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train · 6.32M rows

url stringlengths 14 2.42k	text stringlengths 100 1.02M	date stringlengths 19 19	metadata stringlengths 1.06k 1.1k
https://academy.vertabelo.com/course/standard-sql-functions/aggregate-functions/function-avg/avg	Only this week, get the SQL Complete Track of 9 courses in a special prize of $330$89! Introduction Function COUNT Function AVG 17. Function AVG Functions SUM, MAX, MIN Revision ## Instruction Ok, time to move on. Another function we're going to take a closer look at is AVG, which computes the average value. Let's start with AVG(column): SELECT AVG(price) FROM project; The above query will find the average price for all projects. ## Exercise Find the average number of words from all projects with Spanish (ES) as the target language. ### Stuck? Here's a hint! Use a WHERE clause to pick the lang_to.	2019-04-22 16:57:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35248708724975586, "perplexity": 4758.4579054759015}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578558125.45/warc/CC-MAIN-20190422155337-20190422181337-00409.warc.gz"}
https://www.acmicpc.net/problem/19115	시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율 3 초 512 MB 1 1 1 100.000% ## 문제 As we all know, Master Zhu is the most powerful man in the universe. He has infinite power to protect the world. A magical rooted tree grows in Master Zhu's garden. The tree contains $n$ vertices and $n - 1$ edges. The root of the tree is in vertex $1$. Each vertex $i$ contains an amount of Zhu power equal to $a_i$. Little Rikka is a curious girl: she has $m$ questions to ask to Master Zhu. But now Master Zhu is busy protecting our world, so he wants you to help him answer Rikka's questions. Each Rikka's question has the format "$t$ $u$ $v$ $a$ $b$". • If $t$ is $1$, then $u$ is equal to $v$, and Rikka looks at the subtree rooted in vertex $u$ and wants to know the GCD (greatest common divisor) of $S_a$ and $S_b$, where $S_a$ is the sum of numbers that appear exactly $a$ times in this subtree, and $S_b$ is the sum of numbers that appear exactly $b$ times in this subtree. • If $t$ is $2$, Rikka looks at the simple path between vertices $u$ and $v$ and wants to know the GCD of $T_a$ and $T_b$, where $T_a$ is the sum of numbers that appear exactly $a$ times on this path, and $T_b$ is the sum of numbers that appear exactly $b$ times on this path. Here, for any $x$, we define $\mathrm{GCD} (x, 0) = \mathrm{GCD} (0, x) = x$. ## 입력 The first line of input contains an integer $T$, the number of test cases ($1 \le T \le 10$). The first line of each test case contains two integers $n$ and $m$: the number of vertices in the magical tree and the number of Rikka's questions ($1 \le n, m \le 10^5$). The next line contains $n$ integers $a_1$, $a_2$, $\ldots$, $a_n$: the amount of Zhu power in each vertex ($1 \le a_i \le 10^9$). Each of the next $n - 1$ lines contains two integers $u$ and $v$ and denotes an edge connecting vertices $u$ and $v$ ($1 \le u, v \le n$). It is guaranteed that together, these edges form a tree. Each of the next $m$ lines contains one of Rikka's questions in the format described above ($1 \le u, v \le n$, $1 \le a, b \le n$). ## 출력 For each Rikka's question, print the answer on a separate line. ## 예제 입력 1 1 5 5 1 2 4 1 2 1 2 2 3 3 4 4 5 1 1 1 1 1 1 1 1 1 2 2 1 5 1 1 2 1 5 1 2 2 1 1 2 2 ## 예제 출력 1 4 1 4 1 0	2020-07-06 08:31:33	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22472403943538666, "perplexity": 457.63872652740446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655890157.10/warc/CC-MAIN-20200706073443-20200706103443-00086.warc.gz"}
http://www.deskdr.com/dr/has-anyone-run-the-connection-pooling-for-mysql-tomcat-successfully.html	# Has anyone run the connection pooling for mysql & tomcat successfully? I'm trying to set up connection pooling. I'm following the how-to page at http://jakarta.apache.org/tomcat/tomcat-4.1-doc/jndi-datasource-examples-howto.html But when i test the DBTest/test.jsp file, tomcat displays an error = could not load jdbc driver class 'null'(msdos) i have placed all the required .jar files in the tomcat lib. below is the cofiguration i did to the server.xml file <!-- Example Server Configuration File --> <!-- Note that component elements are nested corresponding to their parent-child relationships with each other --> <!-- A "Server" is a singleton element that represents the entire JVM, which may contain one or more "Service" instances. The Server listens for a shutdown command on the indicated port. Note: A "Server" is not itself a "Container", so you may not define subcomponents such as "Valves" or "Loggers" at this level. --> <Server port="8005" shutdown="SHUTDOWN" debug="0"> <!-- Uncomment these entries to enable JMX MBeans support --> <Listener className="org.apache.catalina.mbeans.ServerLifecycleListener" debug="0"/> <Listener className="org.apache.catalina.mbeans.GlobalResourcesLifecycleListener" debug="0"/> <!-- Global JNDI resources --> <GlobalNamingResources> <!-- Test entry for demonstration purposes --> <Environment name="simpleValue" type="java.lang.Integer" value="30"/> <!-- Editable user database that can also be used by UserDatabaseRealm to authenticate users --> <Resource name="UserDatabase" auth="Container" type="org.apache.catalina.UserDatabase" description="User database that can be updated and saved"> </Resource> <ResourceParams name="UserDatabase"> <parameter> <name>factory</name> <value>org.apache.catalina.users.MemoryUserDatabaseFactory</value> </parameter> <parameter> <name>pathname</name> <value>conf/tomcat-users.xml</value> </parameter> </ResourceParams> </GlobalNamingResources> <!-- A "Service" is a collection of one or more "Connectors" that share a single "Container" (and therefore the web applications visible within that Container). Normally, that Container is an "Engine", but this is not required. Note: A "Service" is not itself a "Container", so you may not define subcomponents such as "Valves" or "Loggers" at this level. --> <!-- Define the Tomcat Stand-Alone Service --> <Service name="Tomcat-Standalone"> <!-- A "Connector" represents an endpoint by which requests are received and responses are returned. Each Connector passes requests on to the associated "Container" (normally an Engine) for processing. By default, a non-SSL HTTP/1.1 Connector is established on port 8080. You can also enable an SSL HTTP/1.1 Connector on port 8443 by following the instructions below and uncommenting the second Connector entry. SSL support requires the following steps (see the SSL Config HOWTO in the Tomcat 4.0 documentation bundle for more detailed instructions): * Download and install JSSE 1.0.2 or later, and put the JAR files into "$JAVA_HOME/jre/lib/ext". * Execute: %JAVA_HOME%\bin\keytool -genkey -alias tomcat -keyalg RSA (Windows)$JAVA_HOME/bin/keytool -genkey -alias tomcat -keyalg RSA (Unix) with a password value of "changeit" for both the certificate and the keystore itself. By default, DNS lookups are enabled when a web application calls request.getRemoteHost(). This can have an adverse impact on performance, so you can disable it by setting the "enableLookups" attribute to "false". When DNS lookups are disabled, request.getRemoteHost() will return the String version of the IP address of the remote client. --> <!-- Define a non-SSL Coyote HTTP/1.1 Connector on port 8081 --> <Connector className="org.apache.coyote.tomcat4.CoyoteConnector" port="8080" minProcessors="5" maxProcessors="75" enableLookups="true" redirectPort="8443" acceptCount="100" debug="0" connectionTimeout="20000" <!-- Note : To disable connection timeouts, set connectionTimeout value to -1 --> <!-- Define a SSL Coyote HTTP/1.1 Connector on port 8443 --> <!-- <Connector className="org.apache.coyote.tomcat4.CoyoteConnector" port="8443" minProcessors="5" maxProcessors="75" enableLookups="true" acceptCount="100" debug="0" scheme="https" secure="true" <Factory className="org.apache.coyote.tomcat4.CoyoteServerSocketFactory" clientAuth="false" protocol="TLS" /> </Connector> --> <!-- Define a Coyote/JK2 AJP 1.3 Connector on port 8009 --> <Connector className="org.apache.coyote.tomcat4.CoyoteConnector" port="8009" minProcessors="5" maxProcessors="75" enableLookups="true" redirectPort="8443" acceptCount="10" debug="0" connectionTimeout="20000" useURIValidationHack="false" protocolHandlerClassName="org.apache.jk.server.JkCoyoteHandler"/> <!-- Define an AJP 1.3 Connector on port 8009 --> <!-- <Connector className="org.apache.ajp.tomcat4.Ajp13Connector" port="8009" minProcessors="5" maxProcessors="75" acceptCount="10" debug="0"/> --> <!-- Define a Proxied HTTP/1.1 Connector on port 8082 --> <!-- <Connector className="org.apache.coyote.tomcat4.CoyoteConnector" port="8082" minProcessors="5" maxProcessors="75" acceptCount="100" debug="0" connectionTimeout="20000" proxyPort="80" useURIValidationHack="false" /> --> <!-- Define a non-SSL legacy HTTP/1.1 Test Connector on port 8083 --> <!-- <Connector className="org.apache.catalina.connector.http.HttpConnector" port="8083" minProcessors="5" maxProcessors="75" enableLookups="true" redirectPort="8443" acceptCount="10" debug="0" /> --> <!-- Define a non-SSL HTTP/1.0 Test Connector on port 8084 --> <!-- <Connector className="org.apache.catalina.connector.http10.HttpConnector" port="8084" minProcessors="5" maxProcessors="75" enableLookups="true" redirectPort="8443" acceptCount="10" debug="0" /> --> <!-- An Engine represents the entry point (within Catalina) that processes every request. The Engine implementation for Tomcat stand alone analyzes the HTTP headers included with the request, and passes them on to the appropriate Host (virtual host). --> <!-- Define the top level container in our container hierarchy --> <Engine name="Standalone" defaultHost="localhost" debug="0"> <!-- The request dumper valve dumps useful debugging information about this instance of Tomcat. If you care only about requests to a particular virtual host, or a particular application, nest this element inside the corresponding <Host> or <Context> entry instead. For a similar mechanism that is portable to all Servlet 2.3 containers, check out the "RequestDumperFilter" Filter in the example application (the source for this filter may be found in "$CATALINA_HOME/webapps/examples/WEB-INF/classes/filters"). Request dumping is disabled by default. Uncomment the following element to enable it. --> <!-- <Valve className="org.apache.catalina.valves.RequestDumperValve"/> --> <!-- Global logger unless overridden at lower levels --> <Logger className="org.apache.catalina.logger.FileLogger" prefix="catalina_log." suffix=".txt" timestamp="true"/> <!-- Because this Realm is here, an instance will be shared globally --> <!-- This Realm uses the UserDatabase configured in the global JNDI resources under the key "UserDatabase". Any edits that are performed against this UserDatabase are immediately available for use by the Realm. --> <Realm className="org.apache.catalina.realm.UserDatabaseRealm" debug="0" resourceName="UserDatabase"/> <!-- Comment out the old realm but leave here for now in case we need to go back quickly --> <!-- <Realm className="org.apache.catalina.realm.MemoryRealm" /> --> <!-- Replace the above Realm with one of the following to get a Realm stored in a database and accessed via JDBC --> <!-- <Realm className="org.apache.catalina.realm.JDBCRealm" debug="99" driverName="org.gjt.mm.mysql.Driver" connectionURL="jdbc:mysql://localhost/authority" connectionName="test" connectionPassword="test" userTable="users" userNameCol="user_name" userCredCol="user_pass" userRoleTable="user_roles" roleNameCol="role_name" /> --> <!-- <Realm className="org.apache.catalina.realm.JDBCRealm" debug="99" driverName="oracle.jdbc.driver.OracleDriver" connectionURL="jdbc:oracle:thin:@ntserver:1521:ORCL" connectionName="scott" connectionPassword="tiger" userTable="users" userNameCol="user_name" userCredCol="user_pass" userRoleTable="user_roles" roleNameCol="role_name" /> --> <!-- <Realm className="org.apache.catalina.realm.JDBCRealm" debug="99" driverName="sun.jdbc.odbc.JdbcOdbcDriver" connectionURL="jdbc:odbc:CATALINA" userTable="users" userNameCol="user_name" userCredCol="user_pass" userRoleTable="user_roles" roleNameCol="role_name" /> --> <!-- Define the default virtual host --> <Host name="localhost" debug="0" appBase="webapps" unpackWARs="true" autoDeploy="true"> <Context path="/my-jsp" docBase="c:\JSP-Files" debug="0" privileged="true" reloadable="true" /> <Context path="" docBase="c:\Inetpub\wwwroot" debug="0" privileged="true" /> <Context path="/sharon" docBase="C:\Tomcat 4.1\webapps\sharon" debug="0" privileged="true" /> <!-- Normally, users must authenticate themselves to each web app individually. Uncomment the following entry if you would like a user to be authenticated the first time they encounter a resource protected by a security constraint, and then have that user identity maintained across all web applications contained in this virtual host. --> <!-- <Valve className="org.apache.catalina.authenticator.SingleSignOn" debug="0"/> --> <!-- Access log processes all requests for this virtual host. By default, log files are created in the "logs" directory relative to$CATALINA_HOME. If you wish, you can specify a different directory with the "directory" attribute. Specify either a relative (to $CATALINA_HOME) or absolute path to the desired directory. --> <!-- <Valve className="org.apache.catalina.valves.AccessLogValve" directory="logs" prefix="localhost_access_log." suffix=".txt" pattern="common" resolveHosts="false"/> --> <!-- Logger shared by all Contexts related to this virtual host. By default (when using FileLogger), log files are created in the "logs" directory relative to$CATALINA_HOME. If you wish, you can specify a different directory with the "directory" attribute. Specify either a relative (to $CATALINA_HOME) or absolute path to the desired directory.--> <Logger className="org.apache.catalina.logger.FileLogger" directory="logs" prefix="localhost_log." suffix=".txt" timestamp="true"/> <!-- Define properties for each web application. This is only needed if you want to set non-default properties, or have web application document roots in places other than the virtual host's appBase directory. --> <!-- Tomcat Root Context --> <!-- <Context path="" docBase="ROOT" debug="0"/> --> <!-- Tomcat Examples Context --> <Context path="/examples" docBase="examples" debug="0" reloadable="true" crossContext="true"> <Logger className="org.apache.catalina.logger.FileLogger" prefix="localhost_DBTest_log." suffix=".txt" timestamp="true"/> <Ejb name="ejb/EmplRecord" type="Entity" home="com.wombat.empl.EmployeeRecordHome" remote="com.wombat.empl.EmployeeRecord"/> <!-- If you wanted the examples app to be able to edit the user database, you would uncomment the following entry. Of course, you would want to enable security on the application as well, so this is not done by default! The database object could be accessed like this: Context initCtx = new InitialContext(); Context envCtx = (Context) initCtx.lookup("java:comp/env"); UserDatabase database = (UserDatabase) envCtx.lookup("userDatabase"); --> <!-- <ResourceLink name="userDatabase" global="UserDatabase" type="org.apache.catalina.UserDatabase"/> --> <!-- PersistentManager: Uncomment the section below to test Persistent Sessions. saveOnRestart: If true, all active sessions will be saved to the Store when Catalina is shutdown, regardless of other settings. All Sessions found in the Store will be loaded on startup. Sessions past their expiration are ignored in both cases. maxActiveSessions: If 0 or greater, having too many active sessions will result in some being swapped out. minIdleSwap limits this. -1 means unlimited sessions are allowed. 0 means sessions will almost always be swapped out after use - this will be noticeably slow for your users. minIdleSwap: Sessions must be idle for at least this long (in seconds) before they will be swapped out due to maxActiveSessions. This avoids thrashing when the site is highly active. -1 or 0 means there is no minimum - sessions can be swapped out at any time. maxIdleSwap: Sessions will be swapped out if idle for this long (in seconds). If minIdleSwap is higher, then it will override this. This isn't exact: it is checked periodically. -1 means sessions won't be swapped out for this reason, although they may be swapped out for maxActiveSessions. If set to >= 0, guarantees that all sessions found in the Store will be loaded on startup. maxIdleBackup: Sessions will be backed up (saved to the Store, but left in active memory) if idle for this long (in seconds), and all sessions found in the Store will be loaded on startup. If set to -1 sessions will not be backed up, 0 means they should be backed up shortly after being used. To clear sessions from the Store, set maxActiveSessions, maxIdleSwap, and minIdleBackup all to -1, saveOnRestart to false, then restart Catalina. --> <!-- <Manager className="org.apache.catalina.session.PersistentManager" debug="0" saveOnRestart="true" maxActiveSessions="-1" minIdleSwap="-1" maxIdleSwap="-1" maxIdleBackup="-1"> <Store className="org.apache.catalina.session.FileStore"/> </Manager> --> <Environment name="maxExemptions" type="java.lang.Integer" value="15"/> <Parameter name="context.param.name" value="context.param.value" override="false"/> <Resource name="jdbc/EmployeeAppDb" auth="SERVLET" type="javax.sql.DataSource"/> <Resource name="jdbc/TestDB" auth="Container" type="javax.sql.DataSource"/> <ResourceParams name="jdbc/TestDB"> <parameter> <name>factory</name> <value>org.apache.commons.dbcp.BasicDataSourceFactory</value> </parameter> <!-- Maximum number of dB connections in pool. Make sure you configure your mysqld max_connections large enough to handle all of your db connections. Set to 0 for no limit. --> <parameter> <name>maxActive</name> <value>100</value> </parameter> <!-- Maximum number of idle dB connections to retain in pool. Set to 0 for no limit. --> <parameter> <name>maxIdle</name> <value>30</value> </parameter> <!-- Maximum time to wait for a dB connection to become available in ms, in this example 10 seconds. An Exception is thrown if this timeout is exceeded. Set to -1 to wait indefinitely. --> <parameter> <name>maxWait</name> <value>10000</value> </parameter> <!-- MySQL dB username and password for dB connections --> <parameter> <name>user</name> <value>javauser</value> </parameter> <parameter> <name>password</name> <value>javadude</value> </parameter> <!-- Class name for mm.mysql JDBC driver --> <parameter> <name>driverClassName</name> <value>org.gjt.mm.mysql.Driver</value> </parameter> <!-- The JDBC connection url for connecting to your MySQL dB. The autoReconnect=true argument to the url makes sure that the mm.mysql JDBC Driver will automatically reconnect if mysqld closed the connection. mysqld by default closes idle connections after 8 hours. --> <parameter> <name>url</name> <value>jdbc:mysql://localhost:3306/javatest?autoReconnect=true</value> </parameter> </ResourceParams> <Resource name="mail/Session" auth="Container" type="javax.mail.Session"/> <ResourceParams name="mail/Session"> <parameter> <name>mail.smtp.host</name> <value>localhost</value> </parameter> </ResourceParams> <ResourceLink name="linkToGlobalResource" global="simpleValue" type="java.lang.Integer"/> </Context> </Host> </Engine> </Service> <!-- The MOD_WEBAPP connector is used to connect Apache 1.3 with Tomcat 4.0 as its servlet container. Please read the README.txt file coming with the WebApp Module distribution on how to build it. (Or check out the "jakarta-tomcat-connectors/webapp" CVS repository) To configure the Apache side, you must ensure that you have the "ServerName" and "Port" directives defined in "httpd.conf". Then, lines like these to the bottom of your "httpd.conf" file: LoadModule webapp_module libexec/mod_webapp.so WebAppConnection warpConnection warp localhost:8008 WebAppDeploy examples warpConnection /examples/ The next time you restart Apache (after restarting Tomcat, if needed) the connection will be established, and all applications you make visible via "WebAppDeploy" directives can be accessed through Apache. --> <!-- Define an Apache-Connector Service --> <!-- <Service name="Tomcat-Apache"> <Connector className="org.apache.catalina.connector.warp.WarpConnector" port="8008" minProcessors="5" maxProcessors="75" enableLookups="true" appBase="webapps" acceptCount="10" debug="0"/> <Engine className="org.apache.catalina.connector.warp.WarpEngine" name="Apache" debug="0"> <Logger className="org.apache.catalina.logger.FileLogger" prefix="apache_log." suffix=".txt" timestamp="true"/> <Realm className="org.apache.catalina.realm.MemoryRealm" /> </Engine> </Service> --> </Server> Pleas4 help!!! you have your driver jar in Tomcat\common\lib? if so, check your classpath, it could be that. ### Similar Messages • Has anyone received the new update for the X6? has anyone received the new update for the X6 with the updated browser? what is the firmware version? 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Again, there's a BADI which allows you to add content, but there's a mismatch in parameters between the FM and BADI. I'm sure they'll sort it out. The only thing left now is to get the item level doc flow to update when pointing to customer reference contract. Again, it's just a case of reverse engineering the data from the IDOC created by the CRMXIF_ORDER_TEST program. Regards Dr Sidewalk • Has anyone run the Identity Management Suite on an OpenSolaris Amazon AMI Hi I want to do some evaluation and training on the IdM Suite and was wondering has anyone succeeded in getting the suite (including the Directroy Server etc) to run on an OpenSolaris image on Amazon EC2? Regards John you have your driver jar in Tomcat\common\lib? if so, check your classpath, it could be that. • Has Anyone sent the iphone in for repair for the low volume issue ??? I called apple last week and spoke with a level on support agent. After he could not solve the volume issue they sent me to level two. the level two tech took the call and told me right away that they were going to send me a new phone. I give him my credit card as a deposit so they would send a new phone and when I had the new phone I could then send the old one back. Well after a few days I called to check on the phone and found out he never placed the order and now they say they want to send it for repair some place in Texas. They did offer the rent me a phone for 29.00 while I wait for repair. I told them no rental for me. How bad is that, a hardware issue and they say they are going to send a new phone and never do then they offer a repair and to rent me a phone. I was wondering if anyone had sent in the phone for this issue yet. I do not think I am going to send it in and I think I am going to get my refund while I still can. I just thought I would check to see if anyone had sent the phone in for repair yet and how it worked out. Andrew How are any of us (Apple users just like you) supposed to have any idea? We weren't there. We don't know the specifics of what happened to your iPhone. Ask the store that repaired it. • Has anyone used the appscript modual for python rather than streight AS? I just discovered appscript and so far I like what I see. has anyone used it? Does it just wrap around actual applescript commands which it then sends to osascript with a system call or does it use the message system directly? Is there anything that it has not yet implemented that might cause problems? To me it seems to be a perfect solution to the clutter that AS seems to be... at least from someone coming from more traditional languages. In startMovie, you need to register the xtra on startMovie axRegister(serial code here) end Then, on your Record Button, something like this: on mouseUp me --start recording session - using 400k as maximum here errOpen=axOpenRecorder(400000) --see if there is an error put errOpen --save the new audio as a file errRecord=axRecordSoundToFile("soundName","c:\path\to\soundfile.wav") --see if there is an error put errRecord end then make sure you close the recorder in stopMovie on stopMovie axCloseRecorder() end You can also make a Stop Recording button that has code like this: on mouseUp me errStop=axStopRecording() put errStop end • Has anyone used the new Quicken for Lion? Before updating to Lion and purchasing the new Quicken which is compatible with Lion, I wanted to see if others have used it yet and if there are any major problems. I have not experienced any problems with the new Quicken for Lion. It's quite different from the old version but it seems to work quite well. After installing Lion, the old version of Quicken was deemed useless. It will not run on Lion, so access it before you update if you intend to extract any info from it. Good luck! • Has anyone fixed the Headstart libraries for Forms 11 ? I have a 100% generated Designer - Forms application using the %65.pll headstart libraries - the so-called Headstart version 6.5i. Currently our production environment is running on Oracle Application Server 10.1.2. It works fine, however, because of several reasons (the underlying Oracle Portal environment is not working properly anymore on Internet Explorer 10) and continuous alerts that our customers may not use Java 6 and should upgrade to Java 7, we have to migrate to 11g. We have installed Fusion Middleware 11.1.1.6, upgraded Portal and recompiled all Forms modules and libraries. Also the Headstart libraries compiled ok. However, when we start a form we get the message that it has been created with an older version of Forms and it quits. The consequence is that i have to migrate the Forms as well with the tool frmplsqlconv. Sadly that fails on the Headstart libraries. For example these errors occur: CG$MESSAGE: The String CALL was found. If it is an occurrence of the Forms Built-In, It should be replaced with CALL_FORM. CG$_SHOW_KEYS: MENU_SHOW_KEYS changed to SHOW_KEYS CG$_PREVIOUS_MENU: The PREVIOUS_MENU Built-in is obsolete and will not compile. CG$_HELP: The MENU_HELP Built-in is obsolete and will not compile. CG$_EXIT: The EXIT_MENU Built-in is obsolete and will not compile. CGNV$FIRST_NAV_ITEM: BREAK changed to DEBUG.SUSPEND Does anyone have Headstart libraries with fixes for these errors? Hello Mark, the problem has been fixed... 1) I tried to migrate the forms to 11g, but that can not be done with headstart... The fmb/pll files should be kept on 10g. 2) The migration documentation is not complete: webutil has been installed completely (in other words, webutil is not migrated) So, steps are: 1) Install webutil 2) Recompile all libraries (including headstart and webutil) 3) Recompile all menus 4) Recompile all forms Then the Forms application works again. Java 7 update 21 is very dramatic. The "vendor" work-around can not be used anymore, like with previous Java 7 versions... It is unbelievable how amateuristic Oracle deals with Java. For me, Java in the client is dead as long as Oracle has the controls. So, the end of Forms is very near. If you are also looking for alternatives, check theformspider.com. Thanks for your help. Best regards, Jan Willem Vermeer • Has anyone found the correct driver for Canon MF4018 printer? I have tried installing all of the available drivers including MF4010 which other users have reported works- I keep getting Error-50 and cannot print anything. If anyone has used any driver for this printer that is compatible with my macbook pro - that could help me out a lot. Since it's a 10.8 issue, why not place a new post in the 10.8 usage forum? DALE • Has anyone solved the fan problem for the U350 64-bit machines? I would have returned it, but it's too late to do so. I've seen a lot of posts on this (the fan running all the time), but the fixes seem to concern the 32-bit machines. Any help would be appreciated. I wish I had gotten the HP dm3 intead _david I'm with you. I'm deeply disappointed with my purchase. To make it worse, Lenovo only has a 21-day return policy and 15% restocking fee. I'm so over you, Lenovo. Never again. • Has anyone purchased the Apple TV for Dummies book? I saw this book yesterday at Border's and was half-tempted to purchase it since Apple does not offer a quality Apple TV user guide. But at$21.95 I thought I would ask here first to see if anyone has purchased the book...and to offer there opinion as to whether or not they think it is worth the money. Input anyone? Thanks. Doug Campbell wrote: The reason I say the Apple instructions are poor are seen in this example. Take a look at #4 & 5 here http://docs.info.apple.com/article.html?artnum=305139#syncing . My Apple tabs do not look like that at all. They did in the 1.0 version but since downloading the new version the only tabs that appear are Summary and Photos. Despite what this link reads, I can no longer synch anything to Apple. my tabs looks exactly like that. the reason you only have 2 tabs is that you have set up itunes as a secondary library (you only get 2 tabs).... as a primary library you get all the tabs and the syncing functions. secondary libraries only provide streaming access. • Has anyone got the Calendar feature for 'Show Holidays calendar' to work ? I have tried most things but cannot get this to work for the UK ! I am under the impression it looks at your regional settings and then adds the holidays for that region. My region is set correctly so I assume it just doesnt work for UK. Yes thats correct & it should showup if already checked. When I checked the https://p15-calendars.icloud.com/holiday/FR_fr.ics also https://p15-calendars.icloud.com/holiday/UK_uk.ics ofcourse it could be any page from p 0- to p 20- but nothing happens from the UK one but the FR it auto downloads does not instal into Calendar it will ask you for permision first. I have many calendars too Europe, Asia etc: This is what info of active Holiday Cal looks like. ### Maybe you are looking for • How to redraw a business process ? Greetings, During a business process definition, the arrows representing the process flows are automatically drawn and hence, sometimes, they superseeds each other, etc. is there any way to redraw a business process flow such that the arrows and node • Using SUBSTRING_INDEX() in SQL Server Hi I started SQL recently as a beginner i came across the above problem. the book i referring is using MySQL and i want to know how can i do the following in SQL Server This is the query as per the example in the book SELECT SUBSTRING_INDEX(locatio • Prouction receipt (One of the interviewr asking the question). QUESTION IS THE:- 2 company codes is production the same material, OR DIFFERENT MATERIAL when we received the material from ONE co code, 50 units, and SECOND co code, 50 units, HOW UR POSTING THE G/L ACC • No color printing on Photosmart 5510 Printer. I have purcheased new cartitgages. I have shaken the cartiratages. I have tried the cleaning feature, realigning, even the old blow on the machine trick from Nintendo days! I am totally lost as to what the issue could be. It will print black, but onl • DIM-00020 error on 8.1.7 to 9.2.0.1 upgrade Hi, Can anyone help us on how to resolve the error we are receiving on upgrade? 1. Installed 9i in a new home 2. Choose Enterprise edition / General installation 3. Installation was sucessful 4. Ran Upgrade assistant from start-program files 5. Got t	2020-06-03 10:19:04	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32747647166252136, "perplexity": 12060.255194555253}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347432521.57/warc/CC-MAIN-20200603081823-20200603111823-00180.warc.gz"}
http://piping-designer.com/index.php/properties/thermodynamics/1977-linear-thermal-expansion-coefficient-2	# Linear Thermal Expansion Coefficient Written by Jerry Ratzlaff on . Posted in Thermodynamics Linear thermal expansion coefficient is a porportional change in the origional length and change in temperature due to the heating or cooling of an object. ## formula $$\alpha_l = \frac { \Delta l } { l_i \Delta T }$$ Where: $$\alpha_l$$ (Greek symbol alpha) = linear thermal expansion coefficient $$\Delta l$$ = initial length minus final length $$l_i$$ = initial length $$l_f$$ = final length $$\Delta T$$ = initial temperature minus final temperature $$T_i$$ = initial temperature $$T_f$$ = final temperature $$\alpha$$ (Greek symbol alpha) = thermal expansion coefficient Solve for: $$\Delta_l = \alpha l_i \Delta T$$ $$l_f = \alpha l_i \Delta T + l$$ $$l_i = \frac {l_f} {\alpha \Delta T +1 }$$ $$\Delta T = \frac {\Delta l}{\alpha l_i }$$ $$T_f = \frac {\Delta l} {\alpha l_i} +T_i$$ $$T_i = T_f \frac {\Delta l} {\alpha l_i}$$	2017-12-13 20:26:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9466755986213684, "perplexity": 5505.096184925511}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948530841.24/warc/CC-MAIN-20171213201654-20171213221654-00068.warc.gz"}
https://eprint.iacr.org/2019/236	## Cryptology ePrint Archive: Report 2019/236 Designated-verifier pseudorandom generators, and their applications Geoffroy Couteau and Dennis Hofheinz Abstract: We provide a generic construction of non-interactive zero-knowledge (NIZK) schemes. Our construction is a refinement of Dwork and Naor’s (FOCS 2000) implementation of the hidden bits model using verifiable pseudorandom generators (VPRGs). Our refinement simplifies their construction and relaxes the necessary assumptions considerably. As a result of this conceptual improvement, we obtain interesting new instantiations: – A designated-verifier NIZK (with unbounded soundness) based on the computational Diffie-Hellman (CDH) problem. If a pairing is available, this NIZK becomes publicly verifiable. This constitutes the first fully secure CDH-based designated-verifier NIZKs (and more generally, the first fully secure designated-verifier NIZK from a non-generic assumption which does not already imply publicly-verifiable NIZKs), and it answers an open problem recently raised by Kim and Wu (CRYPTO 2018). – A NIZK based on the learning with errors (LWE) assumption, and assuming a non-interactive witness-indistinguishable (NIWI) proof system for bounded distance decoding (BDD). This simplifies and improves upon a recent NIZK from LWE that assumes a NIZK for BDD (Rothblum et al., PKC 2019). Category / Keywords: foundations / non-interactive zero-knowledge, computational Diffie-Hellman, learning with errors, verifiable pseudorandom generators Original Publication (with minor differences): IACR-EUROCRYPT-2019	2019-06-17 04:44:31	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8865371346473694, "perplexity": 12302.819741789464}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998376.42/warc/CC-MAIN-20190617043021-20190617065021-00264.warc.gz"}
http://www.d-rhapsody.com/ap-set-rkuy/751dd3-application-injective%2C-surjective-bijective-cours-pdf	Cours maths sup, prépa HEC, BCPST - Duration: 36:48. f invertible (has an inverse) iff , . Afunction ffrom Xto Y is a rule that assigns every element xof Xto a unique yin Y. injection surjection bijection cours pdf admin September 3, 2019 0 Comments Cours d’Algebre superieure. B is bijective (a bijection) if it is both surjective and injective. If f: A ! injection surjection bijection cours pdf admin October 11, 2019 no Comments Cours d’Algebre superieure. Functions can be injections (one-to-one functions), surjections (onto functions) or bijections (both one-to-one and onto). The Gwinnett School of Mathematics, Science, and Technology, AG 5.1 Injective, Surjective, Bijective_Notes.pdf, The Gwinnett School of Mathematics, Science, and Technology â¢ MATH 89. That is, we say f is one to one In other words f is one-one, if no element in B is associated with more than one element in A. (2x+ Y;x Y) Est Un Automorphisme. We write f: X!Y (a) f: Z → Z where f (x) = x + 10 (b) f: R → R where f (x) = x 3 + 2 x 2-x + 1 (c) f: N 0 → N 0 given by f (n) = b n/ 3 c. (The value of the “floor” function b x c is the largest integer that is less than or equal to x. of a function is all possible output values. 29 كانون الأول (ديسمبر) Cours SMAI (S1). Finally, a bijective function is one that is both injective and surjective. è¯ÞëlJÝ¿qÁÌø ÙÈD&ÙB³l¸¿ÜRG$"2YùÛ×åéñ@µé)Þùãhð×¢wÅÀiüRÐr¿D ,BÏ¤0#)çéÈ\|. and/or bijective (a function is bijective if and only if it is both injective and surjective). 15. Functions Solutions: 1. This function g is called the inverse of f, and is often denoted by . Informally, an injection has each output mapped to by at most one input, a surjection includes the entire possible range in the output, and a bijection has both conditions be true. tut05.pdf - MATH2111 Tutorial 5 \u0014 \u0015 x y x 1 Let T R2 \u2192 R3 be the linear transformation defined by T = 3x \u2212 y Is T injective surjective y \u22123x \u2212 y 2 Injective, surjective and bijective maps Definition Let A, B be non-empty sets … This preview shows page 1 - 2 out of 2 pages. This means a function f is injective if a1≠a2 implies f(a1)≠f(a2). A function f:A→B is injective or one-to-one function if for every b∈B, there exists at most one a∈A such that f(s)=t. It is injective (any pair of distinct elements of the domain is mapped to distinct images in the codomain). Applications Lin Eaires - Rebelles.gilles.free.fr F2L(E) Est Bijective Ssi Elle Est Injective Ssi Elle Est Surjective. Think of it as a "perfect pairing" between the sets: every one has a partner and no one is left out. Course Hero is not sponsored or endorsed by any college or university. Discussion We begin by discussing three very important properties functions de ned above. Let f: A! 92 identity, 92 injective, see injection one-to- one, see injection onto, see surjection surjective, it see surjection Fundamental. Note that this is equivalent to saying that f is bijective iff it’s both injective and surjective. 1 in every column, then A is injective. Show that the set of all integers that are multiples of 5 has the same cardinality as the set of all integers. injective surjective bijective darija injective surjective bijective darija. In other words, f: A!Bde ned by f: x7!f(x) So there is a perfect "one-to-one correspondence" between the members of the sets. Injective Bijective Function Deﬂnition : A function f: A ! Lecture 19 Types of Functions Injective or 1-1 Function Function Not 1-1 Alternative Definition for 1-1 29 كانون الأول (ديسمبر) Cours SMAI (S1). Bbe a function. The figure given below represents a one-one function. For example, b … 3. fis bijective if it is surjective and injective (one-to-one and onto). Injective surjective and bijective The notion of an invertible function is very important and we would like to break up the property of being invertible into pieces. injection surjection bijection cours pdf admin May 26, 2019 Leave a comment Cours d’Algebre superieure. Bijective Functions. View CS011Maps02.12.2020.pdf from CS 011 at University of California, Riverside. ... التطبيقات-Les applications - للسنوات الأولى جامعي تخصص ST-SM-STH - Duration: 21:12. List the domain, codomain, and range values for the function. AG 5.1 Injective, Surjective, Bijective_Notes.pdf - Accelerated Geometry 5.1 Injective Surjective Bijective Functions NOTES A function relates each, 5.1 Injective, Surjective, & Bijective Functions, relates each element of a set with exactly one element of. 92 identity, 92 injective, see injection one-to- one, see injection onto, see surjection surjective, it see surjection Fundamental. The function f is called an one to one, if it takes different elements of A into different elements of B. Injective, Surjective, and Bijective Functions De ne: A function An injective (one-to-one) function A surjective (onto) function A bijective (one-to-one and onto) function A few words about notation: To de ne a speci c function one must de ne the domain, the codomain, and the rule of correspondence. When a function, such as the line above, is both injective and surjective (when it is one-to-one and onto) it is said to be bijective. one-to-one and onto (or injective and surjective), how to compose functions, and when they are invertible. View AG 5.1 Injective, Surjective, Bijective_Notes.pdf from MATH 89 at The Gwinnett School of Mathematics, Science, and Technology. E F f (E) On fait pareil pour déterminer graphiquement l’image Lyc Ee Jean Perrin Page 4/7Marseille. Let f : A ----> B be a function. List the domain, codomain, and range values for the function, If every element of the range of a function corresponds to exactly one element, If every element of the range of a function is mapped onto from at least one. 92 identity, 92 injective, see injection one-to- one, see injection onto, see surjection surjective, it see surjection Fundamental. f is injective iff: More useful in proofs is the contrapositive: f is surjective iff: . Christophe Bertault — Mathématiques en MPSI A f (A) L’image f (A)de A par f est l’ensemble des images par f des éléments de A.Graphi-quement, pour déterminer f (A), on projette sur l’axe des ordonnées la portion du graphe de f qui se situe au-dessus de A, comme l’illustre la ﬁgure de droite. Montrer Que F: R2! We show that k π 0 k ≡ i. We say that f is injective if whenever f(a 1) = f(a 2), for some a 1 and a 2 2A, then a 1 = a 2. of a function is all possible input values. This equivalent condition is formally expressed as follow. De nition 15.1. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … (But don't get that confused with the term "One-to-One" used to mean injective). SUPER-INJECTIVE, LEFT-COUNTABLE MANIFOLDS OVER CONTRAVARIANT, STOCHASTICALLY CO-PARABOLIC HOMEOMORPHISMS G. VOLTERRA, S. SYLVESTER, R. RAMANUJAN AND M. KRONECKER Abstract. A function is injective or one-to-one if the preimages of elements of the range are unique. Let Xand Y be sets. This could shed … Not Injective 3. A one-one function is also called an Injective function. De nition 63. A function is bijective if and only if every possible image is mapped to by exactly one argument. 1. Exemple 9. Injective 2. of a function is all actual output values. Accelerated Geometry 5.1 Injective, Surjective, & Bijective Invertible maps If a map is both injective and surjective, it is called invertible. Therefore, we can get to any row by finding the index, and to any index, finding the row. This means, for every v in R‘, there is exactly one solution to Au = v. So we can make a … Maths En PCSI Ann Ee 2019 - 2020 2.2 Rang D’une Application Lin Eaire D E Nition 5. teorie și exemple -Funcții injective, surjective, bijective (exerciții rezolvate matematică liceu): FUNCȚIA INJECTIVĂ În exerciții puteți utiliza următoarea proprietate pentru a demonstra INJECTIVITATEA unei funcții: Funcție f:A->B, A,B⊆R este INJECTIVĂ dacă: ... exemple: jitaru ionel blog It isn't surjective, because$2$in the codomain has no pre... Stack Exchange Network Stack Exchange network consists of 176 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Bijective means both Injective and Surjective together. A bijective function is also called a bijection or a one-to-one correspondence. A function is bijective if it is both injective and surjective. In a sense, it "covers" all real numbers. Cours netprof.fr de Mathématiques / Licence 1 et Prépa Prof : Jonathan. R2 (x;y) 7! If A red has a column without a leading 1 in it, then A is not injective. 29 كانون الأول (ديسمبر) Cours SMAI (S1). 14. It is also not surjective, because there is no preimage for the element $$3 \in B.$$ The relation is a function. Since g is both injective and surjective, it is bijective. View lecture 19.pdf from COMPUTER S 211 at COMSATS Institute Of Information Technology. Likewise, this function is also injective, because no horizontal line will intersect the graph of a line in more than one place. Cours Raisonnements, Ensembles, Applications. Recent interest in functors has centered on examining arithmetic, countably invertible, differentiable categories. A function is a way of matching all members of a set A to a set B. Here is a picture. Let us start with a formal de nition. 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G is both surjective and injective properties functions de ned above a bijection ) if it is surjective injective! one-to-one '' used to mean injective ) & ÙB³l¸¿ÜRG \$ '' 2YùÛ×åéñ @ µé ),...	2021-03-06 16:54:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8539063930511475, "perplexity": 2753.3649655553245}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178375274.88/warc/CC-MAIN-20210306162308-20210306192308-00520.warc.gz"}
https://cs.stackexchange.com/questions/113277/since-the-halting-problem-is-undecidable-does-that-mean-that-there-exists-an-al/113390	# Since the halting problem is undecidable, does that mean that there exists an always undecidable program? The usual demonstration of the halting problem's undecidability involves positing an adversarial machine (call it $$A_0$$) that runs the decider machine (call it $$D_0$$) on itself and performs the opposite of the answer it gets. But it would be possible to construct a machine $$D_1$$, that checked for the exact source code of $$A_0$$ and output the correct answer. Of course then another machine $$A_1$$ that runs $$D_1$$ instead of $$D_0$$ could also be constructed. And so on to any finite $$n$$. So it seems like any given adversarial machine can be thwarted by another larger-indexed decider machine. So it appears that it does not directly follow from that demonstration that there is any single machine that there cannot be a decider machine constructed for. The proposition that there is no single machine that can decide for all cases still holds of course, but I'm interested in that slightly different question of whether there exists a machine that no decider machine can correctly identify whether it halts. Is the answer to that question known? I can imagine a possible answer that any given machine must either halt or not so one of the trivial decider programs that always says the same answer would be correct. But it seems to me that there is a sensible notion of "non-trivially deciding" that would exclude examples like that. But maybe the fact I'm currently unable to describe that notion precisely indicates I'm wrong about that? Edit: I think I now have a way of describing a notion of "non-trivially deciding", although now that name does not fit as well. First we need to change the problem slightly. In this version the decider machines output one of $$halts$$, $$continues$$, or $$unknown$$, indicating that the machine halts, does not halt, or the decider machine does not "know" respectively. So we can call decider machines that are correct in all of the cases that they output $$halts$$ or $$continues$$ "correct" or "honest" decider machines. So now my question is, is there a machine that no single honest decider machine would identify correctly? By "identify correctly" I mean the decider outputs either $$halts$$ or $$continues$$ and that the outputs correctly correspond to the machine under examination's behaviour. By the definition of honest, if the machine under examination halts and the decider outputs $$continues$$ or the machine under examination does not halt, and the decider outputs $$halts$$ then the decider is not honest. So this definition excludes the decider machines that always output the same answer, including the one that always outputs $$unknown$$ by my definition of "identify correctly". Edit 2: To elaborate on my notion of a decider machine correctly identifying a machine's behaviour, we can break the definition into two parts gaining some more vocabulary in the process. First we have the criterion that the decider outputs $$halts$$ or $$continues$$ for that machine. We can call that criterion the identification criterion, and we can say of decider machines that they identify a machine if and only if they out one of $$halts$$ or $$continues$$ on that machine. Second we have the criterion that the decider's output correspond to the to the machine under examination's behaviour. So if the examined machine halts and the decider outputs $$halts$$ the decider is correct about that machine. Similarly if the examined machine does not halt, a decider that outputs $$continues$$ would be correct. It seems useful to include outputting $$unknown$$ as "technically correct". So the full rules would be a decider is correct about a given examined machine if one of the following is true: • The examined machine halts and the decider outputs $$halts$$ or $$unknown$$ • The examined machine does not halt and the decider outputs $$continues$$ or $$unknown$$ We can call this the "correctness" criterion, and say that a decider is correct about a given machine if and only if the above condition is true. We can put the vocabulary back together and say that a decider correctly identifies a given machine if they identify that machine, and they are correct about that machine. So now we can state that the always $$unknown$$ decider does not correctly identify every machine since, while it is always correct about every machine, it does not identify any machines! • "I can imagine a possible answer that any given machine must either halt or not so one of the trivial decider programs that always says the same answer would be correct. But it seems to me that there is a sensible notion of "non-trivially deciding" that would exclude examples like that." Why? – orlp Sep 1 at 10:11 • @orlp I've added what I think to be a precise description of what I wanted to describe. I had an intuition that one existed but I was unable to describe it at the time. – Ryan1729 Sep 1 at 18:31 • It's still unclear to me when a decider is allowed to output "unknown". You say your rules exclude a decider that always returns "unknown", but by what mechanic do you do this? – orlp Sep 1 at 19:02 • @orlp I've now added a more precise definition of "correct identification" and stated explicitly why that definition excluded the always $unknown$ decider. – Ryan1729 Sep 1 at 19:26 • Still trivially avoidable. Consider the decider that simulates the machine for $c$ steps, if it halts before that, it outputs halt, otherwise it outputs unknown. – orlp Sep 1 at 20:47 Suppose you've come up with a machine $$P_0$$ which you claim decides the halting problem. I create a $$Q_0$$ that makes it malfunction somehow (your $$P_0$$ either ends up diverging or gives the wrong answer). The proof of the Halting Problem shows that I can always create such a $$Q_0$$. "Aha!" you say. "But now I can create $$P_1$$, which is exactly like $$P_0$$—except that it checks whether its input is $$Q_0$$ and gives a hardcoded answer if so." Sure, you can do this. But then I can just create a $$Q_1$$ in exactly the same way that I created $$Q_0$$. This is always possible—that's how the proof works. You can show by induction that you can always create a $$P_n$$ that has $$n$$ hardcoded special cases, protecting it against $$n$$ different $$Q$$s. In fact, for any "undecidable program" $$Q$$ I create, you can create a special $$P$$ that can decide it: DoesItHalt(X): if X = Q, return [hardcode whichever answer is correct] else, return true Therefore there is no "universally halting-undecidable program" $$Q_\omega$$. But I can also create a new $$Q$$ that defeats any $$P$$ you make, since you can have as many special cases as you like, but that number must be finite. Therefore there is no "universal halting-decider program" $$P_\omega$$ either (which is the whole point of Turing's proof). The answer to your question is yes. That is exactly the whole point of the Halting Problem: It is impossible to build a recognizer that correctly answers "Yes" or "No" in finite time to the question "Does P halt?" for all P. We don't need to exhibit a P for which all recognizers fail to be able to prove that it exists.	2019-10-19 02:34:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 49, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7468122243881226, "perplexity": 513.4895698258672}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986688674.52/warc/CC-MAIN-20191019013909-20191019041409-00361.warc.gz"}
https://forum.qt.io/topic/31586/compiling-qt-5-1-1-static-on-windows-xp-with-mingw	# Compiling Qt 5.1.1 static on Windows (XP) with MinGW • Hi friends ;-) i am trying to compile Qt 5.1.1 static on my windows xp machine using MinGW. my configure.bat call is: @configure.bat -static -prefix C:\Qt\5.1.1-static -qt-sql-sqlite -opengl desktop@ After configure.bat run, i call mingw32-make and the after some time compilation aborts with error saying uic.exe is missing the library libgcc_s_sjlj-1.dll I can not find this library on my machine (i checked also mingw from another installed Qt version)... But this library doesn't exists at all .... I found some hints to add @-static-gcc -static-g++@ option into the .pro file... But which pro file? I added it into the qt.pro file in Qt source folder but without succsess. Maybe someone has an idea? Greetings, Nando • Back when I was compiling Qt statically, I edited this file: qt-everywhere-opensource-src-5.1.1\qtbase\mkspecs\win32-g++\qmake.conf and added a "-static" to the following variable: QMAKE_LFLAGS I haven't tried to compile Qt5 statically, and maybe I changed that file inside the folder containing the MinGW-version I used to compile, not the Qt-sources. So this is only a guess, hope it helps in any way. • Thanks !!!! That solves the problem! :) i just added @-static -static-libgcc@ to QMAKE_LFLAGS in file qt-everywhere-opensource-src-5.1.1\qtbase\mkspecs\win32-g++\qmake.conf So the lines looks as follows: @QMAKE_LFLAGS = -static -static-libgcc@ Thank you :) [quote author="thEClaw" date="1378358941"]Back when I was compiling Qt statically, I edited this file: qt-everywhere-opensource-src-5.1.1\qtbase\mkspecs\win32-g++\qmake.conf and added a "-static -static-gcc" to the following variable: QMAKE_LFLAGS I haven't tried to compile Qt5 statically, and maybe I changed that file inside the folder containing the MinGW-version I used to compile, not the Qt-sources. So this is only a guess, hope it helps in any way.[/quote] • Happy to hear that still works. :)	2020-10-24 12:34:19	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8480285406112671, "perplexity": 13545.651348725049}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882581.13/warc/CC-MAIN-20201024110118-20201024140118-00271.warc.gz"}
https://www.muchlearning.org/?page=62&ccourseid=1437&sectionid=1604	# Step By Step Calculus » 14.1 - Polar Co-ordinates and Polar Curves Synopsis In the polar co-ordinate system, every point in the plane is described with respect to a fixed point called pole. The polar axis is drawn from the pole horizontally to the right. Each point PP in the plane can be associated with a pair (r,\theta)(r,\theta) where rr is the straight-line distance from the pole OO and \theta\theta is the angle between the line OPOP and the polar axis. One can establish a relationship between the Cartesian co-ordinates and the polar co-ordinates as illustrated here. $\begin{array}{ccc} \begin{array}{\|c\|}\hline \textrm{Polar to Cartesian}\\\hline\\ \left. \begin{array}{l} \cos\theta=\frac{x}{r}\\ \\ \sin\theta=\frac{y}{r} \end{array} \right\}\implies \begin{array}{l} x=r\cos\theta\\ \\y=r\sin\theta. \end{array}\\ \\\hline \end{array} & & \begin{array}{\|c\|}\hline \textrm{\qquad\qquad Cartesian to Polar\qquad\qquad}\\\hline \begin{array}{l}\\ r=\sqrt{x^2+y^2}\\ \\ \theta=\arctan(x,y)\\ \end{array} \\ \\\hline \end{array} \end{array}$ A polar curve represents all points in the plane that satisfy a polar equation of the form r=f(\theta)r=f(\theta) or g(r,\theta)=ag(r,\theta)=a. To find the slope of tangents to a polar curve r=f(\theta)r=f(\theta), we will consider the polar curve in the following parametric form. \displaystyle { \textbf{(Paramteric Form of Polar Curve)}\qquad \left\{\begin{array}{l} x=r\cos(\theta)=f(\theta)\cos(\theta)\\ y=r\sin(\theta)=f(\theta)\sin(\theta) \end{array}\right\} }\displaystyle { \textbf{(Paramteric Form of Polar Curve)}\qquad \left\{\begin{array}{l} x=r\cos(\theta)=f(\theta)\cos(\theta)\\ y=r\sin(\theta)=f(\theta)\sin(\theta) \end{array}\right\} } Then, by the equations seen in the review \displaystyle { \textbf{(Slope of Tangents to Polar Curve)}\qquad \frac{dy}{dx}=\frac{dy/d\theta}{dx/d\theta}=\frac{f'(\theta)\sin\theta+f(\theta)\cos\theta}{f'(\theta)\cos\theta-f(\theta)\sin\theta}. }\displaystyle { \textbf{(Slope of Tangents to Polar Curve)}\qquad \frac{dy}{dx}=\frac{dy/d\theta}{dx/d\theta}=\frac{f'(\theta)\sin\theta+f(\theta)\cos\theta}{f'(\theta)\cos\theta-f(\theta)\sin\theta}. }	2019-01-18 08:20:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9577634334564209, "perplexity": 1593.66081842595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583659944.3/warc/CC-MAIN-20190118070121-20190118092121-00237.warc.gz"}
https://jonnylaw.rocks/posts/2019-06-14-bayesian-linear-regression/index.html	# Bayesian Linear Regression with Gibbs Sampling in R RBayesian Author Jonny Law Published June 14, 2019 Linear regression models are commonly used to explain relationships between predictor variables and outcome variables. The data consists of pairs of independent observations $$(y_i, x_i)$$ where $$y_i \in \mathbb{R}$$ represents the outcome variable of the $$i^\text{th}$$ observation and $$x_i \in \mathbb{R}^m$$ represents the predictors (or covariates) of the $$i^\text{th}$$ observation. The specification for this model is: $y_i = \alpha + x_i^T\beta + \varepsilon_i, \quad \varepsilon_i \sim \mathcal{N}(0, \sigma^2).$ The parameters of the model include the intercept (or overall mean) $$\alpha \in \mathbb{R}$$, the coefficients of the predictor variables, $$\beta \in \mathbb{R}^m$$ is a $$m \times 1$$ column vector and the standard deviation of the un-modelled noise, $$\sigma \in \mathbb{R}$$. ## The Model as a Data Generating Process In order to manufacture a deeper understand of linear regression it is useful to explore the model as a data generating process. This allows us to understand when linear regression is applicable, how to effectively perform parameter inference and how to assess the model fit. If the model is suitable for the application, then synthetic data from the model with appropriately chosen parameters should be indistinguishable from real observed data. The parameters used to generate the simulated data are known and hence inference algorithms should be able to reliably recover these parameters using the simulated data. First consider a simple linear regression (a regression where there is only one predictor variable) which links height to weight. We assume that height will be of adults and measured in cm. This is a continuous variable and we might think that this could be modelled using a Normal distribution with a mean of $$150$$ and a standard deviation of $$20$$. Let’s simulate some values: heights <- rnorm(100, mean = 150, sd = 20) qplot(heights, geom = "histogram") We have simulated 100 heights and plotted them on a histogram. The tallest adults are 200cm and the smallest are 100cm. Now that we have our heights, it remains to choose a suitable value for the parameter $$\alpha$$ which will be the intercept and the coefficient $$\beta$$ which will be multiplied by height to determine the weight in kilograms. In addition, a value of the unmodelled noise $$\sigma$$ must be chosen, this seems reasonable since we know that other factors apart from height determine an individuals weight. alpha <- 60 beta <- 0.3 sigma <- 5 weights <- purrr::map_dbl(heights, ~ rnorm(1, mean = alpha + beta * ., sd = sigma)) qplot(weights, geom = "histogram") For every height, we have simulated an associated weight using purrrs map_dbl. We can plot the height against the weight and see that there is a generally increasing trend, this is expected since our chosen value of the coefficient $$\beta = 0.5$$. qplot(heights, weights) When performing an applied analysis in a business context, it might be tempting to stop here after plotting the relationship between height and weight. However these heights and weights are only a sample of a population - we wish to make statements which pertain to the entire population. If we consider the sample representative of the population then a properly fitted statistical model will allow us to make statements about the population which this sample is drawn from. As an example of a common business problem, this could include sales of a product - we wish to make statements about future sales which we can’t possibly have seen and hence a statistical model is important. ## Fitting the model A parametric model is described by a distribution $$p(y\|\theta)$$ where $$y$$ represents the observed data and $$\theta$$ represents the parameters. These parameters are unknown, but represent properties of the model. The distribution of the observed data is controlled by the values of the parameters, $$\theta$$. The goal of Bayesian inference is to learn which values of the parameters are consistent with the observed data. The parameters are unknown and can’t be determined precisely, however the more data collected the more accurate the posterior inferences can be. In the Bayesian paradigm, the parameters also have a distribution. Before the data is observed, this is referred to as the prior distribution $$p(\theta)$$ which can incorporate the hypothesis of the analyst. The goal is to determine the posterior distribution of the parameters given the observed data, this can be achieved using Bayes theorem: $$p(\theta\|y) = \frac{p(\theta)p(y\|\theta)}{\int_\theta p(\theta)p(y\|\theta)d\theta}$$ The likelihood for linear regression with $$n$$ univariate observations, $$\textbf{y} = y_1,\dots,y_n$$ is written as $p(\textbf{y}\|\psi) = \prod_{i=1}^n\mathcal{N}(\alpha + x_i^T\beta, \tau),$ note that the likelihood is parameterised in terms of the precision $$\tau = \frac{1}{\sigma^2}$$. Standard prior distributions for simple linear regression are chosen to be \begin{align} p(\tau) &= \textrm{Gamma}(\alpha_\sigma, \beta_\sigma), \\ p(\alpha) &= \mathcal{N}(\mu_\alpha, \sigma^2_\alpha), \\ p(\beta) &= \mathcal{N}(\mu_\beta, \sigma^2_\beta). \end{align} ### Gibbs Sampling Gibbs sampling works by alternately sampling from the conditional conjugate distribution. It can often be faster for models which are specified using the conjugate structure, however the choice of prior distribution is not flexible (but the parameterisation is). The algebra below is not required to implement a Gibbs sampling algorithm as there are probabilistic programming languages such as BUGS and JAGS which work out the required maths. Using the likelihood and priors from the section above we can derive the conditionally conjugate posterior distributions: \begin{align} p(\tau\|\textbf{y}, \textbf{x}, \beta, \alpha) &= p(\tau)\prod_{i=1}^np(y_i\|\psi), \\ &= \textrm{Gamma}(\tau\|\alpha_\sigma, \beta_\sigma)\prod_{i=1}^n\mathcal{N}(y_i\|\alpha + x_i^T\beta, \sigma^2), \\ &\propto \tau^{\alpha_\tau-1}e^{-\beta_\tau\tau}\tau^{\frac{n}{2}}\exp\left\{-\frac{\tau}{2}\sum_{i=1}^n(y_i-\alpha - x_i^T\beta)^2\right\}, \\ &= \tau^{\alpha_\tau-1 + \frac{n}{2}}\exp\left\{-\beta_\tau\tau-\frac{\tau}{2}\sum_{i=1}^n(y_i-\alpha - x_i^T\beta)^2\right\},\\ &=\textrm{Gamma}\left(\alpha_\tau+\frac{n}{2}, \beta_\tau +\frac{1}{2}\sum_{i=1}^n(y_i-\alpha - x_i^T\beta)^2\right). \end{align} \begin{align} p(\alpha\|\textbf{y}, \textbf{x}, \beta, \tau) &= \mathcal{N}(\alpha\|\mu_\alpha, \tau_\alpha)\prod_{i=1}^n\mathcal{N}(y_i\|\alpha + x_i^T \beta, \tau), \\ &\propto \tau^{\frac{1}{2}}_\alpha\exp\left\{-\frac{\tau_\alpha}{2}(\alpha-\mu_\alpha)^2\right\}\tau^\frac{n}{2}\exp\left\{-\frac{\tau}{2}\sum_{i=1}^n(y_i-\alpha-x_i^T \beta)^2\right\}, \\ &= \exp\left\{-\frac{\tau_\alpha}{2}(\alpha-\mu_\alpha)^2-\frac{\tau}{2}\sum_{i=1}^n(y_i-\alpha-x_i^T \beta)^2\right\}, \\ &= \exp \left\{ -\frac{1}{2}\left(\alpha^2(\tau_\alpha + n\tau) + \alpha(-2\tau_\alpha\mu_\alpha - 2\tau\sum_{i=1}^n (y_i - x_i^T \beta)) \right) + C \right\}, \\ &= \mathcal{N}\left((\tau_\alpha + n\tau)^{-1}\left(\tau_\alpha + \tau\sum_{i=1}^n (y_i - x_i^T \beta)\right), \tau_\alpha + n\tau\right). \end{align} \begin{align} p(\beta\|\textbf{y}, \textbf{x}, \alpha, \tau) &= \mathcal{N}(\beta\|\mu_\beta, \tau_\beta)\prod_{i=1}^n\mathcal{N}(y_i\|\alpha + x_i^T \beta, \tau), \\ &\propto \tau^{\frac{1}{2}}_\beta\exp\left\{-\frac{\tau_\beta}{2}(\beta-\mu_\beta)^2\right\}\tau^\frac{n}{2}\exp\left\{-\frac{\tau}{2}\sum_{i=1}^n(y_i-\alpha-x_i^T \beta)^2\right\}, \\ &= \exp\left\{-\frac{\tau_\beta}{2}(\beta-\mu_\beta)^2-\frac{\tau}{2}\sum_{i=1}^n(y_i-\alpha-x_i^T \beta)^2\right\}, \\ &= \exp \left\{ -\frac{1}{2}\left(\beta^2(\tau_\beta + \tau\sum_{i=1}^nx_i^2) + \beta(-2\tau_\beta\mu_\beta - 2\tau\sum_{i=1}^n (y_i - \alpha) x_i) \right) + C \right\}, \\ &= \mathcal{N}\left((\tau_\beta + \sum_{i=1}^nx_i^2\tau)^{-1}\left(\tau_\beta + \tau\sum_{i=1}^n (y_i - \alpha )x_i\right), \tau_\beta + \tau\sum_{i=1}^nx_i^2 \right). \end{align} This allows us to construct a Gibbs Sampler for the linear regression model by alternating sampling from the precision, $$\tau$$ given the latest value of the coefficient vector $$\beta$$ and vice versa. The functions to sample from the conditional posterior distributions are written in R as: sample_tau <- function(ys, alpha, beta, alpha0, beta0) { rgamma(1, shape = alpha0 + nrow(ys) / 2, rate = beta0 + 0.5 * sum((ys$y - (alpha + as.matrix(ys$x) %% beta))^2) ) } sample_alpha <- function(ys, beta, tau, mu0, tau0) { prec <- tau0 + tau nrow(ys) mean <- (tau0 + tau * sum(ys$y - as.matrix(ys$x) %% beta)) / prec rnorm(1, mean = mean, sd = 1 / sqrt(prec)) } sample_beta <- function(ys, alpha, tau, mu0, tau0) { prec <- tau0 + tau sum(ys$x * ys$x) mean <- (tau0 + tau * sum((ys$y - alpha) * ys$x)) / prec rnorm(1, mean = mean, sd = 1 / sqrt(prec)) } Then a function which loops through each conditional distribution in turn is defined using the three functions defined above. Each conditional distribution is dependent on the parameter draw made immediately above. gibbs_sample <- function(ys, tau0, alpha0, beta0, m, alpha_tau, beta_tau, mu_alpha, tau_alpha, mu_beta, tau_beta) { tau <- numeric(m) alpha <- numeric(m) beta <- numeric(m) tau[1] <- tau0 alpha[1] <- alpha0 beta[1] <- beta0 for (i in 2:m) { tau[i] <- sample_tau(ys, alpha[i - 1], beta[i - 1], alpha_tau, beta_tau) alpha[i] <- sample_alpha(ys, beta[i - 1], tau[i], mu_alpha, tau_alpha) beta[i] <- sample_beta(ys, alpha[i], tau[i], mu_beta, tau_beta) } tibble(iteration = seq_len(m), tau, alpha, beta) } ys <- tibble(y = weights, x = heights) plan(multiprocess) iters <- future_map_dfr( .x = 1:2, .f = function(x) gibbs_sample( ys, tau0 = 0.5, alpha0 = 60, beta0 = 0.3, m = 1e4, alpha_tau = 3, beta_tau = 2, mu_alpha = 0, tau_alpha = 0.01, mu_beta = 0, tau_beta = 0.01 ), .id = "chain" ) ## Making the Markov chain more efficient In order to get this chain to mix better, the predictor (the height, $$x$$) can be centered by subtracting the mean. This will result in the intercept being higher than when using the untransformed data, since the outcome variable (the weight, $$y$$) is not transformed. In order to recover the value of the parameter gibbs_sample_centered <- function(ys, tau0, alpha0, beta0, m, alpha_tau, beta_tau, mu_alpha, tau_alpha, mu_beta, tau_beta) { tau <- numeric(m) alpha <- numeric(m) beta <- numeric(m) tau[1] <- tau0 alpha[1] <- alpha0 beta[1] <- beta0 mean_x = mean(ys$x) ys$x = ys\$x - mean_x for (i in 2:m) { tau[i] <- sample_tau(ys, alpha[i - 1], beta[i - 1], alpha_tau, beta_tau) alpha[i] <- sample_alpha(ys, beta[i - 1], tau[i], mu_alpha, tau_alpha) beta[i] <- sample_beta(ys, alpha[i], tau[i], mu_beta, tau_beta) } tibble( iteration = seq_len(m), tau, alpha = alpha - mean_x * beta, beta ) } iters_centered <- future_map_dfr( .x = 1:2, .f = function(x) gibbs_sample_centered( ys, tau0 = 0.5, alpha0 = 60, beta0 = 0.3, m = 1e4, alpha_tau = 3, beta_tau = 2, mu_alpha = 0, tau_alpha = 0.01, mu_beta = 0, tau_beta = 0.01 ), .id = "chain" ) iters_centered %>% filter(iteration > 1000) %>% gather(key = "parameter", value, -chain, -iteration) %>% plot_diagnostics_sim(actual_values) The draws from the Gibbs sampling algorithm are draws from the posterior distribution which can be used to produce summaries required for inference using the linear model. Posterior fitted values, ie. a straight line, can be plotted by sampling pairs of values ($$\alpha, \beta$$) from the MCMC output and plotting them using the equation of a straight line ($$y = \alpha + \beta x$$). This gives an indication of the uncertainty in the parameter estimates. ## Citation BibTeX citation: @online{law2019, author = {Jonny Law}, title = {Bayesian {Linear} {Regression} with {Gibbs} {Sampling} in {R}}, date = {2019-06-14}, langid = {en} }	2022-09-28 16:40:21	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.995907723903656, "perplexity": 2339.170514872073}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335257.60/warc/CC-MAIN-20220928145118-20220928175118-00559.warc.gz"}
https://math.stackexchange.com/questions/2319953/finding-poles-and-residues-using-laurent-expansion	# Finding poles and residues using Laurent expansion I would like to find the poles and residues of $$f(z) = \frac {1}{z^2 \sin(\pi (z + \alpha))}$$ Where $0<\alpha<1$. I found the first pole, which is a double pole at $z=0$, and then also there are poles at $z=n-\alpha$. To find the residues I used the Laurent expansion, so for the residue of $z_0 = n - \alpha$ $$f(z) = \frac {a_{-1}}{z-z_0} + a_0 + a_1(z-z_0) + ...$$ I multiplied $f(z)$ by $z-z_0$ and then took the limit as $z \rightarrow z_0$ I don't understand how to then find $a_{-1}$, because I'm not sure what to do after this point: $$\displaystyle \lim_{z\rightarrow z_0} \left[\frac{z-(n-\alpha)}{(n-\alpha)^2 \sin(\pi(z+\alpha))}\right]=a_{-1}$$ I'd appreciate guidance through the method of finding $a_{-1}$ and also what method to use for the $z^2$ pole. The poles at $\;z=n-\alpha\;,\;\;n\in\Bbb Z\;$ are simple , so $$Res_{z=n-\alpha}(f)=\lim_{z\to n-\alpha}\frac{z-(n-\alpha)}{z^2\sin(\pi(z+\alpha))}=\lim_{z\to n-\alpha}\frac1{2z\sin(\pi(z+\alpha)+\pi z^2\cos(\pi(z+\alpha))}=$$$${}$$ $$=\frac1{\pi(n-\alpha)^2\cos\pi n}=\frac{(-1)^n}{\pi(n-\alpha)^2}$$ • To find residue of z^2 pole, would i replace $z-(n-\alpha)$ with $z-0$ to find the residue of $z^2$? Then the z in the numerator and denominator would cancel – inya Jun 12 '17 at 17:36 • @inya The pole at $z=0$ is of order $2$, so you have to use $$res_{z=0} (f) = \displaystyle \lim_{z\to 0} \frac{d}{dz} \left(\frac{z^2}{z^2 \sin(\pi(z+\alpha))}\right)$$ – bob Jun 12 '17 at 17:42 For simple poles, a lot of the time computing the Laurent series isn't the easiest way to do it here are a few tricks: 1) if $f=\frac{h}{g}$ where $h,g$ are holomorphic has a pole at $z=a$ then $Res_{z=a}(f) = \frac{h(a)}{g'(a)}$ 2) or in general, $Res_{z=a}(f) = \lim_{z->a}{(z-a)f(z)}$ (note these only holds for simple poles) So you can use the first trick to find the residues of $n-\alpha$: $Res_{z=n-\alpha}(f) = 1/(\frac{d}{dz}z^2sin(π(z+α))) \|_{z=n-\alpha}$ $=\frac{1}{2zsin(\pi(z+\alpha) + \pi z^2cos(\pi (z-\alpha)))} \|_{z=n-\alpha}$ $=\frac{(-1)^n}{\pi (n-\alpha)^2}$ You can also use trick 2 as you did, to get that to work you can use L'Hopital's rule (as DonAntonio did) Now for the double pole at 0, finding the Laurent series of $sin(\pi (z+ \alpha))$ or $cosec(\pi (z+ \alpha))$ about 0 doesn't look easy so in this case the easiest way might(?) be to use the more general form of trick 2: $Res_{z=a}(f) = \frac{1}{(m-1)!}\lim_{z->a}{\frac{d^{m-1}}{dz^(m-1)}(z-a)^m f(z)}$ , for a pole of order m so in this case: $Res_{z=0}(f) = \frac{d}{dz}cosec(\pi (z+\alpha))\|_{z=0}$ =...	2019-08-18 13:27:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9848197102546692, "perplexity": 185.004835687187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027313889.29/warc/CC-MAIN-20190818124516-20190818150516-00179.warc.gz"}
http://wpressutexas.net/coursewiki/index.php?title=Segment_14_Sanmit_Narvekar	# Segment 14 Sanmit Narvekar Jump to navigation Jump to search ## Segment 14 #### To Calculate 1. Suppose the stopping rule is "flip exactly 10 times" and the data is that 8 out of 10 flips are heads. With what p-value can you rule out the hypothesis that the coin is fair? Is this statistically significant? $\displaystyle \text{Pr(8 or more heads)} = \frac{\binom{10}{8} + \binom{10}{9} + \binom{10}{10}}{2^{10}} = \frac{45 + 10 + 1}{2^{10}} = 0.5469$ If you want a 2 tailed test, since it is symmetric, the pvalue is 0.5469 x 2 = 0.1094. This result is not statistically significant at the 5% or 1% significance levels. 2. Suppose that, as a Bayesian, you see 10 flips of which 8 are heads. Also suppose that your prior for the coin being fair is 0.75. What is the posterior probability that the coin is fair? (Make any other reasonable assumptions about your prior as necessary.) $\displaystyle P(p \| data) = P(data\|p) P(p) =$ 3. For the experiment in the segment, what if the stopping rule was (perversely) "flip until I see five consecutive heads followed immediately by a tail, then count the total number of heads"? What would be the p-value? #### To Think About 1. If biology journals require p<0.05 for results to be published, does this mean that one in twenty biology results are wrong (in the sense that the uninteresting null hypothesis is actually true rather than disproved)? Why might it be worse, or better, than this? (See also the provocative paper by Ioannidis, and this blog in Technology Review (whose main source is this article). Also this news story about ESP research. You can Google for other interesting references.)	2021-03-02 20:41:47	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 2, "math_score": 0.7443629503250122, "perplexity": 865.39394335978}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 5, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178364764.57/warc/CC-MAIN-20210302190916-20210302220916-00530.warc.gz"}
https://technology.amis.nl/2007/06/23/oracle-11g-first-impressions/	# Oracle 11g – First Impressions Marco Gralike The official launch is at hand. In less then 3 weeks Oracle 11g will be presented at the world during a, probably, great launch event in New York. AMIS entered the beta test program in August 2006. It was the first time we participated in beta testing and I think, we are honored and lucky to share now our thoughts and we were allowed to test the software in advance. So living towards the event, lets share some first impressions I got during those first encounters with the new database software. When I installed for the first time the beta software, it was like unwrapping a new present. I like presents (who doesnâ€™t). AMIS will do a lot unwrapping, after the 11g launch, but letâ€™s tell you what my first impressions were (based, for now, on the current Windows version, to make it more visual). Be aware, the following is based on a beta release and a lot can still change or repackaged, when officially launched and delivered at your doorstep. The new and the old After installation of the Oracle Database Windows software, some small items are immediately noticeable. The official launch is at hand. In less than 3 weeks Oracle 11g will be presented at the world during a, probably, great launch event in New York. AMIS entered the beta test program in the end of Juli, early August 2006. It was the first time we participated in beta testing and I think, we are honored (to test the software in advance) and lucky now to share our thoughts. So living towards the event, lets share some first impressions I got during those first encounters with the new database software. When I installed for the first time the beta software, it was like unwrapping a new present. I like presents (who doesnâ€™t). AMIS will do a lot unwrapping, after the 11g launch, but letâ€™s tell you what my first impressions were (based, for now, on the current Windows version, to make it more visual). Be aware, the following is based on a beta release and a lot can still change or repackaged, when officially launched and delivered at your doorstep. ## The new and the old After installation of the Oracle Database Windows software, some small items are immediately noticeable. One of my favorites is gone: the sqlplusW.exe executable. I shouldnâ€™t have been surprised, because this was announced a long time ago, now it finely was excluded from the trench lines included its web variant: iSQLPlus. Some of you will see this as a great step forward. I will dearly miss my companion on Windows, because the Windows command shell is not one of my favorite shells, so I will have to find an alternative (or maybe execute it from within Cygwin). Donâ€™t be afraid, the actual sqlplus.exe is still packaged with the software. I worked with Oracle on Windows since Windows NT 3.0. So after a long line of changing from sqldba.exe to svrmgrl.exe to sqlplus.exe; now the sqlplus.exe executable is here to stay. There are still some little differences between Windows and other operating systems, regarding naming and utiltities, but these becoming the exception to the rule, which makes, for instance, describing what you are doing and writing documentation more general and more applicable to more operating systems. What came in itâ€™s place? SQLDeveloper. As said, a lot of you, will now stand-up and cheer, especially because it becomes a very interesting and powerful tool to do your database and programming work. After installation on Windows a new directory is added (C:\Oracle\product\11.1.0\db_1\sqldeveloper) where SQLDeveloper and itâ€™s supporting packaging reside. Whatâ€™s also immediately noticeable? APEX ! From 11g and probably onwards, APEX has claimed its own place / directory (C:\Oracle\product\11.1.0\db_1\apex) and will be installed when you install the database software. I guess I donâ€™t have to mention much about APEX, it is already here for a while, and it is a great environment to setup small web applications and more (who knows how mature this software environment will become in the future!). ## Fault Diagnosabilty Infrastructure (FDI) In the software directory structure, a small directory called â€œdiagâ€ is created (and easily overlooked) which is the first sign of big steps regarding manageability of, among others, diagnosing and tracing database and client events. The original bdump, udump and cdump structures, being dedicated for tracing and alert have been replaced (the first steps are now at hand) by the new Fault Diagnosabilty Infrastructure. ### Manageability All information about diagnose information, alerting and tracing and more, will now reside in one place. This has a lot of advantages regarding manageability of all this kind of information for all databases on one node. It is the first step to the new diagnosable infrastructure and one of the consequences is that a lot of information is not presented in plain text, but now shown in XML format. ### New tooling One of the new tool introduced in 11g is the ADRCI tool that can present you the XML information in the diag directory structure, in the old known format or, for example, grep on things like â€œORA-â€œ from the log.xml (new alert.log replacement). It has also fun stuff like â€“tail parameter where the tool shows the same behavior like the â€œtail â€“fâ€ on Linux or UNIX (and we are still talking Windows environment here!). So when I was talking about annoying old Windows command shell behavior, here the new software gives us a hand with Linux, UNIX common solutions. Maybe after a while I donâ€™t have to use alternatives like Cygwin or the sourceforge utility set on Windows, which you can find by the way at http://unxutils.sourceforge.net, because there will be an option, in this case, with the Oracle software embedded alternative (like the ADRCI tool example already shows). The old alert and trace files are not completely replaced by this new infrastructure and can still be found. Most of them reside now in the directory O:\diag\rdbms\beta4\beta4\trace. My example Windows database has the ORACLE_SID â€œbeta4â€. This is reflected in the directory diag structure by recursively â€œrdbmsâ€, database name â€œbeta4â€, database SID â€œbeta4â€ and then a â€œtraceâ€ directory. ## Using the Database Configuration Assistant Regarding new Oracle software, my first steps always start with using the dbca utility, aka the Database Configuration Assistant tool, to create an out of the box demo environment. If I have time, that is, if I take the time, I will use the Database Configuration Assistant for creating a demo environment based on scripting (the â€œcustom databaseâ€ option). So I will avoid the RMAN restore actions and it will give me database scripting which I can explore. By doing this, it will give me a first impression of; whatâ€™s new, whatâ€™s changed, etc.â€¦ The downside is, because I almost always use my laptop for such an exercise, or a small virtual machine environment, that It will take more time to create the database (its build from scratch), because my laptop isn’t as powerful as a server environment (at least mine isn’t). ### More security aware Most of the starting screens are the same as you and I are used to. Some are not. One of these screens announces the more tightened security policies and possibilities under Oracle 11g. A screen is presented with the new â€œEnhanced default 11g Securityâ€ settings or â€œRevert to the pre-11g default Securityâ€ settings. Among others, you enable here, when choosing the default 11g Security option, auditing and using a new default password profile. ### More options The Database Configuration Assistant Database options screen shows options for â€œOracle Database Vaultâ€ and â€œOracle Database Options for .Netâ€. The Standard Database Components screen enables you now to install APEX via the Database Configuration Assistant. ### Improved It now also has an option to customize XMLDB features, in this case to enable or disable the Protocol Server and set the desired ports for HTTP(s) and WebDAV or FTP(s). Knowing how many times these kinds of questions are asked on the OTN XMLDB forum, this is a welcome addition for a lot of people, and probably also simple to implement because this it is nowadays very easy to enable or disable the Protocol Server via the dbms_xdb package. But then again, isnâ€™t it always easy, if you know howâ€¦ ### New features The next Initialization panel show one of the other new features: Automatic Memory Management. This is already discussed a little bit on the internet and if possible I will discuss this in a later post. Under the â€œAll Initialization Parametersâ€ button you are able to see (under â€œshow advancedâ€) that on my desktop these settings are influenced by MEMORY_MAX_TARGET and MEMORY_TARGET initialization parameters. SGA and PGA can now be controlled as one, by Oracle (the next step after the introduction of SGA_TARGET and SGA_MAX_SIZE). After setting the parameters according to you wishes, as you are used, the next screen will show you a summery and after that gives you the option to create the database (et all: APEX, XMLDB, etc) and or create scripts. ### Wrap-up This will now give a glance at the database create scripts generated in the default %ORACLE_BASE%\admin\%ORACLE_SID%\scripts directory (Linux/Unix notations would have been $ORACLE_BASE\admin\$ORACLE_SID\scripts). Examining the scripting will give you an awful lot of new information of how things have been changed or how new features are implemented. This concludes this first post. Of course there is still a lot to explain, but there are to many things that have been improved, changed, discarded or altered to mention in this first post. More can be expected here or, if you are interested in XMLDB features will come up on my XMLDB (promo) site http://blog.gralike.com 😉 Marco ## Disclaimer! The information demonstrated and shared here is based on Oracle beta software. The following is intended to outline Oracle’s general product direction. It is intended for information purposes only, and may not be incorporated into any contract. It is not a commitment to deliver any material, code, or functionality, and should not be relied upon in making purchasing decisions. The development, release, and timing of any features or functionality described for Oracle’s products remains at the sole discretion of Oracle. ## 3 thoughts on “Oracle 11g – First Impressions” 1. I am looking to build a proper website that will enable viewers to leave information etc. Along with other interesting features. I am planning to use ASP, C#, SQL express and some tool for the web GUI. I would be interested in your comments and suggestions. Very kind regards, Ravji 2. Marco Gralike says: 3. Doug Burns says: Thanks for that, Marco. I haven’t been involved in beta testing, so it’s interesting stuff. Cheers, Doug ## SQL Challenge - Planning a Conference Schedule Facebook0TwitterLinkedinComing Wednesday, we organize the fourth AMIS Academy (Wednesday 27th June – free mini-conference at our place), a mini-conference with 16 presentations in four consecutive timeslots. One of our challenges in organizing this conference is planning the presentations. Ideally, every one can visit as many of their preferred sessions as […]	2020-07-08 23:23:34	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3705917000770569, "perplexity": 2848.9308343815114}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655897707.23/warc/CC-MAIN-20200708211828-20200709001828-00491.warc.gz"}
https://gm0.copperforge.cc/en/stable/docs/robot-design/power-transmission/gears.html	# Gears¶ Gears, like sprockets and pulleys, are used in power transmission for three common applications: changing the direction of power, changing the amount of torque, and changing RPM. Gears are a less common transmission option than chain, but are still very viable for most use cases. Gears are equally as reliable as chain, but can’t be used for transferring power over long distances. Many teams dislike gears when using kit-based channels because the hole pattern limits which combinations of gears can be used. Consequently, it may be difficult to achieve a desired specific gear ratio. However, with systems, it’s very easy to use different ratios, since the gears can be moved around in extrusion. Gears are made in different materials, with the most common being 7075 aluminum. Never mesh plastic and metal gears together. It is acceptable to mesh different types of metal gears together, as long as they have the same diametral pitch. It is advised to stay away from TETRIX aluminum gears as they wear down very easily. Some REV gears are made out of Delrin, a self-lubricating plastic. It is a durable material, but keep in mind that it is very possible to strip the bore using a plastic gear. Thus, we advise using the REV Hex Hub Strengthener to avoid stripping the bore on Delrin gears. Bevel gears are a special type of gear that allows power transmission in two different planes. It is especially useful in tight spaces where a regular motor mounting position would not work. ## Terms¶ • Module refers to the amount of diametral pitch in millimeters per tooth. Simply, it refers to the tooth size. Typically, gears of the same material from the same manufacturer should have the same module. * Diametral pitch (DP) refers to the gear tooth size. It is expressed as the number of teeth per inch of pitch diameter. Teeth size varies inversely with DP. * Pitch diameter (PD) refers to the diameter of the imaginary pitch circle that is drawn when the gear is meshed with the pitch circle of another gear. For gears, PD < OD. \begin{align}\begin{aligned}PD = Module * Number\ of\ Teeth\\PD = \frac{Number\ of\ Teeth}{PD}\\PD = OD - (2 * Module)\end{aligned}\end{align} • Outer diameter (OD) refers to the actual outside diameter of the gear. Simply, it is the circle that the outer face of the tooth draws when it rotates around. • Pitch circle refers to an imaginary circle that contacts the pitch circle of any other gear with which it is in mesh. Basically, each gear has a pitch circle. When gear 1 is meshed with gear 2, the pitch circles of both gears should touch exactly in the middle of where the teeth interlock with each other. ## Meshing Gears¶ Note Be sure to never gears that are not of the same diametral pitch. (A notable exception is 32 diametral pitch and 0.8 MOD gears. These are close enough to be perfectly fine.) When meshing gears, it is important that the gears are not too loose nor too tight. If the gears are too loose, the teeth will easily wear out, decreasing its longevity. If the gears are too tight, however, they will have too much friction and possibly grind or bind up. The ideal way to mesh gears are to make sure the teeth interlock and just touch the base of the gear. Attention If possible, it’s best to avoid meshing gears with a clamping motor mount – due to the sensitivity of the mesh, even the slightest movement of the motor inside the clamping mount can cause the gears to slip or damage each other. Calculating center-to-center distances using gears is quite simple. In order to calculate the desired center distance between two given gears, you must know the number of teeth for each gear and the diametral pitch of your gears (the number of teeth per inch of the gear’s diameter). With these two pieces of information, you can use the equation $$D=\frac{T_{1}+T_{2}}{P}$$. In this equation, $$D$$ is the distance between the center of both gears, $$T_1$$ and $$T_2$$ are the number of teeth of each gear in question, and $$P$$ is the diametral pitch of the gears. The module (abbreviated MOD) of a gear is used similarly to diametral pitch. It is the number of millimeters of the gear’s diameter per tooth of the gear. The equation to find center distance $$D$$ is $$D = \frac{(T_{1} + T_{2}) * M}{2}$$, where $$T_{1}$$ and $$T_2$$ are the number of teeth of each gear in question, and $$M$$ is the module of the gear. Additionally, it is possible to average the pitch diameters of the two gears to find the correct center-to-center distance. Correct gear mesh As with sprockets, it is important to line up the gears so that they do not accidentally slip. Especially when using extrusion, it is possible that the gear may not be parallel to the extrusion, as the two supporting ends may not be perfectly in line with one another. It is imperative that the gear be lined up as straight as possible to prevent damage or gear binding. It is highly recommended to use white lithium grease or a similar lubricant between the gears to reduce friction and possible binding. • Gears are a solid and proven power transmission method. Early examples of gears date back to the 4th century BC, so you’re using technology with millennia of development behind it. When it comes to gears, there’s not much that we haven’t figured out. • Gears are simple to use with both channel and extrusion. On channel, your gears are already spaced correctly - you just need to choose the right pair of gears. Extrusion gives you even more flexibility - just slide your gears into mesh, and you can have whatever ratio you want. • Gears can give you big reductions in small areas. Depending on the gear combination, one can achieve big ratios in reduction in very small spaces (for example, a 10 tooth gear and a 100 tooth gear will take much less space than a 10 tooth sprocket and a 100 tooth sprocket). • Gears require no tensioning: once the spacing is correct, the gears will operate quickly. Unlike chain or belt, there is nothing further transferring the power, which cuts out the need to properly tension chain or belt. This of course has the drawback of not being able to transfer power far distances.	2021-02-26 19:37:56	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4628128111362457, "perplexity": 1218.150164811108}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178357935.29/warc/CC-MAIN-20210226175238-20210226205238-00309.warc.gz"}
http://tex.stackexchange.com/questions/83085/how-to-improve-listings-display-of-json-files?answertab=oldest	# How to improve listings display of JSON files? I was wondering if there is a good way for JSON files to be listed with the listings package. The only language definition I could come up with, is this: \lstdefinelanguage{json} { morestring=[b]", morestring=[d]' } Now, this highlights the strings used in JSON files, but the important syntactical things in JSON are the curly braces, the square brackets, commas, and colons. I have sadly no Idea how I could make them be highlighted in a different manner. I tried adding { and } as identifier or as keywords, but it didn't work. I'd really like to make listed JSON files appear nicer, since on a project I need to document I'd really need it. Also, I couldn't find a JSON definition for that on the internet, anywhere else. On a more general thought: can I highlight all numerals with listings? - the full json definition is on the page json.org – David Carlisle Nov 17 '12 at 15:04 @DavidCarlisle yes, I know that, but I still don't know how to construct a language definition for listings. Symbols such as { are not accepted as keywords. Or I'm doing something wrong. – polemon Nov 17 '12 at 15:39 ah sorry I misread your comment – David Carlisle Nov 17 '12 at 15:55 I updated my answer; I initially overlooked the numerals issue; now I've added it to my answer. – Gonzalo Medina Nov 17 '12 at 16:55 both single- and double-quoted strings should probably have the [b] type as they are backslash-escaped in JSON (and Javascript). – mlc Apr 8 at 20:01 Here's one possibility for the colon, comma, braces, square brackets, and numbers, using the literate key: \documentclass{article} \usepackage{bera}% optional: just to have a nice mono-spaced font \usepackage{listings} \usepackage{xcolor} \colorlet{punct}{red!60!black} \definecolor{background}{HTML}{EEEEEE} \definecolor{delim}{RGB}{20,105,176} \colorlet{numb}{magenta!60!black} \lstdefinelanguage{json}{ basicstyle=\normalfont\ttfamily, numbers=left, numberstyle=\scriptsize, stepnumber=1, numbersep=8pt, showstringspaces=false, breaklines=true, frame=lines, backgroundcolor=\color{background}, literate= *{0}{{{\color{numb}0}}}{1} {1}{{{\color{numb}1}}}{1} {2}{{{\color{numb}2}}}{1} {3}{{{\color{numb}3}}}{1} {4}{{{\color{numb}4}}}{1} {5}{{{\color{numb}5}}}{1} {6}{{{\color{numb}6}}}{1} {7}{{{\color{numb}7}}}{1} {8}{{{\color{numb}8}}}{1} {9}{{{\color{numb}9}}}{1} {:}{{{\color{punct}{:}}}}{1} {,}{{{\color{punct}{,}}}}{1} {\{}{{{\color{delim}{\{}}}}{1} {\}}{{{\color{delim}{\}}}}}{1} {[}{{{\color{delim}{[}}}}{1} {]}{{{\color{delim}{]}}}}{1}, } \begin{document} \begin{lstlisting}[language=json,firstnumber=1] "id": "file", "value": "File", "popup": { {"value": "New", "onclick": "CreateNewDoc()"}, {"value": "Open", "onclick": "OpenDoc()"}, {"value": "Close", "onclick": "CloseDoc()"} ] } }} 0123456789 \end{lstlisting} \end{document} - One issue is that in a number-alphabet combination (such as a web address), the numbers also get highlighted in the same manner as standalone numbers, while alphabets don't get highlighted, which makes it a little bit weird. – AnonJ Dec 14 at 6:47	2014-12-19 21:10:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9267621040344238, "perplexity": 2804.5754335130723}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1418802768957.83/warc/CC-MAIN-20141217075248-00131-ip-10-231-17-201.ec2.internal.warc.gz"}
https://www.codingame.com/training/easy/hidden-messages-in-images	• 223 ## Learning Opportunities This puzzle can be solved using the following concepts. Practice using these concepts and improve your skills. ## Goal Steganography in images is to hide information in pixels of images imperceptibly to the human eye. In this problem there are ASCII messages hidden in the image pixels. More specifically, the least significant bit of each pixel represents a piece of the ASCII message. Every 8 consecutive bits we have a byte, convert that byte into an ASCII value. To make your life easier, images will always have a number of pixels multiple of 8. Print all ASCII characters extracted from the image. Example Given an input image with width = 4 and height = 4 106 19 134 22 161 192 98 184 52 51 97 88 208 63 58 25 106 => 01101010 => less significant bit => 0 19 => 00010011 => less significant bit => 1 134 => 10000110 => less significant bit => 0 22 => 00010110 => less significant bit => 0 161 => 10100001 => less significant bit => 1 192 => 11000000 => less significant bit => 0 98 => 01100010 => less significant bit => 0 184 => 10111000 => less significant bit => 0 52 => 00110100 => less significant bit => 0 51 => 00110011 => less significant bit => 1 97 => 01100001 => less significant bit => 1 88 => 01011000 => less significant bit => 0 208 => 11010000 => less significant bit => 0 63 => 00111111 => less significant bit => 1 58 => 00111010 => less significant bit => 0 25 => 00011001 => less significant bit => 1 Extracted bits => 0100100001100101 Split binary information into bytes => [ "01001000", "01100101"] Map bytes to ASCII => ["H", "e"] Output => He Input Line 1: Two integers w, h for the dimensions of the image. Next h lines: w space separated integers for the pixels of the image. Output ASCII message extracted from the image Constraints 8 ≤ w,h ≤ 50 w*h % 8 == 0 Example Input 8 12 220 251 30 182 233 122 150 30 132 101 135 212 246 201 128 203 62 33 39 70 73 175 218 140 44 165 9 140 83 67 34 100 142 75 125 242 49 175 209 37 252 26 123 6 186 72 230 94 218 85 228 205 146 67 219 187 194 159 81 190 51 235 41 121 208 33 245 71 172 218 97 130 122 31 135 198 135 249 174 28 162 109 149 216 156 195 140 10 100 252 1 164 150 22 144 109 Output Hello World! A higher resolution is required to access the IDE Join the CodinGame community on Discord to chat about puzzle contributions, challenges, streams, blog articles - all that good stuff! Online Participants	2021-08-03 00:09:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28817591071128845, "perplexity": 1247.4048634885855}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154408.7/warc/CC-MAIN-20210802234539-20210803024539-00326.warc.gz"}
https://scicomp.stackexchange.com/questions/26767/dirichlet-term-in-error-estimations	# Dirichlet term in error estimations I am working on a method based on moving least square approximation where shape functions do not satisfy Kroneker Delta property. So Dirichlet boundary condition should be enforced. I usually used penalty method for that. In the error estimation based on residual I used the following for Poisson equation: \begin{align} \eta^2=h_T^2\Vert \Delta u+f \Vert^2+h_T^{-1} \Vert u-g_D\Vert^2_{\partial \Omega}. \end{align} where \begin{align} -\Delta u=f, \quad u_{\|\partial \Omega}=g_D. \end{align} Also, it should be noted that, because of the shape functions there is no jump between the internal elements. The problem is that penalty parameter $\gamma$ should be bigger than $1e3$ to get good result. But for large $\gamma$ the effect of adaptive technique is not really good. All the time results by adaptive refinement is better than uniform. But when $\gamma$ is smaller for example $\gamma< 1e2$ the difference is remarkable. By these results I guess the term relates to Dirichlet boundary should be change by $\gamma$. But how?	2021-10-18 03:35:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9771100282669067, "perplexity": 529.3837687731288}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585196.73/warc/CC-MAIN-20211018031901-20211018061901-00165.warc.gz"}
https://techwhiff.com/learn/birthaay-paradox-take-2-homework-unanswered-at/441715	# Birthaay Paradox: Take 2 Homework. Unanswered At the end of June, a bunch of customers all... ###### Question: Birthaay Paradox: Take 2 Homework. Unanswered At the end of June, a bunch of customers all having birthdays in July enter a bakery to order cakes for their July birthday celebrations. How many such customers must there be so that there is at least a 50% chance (>=.5 probability) that at least two of them were born on the same day in July (ignore the year). Assume that there are no other customers in the store and that there are no concerns about social distancing etc. Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a 5 b 7 с 9 d 11 e 13 f 15 g 17 h 19 .- 21 i 23 Linear Congruential Generator Homework • Unanswered Which of the following criteria are necessary and sufficient for a Linear Congruential Generator Xn+1 (aXn + b)modm- with non-zero b - to have a full period m (i.e. all m numbers in 0... m-1 are obtained before the cycle repeats itself)? n+1 = Multiple answers: Multiple answers are accepted for this question Select one or more answers and submit. For keyboard navigation... Show More a the greatest common divisor of a and is 1 b a-1 is divisible by 4 if m is divisible by 4 с a-1 is divisible by all prime factors of m d None of the above Linear Congruential Generator: Example 2 Homework • Unanswered What is the period-length of the Linear Congruential Generator Xn+1 = (1Xn + 5)mod13 with seed Xo = 1? Numeric Answer: 0 Cannot be empty #### Similar Solved Questions ##### With Medicare Access and CHIP Reauthorization, what score must Merit Based Incentive Payments System eligible clinicians... With Medicare Access and CHIP Reauthorization, what score must Merit Based Incentive Payments System eligible clinicians achieve to receive the maximum number of points in the composite score and what are the maxiumum number of points?... ##### You decide to build a small generator by rotating a coiled wire inside a static magnetic... You decide to build a small generator by rotating a coiled wire inside a static magnetic field of 0.34 T. You construct the apparatus by coiling wire into 3 loops of radius 0.17 m. If the coils rotate at 2.0 revolutions per second and are connected to a device with 140Ω resistance, calculate t... ##### 1. An average nerve axon is about 5x10-6m in radius, and the axoplasm that composes the... 1. 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Identify Mendel’s particles and briefly explain the mechanism behind each of his two laws.... ##### How do you convert -220 degrees to radians without a calculator? How do you convert -220 degrees to radians without a calculator?... ##### A 25 KVA 380/100 V conventional (two winding) transformer is to be used as an auto... A 25 KVA 380/100 V conventional (two winding) transformer is to be used as an auto transformer. Sauto = kVA according to the configuration is 090 IL Vu = 480 source 192 VL= 380 load 31.58 120 48 95 None of these... ##### Write a function rule the relates the inout X and output Y: (0,1), (1,4), (2,7), (3,10) please help write a function rule the relates the inout X and output Y: (0,1), (1,4), (2,7), (3,10)please help! I can't get this one.....	2022-11-27 02:46:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3559742867946625, "perplexity": 2482.6590271189084}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710155.67/warc/CC-MAIN-20221127005113-20221127035113-00185.warc.gz"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?t=26344	## Irreversible Expansion $w=-P\Delta V$ and $w=-\int_{V_{1}}^{V_{2}}PdV=-nRTln\frac{V_{2}}{V_{1}}$ Abigail Urbina 1K Posts: 102 Joined: Thu Jul 27, 2017 3:01 am ### Irreversible Expansion I know that Dr. Lavelle went over this in lecture yesterday a little bit, but can someone please explain to me exactly what an irreversible expansion is? And why is it irreversible? If I understand this correctly, I know that a reversible expansion can be reversed through an infinitesimal change (small fluctuation) in the internal and external pressures. Also, work is a reversible process when the system is at equilibrium. Can someone please give a more specific conceptual definition of irreversible expansion and how it differs with reversible expansion? Katie Lam 1B Posts: 52 Joined: Fri Sep 29, 2017 7:06 am ### Re: Irreversible Expansion Irreversible expansion is irreversible because pressure is reduced much more quickly than in a reversible reaction, where the pressure changes very slowly and maximum work is done. In irreversible processes, the system is not in thermodynamic equilibrium the entire time while in reversible processes, it is. Sarkis Sislyan 1D Posts: 31 Joined: Thu Jul 27, 2017 3:00 am ### Re: Irreversible Expansion Dr. Lavelle gave the example in lecture of a piston with internal pressure of 2 atm and an external pressure of 1 atm. With nothing being done to keep the piston in place (such as a pin being inserted), the internal pressure would push up against the weaker external pressure in a sudden movement. This is an irreversible reaction. A reversible reaction instead would have both the internal and external pressure be equivalent at 2 atm. In this case, there would need to be many many small movements in order to raise the piston. In this case, the reaction can be reversed by making infinitesimally small changes to factors such as pressure, but in an irreversible reaction, this is not the case. Yeyang Zu 2J Posts: 58 Joined: Fri Sep 29, 2017 7:06 am ### Re: Irreversible Expansion First, reversible process is one that can be reversed by an infinitely small change in infite-small change for example, 2 systems are both under 2 atm pressure, they could push/pull each other with a tiny small change in volume, it works the same for both directions however, if the 2 system are one 1 atm and another 2 atm, push/pull to two different directions representing two different results due to the pressure difference	2020-10-30 19:26:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.575285017490387, "perplexity": 848.564299246231}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107911229.96/warc/CC-MAIN-20201030182757-20201030212757-00173.warc.gz"}
https://clay6.com/qa/48689/the-value-of-13c-2-13c-3-13c-4-13c-is	The value of $13C_2+13C_3+13C_4+....13C_{13}$ is $\begin{array}{1 1}(A)\;2^{13}-13\\(B)\;2^{13}-14\\(C)\;\text{an odd No. }\neq 2^{13}-12\\(D)\;\text{an even No. }\neq 2^{13}-14\end{array}$	2020-09-18 17:50:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6164352297782898, "perplexity": 50.99795003572028}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400188049.8/warc/CC-MAIN-20200918155203-20200918185203-00770.warc.gz"}
https://math.stackexchange.com/questions/1547915/use-complex-integrals-residue-to-evaluate-int-0-infty-fracdxx13-1	# Use Complex Integrals/ Residue to evaluate $\int_0^\infty \frac{dx}{(x+1)^3 + 1}$ Use Complex Integrals/ Residue to evaluate $\int_0^\infty \frac{dx}{(x+1)^3 + 1}$ I'm not sure how to do this integration. It looks like partial fractions but I'm unsure. • are u forced to use residue theorem? this integral is easier solved by other methods – tired Nov 26 '15 at 23:34 Generally, we can evaluate integrals of the form $$\int_0^{\infty} dx \, f(x)$$ using a contour integral of the form $$\oint_c dz \, f(z) \log{z}$$ As long as $f$ is sufficiently well-behaved at the origin and at infinity and in between, we have $$-i 2 \pi \int_0^{\infty} dx \, f(x) = i 2 \pi \sum_k \operatorname*{Res}_{z=z_k} f(z) \log{z_k}$$ In this case $$f(z) = \frac1{(1+z)^3+1}$$ so that, for $k \in \{0,1,2\}$: $$z_k = -1 + e^{i (2 k+1) \pi/3} = -\left [1-\cos{(2 k+1) \frac{\pi}{3}}\right ] + i \sin{(2 k+1) \frac{\pi}{3}}$$ Thus, $$\int_0^{\infty} \frac{dx}{(1+x)^3+1} = -\sum_{k=0}^2 \frac{\log{z_k}}{3 e^{i 2 (2 k+1) \pi/3}}$$ where \begin{align}\log{z_k} &= \log{\|z_k\|} + i \arg{z_k} \\ &= \log{2 \left \| \sin{(2 k+1) \frac{\pi}{6}} \right \|} - i \arctan{\cot{(2 k+1) \frac{\pi}{6}}} \\ &= \log{2} - i \frac{\pi}{2} + \log{\sin{(2 k+1) \frac{\pi}{6}}} + i (2 k+1) \frac{\pi}{6}\end{align} so that \begin{align}\sum_{k=0}^2 \frac{\log{z_k}}{3 e^{i 2 (2 k+1) \pi/3}} &= -i \frac13 \frac{\pi}{3} e^{-i 2 \pi/3} + \frac13 \log{2} e^{-i 2 \pi} + i \frac13 \frac{\pi}{3} e^{i 2 \pi/3}\\ &= -\frac{2 \pi}{9} \sin{\frac{2 \pi}{3}} + \frac13 \log{2}\end{align} Finally, we may conclude that $$\int_0^{\infty} \frac{dx}{(1+x)^3+1} = \frac{\pi}{3 \sqrt{3}} - \frac13 \log{2}$$ This agrees with a numerical integral in Mathematica v 9.0. We have $$I = \int_0^{\infty} \dfrac{dx}{(1+x)^3+1} = \int_1^{\infty} \dfrac{dx}{x^3+1} = \int_1^0 \dfrac{-dx/x^2}{1/x^3+1} = \int_0^1 \dfrac{xdx}{1+x^3}$$ Hence, $$I = \int_0^1\dfrac{x+1}{3(x^2-x+1)}dx - \int_0^1\dfrac{dx}{3(x+1)} = \dfrac{\pi}{3\sqrt{3}}-\dfrac{\log2}3$$ $$I=\int_{0}^{+\infty}\frac{dx}{(x+1)^3+1}=\int_{1}^{+\infty}\frac{dx}{x^3+1}=\int_{0}^{1}\frac{x}{1+x^3}\,dx$$ The roots of $1+x^3$ lie at $-1,\xi=\frac{1+i\sqrt{3}}{2},\bar{\xi}=\frac{1-i\sqrt{3}}{2}$ and they are simple. Since: $$\text{Res}\left(\frac{x}{1+x^3},x=-1\right) = -\frac{1}{3}$$ the partial fraction decomposition of $\frac{x}{1+x^3}$ is given by: $$\frac{x}{1+x^3} = -\frac{1}{3(x+1)}+\frac{1+x}{3(1-x+x^2)}$$ and: $$I = \frac{1}{2}-\frac{1}{5}+\frac{1}{8}-\frac{1}{11}+\ldots = \color{red}{-\frac{\log(2)}{3}+\frac{\pi}{3\sqrt{3}}}.$$ • Jack, no offense, but your previous answer was wrong and your correction was merely a change to the correct answer provided by others. I think you really should show correction to a step as well. For example, are you sure your partial fractions decomposition is correct? Hint: @Leg got it right. – Ron Gordon Nov 27 '15 at 10:44 • @RonGordon: no offense took, but I simply forgot to divide by three, then fixed it wrong. The decomposition $$\frac{x}{1+x^3}=-\frac{1}{3(x+1)}+\frac{1+x}{3(1-x+x^2)}$$ is now correct. – Jack D'Aurizio Nov 27 '15 at 10:48 • Jack, with you I figured it was something as trivial as that. – Ron Gordon Nov 27 '15 at 10:56 HINT: $$\int\frac{1}{\left(x+1\right)^3+1}\space\text{d}x=$$ Substitute $u=x+1$ and $\text{d}u=\text{d}x$: $$\int\frac{1}{u^3+1}\space\text{d}u=$$ $$\int\left(\frac{2-u}{3(u^2-u+1)}+\frac{1}{3(u+1)}\right)\space\text{d}u=$$ $$\frac{1}{3}\int\frac{2-u}{u^2-u+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$\frac{1}{3}\int\left(\frac{3}{2(u^2-u+1)}-\frac{2u-1}{2(u^2-u+1)}\right)\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$-\frac{1}{6}\int\frac{2u-1}{u^2-u+1}\space\text{d}u+\frac{1}{2}\int\frac{1}{u^2-u+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ Substitute $s=u^2-u+1$ and $\text{d}s=(2u-1)\space\text{d}u$: $$-\frac{1}{6}\int\frac{1}{s}\space\text{d}s+\frac{1}{2}\int\frac{1}{u^2-u+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$-\frac{\ln\|s\|}{6}+\frac{1}{2}\int\frac{1}{u^2-u+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$-\frac{\ln\|s\|}{6}+\frac{1}{2}\int\frac{1}{\left(u-\frac{1}{2}\right)^2+\frac{3}{4}}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ Substitute $p=u-\frac{1}{2}$ and $\text{d}p=\text{d}u$: $$-\frac{\ln\|s\|}{6}+\frac{1}{2}\int\frac{1}{p^2+\frac{3}{4}}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$-\frac{\ln\|s\|}{6}+\frac{1}{2}\int\frac{4}{\frac{4p^2}{3}+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$-\frac{\ln\|s\|}{6}+\frac{2}{3}\int\frac{1}{\frac{4p^2}{3}+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ Substitute $2=\frac{2p}{\sqrt{3}}$ and $\text{d}w=\frac{2}{\sqrt{3}}\space\text{d}p$: $$-\frac{\ln\|s\|}{6}+\frac{1}{\sqrt{3}}\int\frac{1}{w^2+1}\space\text{d}u+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ $$-\frac{\ln\left\|s\right\|}{6}+\frac{\arctan\left(w\right)}{\sqrt{3}}+\frac{1}{3}\int\frac{1}{u+1}\space\text{d}u=$$ Substitute $v=u+1$ and $\text{d}v=\text{d}u$: $$-\frac{\ln\left\|s\right\|}{6}+\frac{\arctan\left(w\right)}{\sqrt{3}}+\frac{1}{3}\int\frac{1}{v}\space\text{d}v=$$ $$-\frac{\ln\left\|s\right\|}{6}+\frac{\arctan\left(w\right)}{\sqrt{3}}+\frac{\ln\left\|v\right\|}{3}+\text{C}=$$ $$-\frac{\ln\left\|s\right\|}{6}+\frac{\arctan\left(\frac{2p}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\ln\left\|v\right\|}{3}+\text{C}=$$ $$-\frac{\ln\left\|s\right\|}{6}+\frac{\arctan\left(\frac{2\left(u-\frac{1}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\ln\left\|v\right\|}{3}+\text{C}=$$ $$-\frac{\ln\left\|u^2-u+1\right\|}{6}+\frac{\arctan\left(\frac{2\left(u-\frac{1}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\ln\left\|u+1\right\|}{3}+\text{C}=$$ $$-\frac{\ln\left\|(x+1)^2-(x+1)+1\right\|}{6}+\frac{\arctan\left(\frac{2\left((x+1)-\frac{1}{2}\right)}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\ln\left\|(x+1)+1\right\|}{3}+\text{C}=$$ $$\frac{1}{6}\left(-\ln\left\|x^2+x+1\right\|+2\ln\left\|x+2\right\|+2\sqrt{3}\arctan\left(\frac{2x+1}{\sqrt{3}}\right)\right)+\text{C}$$ $$\lim_{n\to\infty}\left[\frac{1}{6}\left(-\ln\left\|x^2+x+1\right\|+2\ln\left\|x+2\right\|+2\sqrt{3}\arctan\left(\frac{2x+1}{\sqrt{3}}\right)\right)\right]_{0}^{n}=$$ $$\lim_{n\to\infty}\left(\frac{1}{18}\left(-3\ln\|n^2+n+1\|+6\ln\|n+2\|+6\sqrt{3}\arctan\left(\frac{2n+1}{\sqrt{3}}\right)-\pi\sqrt{3}-\ln(64)\right)\right)$$	2019-10-22 16:47:49	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9991326928138733, "perplexity": 911.3288958550933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00155.warc.gz"}
http://openstudy.com/updates/56045f9ee4b033021d80b109	## anonymous one year ago (I know this is totally irrelevant but hardly anyone is on Chemistry) Write a chemical equation for the combustion of each of the following substances. If a compound contains carbon and hydrogen, assume that carbon dioxide gas and liquid water are produced. (Use the lowest possible whole number coefficients. Include states-of-matter under the given conditions in your answer.) (a) solid barium 1. ParthKohli Well, what do you think? 2. anonymous I honestly have no clue as to what I should do 3. ParthKohli $\rm Ba ~(s) + O_2~(g) \longrightarrow \cdots$ 4. anonymous Ba_{2}O(s)? 5. anonymous $Ba _{2}$ 6. ParthKohli In elemental states, you're looking at reactions like these:$\rm C~(s) + O_2~(g) \longrightarrow CO_2~(g)$$\rm Na + O_2 \longrightarrow Na_2 O$$\rm N + O_2 \longrightarrow NO_2$ 7. ParthKohli Why $$\rm Ba_2 O$$? Why not $$\rm Ba_2 O_3$$ or $$\rm BaO_2$$ or $$\rm BaO$$? 8. anonymous Oh yeah then BaO right? 9. anonymous Since Ba has a +2 charge and O has a -2 charge 10. anonymous right? 11. anonymous Hello? 12. ParthKohli Yes, right! 13. anonymous Yay! 14. anonymous So for my other questions do I just add $O _{2}$ 15. anonymous because that was the main place as to where I was confused 16. ParthKohli That's what combustion is, right? 17. anonymous I think my teacher didn't cover this too thoroughly and he moves from subect to subject pretty quickly as well 18. anonymous Anyways thank you so much!!!! 19. ParthKohli No problem :)	2016-10-27 07:06:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5913843512535095, "perplexity": 5099.305125125507}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721142.99/warc/CC-MAIN-20161020183841-00365-ip-10-171-6-4.ec2.internal.warc.gz"}
http://islam.wikia.com/wiki/Alhazen%27s_problem	## FANDOM 531 Pages Ibn al-Haytham's work on catoptrics in Book V of the Book of Optics contains the important Islamic mathematical problem known as Alhazen's problem. ## Geometric formulationEdit The problem comprises drawing lines from two points in the plane of a circle meeting at a point on the circumference and making equal angles with the normal at that point. This is equivalent to finding the point on the edge of a circular billiard table at which a cue ball at a given point must be aimed in order to canon off the edge of the table and hit another ball at a second given point. Thus, its main application in optics is to solve the problem, "Given a light source and a spherical mirror, find the point on the mirror where the light will be reflected to the eye of an observer." This leads to an equation of the fourth degree.[1][2][3] ## Sums of powers and integral calculusEdit This eventually led Ibn al-Haytham to derive the earliest formula for the sum of the fourth powers, and using an early proof by mathematical induction, he developed a method for determining the general formula for the sum of any integral powers. He used his result on sums of integral powers to perform an integration, in order to find the volume of a paraboloid. He was thus able to find the integrals for polynomials up to the fourth degree, and came close to finding a general formula for the integrals of any polynomials. This was fundamental to the development of infinitesimal and integral calculus.[4] He also contributed to calculus with the following geometric infinite series:[5] $\frac{1}{1-x} = 1 + x + x^2 + x^3 + \dots$ for $\|x\|<1$[6] ## InfluenceEdit Ibn al-Haytham solved the problem using conic sections and a geometric proof, but Alhazen's problem remained influential in Europe, when later mathematicians such as Christiaan Huygens, James Gregory, Guillaume de l'Hôpital, Isaac Barrow, and many others, attempted to find an algebraic solution to the problem, using various methods, including analytic methods of geometry and derivation by complex numbers.[7] Over the centuries, Ibn al-Haytham's contributions to integral calculus showed up in the work of various mathematicians. According to mathematics historian Victor J. Katz: "Ibn al-Haytham's formula for the sum of fourth powers shows up in other places in the Islamic world over the next few centuries. It appears in the work of Abu-l-Hasan ibn Haydur (d. 1413), who lived in what is now Morocco, and in the work of Abu Abdallah ibn Ghazi (1437-1514), who also lived in Morocco. Furthermore, one also finds the formula in The Calculator's Key of Ghiyath al-Din Jamshid al-Kashi (d. 1429), a mathematician and astronomer whose most productive years were spent in Samarkand, now in Uzbekistan, in the court of Ulugh Beg." Ibn al-Haytham's equation also later showed up in Indian mathematics, specifically the Kerala school of astronomy and mathematics in the 16th century.[4] An algebraic solution to Alhazen's problem was finally found in 1997 by the Oxford mathematician Peter M. Neumann.[8] Recently, Mitsubishi Electric Research Labs (MERL) researchers Amit Agrawal, Yuichi Taguchi and Srikumar Ramalingam solved the extension of Alhazen's problem to general rotationally symmetric quadric mirrors including hyperbolic, parabolic and elliptical mirrors .[9] They showed that the mirror reflection point can be computed by solving an eighth degree equation in the most general case. If the camera (eye) is placed on the axis of the mirror, the degree of the equation reduces to six .[10] Alhazen's problem can also be extended to multiple refractions from a spherical ball. Given a light source and a spherical ball of certain refractive index, the closest point on the spherical ball where the light is refracted to the eye of the observer can be obtained by solving a tenth degree equation.[10] ## References Edit 1. MacKay, R. J.; Oldford, R. W. (August 2000), "Scientific Method, Statistical Method and the Speed of Light", Statistical Science 15 (3): 254–78 2. Weisstein, Eric. "Alhazen's Billiard Problem". Mathworld. Retrieved on 2008-09-24. 3. 4.0 4.1 Victor J. Katz (1995), "Ideas of Calculus in Islam and India", Mathematics Magazine68 (3): 163–174 [165-9 & 173-4] 4. Edwards, C. H., Jr. 1979. The Historical Development of the Calculus. New York: Springer-Verlag. 5. "On the Use of Series in Hindu Mathematics" (1936). Osiris 1: 606–628. doi:10.1086/368443. 6. John D. Smith (1992), "The Remarkable Ibn al-Haytham", The Mathematical Gazette 76 (475): 189–198 7. Highfield, Roger (1 April 1997), "Don solves the last puzzle left by ancient Greeks", Electronic Telegraph 676, archived from the original on 2004-11-23, retrieved 2008-09-24 8. Agrawal, Amit; Taguchi, Yuichi; Ramalingam, Srikumar (2011), Beyond Alhazen's Problem: Analytical Projection Model for Non-Central Catadioptric Cameras with Quadric Mirrors, IEEE Conference on Computer Vision and Pattern Recognition 9. 10.0 10.1 Agrawal, Amit; Taguchi, Yuichi; Ramalingam, Srikumar (2010), Analytical Forward Projection for Axial Non-Central Dioptric and Catadioptric Cameras, European Conference on Computer Vision	2017-06-29 00:15:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 2, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8558406233787537, "perplexity": 1720.5957852891108}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323808.56/warc/CC-MAIN-20170629000723-20170629020723-00485.warc.gz"}
https://www.physicsforums.com/threads/electrostatic-repulsive-force-between-parallel-plates.794088/	# Electrostatic repulsive force between parallel plates ## Main Question or Discussion Point Hi I was thinking about two parallel plates with same charges (there's no electrical field between them). How can we calculate the repulsive force? Does anyone have any ideas besides numerical integration? Thanks Related Other Physics Topics News on Phys.org Simon Bridge Homework Helper Welcome to PF, For two infinite parallel planes of charge (note: not two real parallel pates) the net field between them is zero. Consider a situation you are familiar with, two point charges: the field at each point charge is infinite - how do you normally compute the force between them (using fields)? It's the same for each plate. So what I understand from your suggestion is that I can have a first order estimation of repulsive force by calculating available charges on each plate (Q1 = Q2) and use Coulomb's law as k.Q1.Q2/(d^2), is that right? But I'm a little confused here since I have reached a contradiction for attraction force between oppositely charged plates of a capacitor: Approach 1 = Force is calculated by differentiating electrostatic energy as: Approach 2 = Coulomb's Law: Neglecting constant coefficients, the effect of distance "x" is 2 orders of magnitude different. What am I missing here? Would it be possible for you to clarify this for me? Thanks Welcome to PF, For two infinite parallel planes of charge (note: not two real parallel pates) the net field between them is zero. Consider a situation you are familiar with, two point charges: the field at each point charge is infinite - how do you normally compute the force between them (using fields)? It's the same for each plate. Simon Bridge Homework Helper So what I understand from your suggestion is that I can have a first order estimation of repulsive force by calculating available charges on each plate (Q1 = Q2) and use Coulomb's law as k.Q1.Q2/(d^2), is that right? No. I am saying that you should think more carefully about how you normally do other, simpler, electrostatic calculations. In the case of 2 point charges, the electric field at each charge is infinite and yet you can still get a sensible answer for the force between them. How do you do that? This goes to the heart of your initial misunderstanding. The net field is zero - between the plates, but you don't use the net field everywhere to calculate the force. (Technically the net field at the position of the plates is undefined, anyway.) In the case of 2 point charges, the electric field at each charge is infinite and yet you can still get a sensible answer for the force between them. How do you do that? Well in this case I know that electric field around each point charge is calculated as: kQ/(r2) (undefined at the position of point charge) and the force is defined as F=q.E which results in kQq/(r2). I believe I can use the same approach for attracting parallel plates: Total net field between plates is Q/(εArea) and Force is equal to total charge on each plate multiplied by this electric field. So I can write F = Q.E = (Q2)/(εArea) and substituting for Q we end up having F=½AreaεV2/d2. This is the exact same thing when I differentiate the electrostatic energy. I don't know what I am missing here that I cannot relate this basic concept to repulsive parallel plate, as you mentioned this originates from my initial misunderstanding of the concept. I really appreciate if you could provide me with more hints so I can get back onto right track. Thank you Simon Bridge Homework Helper Well in this case I know that electric field around each point charge is calculated as: kQ/(r2) (undefined at the position of point charge) and the force is defined as F=q.E which results in kQq/(r2). ... you skipped over a bit there ... please concentrate: what did you say the electric field at the position of the charge was? Basically - the field at the charge is undefined, but that does not stop you calculating the force on the charge due to the other charge. For the force on charge 1 due to charge two you write: $\vec F = q_1\vec E_2$ Notice what E2 isn't? It is not the total field from both charges combined. It is the field from the second charge alone ... as if q1 were not there. For this problem, the charge does not see its own electric field. It's the same with the plates - the force on plate 1 due to plate 2 is what you want to calculate. But in post #1 you observed that the field between the plates is zero! But the field due to plate 2 between the plates is not zero. It is the total combined field that is zero. If the field due to plate 1 is E1 and the field due to plate 2 is E2, then a charge q somewhere other than on one of the plates gets force $\vec F = q(\vec E_1+\vec E_2)$, this will be zero between the plates... but the same charge at[] the position of plate 1 gets force $\vec F = q\vec E_2$ ... see? There are two basic ways to work out the force by brute, um, force... you can use coulombs law on each charge element, or you can work out how the energy stored in that system changes with the separation of the plates. I suspect this is something you should do ... compare the result with the electric fields for each plate separately. Involves calculus I'm afraid - but after that you just remember the result. The shortcut would be to realize that it is the same force as for oppositely charged plates, but with the opposite sign. In fact, we are assuming a uniform charge distribution - that only happens for an insulator. ----------------------------- [*] ... when q is a part of the plate. All charges in the plate will see the forces due to all the other charges in the plate. But, since this is an electrostatic system, the internal forces all cancel out. Last edited:	2020-03-28 12:01:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7846904993057251, "perplexity": 408.2795407550736}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370491857.4/warc/CC-MAIN-20200328104722-20200328134722-00424.warc.gz"}
https://www.cheenta.com/a-trigonometric-relation-and-its-implication-from-vietnam-national-mathematical-olympiad/	Select Page # Understand the problem Prove that a triangle $ABC$ is right-angled if and only if $$\sin A + \sin B + \sin C = \cos A + \cos B + \cos C + 1$$ Trigonometry Medium ##### Suggested Book Challenge and Thrill of Pre-college Mathematics Do you really need a hint? Try it first! Familiarity with the trigonometric identities associated with a triangle is a must for any aspiring Olympian. Check the list given in the reference. $ABC$ is right-angled iff $\cos A\cos B\cos C=0$. Show that $\cos A\cos B\cos C=\frac{s^2-(2R+r)^2}{4R^2}$. Combining hints 2 and 3, we see that $ABC$ is right-angled iff $s=2R+r$. We know that $\sin A+\sin B+\sin C=\frac{s}{R}$ and $\cos A+\cos B+\cos C=1+\frac{r}{R}$, hence $ABC$ is right-angled iff $\sin A+\sin B+\sin C=1+\cos A+\cos B+\cos C$.	2019-08-23 10:52:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 22, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8041146993637085, "perplexity": 739.8815164964849}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027318375.80/warc/CC-MAIN-20190823104239-20190823130239-00444.warc.gz"}
https://www.gamedev.net/forums/topic/129989-nv_occlusion_query-extention-for-occlusion-culling/	#### Archived This topic is now archived and is closed to further replies. # NV_OCCLUSION_QUERY extention for occlusion culling This topic is 5833 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts Hi, I want to use the NV_OCCLUSION_QUERY extention for occlusion culling in an octree (with front to back rendering) This is the source code for rendering the AABB containing the triangles, and testing if they are visible. glDisable(GL_CULL_FACE); glColorMask(GL_FALSE, GL_FALSE, GL_FALSE, GL_FALSE); glDepthMask(GL_FALSE); glBeginOcclusionQueryNV(cull_box2); glPushMatrix(); glTranslatef(bb.mid[0],bb.mid[1],bb.mid[2]); glScalef(bb.len[0],bb.len[1],bb.len[2]); glutSolidCube(1.0); glPopMatrix(); glEndOcclusionQueryNV(); glColorMask(GL_TRUE, GL_TRUE, GL_TRUE, GL_TRUE); glDepthMask(GL_TRUE); glEnable(GL_CULL_FACE); GLuint pixelCount=0; glGetOcclusionQueryuivNV( cull_box2 , GL_PIXEL_COUNT_NV, &pixelCount); if (pixelCount>pixel_threshold) render triangles of AABB with display list Problem is, the code is slower with culling then without occlusion culling (just rendering with display list), even though a lot less triangles are rendered with occlusion culling. Especially when de depth of the octree is getting bigger (>4) it slows very much (i guess because of the begin- and end-occlusion query, i used some timing queries to find out where the bottleneck was). Note that with depth 2 of 3 (not too many occlusion querys) there is a significant win over non occlusion culling when e.g. inside a certain model, but with larger octree depths the overhead of occlusion queries and octree seem to win, and there are less fps. In nvidia slides (http://www.nvidia.com/dev_content/gdc2002/GDC2002_occlusion_files/frame.htm) was a note : "Do other CPU computation while queries are being made " Should i use a separate thread to perform the occlusion queries, or do the occlusion queries already run in an seperate thread ? Is it normal that the queries become a bottleneck when used frequently ? With large octree depth, octree rendering without culling is even faster then with culling (with queries). With depth 5 there are like 1000''s / 10000''s of occlusion queries. Can this be a bottleneck ? How can i fix this problem ? tia, and merry christmas Roel Martens ##### Share on other sites You can try interleaving the querries: int num_octree_nodes = 8; /* typical value */for (i = 0; i < num_octree_nodes; i++) { glBeginOcclusionQueryNV(cull_box); glPushMatrix(); glTranslatef(bb.mid[0],bb.mid[1],bb.mid[2]); glScalef(bb.len[0],bb.len[1],bb.len[2]); glutSolidCube(1.0); glPopMatrix(); glEndOcclusionQueryNV();}for (i = 0; i < num_octree_nodes; i++) { GLuint pixelCount=0; glGetOcclusionQueryuivNV(cull_box[i] , GL_PIXEL_COUNT_NV, &pixelCount); if (pixelCount>pixel_threshold) render triangles of AABB with display list} Note that glGetOcclusionQueryuivNV implies a glFlush, which is why your current code is slower. ##### Share on other sites To add to my last post, you cuold probably split that last loop in two to not have the glFlush overhead inserted in your render loop. GLuint pixelCount[num_octree_nodes];for (i = 0; i < num_octree_nodes; i++) { glGetOcclusionQueryuivNV(cull_box , GL_PIXEL_COUNT_NV, &pixelCount[i]);}for (i = 0; i < num_octree_nodes; i++) { if (pixelCount[i]>pixel_threshold) render triangles of AABB with display list} ##### Share on other sites Oh, and please don''t cross post on 3 forums, Mr Impatience. I just found this thread on FlipCode and OpenGL.org... ##### Share on other sites i add myself to the ap.. thought it was not me that posted it don''t crosspost. even over forums, its annyoing "take a look around" - limp bizkit ##### Share on other sites for (i = 0; i < num_octree_nodes; i++) { test if bb is visible } i think the problem here is, that you cannot know the visibility of the other octree nodes, because it can change because of rendering other octree nodes. So you gotta check a bb for visibility, and if visible render its triangles, i guess.. -- I''m writing this because i do a thesis on occlusion culling and want to make an implementation which shows the advantages of occlusion culling with the NV_OCCLUSION_QUERY extention. I guess octrees are not a very good way to use the query, because it''s not as fast when used this way, so i''m thinking of using object based files (like xgl), and draw bb rond object for testing visibility with the query. Are there any other file formats where you can distinct seperate objects in the file (e.g. houses in a city xgl file), and are there download locations for sample (city?) files, or even modellers would do fine. ##### Share on other sites Each octree has 8 nodes. Check all 8 nodes, and only then check their children. 1. 1 2. 2 Rutin 16 3. 3 4. 4 5. 5 • 26 • 9 • 11 • 9 • 9 • ### Forum Statistics • Total Topics 633715 • Total Posts 3013496 ×	2018-12-14 17:49:52	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.251971572637558, "perplexity": 8679.554394674513}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826145.69/warc/CC-MAIN-20181214162826-20181214184826-00366.warc.gz"}
http://bababadalgharaghtakamminarronnkonnbro.blogspot.com/2012/06/kempe-tree-data-structure-for.html	## Monday, June 25, 2012 ### Introduction This post describes two variations on tree structure that I've used in some programming problems for solving variations of the range query/update problem. I haven't seen anyone else use it before, so for the moment I'm going to call it the Kempe tree, named after my great-grandfather who was also named Richard Kempe. Suppose we are given a list of data $$a_0, a_1, \ldots, a_{n-1}$$. In general terms, range update data structure supports the following type of operation: $update( i, j, x ): a_k \leftarrow x \text{ for all } k \in \{ i, i+1, \ldots, j \}$ Similarly, a range query data structure supports the following type of operation: $query( i, j ) = f( a_i, a_{i+1}, \ldots, a_{j} )$ (Here $$f$$ is taken to be some function we can aggregate over a large number of values, like $$\min$$, $$+$$, etc....) Both of these operations are expected to be reasonably fast, usually taking at most $$O( n )$$ steps. As an example, segment trees and Fenwick trees (or binary-indexed trees) are range query data structures. Segment trees with lazy propagation support both range queries and range updates. The Kempe tree is a data structure that supports either fast range updates and single-element queries, or fast range queries and single-element updates, but not both simultaneously. (Okay, fine, it can support both, provided one is $$O( \log^2 n )$$. But more on that later.) Why, then, should I use a Kempe tree, you ask? The main reason is that it uses numerical tricks to make it easier to code, the same reason why the Fenwick tree is sometimes used instead of the segment tree. (This also means that, for all intents and purposes, Kempe trees will never be used outside of competition programming.) ### Range Traversals The Kempe tree, like the Fenwick tree, is an array-based tree. Suppose we have $$n$$ data entries, a[0], a[1], ..., a[n-1]; then we require an array of size $$N + n$$, where $$N$$ is the smallest power of $$2$$ that is $$\geq n$$. Let tree[i] denote this array. The entries of tree[i] are allocated as follows: • Elements a[0], a[1], ..., a[n-1] are stored in entries tree[N], tree[N+1], ..., tree[N+n-1], respectively. • The parent node for any entry tree[i] is tree[i/2]. • Likewise, a non-leaf node tree[i] has children tree[2i] and tree[2i+1]. • The root of the tree is tree[1]. See the following image for a description of the mapping. Numbers in the tree nodes denote position in the array tree[i]. We say a tree node governs the array entries that are its descendants. For some range a[i], a[i+1], ..., a[j], the following algorithm finds the minimal set of tree nodes tree[x[0]], tree[x[1]], ..., tree[x[m-1]] that govern a[i], a[i+1], ..., a[j]: vector find_governing_nodes( int i, int j ) { vector ans; i += N, j += N; while( i <= j ) { if( i % 2 == 1 ) ans.push_back( i ); if( j % 2 == 0 ) ans.push_back( j ); i = ( i + 1 ) / 2; j = ( j - 1 ) / 2; } return ans; } A sketch of the proof for the correctness of the algorithm is the following. We start with i and j at the ends of the interval we are interested in. We process the interval by moving i and j up the tree, and by 'pulling' them together. If moving either i or j shrinks the interval during the next step, then we add them to the list of governing nodes. The following image illustrates the process in action: 1. We wish to query the range $$[1, 5]$$. i and j are initialised to 9 and 13, respectively. 2. Since 9 would jump out of its subtree during the next move, we add 9 to the list of governing nodes. 3. We move i to 5 and j to 6. Both i and j will jump out of their respective ranges during the next move, so we add both 5 and 6 to the list of governing nodes. 4. i gets moved to 3, and j to 2. This is an invalid range, so we break and return the list [9, 5, 6]. ### Range Queries and Singleton Updates We now present an example of a tree structure that can handle updates to single elements and range queries. The function we will try to query is the sum function. // define MAX to be some really big number int tree[MAX], N; // initialises a tree for n data entries int init( int n ) { N = 1; while( N < n ) N = 2; for( int i = 1; i < N + n; i++ ) tree[i] = 0; } // compute the product a[i] + a[i+1] + ... + a[j] int range_sum( int i, int j ) { int ans = 1; for( i += N, j += N; i <= j; i = ( i + 1 ) / 2, j = ( j - 1 ) / 2 ) { if( i % 2 == 1 ) ans += tree[i]; if( j % 2 == 0 ) ans += tree[j]; } return ans; } // set a[i] = val void update( int i, int val ) { int diff = val - tree[i+N]; for( int j = i + N; j; j /= 2 ) tree[j] += diff; } ### Range Updates and Singleton Queries The following example will allow us to increment a range, while allowing us to query the result on a singleton value. // define MAX to be a really big number int tree[MAX], N; // initialises a tree for n data entries int init( int n ) { N = 1; while( N < n ) N = 2; for( int i = 1; i < N + n; i++ ) tree[i] = 0; } // increments a[k] by val for all k between i and j, inclusive void range_increment( int i, int j, int val ) { for( i += N, j += N; i <= j; i = ( i + 1 ) / 2, j = ( j - 1 ) / 2 ) { if( i % 2 == 1 ) tree[i] += val; if( j % 2 == 0 ) tree[j] += val; } } // compute a[i] int query( int i ) { int ans = 0; for( int j = i + N; j; j /= 2 ) ans += tree[j]; return ans; } ### Final Remarks We can easily extend the tree to support many types of functions, such as the product function, min, max, set union, set intersection, and so forth. Unfortunately, under the current scheme, the tree cannot simultaneously support range updates and queries. There is a way to support both operations, provided that one operation takes $$O( \log n )$$ and the other takes $$O( \log^2 n )$$. (The proof of this is left to the reader.) Thus, Kempe trees do not provide as much functionality as segment trees, but are generally somewhat easier to code.	2017-09-26 17:55:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6084176301956177, "perplexity": 1313.3142875790718}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818696677.93/warc/CC-MAIN-20170926175208-20170926195208-00108.warc.gz"}
https://brilliant.org/problems/simple-properties-of-determinants/	# Simple properties of determinants Algebra Level 2 If $$A$$ is a $$3\times 3$$ matrix such that $$\det(A)=-2,$$ what is $$\det\left(3A^{-1}\right)?$$ ×	2018-07-22 05:07:13	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35427212715148926, "perplexity": 940.5330234906196}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676593010.88/warc/CC-MAIN-20180722041752-20180722061752-00515.warc.gz"}
https://math.stackexchange.com/questions/2610632/convergence-divergence-of-these-series	# Convergence/divergence of these series $\{a_n\}$ is a sequence of positive real numbers such that $\sum_{n=1}^\infty a_n$ is convergent. Which of the following series are convergent? 1. $$\sum_{n=1}^\infty \frac{a_n}{1 + a_n}$$ 2. $$\sum_{n=1}^\infty \frac{a_n^\frac{1}{4}}{n^\frac{4}{5}}$$ 3. $$\sum_{n=1}^\infty na_n\sin\frac{1}{n}$$ 1) looks convergent to me by the comparison test: $\frac{a_n}{1 + a_n} < a_n$ and $\sum_{n=1}^\infty a_n$ converges. I have no idea what to do for 2) and 3). I have tried to use Dirichlet's test, but couldn't figure out anything that worked. Edit: I just realized 3) could be done with the limit form of the comparison test: $n \sin \frac{1}{n}$ has positive terms for large enough $n$, and $$\lim_{n \rightarrow \infty} \frac{na_n \sin \frac{1}{n}}{a_n} = 1$$ I still don't know how to do 2) though. • For 2, you can either use Hölder's inequality (which is a generalization of Cauchy-Schwarz inequality) to obtain $$\sum_{n=1}^{\infty} \frac{a_n^{1/4}}{n^{4/5}} \leq \left( \sum_{n=1}^{\infty} a_n \right)^{1/4} \left( \sum_{n=1}^{\infty} \frac{1}{n^{16/15}} \right)^{3/4} < \infty$$ or use Young's inequality (which is a generalization of AM-GM inequality) to obtain $$\sum_{n=1}^{\infty} \frac{a_n^{1/4}}{n^{4/5}} \leq \sum_{n=1}^{\infty} \left( \frac{1}{4}\cdot a_n + \frac{3}{4} \cdot\frac{1}{n^{16/15}} \right) < \infty.$$ • For 3, notice that $n \sin(1/n) \to 1$ as $n\to \infty$ and hence $n \sin(1/n)$ is bounded. So if $M > 0$ is a bound of $n \sin(1/n)$ then $$\sum_{n=1}^{\infty} \left\| n a_n \sin(1/n) \right\| \leq \sum_{n=1}^{\infty} M a_n < \infty.$$ In fact, if you are aware of the inequality $\left\|\sin x\right\| \leq \left\|x\right\|$ which holds for all $x \in \mathbb{R}$ then you directly obtain $$\sum_{n=1}^{\infty} \left\| n a_n \sin(1/n) \right\| \leq \sum_{n=1}^{\infty} a_n < \infty.$$	2019-05-25 11:53:53	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9386314153671265, "perplexity": 81.78737126227642}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232258003.30/warc/CC-MAIN-20190525104725-20190525130725-00096.warc.gz"}
http://meteothinker.com/docs/meteoinfolab/meteolib/meteo/uv2ds.html	# uv2ds¶ mipylib.meteolib.meteo.uv2ds(u, v) Calculate wind direction and wind speed from U/V. Parameters: u – (array_like) U component of wind field. v – (array_like) V component of wind field. Wind direction and wind speed.	2018-03-18 07:46:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6586995720863342, "perplexity": 11443.913156728446}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645550.13/warc/CC-MAIN-20180318071715-20180318091715-00798.warc.gz"}
http://aux.planetmath.org/proofthateulervarphifunctionismultiplicative	# proof that Euler $\varphi$ function is multiplicative Suppose that $t=mn$ where $m,n$ are coprime. The Chinese remainder theorem (http://planetmath.org/ChineseRemainderTheorem) states that $\gcd(a,t)=1$ if and only if $\gcd(a,m)=1$ and $\gcd(a,n)=1$. In other words, there is a bijective correspondence between these two sets: • $\{a:a\equiv 1\pmod{t}\}$ • $\{a:a\equiv 1\pmod{m}\text{ and }a\equiv 1\pmod{n}\}$ Now the number of positive integers not greater than $t$ and coprime with $t$ is precisely $\varphi(t)$, but it is also the number of pairs $(u,v)$, where $u$ not greater than $m$ and coprime with $m$, and $v$ not greater than $n$ and coprime with $n$. Thus, $\varphi(mn)=\varphi(m)\varphi(n)$. Title proof that Euler $\varphi$ function is multiplicative ProofThatEulervarphiFunctionIsMultiplicative 2013-03-22 15:03:40 2013-03-22 15:03:40 Wkbj79 (1863) Wkbj79 (1863) 12 Wkbj79 (1863) Proof msc 11A25 EulerPhiFunction MultiplicativeFunction EulerPhifunction	2018-03-20 02:16:02	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 20, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9552269577980042, "perplexity": 384.04268496969377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647251.74/warc/CC-MAIN-20180320013620-20180320033620-00254.warc.gz"}
http://thompsonsed.co.uk/programming-fractal-art-using-tensorflow	Programming fractal art using tensorflow Fractals are undeniably beautiful. The self-similar, highly complex patterns reflect elements of the natural world, yet appear geometric and almost alien in their organisation. I decided generate some using python and tensorflow as a short mini-project. There are a tonne of resources online for generating fractals in any programming language – I made particular use of this GitHub repo by hzy46this blog over on IBM and this reddit post for colouring – so this a relatively quick exercise, but rewarding! You can find all the code I wrote for this exercise over on GitHub – check out the jupyter notebooks there for examples and explanations. The two most famous fractals are the Mandelbrot set and the Julia set. My algorithm for producing either set first requires defining a complex matrix (the “grid”) on which to operate. Then we can use tensorflow to perform the Mandelbrot/Julia algorithm. Tensorflow’s matrix algebra provides an easy method for fast computation of the fractals with built-in hardware acceleration, a useful feature for our fractals, which repeat the same operation many times on every cell in the matrix. With our grid, plus “threshold” and “iterations” parameters, the Mandelbrot algorithm is: # Define the tensorflow variables c = tf.constant(grid.astype(np.complex64)) z = tf.Variable(c) n = tf.Variable(tf.zeros_like(c, tf.float32)) # Start the tensorflow session with tf.Session(): tf.global_variables_initializer().run() # Define the main mandelbrot algorithm - either take the square plus x, or keep z z_out = tf.where(tf.abs(z) < threshold, z 2 + c, z) not_diverged = tf.abs(z_out) < threshold # Create a group of tensorflow operations step = tf.group( z.assign(z_out), # Run the operations for a set number of steps for i in range(iterations): step.run() We now have filled our grid with complex values from the algorithm. For colouring the cells according to their complex value, we define a few options: • If the absolute value of the cell is below some minimum threshold, we display the background colour (black by default). • Otherwise, a function maps complex values to (logarithmic) real values so that we can colour them. • Depending on the final value, we then have two sets of ratios of RBG colour – one for the overall background, and one for the highlights on the edges of the complex fractal structure. With this all together, we use the following code for each cell, where the threshold and colour ratios (r1, r2, r3, b1, b2 and b3) are globally defined. def colour(z, i): """ Gets the colour of a z and step value. :param z: the z value from the mandelbrot set :param i: the step value :rtype: list :return: list containing the RGB colours """ if abs(z) < threshold: return 0, 0, 0 v = np.log2(i + threshold - np.log2(np.log2(abs(z)))) / threshold if v < 1.0: return v b1, v b2, v b3 # coloured tones else: v = max(0, 2 - v) return v r1, v r2, v ** r3 # sepia tones Now we can experiment with different colouring for some better-looking fractals. Or explore different areas of the fractal. And now theJulia set. The Julia set has a periodicity. For some $$\theta$$, we have $$c=-(a-r cos(\theta)) – (b + r sin(\theta))i$$ where $$a$$ and $$b$$ are constants defining the initial shape and $$r$$ defines the amount of variation over a single period. Using this periodic formula on $$\theta$$, and therefore on $$c$$, we can produce an animation of the Julia set. Cool, right? I’d recommend writing your own fractal generator and trying to generate some fractal art for yourself.	2020-12-05 06:02:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41585955023765564, "perplexity": 2311.838383590434}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141746320.91/warc/CC-MAIN-20201205044004-20201205074004-00530.warc.gz"}
https://www.esaral.com/q/what-are-the-points-on-the-x-axis-whose-perpendicular-distance-from-the-15301	Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too! # What are the points on the x-axis whose perpendicular distance from the Question: What are the points on the x-axis whose perpendicular distance from the line $\frac{x}{3}+\frac{y}{4}=1$ is 4 units? Solution: Given: perpendicular distance is 4 units and line $\frac{x}{3}+\frac{y}{4}=1$ To find : points on the x-axis Formula used: We know that the length of the perpendicular from (m,n) to the line ax + by + c = 0 is given by, $D=\frac{\|a m+b n+c\|}{\sqrt{a^{2}+b^{2}}}$ The equation of the line is $4 x+3 y-12=0$ Any point on the $x$-axis is given by $(x, 0)$ Here $m=x$ and $n=0, a=4, b=3, c=-12$ and $D=4$ units $D=\frac{\|4(x)+3(0)-12\|}{\sqrt{4^{2}+3^{2}}}=4$ $D=\frac{\|4 x-12\|}{\sqrt{16+9}}=\frac{\|4 x-12\|}{\sqrt{25}}=\frac{\|4 x-12\|}{5}=4$ $\|4 x-12\|=4 \times 5=20$ $4 x-12=20$ or $4 x-12=-20$ $4 x=20+12$ or $4 x=-20+12$ $4 x=32$ or $4 x=-8$ $x=32 / 4=8$ or $x=(-8) / 4=-2$ (8,0) and (2,0)are the points on the x-axis whose perpendicular distance from the line is 4 units	2023-01-30 08:55:28	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6240249276161194, "perplexity": 370.69858260560915}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499804.60/warc/CC-MAIN-20230130070411-20230130100411-00711.warc.gz"}
https://www.tutorialspoint.com/understanding-the-npm-scripts-in-node-js	# Understanding the npm scripts in node.js Node.jsServer Side ProgrammingProgramming So far we are running our App.js using following command − ## Node App.js We can use npm scripts to run or debug our app. How to start a node project Command is − npm init Above command will initiate a project, it will ask few questions about project name and starting file name etc. As we have App.js file already give App.js file as starting entry file name. npm init command will create a package.json file from where dependencies for project can be added/updated/removed. Package.json file looks like this, Its in json file format as per file extension suggests − { "name": "dev", "version": "1.0.0", "description": "", "main": "App.js", "scripts": { "test": "echo \"Error: no test specified\" && exit 1" }, "author": "", } Main is entry file name , which is App.js file here. We can see there are scripts for test as well added by default. We can customize the scripts as per our requirement. Lets add a start script for App.js to run. In scripts section add below entry in it − "scripts": { "test": "echo \"Error: no test specified\" && exit 1", "start": "node App.js" } Now, we don’t need to manually use node App.js to run application instead we can npm script − ## npm start start and test are a reserved keyword in npm scripts. If we want to create a script name other than start like − “dev”: “node App.js” Then to run it, we will have to execute npm run dev , notice the use of run keyword after npm . Package.json file holds the dependencies and dev-dependencies for a project. The other people will have to just execute npm install to get those dependencies in their project. The dependencies which are required only during development of application are installed using npm install –save-dev library_name if any library needs to installed globally in local system, npm install –g library-name -g flag denotes the global install of the library, now we can use that library in other projects without need to install it again. Webpack library helps in building a project into a defined structure , we can customize as per project requirement. Published on 13-May-2020 15:44:28	2021-05-06 10:48:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19734258949756622, "perplexity": 11434.696252128279}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988753.91/warc/CC-MAIN-20210506083716-20210506113716-00466.warc.gz"}
https://stats.stackexchange.com/questions/242878/keeping-getting-wrong-answer-calculating-confidence-intervals	Keeping getting wrong answer calculating confidence intervals I was given the following: A sample of 16 domestic cars is made whose average fuel economy is 30.313 and a standard deviation of 4.7583. A sample of 10 imported cars is made whose average fuel economy is 32.012 with a standard deviation of 8.878. Find a 95% confidence interval for the difference between the two means. I attempted to do the calculation but but my answer was incorrect and the online homework system said the answer was (-7.192, 3.794) What I did was the formula $t_{\frac{\alpha}{2}}$ $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$ for the margin of error. I was a little unsure of what degrees of freedom I should use but i noticed by looking at the table there was not a single value on the table that would get me the answer the system said. the $t$ value would have to be 1.801518 and the limiting value of the $t$ is the $z$ value of 1.96. So am I using the wrong formula or is the system just wrong? I looked at a few other problems I war marked incorrect for saw similar things. • I think that 95% CI would be what you would get if you did a two-sample t test with equal variances. Your formula, however, is for unequal variances. What did you your calculation yield? – Dimitriy V. Masterov Oct 28 '16 at 1:02 • The value I got for the square root part of it was 2.106. I have heard different things about the right number of degrees of freedom,I think the rule in this case would be the smaller of $n_1 -1$ and $n_2 -1$ which would be 9 in this case. That gives a $t$ value of 2.262. Then the CI would be (-7.220932 ,3.065) – Elliot Oct 28 '16 at 1:18 • As @DimitriyV.Masterov points out that is not the df in this case. – mdewey Oct 28 '16 at 11:12 The difference in means is $$30.313-32.012=-1.699.$$ Assuming equal variances, the pooled standard error of the difference is $$\left(\frac{(16-1) \cdot 4.7583^2+(10-1) \cdot 8.878^2}{16+10-2} \right)^{0.5} \cdot \left(\frac{1}{16}+\frac{1}{10} \right)^{0.5} = 2.66506$$ The inverse t-tail value with 24 degrees of freedom (total sample size, minus the the two means) is 2.0638986. Putting these together means that 95% CI is $$-1.699\pm2.0638986 \cdot 2.66506=[-7.1994135,3.8014135]$$ This is near the online answer and agrees with computer: . ttesti 16 30.313 4.7583 10 32.012 8.878 Two-sample t test with equal variances ------------------------------------------------------------------------------ \| Obs Mean Std. Err. Std. Dev. [95% Conf. Interval] ---------+-------------------------------------------------------------------- x \| 16 30.313 1.189575 4.7583 27.77748 32.84852 y \| 10 32.012 2.80747 8.878 25.66106 38.36294 ---------+-------------------------------------------------------------------- combined \| 26 30.96646 1.281078 6.532243 28.32803 33.60489 ---------+-------------------------------------------------------------------- diff \| -1.699 2.66506 -7.199414 3.801414 ------------------------------------------------------------------------------ diff = mean(x) - mean(y) t = -0.6375 Ho: diff = 0 degrees of freedom = 24 Ha: diff < 0 Ha: diff != 0 Ha: diff > 0 Pr(T < t) = 0.2649 Pr(\|T\| > \|t\|) = 0.5298 Pr(T > t) = 0.7351 • Alright thank you. So the formula I used is when we dont have equal variances? – Elliot Oct 28 '16 at 14:57 • Also what is the correct df when I use the formula that I was using? – Elliot Oct 28 '16 at 16:20 • @Elliot You can find the formulas here. – Dimitriy V. Masterov Oct 28 '16 at 17:32	2019-11-17 03:19:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6190376281738281, "perplexity": 739.5361948335232}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496668782.15/warc/CC-MAIN-20191117014405-20191117042405-00487.warc.gz"}
https://onegoverningbody.com/find-the-data-range-1-2-2-3-3-3-4-5-5-5/	# Find the Data Range 1 , 2 , 2 , 3 , 3 , 3 , 4 , 5 , 5 , 5 , , , , , , , , , Subtract the minimum data value from the maximum data value to find the data range. In this case, the data range is . Find the Data Range 1 , 2 , 2 , 3 , 3 , 3 , 4 , 5 , 5 , 5 We can help to solve your math questions ### Our Math Experts They can help to solve your math problems Scroll to top	2022-09-25 08:17:36	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.933434247970581, "perplexity": 107.48320029980006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334515.14/warc/CC-MAIN-20220925070216-20220925100216-00231.warc.gz"}
https://quantumcomputing.stackexchange.com/tags/oracles/info	Often, such operations are defined using a classical function $$f:\{0,1\}^n \rightarrow\{0,1\}^m$$ which takes an $$n$$-bit binary input and produces an $$m$$-bit binary output.	2020-05-27 02:47:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 3, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9360709190368652, "perplexity": 292.6771893781146}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347392057.6/warc/CC-MAIN-20200527013445-20200527043445-00080.warc.gz"}
http://dms.umontreal.ca/~andrew/2012.php	### 2012 Publications #### Sharp transitions in making squares (with Ernie Croot, Robin Pemantle and Prasad Tetali) Annals of Mathematics, 175 (2012), 1507-1550. In the fastest-performing integer factoring algorithms, one creates a sequence of integers (in a pseudo-random way) and wishes to rapidly determine a subsequence whose product is a square. In 1994 Pomerance stated the following problem which encapsulates all of the key issues: Select integers $$a_1, a_2, \ldots$$ at random from the interval $$[1, x]$$ , until some (non-empty) subsequence has product equal to a square. Find a good estimate for the expected stopping time of this process. A good solution should allow one to determine the optimal choice of parameters in many factoring algorithms. Pomerance (1994), using an idea of Schroeppel (1985), showed that with probability $$1 - o(1)$$ the first subsequence whose product equals a square occurs after at least $$J_0^{1-o(1)}$$ integers have been selected, but no more than $$J_0$$, for an appropriate (explicitly determined) $$J_0 = J_0(x)$$ . We tighten Pomerance?s interval to $$[(\pi/4)(e^{-\gamma}-o(1)) J_0, (e^{-\gamma}+o(1)) J_0]$$ , where $$\gamma$$ is the Euler-Mascheroni constant, and believe that the correct interval is $$[ (e^{-\gamma}-o(1)) J_0, (e^{-\gamma}+o(1)) J_0]$$ , a "sharp threshold". In our proof we confirm the well-established belief that, typically, none of the integers in the square product have large prime factors. The heart of the proof of our upper bound lies in delicate calculations in probabilistic graph theory, supported by comparative estimates on smooth numbers using precise information on saddle points. Article #### Zeta functions for ideal classes in real quadratic fields, at $$s=0$$ (with Andras Biro) Journal of Number Theory, 132 (2012), 1807-1829. For any given fractional ideal $$I$$ of a real quadratic field, Jozsef Beck introduced the twisted partial zeta function $$\zeta_I(s,\chi) := \sum_a \chi(Na)/(Na)^s$$, where the sum is over all integral ideals that are equivalent to $$I$$, and $$\chi$$ is some Dirichlet character. We give a short, easily computable formula to evaluate $$\zeta_I(0,\chi)$$ in terms of the cycle of reduced quadratic forms associated with $$I$$. We generalize our formula to $$\zeta_I(1-k,\chi)$$ for all integers $$k\geq 1$$, and discuss connections between these formulae and small class numbers. Article #### Primitive prime factors in second-order linear recurrence sequences, Acta Arithmetica, 155 (2012), 431-452. For a class of Lucas sequences $$\{ x_n\}_{n\geq 0}$$ , we show that if $$n$$ s a positive integer then $$x_n$$ has a primitive prime factor which divides $$x_n$$ to an odd power, except perhaps when $$n =$$ 1, 2, 3 or 6. This has several desirable consequences. Article	2017-11-23 16:38:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7498196959495544, "perplexity": 365.1321756749638}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806844.51/warc/CC-MAIN-20171123161612-20171123181612-00470.warc.gz"}
http://www.zora.uzh.ch/id/eprint/30517/	From the Lifshitz tail to the quenched survival asymptotics in the trapping problem Fukushima, R (2009). From the Lifshitz tail to the quenched survival asymptotics in the trapping problem. Electronic Communications in Probability, 14:435-446. Abstract The survival problem for a diffusing particle moving among random traps is considered. We introduce a simple argument to derive the quenched asymptotics of the survival probability from the Lifshitz tail effect for the associated operator. In particular, the upper bound is proved in fairly general settings and is shown to be sharp in the case of the Brownian motion among Poissonian obstacles. As an application, we derive the quenched asymptotics for the Brownian motion among traps distributed according to a random perturbation of the lattice. Abstract The survival problem for a diffusing particle moving among random traps is considered. We introduce a simple argument to derive the quenched asymptotics of the survival probability from the Lifshitz tail effect for the associated operator. In particular, the upper bound is proved in fairly general settings and is shown to be sharp in the case of the Brownian motion among Poissonian obstacles. As an application, we derive the quenched asymptotics for the Brownian motion among traps distributed according to a random perturbation of the lattice. Statistics Citations Detailed statistics	2017-12-16 11:01:21	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8696495294570923, "perplexity": 372.05479399224157}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948587577.92/warc/CC-MAIN-20171216104016-20171216130016-00769.warc.gz"}
https://ideas.repec.org/p/hal/wpaper/hal-00613216.html	My bibliography Save this paper # Equilibrium model with default and insider's dynamic information ## Author Listed: • Luciano Campi () (CEREMADE - CEntre de REcherches en MAthématiques de la DEcision - Université Paris-Dauphine - CNRS - Centre National de la Recherche Scientifique, FiME Lab - Laboratoire de Finance des Marchés d'Energie - EDF R&D - EDF R&D - EDF - EDF - CREST - Université Paris-Dauphine) • Umut Cetin (Department of Statistics, LSE - LSE - London School of Economics and Political Science) • Albina Danilova (LSE - Department Mathematics [London] - LSE - London School of Economics and Political Science) ## Abstract We consider an equilibrium model á la Kyle-Back for a defaultable claim issued by a given firm. In such a market the insider observes \emph{continuously in time} the value of firm, which is unobservable by the market maker. Using the construction of a dynamic Bessel bridge of dimension $3$ in Campi, \c Cetin and Danilova (2010), we provide the equilibrium price and the optimal insider's strategy. As in Campi and \c Cetin (2007), the information released by the insider while trading optimally makes the default time predictable in market's view at the equilibrium. We conclude the paper by comparing the insider's expected profits in the static and dynamic private information case. We also compute explicitly the value of insider's information in the special cases of a defaultable stock and a bond. ## Suggested Citation • Luciano Campi & Umut Cetin & Albina Danilova, 2011. "Equilibrium model with default and insider's dynamic information," Working Papers hal-00613216, HAL. • Handle: RePEc:hal:wpaper:hal-00613216 Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00613216 as File URL: https://hal.archives-ouvertes.fr/hal-00613216/document ## References listed on IDEAS as 1. Luciano Campi & Umut Çetin, 2007. "Insider trading in an equilibrium model with default: a passage from reduced-form to structural modelling," Finance and Stochastics, Springer, vol. 11(4), pages 591-602, October. 2. Back, Kerry & Pedersen, Hal, 1998. "Long-lived information and intraday patterns," Journal of Financial Markets, Elsevier, vol. 1(3-4), pages 385-402, September. 3. Xin Guo & Robert Jarrow & Haizhi Lin, 2008. "Distressed debt prices and recovery rate estimation," Review of Derivatives Research, Springer, vol. 11(3), pages 171-204, October. 4. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November. 5. Back, Kerry, 1992. "Insider Trading in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 5(3), pages 387-409. Full references (including those not matched with items on IDEAS) ## Citations Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item. as Cited by: 1. Campi, Luciano & Cetin, Umut & Danilova, Albina, 2013. "Explicit construction of a dynamic Bessel bridge of dimension 3," LSE Research Online Documents on Economics 45263, London School of Economics and Political Science, LSE Library. ### NEP fields This paper has been announced in the following NEP Reports: ## Corrections All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:wpaper:hal-00613216. 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RePEc uses bibliographic data supplied by the respective publishers.	2018-06-21 20:22:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26409968733787537, "perplexity": 7939.703072222866}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864257.17/warc/CC-MAIN-20180621192119-20180621212119-00417.warc.gz"}
http://planetmath.org/SzemeredisTheorem	# Szemerédi’s theorem Let $k$ be a positive integer and let $\delta>0$. There exists a positive integer $N=N(k,\delta)$ such that every subset of $\{1,2,\ldots,N\}$ of size (http://planetmath.org/Cardinality) $\delta N$ contains an arithmetic progression of length $k$. The case $k=3$ was first proved by Roth[4]. His method did not seem to extend to the case $k>3$. Using completely different ideas Szemerédi proved the case $k=4$ [5], and the general case of an arbitrary $k$ [6]. The best known bounds for $N(k,\delta)$ are $e^{c(\log\frac{1}{\delta})^{k-1}}\leq N(k,\delta)\leq 2^{2^{\delta^{-2^{2^{k+9% }}}}},$ where the lower bound is due to Behrend[1] (for $k=3$) and Rankin[3], and the upper bound is due to Gowers[2]. For $k=3$ a better upper bound was obtained by Bourgain $N(3,\delta)\leq c\delta^{-2}e^{2^{56}\delta^{-2}}.$ ## References • 1 Felix A. Behrend. On the sets of integers which contain no three in arithmetic progression. Proc. Nat. Acad. Sci., 23:331–332, 1946. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0060.10302Zbl 0060.10302. • 2 A new proof of Szemerédi’s theorem. Geom. Funct. Anal., 11(3):465–588, 2001. Preprint available at http://www.dpmms.cam.ac.uk/ wtg10/papers.htmlhttp://www.dpmms.cam.ac.uk/ wtg10/papers.html. • 3 Robert A. Rankin. Sets of integers containing not more than a given number of terms in arithmetical progression. Proc. Roy. Soc. Edinburgh Sect. A, 65:332–344, 1962. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0104.03705Zbl 0104.03705. • 4 Klaus Friedrich Roth. On certain sets of integers. J. London Math. Soc., 28:245–252, 1953. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0050.04002Zbl 0050.04002. • 5 Endre Szemerédi. On sets of integers containing no four elements in arithmetic progression. Acta Math. Acad. Sci. Hung., 20:89–104, 1969. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0175.04301Zbl 0175.04301. • 6 Endre Szemerédi. On sets of integers containing no $k$ elements in arithmetic progression. Acta. Arith., 27:299–345, 1975. http://www.emis.de/cgi-bin/zmen/ZMATH/en/quick.html?type=html&an=0303.10056Zbl 0303.10056. Title Szemerédi’s theorem SzemeredisTheorem 2013-03-22 13:19:40 2013-03-22 13:19:40 bbukh (348) bbukh (348) 17 bbukh (348) Theorem msc 11B25 msc 05D10	2018-03-21 16:59:30	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 16, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7751554846763611, "perplexity": 871.9691735981231}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257647671.73/warc/CC-MAIN-20180321160816-20180321180816-00015.warc.gz"}
https://en.x-mol.com/paper/article/1430590743928094720	Find Paper, Faster Example：10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502 The Finite-Element with Discontiguous-Support Method Nuclear Science and Engineering (IF1.381), Pub Date : 2021-08-25, DOI: 10.1080/00295639.2021.1932224 Abstract Energy discretization of the transport equation is difficult due to numerous strong, narrow cross-section (XS) resonances. The standard traditional multigroup (MG) method can be sensitive to approximations in the weighting spectrum chosen for XS averaging, which can lead to inaccurate treatment of important phenomena such as self-shielding. We generalize the concept of a group to a discontiguous range of energies to create the Finite-Element with Discontiguous-Support (FEDS) method. FEDS uses clustering algorithms from machine learning to determine optimal definitions of discontiguous groups. By combining parts of multiple resonances into the same group, FEDS can accurately treat resonance behavior even when the number of groups is orders of magnitude smaller than the number of resonances. In this paper, we introduce the theory of the FEDS method and describe the workflow needed to use FEDS, noting that ordinary MG codes can use FEDS XSs without modification, provided these codes can handle upscattering. This allows existing MG codes to produce FEDS solutions. In the context of light water reactors, we investigate properties of FEDS XSs compared to MG XSs and compare $k$-eigenvalue and reaction rate quantities of interest to continuous-energy Monte Carlo, showing that FEDS provides higher accuracy and less cancellation of error than MG with expert-chosen group structures.	2021-12-05 23:19:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.43685656785964966, "perplexity": 2828.5181273670405}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363226.68/warc/CC-MAIN-20211205221915-20211206011915-00391.warc.gz"}
http://mathhelpforum.com/algebra/92561-series-print.html	# Series • June 11th 2009, 08:20 AM metlx Series How would I write this series with the $\Sigma$ sign and all: 25 (1 + 2.04 + 3.04 + 4.08 + 5.08 + 6.12 + 7.12 + 8.16 ...) OR 25 + 51 + 76 + 102 + 127 .... • June 11th 2009, 08:54 AM TheAbstractionist $\sum_{n\,=\,0}^k25\left(n+0.04\left\lfloor\frac n2\right\rfloor\right)$ $=\quad\sum_{n\,=\,0}^k\left(25n+\left\lfloor\frac n2\right\rfloor\right)$ • June 11th 2009, 08:58 AM Right I see the abstractionist is also looking at this thread so by the time i post this he''ll have a better answer down probably... Do it as two sums... $\bigg{(} \bigg{(} 25 \sum_{n=0}^\infty 2n \bigg{)} + n \bigg{)} + \bigg{(} \bigg{(} 25 \sum_{n=0}^\infty (2n+1) \bigg{)} + n \bigg{)}$ • June 11th 2009, 09:24 AM Soroban Hello, metlx! Quote: Write in sigma-notation: $(a)\;\;S \;=\;25\,\bigg(1 + 2.04 + 3.04 + 4.08 + 5.08 + 6.12 + 7.12 + 8.16 + \hdots\bigg)$ This is quicky tricky . . . $\text{We have: }\;S \;=\;\;25\bigg(1 + \underbrace{2.04 + 3.04} + \underbrace{4.08 + 5.08} + \underbrace{6.12 + 7.12} +$ $\underbrace{8.16 + 9.16} + \hdots\bigg)$ . . . . . . $S \;=\;25\bigg(1 + 5.08 + 9.16 + 13.24 + 17.32 + \hdots\bigg)$ . . . . . . $S \;=\;25\bigg([1 + 0(0.8)] + [5 + 1(0.08)] + [9 + 2(0.8)] + [13 + 3(0.8)] + \hdots\bigg)$ . . . . . . $S \;=\;25\sum_{k=0}^n\bigg((4k+1) + k(0.8)\bigg) \;=\;25\sum_{k=0}^n\bigg(4.8k + 1\bigg)$ Quote: $(b)\;\;S \;=\;25 + 51 + 76 + 102 + 127 + \hdots$ This too is tricky. .The pattern is: add 26, add 25, add 26, add 25, . . . $\text{We have: }\;S \;=\;\underbrace{25 + 51} + \underbrace{76 + 102} + \underbrace{127 + 153} + \underbrace{178 + 204} + \hdots$ . . . . . . $S \;=\;76 + 178 + 280 + 382 + \hdots$ . which has a common difference of 102 Therefore: . $S \;=\;\sum_{k=0}^n\bigg(76 + 102k\bigg)$	2014-10-25 09:53:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9326965808868408, "perplexity": 785.2097651994843}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414119648008.18/warc/CC-MAIN-20141024030048-00247-ip-10-16-133-185.ec2.internal.warc.gz"}
http://www.icmsquare.net/index.php/program/submissions	### Submissions ##### Asymptotic solution of natural convection in a uniformly Joule-heating shallow cavity xiaohui zhang, Soochow University, , China Abstract: The steady laminar two-dimensional Joule heating natural convection is investigated using asymptotical analysis, the fluid is in a rectangular cavity, the direct current contributes heat for heating the process medium by a pair of plate electrodes, the top wall is cooled with atmosphere and all the other walls are kept thermally insulated. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the vertical dimension of cavity to the horizontal dimension of cavity, goes to zero. The numerical experiments are also carried out to compare with the asymptotic solution of the steady two-dimensional Joule heating convection. The asymptotic results indicate that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio. ##### Ab-initio simulation of the ionization and fragmentation of acetylene by strong femtosecond laser pulses Kalman Varga, Vanderbilt, Physics, United States Abstract: The electron and nuclear dynamics of acetylene when interacting with strong short laser pulses has been simulated in the framework of real–space Time Dependent Density Functional Theory (TDDFT) and molecular dynamics. The stretching and dissociation of individual bonds are reported, and are shown to depend on the laser field intensity and orientation relative to the laser polarization. The ionization dynamics, including ionization from individual Kohn–Sham orbitals, is also reported. The orbital ionization dynamics are shown to vary with an increase in the intensity of the laser field. ##### Ab-initio study of the structural and electronic properties of cadmium telluride CdTe and its alloy cadmium zinc telluride Cd1-xZnxTe Louiza Messaadia , Physics Laboratory at Guelma, University 8 Mai 1945 Guelma, Department of Materials Science, Algeria Abstract: The scope of this investigation is to make a clear contrast between the structural and electronic properties of cadmium telluride CdTe and its alloy cadmium zinc telluride Cd1-xZnxTe using first principles calculations based on density functional theory within the local density approximation (LDA). A supercell with 2×2×2 unit cells has been considered in the calculations. Structural parameters and electronic densities of states are shown to discuss the effects of local environment induced by Zn impurity on the structure of zinc- blend CdTe. Our results are in good agreement with some theoretical studies. ##### Ab-initio study of the structural and electronic properties of cadmium telluride CdTe and its alloy cadmium zinc telluride Cd1-xZnxTe Louiza Messaadia , Physics Laboratory at Guelma, University 8 Mai 1945 Guelma, Department of Materials Science, Algeria Abstract: The scope of this investigation is to make a clear contrast between the structural and electronic properties of cadmium telluride CdTe and its alloy cadmium zinc telluride Cd1-xZnxTe using first principles calculations based on density functional theory within the local density approximation (LDA). A supercell with 2×2×2 unit cells has been considered in the calculations. Structural parameters and electronic densities of states are shown to discuss the effects of local environment induced by Zn impurity on the structure of zinc- blend CdTe. Our results are in good agreement with some theoretical studies. ##### Canonical Quantization of the Reissner-Nordstr\"om Black Hole via Conditional Symmetries Evangelos Melas, Technological Educational Institution of Patras, Department of Management, Greece Abstract: We use the conditional symmetry approach to study the $r$-evolution of a minisuperspace spherically symmetric model both at the classical and quantum level. After integration of the coordinates $t$, $\theta$ and $\phi$ in the gravitational plus electromagnetic action the configuration space dependent dynamical variables turn out to correspond to the $r$-dependent metric functions and the electrostatic field. In the context of the formalism for constrained systems (Dirac - Bergmann, ADM) with respect to the radial coordinate $r$, we set up a point-like reparametrization invariant Lagrangian. It is seen that, in the constant potential parametrization of the lapse, the corresponding minisuperspace is a Lorentzian three-dimensional flat manifold which obviously admits six Killing vector fields plus a homothetic one. The weakly vanishing $r$-Hamiltonian guarantees that the phase space quantities associated to the six Killing fields are linear holonomic integrals of motion. The homothetic field provides one more rheonomic integral of motion. These seven integrals are shown to comprise the entire classical solution space, i.e. the space-time of a Reissner-Nordstr\"om black hole, the $r$-reparametrization invariance since one dependent variable remains unfixed, and the two quadratic relations satisfied by the integration constants. We then quantize the model using the quantum analogues of the classical conditional symmetries, and show that the existence of such symmetries yields solutions to the Wheeler-DeWitt equation which, as a semiclassical analysis shows, exhibit a good correlation with the classical regime. Finally, we use the resulting wave functions to investigate the possibility of removing the classical singularities. ##### A mathematical characterization of the gel point in sol-gel transition Ayse Humeyra Bilge, Kadir Has University, Fculty of Engineerin and Natural Sciences, Turkey Abstract: We model the sol-gel transition in terms of Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models and compare with experimental results. We show, numerically, that the gel point" described as the onset of the gelation phenomena and measured experimentally, corresponds to an accumulation point of the extreme values of the derivatives of the gelation curve. We define the critical point of a sigmoidal curve" as the limit of the points where the derivatives reach their extreme values, provided that this limit exists. ##### Multiscale continuation algorithms for binary Rydberg-dressed Bose-Einstein condensates Cheng-Sheng Chien, Chien Hsin University of Science and Technology, Department of Computer Science and Information Engineering, Taiwan Abstract: We present two multiscale continuation algorithms for binary Rydberg-dressed Bose-Einstein condensates which are governed by a system of the Gross-Pitaevskii equations (GPEs). First we describe a three-parameter continuation algorithm to trace the ground state solution curve of the GPEs, where we use the chemical potentials λ1 and λ2 together with an artificial parameter ν0 belong to [0, ν] as the three continuation parameters. Here ν0 is used to control the value of the parameter μ12 for the integration term, say μ12 = ν0 × μ0 for some μ0. Besides, the parameters μ11 = μ22 are fixed. Next, we describe a four-parameter continuation algorithm to trace the ground state solutions of the GPEs. At the beginning we use the two-parameter continuation algorithm described by Wang and Chien [CiCP, 2013] to trace the ground state solution curves of the GPEs with the coefficients of the integration terms μ11 = μ22 = μ12 = 0. When the constraint conditions \|\|ψ1\|\| = \|\|ψ2\|\| = 1 are satisfied, we use the chemical potentials λ1 and λ2 together with two additional parameters ν0 belong to [0, ν] and ν1 belong to [0, ν*] as the four continuation parameters and proceed again to trace the ground state solution curves, where μ11 = μ22 = ν1 × μ1 for some μ1. Since the parameters μ11 = μ22 and μ12 have different scales, the parameter ν1 reaches the desired value earlier than the parameter ν0. Then we reduce the four-parameter continuation algorithm to the three-parameter one, and proceed to trace the ground state solution curves until the desired ground state solutions are obtained. The proposed multiscale/multi-parameter continuation algorithms have the advantage that we can obtain the contours of the wave functions ψ1 and ψ2 for various values of μ11 = μ22 belong to [0, μ] and μ12 belong to [0, μ*], where we only need to trace the ground state solution curve once. Our numerical experiments show that the proposed algorithms outperform the classical continuation algorithm, and is very competitive compared to other numerical methods for treating similar problems. ##### BICEP2, inflation and quantum fluctuations Prof. Dr. Emilio Elizalde, ICE-CSIC and IEEC Barcelona, , Spain Sergei Odintsov, ICREA and ICE (CSIC-IEEC), Theoretical Physics and Cosmology , Spain Abstract: After a short review of a few basic notions around the Big Bang theory, a summary will be given of the impacting results of BICEP2, together with the subsequent reactions of cosmologists and theoretical physicists. While some basic models of inflation can accommodate the new results, they seem to exclude, on the contrary, other popular and very important families of inflationary models. And it is quite difficult to explain, simultaneously, the previous results of PLANCK together with the new data. The fundamental question has also arisen: have we finally found indeed the footprints of the very elusive quantum gravity? ##### Unification of inflation with dark energy era in modified gravity Sergey Odintsov, ICREA and ICE(CSIC-IEEC), Cosmology, Spain Abstract: We review the unification of inflation with dark energy within modified F(R) gravity. Several models are presented, their properties are described. Some applications- like massive neutron stars from F(R) gravity are also mentioned. Finally, the unification of early-time with late-time acceleration is also considered in modified Gauss-Bonnet gravity. ##### Supersymmetric extension of a coupled Korteweg-de Vries system Adrián Sotomayor, Antofagasta University, Mathematics, Chile Alvaro Restuccia, Antofagasta University, Physics, Chile Abstract: We obtain a supersymmetric extension of a coupled KdV system. This system arises from a complexiﬁcation of real KdV equation. The system has an inﬁnite sequence of conserved quantities involving the even and odd ﬁelds describing the new system. This inﬁnite se- quence can be obtained from a supersymmetric Gardner equation via a Gardner integrable deformation. We also ﬁnd the hamiltonian and the Poisson structure of the system. ##### One dark matter mystery: halos in the cosmic web Abstract: The current cold dark matter cosmological model explains the large scale cosmic web structure but is challenged by the observation of a relatively smooth distribution of matter in galactic clusters. We consider various aspects of modeling the dark matter around galaxies as distributed in smooth halos and, especially, the structure of the dark matter halos seen in cosmological N-body simulations. We conclude that the problems of the cold dark matter cosmology on small scales are more serious than normally admitted. ##### Stabilizability of stochastic nonlinear hybrid systems Ewelina Seroka, Cardinal Stefan Wyszynski University in Warsaw, Faculty of Mathematics and Natural Sciences, Poland Abstract: The problem of the asymptotic stabilizability in probability of a class of stochastic nonlinear control hybrid systems (with a linear dependence of the control) with any, state dependent and markovian switching rule is considered in the paper. It is assumed that the trivial solution of unforced hybrid system is stable in probability (wherein some of subsystems of unforced hybrid systems can be unstable). By applying the stabilizing control the trivial solution of hybrid system becomes asymptotically stable in probability. To solve the issue, the Lyapunov technique including a common, single, multiple Lyapunov function, the hybrid control theory and some results of P. Florchinger for stochastic non-hybrid systems, are used. Moreover, in the case of hybrid systems with markovian switching rule, results of R.Z. Khasminskii, C. Zhu, G. Yin are applied. Sufficient conditions for the asymptotic stabilizability in probability for a considered class of hybrid systems are formulated. Also the stabilizing control in a feedback form is considered. Furthermore, in the case of hybrid systems with the state dependent switching rule, a method for a construction of stabilizing switching rules is proposed. Obtained results are illustrated by examples and numerical simulations. ##### Microscopic black hole stabilization via the uncertainty principle Constantinos G. Vayenas, University of Patras, , Greece Abstract: We study the properties of bound states consisting of relativistic rotating particles [1] and formed via stabilization of microscopic black holes due to the uncertainty principle [1-3]. We show that the combination of Schwarzschild or Reissner-Nordström geodesics with the uncertainty principle, expressed via the Compton wavelength of the confined mass, leads to Planckian or sub-Planckian states with the mass and other properties of hadrons, formed via the confinement of much lighter relativistic particles. The concepts of generalized Uncertainty Principle (GUP) [4] and Generalized Event Horizon (GEH) [3] in relation to these states are also discussed. 1. C.G. Vayenas, S. Souentie, A. Fokas, Physica A, 405 (2014) 360-379. 2. C.G. Vayenas, S. Aretakis, A. Fokas and D. Grigoriou, in preparation (2014). 3. B.J. Carr, arXiv:1402.1427v1 [gr-qc] (2014). 4. S. Das, E.C. Vagenas, Can. J. Phys. 87 (2009) 233-240. ##### Computer Simulation of Fire Dynamics in Industrial Hall Jan Glasa, Institute of Informatics, Slovak Academy of Sciences, , Slovakia (Slovak Republic) Abstract: In this paper, computer simulation of smoke spread dynamics in industrial hall is investigated. A set of simulations of fire in three industrial halls with the same geometry varying in the height of ceiling is realized using the CFD-based fire field model, FDS, version 6. The obtained simulation results are described focusing on the impact of the ceiling height and fire barriers on the fire course and smoke spread dynamics. ##### Feedback Stabilization of an Oscillating Vertical Cylinder by POD Reduced-Order Model Gilles Tissot, PPRIME Institute, Fluides, Thermique, Combustion, France Laurent CORDIER, PPRIME Institute, Fluides, Thermique, Combustion, France Bernd NOACK, PPRIME Institute, Fluides, Thermique, Combustion, France Abstract: The objective of this paper is to demonstrate the use of Reduced-Order Models (ROM) based on Proper Orthogonal Decomposition (POD) to stabilize by vertical oscillations the flow over a circular cylinder for a Reynolds number equal to 60. The 2D Navier-Stokes equations are first solved by a finite element method with COMSOL Multiphysics in which the moving mesh is introduced via ALE. Since in Fluid-Structure Interaction, the POD algorithm cannot be applied directly, we then implement the fictitious domain method of Glowinski et al. (1999) where the solid domain is treated as a fluid undergoing an additional constraint. The POD-ROM is then classically obtained by projecting the Navier-Stokes equations on a small number of POD modes. At this level, the cylinder movement is enforced in the POD-ROM through the introduction of Lagrange multipliers. A Linear Quadratic Regulator framework is used to determine the optimal control law, in our case the vertical velocity of the cylinder, such that the flow is stabilized. After linearization of the POD-ROM around the steady flow state, the optimal linear feedback gain is obtained as solution of a Generalized Algebraic Riccati Equation. Finally, when the optimal feedback control is applied, it is shown that the flow converge rapidly to the steady state. In addition, a vanishing control is obtained proving the efficiency of the control approach. ##### Inference of Transcriptional Network for Pluripotency in mouse Embryonic Stem Cells Sachiyo Aburatani, National Institute of Advanced Science and Technology, Computational Biology Research Center, Japan Abstract: In embryonic stem cells, some transcription factors (TFs) are known to maintain the pluripotent process. To gain insights into the regulatory system to control pluripotency, I inferred regulatory relationships between TFs, which expressed in ES cells. In this study, I applied a method based on structural equation modelling (SEM), combined with factor analysis, to 649 expression profiles of 19 TF genes measured in mouse ES (mES) cells. By the factor analysis, 19 TF genes were regulated by several unmeasured factors. Since the known cell reprogramming TF genes (Pou5f1, Sox2, Nanog and Klf4) were regulated by the different factors, the each estimated factor is considered to be an input signal transduction to control pluripotency in mES cells. In the inferred network model, TF proteins were also arranged as unmeasured factors which control the other TFs. The interpretation of the inferred network model allowed us to reveal the regulatory mechanism for controlling pluripotency in ES cells. ##### MPR Supported Multiscale Initialization of Transfer Functions for Interactive 3D Visualization Merve Ozdemir, Dokuz Eylül University, Electrical and Electronics Engineeing, Turkey Alper Selver, Dokuz Eylül University, Electrical and Electronics Engineering, Turkey Oguz Dicle, Dokuz Eylül University, Radiology, Turkey Abstract: Visualization aims to produce clear and informative pictures of the important structures in a dataset. Depending on the application, this requires interactive determination of visual parameters such as opacity and color. In volume rendering technique, combinations of these visual parameters can be determined during the rendering pipeline. During the generation of volume rendered images, Transfer Function (TF) specification is the step where these adjustments can be done. Therefore, it is crucial and important to design accurate TFs to produce meaningful and intelligible 3-D images. However, TF design is a very difficult task because of the availability of various possibilities in extensive search spaces of TFs. Since this flexibility of search space cannot be kept in strict bounds, specification of an appropriate TF is a challenging problem where effective initial TF designs should be generated prior to the optimization that is controlled by the user. Moreover, advanced user interaction interfaces and data exploration tools should be provided for fulfilling user expectations. To overcome the difficulty of initial TF generation generally a number of predefined TF presets are used as starting point (so called initial TF design). The main idea behind this approach is that certain types of volume data are standardized in the range of data values and special sub-ranges are assigned to the same type of structure (Thus, predefined TFs are adjusted due to these ranges). However, volumetric data usually have varying characteristics even in different samples of the same application. For instance, in medical imaging, depending on different modality settings, injection of a contrast media or environmental circumstances, the sub-ranges of the tissues may vary significantly. Similarly in natural stone analysis, the ingredients of brecciated rocks differ significantly from each other which prevent the use of pre-defined ranges for analysis. For these reasons, a limited number of TF presets cannot be enough to cover all possible cases and to provide useful initial TFs. In order to create a useful initial TF that provides a good basis prior to optimization, an automatic sub-range detection method that finds the intensity range for each structure of interest is needed. Moreover, it is necessary to integrate the developed method into the TF design procedure without losing user control and interaction over the search space. By addressing this problem, a semi-automatic method for initial generation of TFs is introduced in this study. The proposed approach is based on modeling the search space in a hierarchical manner using gaussian functions. The search space is constructed with generalized Volume Histogram Stack (VHS) which can be determined by the user by interacting with Multi Planar Reconstruction (MPR) images of the volume data. VHS is recently introduced in as a new domain which is created by aligning the histograms of the image slices of a CT/MR series. Histograms were generated from orthogonal directions of slice planes, namely, axial, coronal and saggital. Thus, VHS can represent the intensity values of the tissues as well as their spatial information and local distributions (via lobes in VHS) which are not available in conventional volume histograms. The tissues which are at different slices but with similar gray level distributions can clearly be distinguished by using this spatial information. Then, a tissue (a structure of interest) can effectively be visualized by determining its corrsponding lobe(s) in VHS, which represents that structure of interest, and by assigning a color-opacity value to that lobe. In this study, VHS data is further generalized in such a way that it is possible to calculate VHS on an arbitrary aligned axis (i.e. a slice plane with an arbitrary normal vector, not aligned with x, y or z) which can be obtained with the help of not only MPR but also of Curved MPR or Oblique sectioning techniques. A generalized VHS can be generated not only for slice based medical image series but all volumetric data as long as spacing values in 3D is known. With the help of this expansion, the VHS becomes an effective new domain as a search space for TF specification on any kind of 3D data. Although extending the implementation of VHS to work along an arbitrary axis or with an arbitrary surface would provide many advantages, it should still be supported by a lobe detection method. Because, when two or more structure of interest have overlapping intensity values and if their spatial location also overlaps at some degree, they construct overlapping regions which produce hardly recognizable minor lobes (or side parts of main lobes) due to the domination by the major ones. The proposed multiscale and hierarchical modeling strategy applied on generalized VHS allows recognizing suppressed lobes corresponding to suppressed structures and also for representing the overlapping regions which are parts of the lobes but can not be represented by the clusters associated to the lobes due to the overlapping. The developed strategy allows the integration of spatial knowledge, local distribution of the structures and their intensity information into the TF while preserving the user control. The proposed method is applied to 10 MRI datasets for abdominal tissue/organ visualization. The results show that, the proposed approach effectively increases performance on classification of abdominal organs. ##### Some of the cosmological funds gravitational theories F(T,\Theta) Faezeh, Kiani, , Iran (Islamic Republic of) Abstract: we study a new type of modified teleparallel gravity of the form F(T,\Theta) in which T, the torsion scalar, is coupled with $\Theta$, the trace of the stress-energy tensor. We also study the minimal and non-minimal coupling by the dynamical system approach. In this Model, the crossing the phantom divide, the existence of de Sitter solution and its stability are investigated in the non-minimal version. ##### Automatic Method to Classify Images Based on Multiscale Fractal Descriptors and Paraconsistent Logic Eduardo Pavarino, São Paulo State University (UNESP), Department of Computer Science and Statistics (DCCE), Brazil Leandro Alves Neves, São Paulo State University (UNESP), Department of Computer Science and Statistics - DCCE, Brazil Marcelo Zanchetta do Nascimento, Federal University of Uberlândia, FACOM, Brazil Moacir Fernandes de Godoy, FAMERP - São José do Rio Preto, Transdisciplinary Center for Study of Chaos and Complexity (NUTECC), Brazil Pedro Francisco de Arruda, FAMERP - São José do Rio Preto, , Brazil Leandro Neves, São Paulo State University, DCCE, Brazil Dalísio de Santi Neto, Hospital de Base de São José do Rio Preto, Department of Pathology, Brazil Abstract: In this study is presented an automatic method to classify images from fractal descriptors as decision rules, such as multiscale fractal dimension and lacunarity. The proposed methodology was divided in three steps: quantification of the regions of interest with fractal dimension and lacunarity, techniques under a multiscale approach; definition of reference patterns, which are the limits of each studied group; and, classification of each group, from the combination of the reference patterns with signals maximization (an approach commonly considered in paraconsistent logic). As a first application, the proposed method was used to classify histological prostatic images with 40x of magnification, aiming the diagnostic of prostate cancer. The investigated groups were normal, hyperplasia and cancer. The accuracy levels were important, overcoming those obtained with Support Vector Machine (SVM), Radial Basis Function Network (RBFNetwork) and Best-first Decicion Tree (BFTRee) classifiers: well know and widely applied techniques to recognize patterns. The proposed technique was better than SVM and RBFNetwork in all tests with both stroma and lumen and only with stroma, respectively. Regarding the BFTree classifier, the developed method was better in, approximately, 67% of the comparisons. The groups with better results were normal versus hyperplasia and normal versus cancer, being the region of stroma the more significant to distinguish the prostate cancer. Thus, the proposed approach allows recognize and classify patterns in studied context, offering the advantage of giving comprehensive models to the specialists. ##### Approximate best proximity points of cyclic self-mapsand cyclic asymptotic regularity Manuel de la Sen, University of the Basque Country, IIDP, Spain Abstract: This manuscript relies on 2-cyclic self-mappings by giving a simple formal development to join some useful concepts, and related results, like those of approximate best proximity points of cyclic self-mappings, the approximate best proximity (respectively, partial best proximity) point property or the cyclic asymptotic regularity. A formal mathematical development is given which brings together the concepts of approximate best proximity points of cyclic self-mappings, approximate best proximity (respectively, partial best proximity) point property and cyclic asymptotic regularity of cyclic self-mappings. There are also further induced results available for the approximate fixed points of the composite self-mapping obtained from the composition of the original one with itself which follow from the approximate best proximity point properties and those related ones of cyclic asymptotic regularity . ##### Clusters and molecules in extreme light Eric Suraud, Universite Paul Sabatier, Lab. Phys. Theorique, France Abstract: The progress in laser technology over the last decades has opened up new avenues for the explo- ration of properties of clusters and molecules. A laser pulse is characterized by its frequency but also by the laser intensity as well as the laser time profile. While for years the variations of these parame- ters were heavily constrained by technology, the last two decades and even more so the last years have seen tremendous increases in the range of attainable parameters. This is true for intensity, which since the 1990’s can reach huge values which can lead to very large energy deposits and possibly violent disintegration of the irradiated species. But this is also true for the tuning of the time profile which can now be tailored up to time scales of the order of magnitude of electronic motion and even below. This allows the follow up of the detail of electronic dynamics at its own ”natural” time. The latest breaktroughs were attained in terms of laser frequency with the ongoing possibility of reaching very large frequencies up the X domain. This opens up new possibilities of imaging which are progressively being explored. We shall discuss some of these directions of investigation, taking examples in cluster and molecular physics. We shall especially discuss the case of high intensity and short time pulses for which a sizable amount of results have already been attained. We shall also discuss in detail the case of very short times (attoseconds) which are becoming more and more studied. [1] Mechanisms of cluster ionization in strong laser pulses, U. Saalmann, C. Siedschlag,, J. M. Rost, J. Phys. B 39 (2006) R39. [2] Non linear electron dynamics in metal clusters, F. Calvayrac, P. G. Reinhard, E. Suraud, C. Ullrich, Phys. Reports 337(2000)493-578 [3] Laser-driven nonlinear cluster dynamics, Th. Fennel, K.-H. Meiwes-Broer, J. Tiggesbumker, P.-G. Reinhard, P. M. Dinh, E. Suraud, Rev. Mod. Phys. in press, 2010, http://arxiv.org/abs/0904.2706 [4] Probing Time-Dependent Molecular Dipoles on the Attosecond Time Scale, C. Neidel et al Phys. Rev. Lett 111 (2013) 033001. ##### Multi-parameter continuation and collocation methods for rotating multi-component Bose-Einstein condensates Yun-Shih Wang, Chien Hsin University of Science and Technology, , Taiwan Abstract: We describe multi-parameter continuation methods combined with spectral collocation methods (SCM) for computing numerical solutions of rotating two-component Bose-Einstein condensates (BECs), which are governed by the Gross-Pitaevskii equations (GPEs). Various types of orthogonal polynomials are used as the basis functions for the trial function space. A novel multi-parameter/multiscale continuation algorithm is proposed for computing the solutions of the governing GPEs, where the chemical potential of each component and angular velocity are treated as the continuation parameters simultaneously. The proposed algorithm can effectively compute numerical solutions with abundant physical phenomena. Numerical results on rotating two-component BECs are reported. ##### Two reliable approaches involving Haar wavelet method and Optimal Homotopy Asymptotic method for the solution of fractional Fisher type equation SANTANU SAHA ROY, NATIONAL INSTITUTE OF TECHNOLOGY ROURKELA, MATHEMATICS, India Abstract: In this article, two reliable techniques, Haar wavelet method and optimal homotopy asymptotic method (OHAM) are presented. Haar wavelet method is an efficient numerical method for the numerical solution of fractional order partial differential equation like Fisher type. The approximate solutions of the fractional Fisher type equation are compared with the optimal homotopy asymptotic method as well as with the exact solutions. Comparisons between the obtained solutions with the exact solutions exhibit that both the featured methods are effective and efficient in solving nonlinear problems. However, the results indicate that optimal homotopy asymptotic method provides more accurate value than Haar wavelet method. ##### Atomistic and Continuum Simulations of Nanoscale Pattern formation on Alloy Surfaces by Ion Beam Sputtering Bharathi Srinivasan, Institute of High Performance Computing, Engineering Mechanics, Singapore Ramanarayan Hariharaputran, Insititute of High Performance Computing, Materials Science & Engineering, Singapore Yong Wei Zhang, Institute of High Performance Computing, EM, Singapore Abstract: Nanoscale surface pattern creation is a topic of recent research interest due to its relevance in optoelectronic devices. Sputtering by low energy ion beam is one of the techniques used to achieve self-assembled morphological patterns on surfaces. In alloy surfaces, both morphological and compositional patterns are created due to interplay of various factors such as diffusion, sputter removal and elastic misfit. Temperature, flux of the incident ion beam and the elastic interactions arising out of misfit stresses dominate the self-assembly of these nanostructures. Here we present the results from both kinetic Monte Carlo simulations and a nonlinear continuum model on the influence of these parameters on the dynamics of pattern formation in alloy surfaces by ion beam sputtering. ##### Some properties of light mesons in a strong magnetic field in context of the SU(3) lattice gauge theory Elena Luschevskaya, Institute of Theoretical and Experimental Physics, Laboratory of theoretical and nuclear physics, Russian Federation Abstract: We calculated the correlators of vector, axial and pseudoscalar currents in external strong abelian magnetic field in $SU(3)$ gluodynamics. The masses of neutral and charged $\rho$ and $A$ mesons with various spin projections to the external magnetic field $B$ have been calculated. We found that the masses of neutral mesons with zero spin $s=0$ decrease, while the masses of the $\rho$ and $A$ mesons with spin $s=\pm 1$ increase in increasing magnetic field. The masses of charged vector and axial mesons with nonzero spins diminish, but the masses of the same mesons with zero spin grow with the field value. ##### Trans-dimensional Monte Carlo sampling applied to the magnetotelluric inverse problem Eric Mandolesi, Dublin Institute for Advanced Studies, Geophysics, Ireland Nicola Piana Agostinetti, Dublin Institute for Advanced Studies, Geophysics, Ireland Abstract: The data required to build geological models of the subsurface are often unavailable from direct measurements or well logs. In order to image the subsurface geological structures several geophysical methods have been developed. The magnetotelluric (MT) method uses natural, time-varying electromagnetic (EM) fields as its source to measure the EM impedance of the subsurface. The interpretation of these data is routinely undertaken by solving inverse problems to produce 1D, 2D or 3D electrical conductivity models of the subsurface. In classical MT inverse problems the investigated models are parametrized using a fixed number of unknowns (i.e. fixed number of layers in a 1D model, or a fixed number of cells in a 2D model), and the non-uniqueness of the solution is handled by a regularization term added to the objective function. This study presents a different approach to the 1D MT inverse problem, by using a trans-dimensional Monte Carlo sampling algorithm, where trans-dimensionality implies that the number of unknown parameters is a parameter itself. This construction has been shown to have a built-in “Occam’s razor”, so that the regularization term is not required to produce a simple model. The influences of subjective choices in the interpretation process can therefore be sensibly reduced. The inverse problem is solved within a Bayesian framework, where posterior probability distribution of the investigated parameters are sought, rather than a single best-fit model, and uncertainties on the model parameters, and their correlation, can be easily measured. ##### Classification of Histological Images Based on the Stationary Wavelet Transform Sidon, Federal University of ABC , CMCC Centro de Matemática, Computação e Cognição, Brazil Yan Duarte, Federal University of ABC , CMCC Centro de Matemática, Computação e Cognição, Brazil Marcelo Zanchetta do Nascimento, Federal University of Uberlândia, FACOM, Brazil Leandro Neves, São Paulo State University, DCCE, Brazil Valério Batista, Federal University of ABC, CMCC, Brazil Abstract: Non-Hodgkin lymphomas are of many distinct types, and different classification systems make it difficult to diagnose them correctly. Many of these systems classify lymphomas only based on how they look under a microscope. In 2008 the World Health Organisation (WHO) introduced the most recent system, which also considers the chromosome features of the lymphoma cells and the presence of certain proteins on their surface. The WHO system is the one that we apply in this work. Herewith we present an automatic method to classify histological images of three types of non-Hodgkin lymphoma. Our method is based on the Stationary Wavelet Transform (SWT), and it consists of three steps: 1) extracting sub-bands from the histological image through SWT, 2) applying Analysis of Variance (ANOVA) to clean noise and select the most relevant information, 3) classifying it by the Support Vector Machine (SVM) algorithm. The kernel types Linear, RBF and Polynomial were evaluated with our method applied to 339 images of lymphoma from the National Institute on Aging. We concluded that the following combination led to the most relevant results: detail sub-band, ANOVA and SVM with Linear and RBF kernels. ##### Family of higher order exponential variational integrators Odysseas Kosmas, University of Erlangen-Nuremberg, Mechanical Engineering, Germany Sigrid Leyendecker, University of Erlangen-Nuremberg, Mechanical Engineering, Germany Abstract: In the present work we derive a family of higher order exponential variational integrators for the numerical integration of systems with oscillatory solutions. To increase the order of variational integrators, first the discrete Lagrangian in any time interval is defined as a weighted sum of the evaluation of the continuous Lagrangian at intermediate time nodes while expressions for configurations and velocities are obtained using interpolating functions that can depend on free parameters. Secondly, in order to chose those parameters appropriately, exponential integration techniques are embedded. Focusing on highly oscillatory problems, we then split their potential energy into a fast and a slow component and use different quadrature rules for the different potentials. Finally, we study the behavior of this family of integrators in numerical tests. ##### Analysis on the use of Multi-Sequence MRI Series for Segmentation of Abdominal Organs Esref Selvi, Dokuz Eylül University, Institute of Natural and Applied Sciences, Turkey Emre Kavur, Dokuz Eylül University, Institute of Natural and Applied Sciences, Turkey Alper Selver, Dokuz Eylül University, Electrical and Electronics Engineering, Turkey Oguz Dicle, Dokuz Eylül University, Radiology, Turkey Abstract: Segmentation of abdominal organs from MRI data sets is a challenging task due to various limitations and artefacts. During the routine clinical practice, radiologists use multiple MR sequences in order to analyze different anatomical properties. These sequences have different characteristics in terms of acquisition parameters (such as contrast mechanisms and pulse sequence designs) and image properties (such as pixel spacing, slice thicknesses and dynamic range). For a complete understanding of the data, computational techniques should combine the information coming from these various MRI sequences. These sequences are not acquired in parallel but in a sequential manner (one after another). Therefore, patient movements and respiratory motions change the position and shape of the abdominal organs. In this study, the amount of these effects is measured using three different symmetric surface distance metrics performed to three dimensional data acquired from various MRI sequences. The results are compared to intra and inter observer differences and discussions on using multiple MRI sequences for segmentation and the necessities for registration are presented. ##### Spherical Target Recognition using Time-Domain Multiscale Approximation of Scattered Signals Mehmet Taygur, Dokuz Eylül University, Electrical and Electronics Engineeing, Turkey Alper Selver, Dokuz Eylül University, Electrical and Electronics Engineering, Turkey Yesim Zoral, Dokuz Eylül University, Electrical and Electronics Engineeing, Turkey Abstract: Classification of similar shaped objects from scattered electromagnetic waves is a difficult problem to solve, as it heavily depends on the aspect angle. Eliminating the effects of the aspect angle is possible by extracting distinguishable features from the scattered signals. These features should be robust to noise effects especially at SNR levels, where noise effects become dominant on the scattered signal. In this paper, we propose a target classification method, which uses a structural feature set extracted from scattered signal. Prior to feature extraction, a multi-scale approximation is performed using hierarchical radial basis function network topology to suppress the effects of noise on scattered signal. After principle component analysis, k-fold cross validation based experiments is performed. Results show that spherical targets are recognized successfully up to -10dB SNR. ##### A Mathematical Model for Analyzing Surface Plasmon Polariton Propagation through a Schottky-Junction-Based Plasmonic Amplifier Abdolber Mallah Livani, Amirkabir University, Electrical Engineering, Iran (Islamic Republic of) Hassan Kaatuzian, Amirkabir University of Technology, Photonics Research Laboratory (PRL), Electrical Engineering Dept., Iran, Islamic Republic Of Abstract: We have devised a simple model for describing an amplifier which operates on Surface Plasmon Polaritons (SPPs). A semiconductor is considered instead of dielectric which its interface with metal can support TM polarized SPP propagation. Metal-Semiconductor interface in particular conditions can be regarded as a Schottky junction that has the capability of being pumped electrically. So compensation of propagation losses is possible and beyond that, amplification occurs. This configuration has advantages such as simple fabrication process and compact size. However, designing such an amplifier with too many effects that arise in a Schottky junction may be an extremely difficult process. So a simplified model which regards essential effects and ignores non important ones is useful. In this work, gold has brought in contact with n+-doped In0.53Ga0.47As as semiconductor to form a Schottky junction. Concentration of doping in semiconductor is 9.3×1017cm-3. To estimate optical gain, at first, we solve drift-diffusion currents, continuity and Poisson’s equations to calculate carrier densities then using wave analysis, power density will be obtained. In 0.8V forward bias, optical gain of In0.53Ga0.47As is estimated around 2000cm-1 which is required for compensation of ohmic losses in metal for SPP. Current density in this forward bias is 104A/cm2 which is a typical current density. ##### Multicriteria optimization for wind farm layout design and assessment: Effective implementation of the Weighted Sum and Lexicographical methods Daniela Borissova, Information and Communication Technologies – Bulgarian Academy of Sciences, Information Processes and Decision Support Systems, Bulgaria Ivan Mustakerov, Information and Communication Technologies – Bulgarian Academy of Sciences, Information Processes and Decision Support Systems, Bulgaria Abstract: The design of a reliable and cost-effective industrial wind power farm is a prerequisite for the effective use of wind power as an alternative resource of renewable energy. The optimal layout could be defined by proper mathematical modeling involving explicitly multiple criteria in decision-making environment. The multicriteria approach is well suited for testing various design scenarios. Having in mind that designers usually prefer more flexible and transparent approaches, the multicriteria optimization could be used as a wind farm design simulation tool. In contrast to single criterion optimization, multiple criteria decision making is concerned with solving decision problems to choose the “best” alternative from a set of available alternatives, where the “best” can be interpreted as “the most preferred alternative” of decision maker. The multicriteria methods reflect more precisely the decision maker preferences in respect of wind farm layout design. The paper presents a multicriteria optimization approach for wind farm layout design by formulation of mixed integer problem for simultaneously determination of number, type and turbines placement taking into account the specifics of given wind area and decision maker preferences. A methodology for assessment of wind farm layout design by multicriteria optimization is proposed. The solutions results assist the project manager to assess the wind farm project on the early design stage. The weighted sum and lexicographical method are used to assess the effectiveness of wind farm layout design. Numerical case study examples of wind farm layout design demonstrate that both methods adequately reflect different criteria importance for different wind conditions of a particular site. During the simulation process, different points of view are analyzed to get Pareto-optimal alternatives. The wind farm energy output and costs corresponding to different Pareto-optimal alternatives under different wind directions are illustrated. ##### An algorithm for optimal design of wind farm layout over complex terrain Ivan Mustakerov, Information and Communication Technologies – Bulgarian Academy of Sciences, Information Processes and Decision Support Systems, Bulgaria Daniela Borissova, Information and Communication Technologies – Bulgarian Academy of Sciences, Information Processes and Decision Support Systems, Bulgaria Abstract: The paper concerns problem for optimal design of wind farm layout over complex terrain. When trying to make wind energy project economically viable, wind turbines type and placement are important design parameters that constitute a significant part of the overall project costs. Generally, the energy production is the major factor that has to be considered for economic success of a wind farm project, but in reality it has to be evaluated toward associated costs. It is essential to evaluate the relation of costs and energy production of wind farm on the early design stages. A combinatorial optimization model for determination of the wind turbines type and wind farm layout is described. This model is used in an algorithm for evaluating of different layouts over given terrain with preferable and not preferable zones for wind turbines placement. The basic steps of the algorithm are: definition of first k optimal types and corresponding numbers of wind turbines; determination of wind farm layouts for each type of turbines for given wind site specifics; calculation of the expected farm output potential and related costs for each layout; choice of the turbine’s type toward the best ratio of wind farm output potential and related costs. The algorithm is tested numerically for real turbines type’s data for given site dimensions and terrain specifics. The numerical illustration showed the applicability of the proposed algorithm. Using of this approach contributes the preliminary evaluation of wind farm effectiveness on the design stage of wind farm project development. It can be implemented as reasonable decision making tool for effective wind farm design. Some illustrative layouts for different wind turbines types defined by means of the described algorithm for uniform and predominant wind directions are shown. ##### Cooperative particle motion and dissipative solitary waves in complex (dusty) plasmas Sergey Zhdanov, MPE, , Germany Abstract: As an important element of self-organization, cooperative particle motion is present in many physical, astrophysical and biological systems. A particularly interesting and challenging topic is to study dynamic cooperativity at local and intermediate scales. As a rule, cooperative dynamics, bringing to life ’abnormal’ effects like enhanced diffusion, self-dragging, or self-propelling of particles, hold aspects of ’strange’ kinetics. Such kind of cooperative behavior was evidenced for string-like formations of colloidal rods, dynamics of mono- and di-vacancies in 2d colloidal crystals and in complex plasmas. Strongly coupled complex (dusty) plasmas give us a unique opportunity to go beyond the limits of continuous media and study various generic processes occurring in liquids or solids in real time and at the kinetic level. There is a certain advantage to experiment with complex plasmas merely because these systems are easy to manipulate in a controllable way. Externally manipulated ’dust molecules’, self-assembled strings in driven 3d particle clusters and dissipative solitary waves are noticeable examples. The results of recent experiments showing microparticle cooperative movements occurring under natural conditions are reviewed and interpreted. ##### GPU Computing in Bayesian Inference of Realized Stochastic Volatility Model Tetsuya Takaishi, Hiroshima University of Economics, , Japan Abstract: Recently the realized stochastic volatility model has been proposed to infer volatility of financial time series. We perform the Bayesian inference of the realized stochastic volatility model by the Hybrid Monte Carlo algorithm. The Hybrid Monte Carlo algorithm can be parallelized and thus performed on the GPU. The GPU code is developed with CUDA Fortran. We compare the computational time in performing the Hybrid Monte Carlo algorithm on GPU (GTX 760) and CPU (Intel i7-4770 3.4GHz) and find that the GPU can be up to 17 times faster than the CPU. We also code the program with OpenACC and find the similar speedup with OpenACC. ##### Magnetic phase transition in the spin-fluctuation theory Nikolai Melnikov, Lomonosov Moscow State University, Computational Mathematics and Cybernetics, Russian Federation Georgiy Paradezhenko, Lomonosov Moscow State University, Computational Mathematics and Cybernetics, Russian Federation Abstract: The effect of spin fluctuations on the magnetic phase transition is studied by the functional integral method. The pair interaction between magnetic moments at finite temperatures is replaced by the interaction with the fluctuating exchange field. Magnetic characteristics are obtained by the integrataion over the fluctuating field configurations, which requires an appropriate approximation. A characteristic feature of the Gaussian approximation is the first-order phase transition. We present a renormalization method that takes into account the fourth-order terms of the free energy in the fluctuating field. By the example of the Ising model, we demonstrate that the renormalized Gaussian approximation yields the second-order phase transition, which is observed in experiment. ##### Interaction of strong laser pulses and nanostructures Kalman Varga, Vanderbilt, Physics, United States Abstract: Attosecond science has brought “an era of control of the quantum world” enabling scientists to observe the electron dynamics in molecules and solids directly on their natural length (Angstrom) and time (sub-femtosecond) scales. We will present our study of electron and nuclear dynamics induced by strong laser pulses in the framework of the time-dependent density functional theory in real-time and real-space. Several prototypical examples will be used to highlight the correlated electron and nuclear dynamics in strong fields, including Coulomb explosion of clusters, laser-enhanced field emission from nanostructures, and laser-assisted desorption of hydrogen from surfaces of silicon clusters and graphene flakes. ##### On the computer simulations of electron states of ionic nanosystems with extended defects Yury K. Timoshenko, Voronezh State University, Department of Mathematical and Applied Analysis, Faculty of Applied Mathematics, Informatics, and Mechanics, Russian Federation Abstract: Yury K. Timoshenko The electron states of nanosystems of ionic compounds AgCl and KCl with extended defects (charged defects, edge dislocations) were under consideration. The semi-empirical tight-binding approximation and different calculation methods were used. The obtained results and efficiency of calculation schemes are discussed. This work is an improvement of our early investigations [1-3]. References 1. Timoshenko Yu K and Shunina V A Surface Sci. 603 2564 (2009) 2. Timoshenko Yu K and Shununa V A Proc. of SPIE 7396 73960T (2009) 3. Timoshenko Yu K Journal of Physics: Conference Series 490 (2014) 012173 doi:10.1088/1742-6596/490/1/012173 ##### Computational Simulation of Semiconductor Laser with Optical Injection gulnaz, Kazakh National Technical university, Department of Applied Physics, Kazakhstan Abstract: In this paper we study the dynamics of a semiconductor laser with optical injection. The time behaviour of solutions of a system of three coupled nonlinear rate equations, describing the electric field amplitude and the carrier concentration and the phase difference within the resonator, is discussed both qualitatively and numerically. We then concentrate on the periodic orbits that emanate from Hopf bifurcations. Depending on the injection strength and the phase difference two types of oscillations can be found, such as relaxation and periodic oscillations. ##### Numerical solution of a single charged particle under the Spatial Cyclotron Autoresonance Conditions JESUS GONZALEZ, UNIVERSIDAD DEL MAGDALENA, DEPARTAMENTO DE FISICA, Colombia Eduardo Orozco, Universidad Industrial de Santander, Physics, Colombia VALERIY DUGAR ZHABON, Universidad Industrial de Santander, Escuela de Física, Colombia Abstract: Relativistic dynamics of a single charged particle, accelerated in the cyclotron resonance conditions by TE11P waves in the stationary and inhomogeneous electric and magnetic fields is studied. The magnetic field is increased in the direction of the charged particle movement, so that the electron are in the spatial cyclotron autoresonance conditions. The electrostatic field has a suitable profile, which opposes the diamagnetic force associated with the mirror effect. By using a numerical solution of the Newton-Lorentz equation of motion, with the Leap-frog Boris scheme, a simulation of the system was made. The electric and magnetic fields at particle positions are calculated by using a bilinear interpolation method. It is shown that the resonant interaction of the electron with the electromagnetic wave can be prolonged in the static electric field; as a result the beam gets a larger energy. The numerical experiments are carried out with the TE113, and TE114 microwave fields of 0.1 GHz and 2.45 GHz, respectively, of 6 kV/cm amplitude. ##### Poisson structure on the phase space associated to the hamiltonian dynamics of coupled Korteweg-de Vries type equations Alvaro Restuccia, Antofagasta University, Physics, Chile Adrián Sotomayor, Antofagasta University, Mathematics, Chile Abstract: We present the hamiltonian structures for a wide class of coupled Korteweg-de Vries systems, including the Gear and Grimshaw system that models the strong interaction of internal waves in a stratified liquid and the system of Lou , Tong , Hu and Tang that describes a two layer fluid model. Among the hamiltonian structures of these systems we found new Poisson algebras which define consistent algebras of observables. ##### Modeling of strain in magnetic media by method movable cellular automata Victor V. Usachev, Far Eastern Federal University, The School of Natural Sciences, Russian Federation Petr Andriushchenko, Far Eastern Federal University, , Russian Federation Leonid Afremov, Far Eastern Federal University, Department of theoretical and experimental physics, Russian Federation Abstract: This paper represents ideas of the application of the method Movable Cellular Automata for modeling the distribution of magnetic particles in an elastic non magnetic matrix. The basic principles of mathematical model and algorithms is shown below. The model is represented as an ensemble of N discrete elements (automata), which identified the characteristic physical properties, rules of interaction and the possible states. Nearby automata capable of forming bonds with each other. Each machine can have 4 neighbors in a square package or 6 neighbors in the dense packing in the 2D model. Bound pair belong the same piece of material, and pair of unrelated automata belong to different fragments. The criterion for the formation of link and the link gap is the distance between the automata. The part of automata uniformly magnetized and interact with each other like magnetic dipoles. The special conditions can be given for certain groups of automata, for example, the lower layer can be fixed, and the upper layer can be influenced by an external force. Critical integration time step dt affects the accuracy of the calculations. Speed of sound in the medium venv possible to use for evaluate dt: dt = 0.25(d/ venv), venv = √ (K/ρ + 4G/3ρ), ρ - density, K - bulk compression modulus, G - shear modulus. In the case of different types of automata the smallest of their respective times is accepted. Offset the automaton from its position at the previous step is calculated according to the Werle’s scheme. At each step of integration the forces, acting on the automaton by the system is calculated, after a new speed and new coordinates of automata is calculated. The resultant force is the sum of the elastic and viscous forces, as well as force of the magnetic interaction automata. ##### Time Dependent Quantum Transport in Nano Structures Hang XIE, The University of Hong Kong,, Department of Chemistry, Hong Kong Abstract: In the modern electronics industry, the devices’ scale is in the range of nanometers. In this range the classical description for the electron transport is not suitable and the quantum mechanics will be implemented. We have developed a type of time-dependent-quantum-transport method based on the non-Equilibrium Green’s function theory. This method introduces some auxiliary density matrices to replace the complicated combinations of self-energies and the Green’s functions. So a series of coupling equation of motions are derived instead of solving the differential-integral equations in the traditional quantum dissipation systems, which is very time-consuming. In the practical calculations we use a Lorentzian-Pade expansion scheme to transform the energy integral of spectrum functions into finite summations. An automatic Lorentzian fitting algorithm for the complicated lead spectrum matrices is also developed. For the large systems, we implement a parallel algorithm to deal with the huge memory of the auxiliary density matrices. With this method, we have calculated some dynamic electron response in nano structures. We observe different ‘overshooting’ phenomena in graphene nanoribbons which result in the profiles of the density of states near the Fermi level. We also calculated the transient current in some carbon nanotubes. We find that under a rapid-rising stepwise bias, there exist a lot of high frequency current excitation in these carbon nanotubes. ##### Computational analysis of difenoconazole interaction with soil chitinase Diana-Larisa VLADOIU, West University of Timisoara, Biology-Chemistry, Romania Alecu Aurel Ciorsac, Politehnica University of Timișoara, Physical Education and Sport, Romania Marioara Nicoleta Filimon, West University of Timisoara, Biology-Chemistry, Romania Vasile Ostafe, West University of Timișoara, Biology-Chemistry, Romania ISVORAN ADRIANA, West University of Timisoara, Biology-Chemistry, Romania Abstract: Difenoconazole (DFC) is a fungicide managing to control a comprehensive range of fungi causing diseases of field crops. It usually comes into contact with soil, where it may undergo a variety of transformations and/or causes the loss of soil fertility or environmental damages. Within this study we use a computational approach to investigate the potential binding of DFC to soil chitinases. Computational characterization of the substrate binding sites of Serratia marcescens and Bacillus cereus chitinases using Fpocket tool reflects the role of hydrophobic residues for the substrate binding and the high local hydrophobic density of both sites. Molecular docking study reveals that difenoconazole is able to bind to Serratia marcescens and Bacillus cereus chitinases active sites, the binding energies being comparable. These results are in good agreement with the logP value (4.86) of DFC and published data reflecting that difenoconosale and its stereoisomers are degraded by soil microflora. ##### Ring Dark Solitons in Toroidal Bose-Einstein Condensates Lauri A. Toikka, University of Turku, Department of Physics and Astronomy, Finland Kalle-Antti Suominen, University of Turku, Department of Physics and Astronomy, Finland Abstract: Ring dark solitons (RDSs) are examples of nonlinear quantum states that can be supported by a Bose-Einstein condensate (BEC). Unlike the well-known planar dark solitons, exact analytic expressions for RDSs are not known. We address this problem by presenting exact localised soliton-like solutions to the radial Gross-Pitaevskii equation. To date, RDSs have not been experimentally observed in cold atomic gases, either. To this end, we propose two protocols for their creation in experiments. In addition, we present results regarding the dynamics and stability of RDSs. Under certain trapping potentials, we show that the decay of RDSs into circular arrays of vortex-antivortex pairs can be reversible, but eventually the decay leads to a state with some properties of quantum turbulence. ##### Ferromagnetic/superconducting interface in a hybrid nanoscopic disc JESUS GONZALEZ, UNIVERSIDAD DEL MAGDALENA, DEPARTAMENTO DE FISICA, Colombia JOSE BARBA, Universidad Nacional de Colombia, Departamento de Física, Colombia Abstract: The oscillations exhibited by the magnetization of superconducting nano and mesoscopics structures as a function of the applied magnetic field has attracted attention in the last few years. Nano/Mesoscopic hybrid systems in contact with ferromagnets exhibit interesting transport properties related to the influence of the exchange field on the density of states of clean ferromagnetic structures in contact with superconductor. In this work we study the vortex configurations in a superconducting disk with one central defect inside. The sample is surrounded by a ferromagnetic medium. We calculate the spatial distribution of the Cooper pairs and the phase of the superconducting order parameter and obtain magnetization, free energy and vorticity curves as a function of the magnetic applied field. We found that the first vortex penetration field decrease when a ferromagnetic/superconducting interface is used. ##### The Solutions of the equations of pulse propagation in optical fibers Yuliya Zhiganshevna Pchelkina, Samara State Aerospace University (SSAU), The Department of applied mathematics, Russian Federation Ivan Alimenkov, Samara State Aerospace University (SSAU), Applied mathematics, Russian Federation Abstract: The solution of the equation of propagation of optical pulses in optical fibers is founded in quadratures. The expanded equation of propagation of optical pulses in silica optical fibers is displayed. The localized solution is founded. The decision of the extended equation of propagation of optical pulses in optical fibers for arbitrary functions of the response of a nonlinear medium for external harmonic perturbation is founded in quadratures . ##### Mathematical Modelling on Chemically Reacting Boundary Type Flow under Reduced Gravity Conditions Wang Hui Ying, University of Poitiers, Pprime-CNRS, France Abstract: A fire on board spacecraft is, though unlikely owe to strict safety measures, one of the scenarios with the highest damage potential for hardware and crew. In spacecraft, where buoyancy is negligible, the flow is limited to that induced by the ventilation system with a characteristic velocity of 0.2 m/s. Therefore, the flow is expected to be laminar. The most likely scenario of a flame incidentally initiated and spread on board spacecraft is a wall of combustible material adjacent to a low Reynolds number gas flow (forced by the venting system) and exposed to a critical ignition source. When analysing a combustion process, transport equations can be scaled and characteristic parameters can be extracted. In normal-gravity, a buoyantly induced velocity generates an upper limit for all time scales and dominates all forms of transport. All forms of transport slower than natural convection can thus be neglected. In micro-gravity this upper limit disappears and different phenomena, negligible in normal gravity, become relevant and sometimes of great importance. This is the case for all combustion processes related to fire and in particular the estimation of material flammability. Ignition includes solid and gas phase processes. Those related to the solid phase are relevant to the material and can be extrapolated to micro-gravity. The processes related to the gas phase are affected by buoyancy and thus require further attention. Under conditions of reduced gravity where the effects of buoyancy are small, due to the absence of natural convection, time scales associated with combustion processes are much longer and radiation can be the predominant mode of heat transfer even for small diffusion flames. Soot production is enhanced with increasing residence times, further emphasizing the role of radiation. Thus the ability to control soot formation and radiative emissions in nonpremixed combustion is of extreme importance to spacecraft fire safety. The research presented tends to provide fundamental numerical knowledge on co-current, boundary type flame spread. The objective of this work is to use the detail from the numerical simulations to gain further insight into the effects of the fuel injection rate on the soot formation and associated heat flux on a boundary layer diffusion flame. To understand and analyze the flame spread under conditions of reduced gravity, the most important issue is the identification of the flame position/ geometry and associated heat flux. A numerical study is performed to give a quantitative description of soot formation and associated radiation flux with different fuel injection rate. The strong coupling between soot and radiation are studied in three-dimensional flames by solving the Navier-Stokes fluid dynamic equations of elliptic, reacting flow. Binary diffusion coefficients, thermal conductivity and viscosity coefficients are all temperature and composition dependent. Investigations on the effects of fuel (ethylene) injection rate on the geometric characteristics, localisation and stability of the boundary diffusion flame are performed. The computed soot volume fraction is compared with experimental data from a laminar ethylene diffusion flame established over a horizontal flat plate in micro-gravity environment, and a relatively good agreement is attained. An increase of fuel injection velocity results in a significant increase in integrated soot formation. A stable symmetrical flame and counter-rotating vortex in the cross-section is generated even under microgravity conditions with an increase of fuel injection velocity. The extent of the flame in cross-stream plane surpasses significantly the pyrolysis zone. Development of the counter-rotating vortex leads to the formation of the kidney-shape structure on the cross-stream plane for the temperature. This allows soot particle for long residence times before crossing the flame sheet at fuel-rich conditions, and enhances soot formation. ##### A different model for open vehicle routing problem Semih ONUT, Yildiz Technical University, , Turkey Mehmet Kamber, Yildiz Technical University, , Turkey Abstract: Open vehicle routing problem (OVRP) is a generalization of vehicle routing problem (VRP) where vehicles do not require to return to the depot. A new variant of OVRP, heterogeneous fleet balanced open vehicle routing problem (HFBOVRP), is studied in this study. There are more than one types of vehicles which can be assigned to tours, so the problem is a heterogeneous fleet OVRP. First objective is to minimize the total transportation cost. The second objective is to balance the tour lengths. Some theoretical instances are generated and problems are solved by optimization methods. ##### The Analysis of a Reactive Hydromagnetic fluid flow in a channel through a Porous Medium with Convective Cooling. Hassan Anthony R., Tai Solarin University of Education, Ijagun, Ogun State, Department of Mathematics, Nigeria Abstract: This study investigates the analysis of a reactive hydromagnetic fluid flow between two parallel plates through a porous medium with convective boundary conditions. Neglecting the consumption of the material which is exothermic under Arrhenius kinetics; it is assumed that the flow system exchanges heat with the ambient following Newton’s cooling law. Analytical solutions of the nonlinear dimensionless equations governing the fluid flow are obtained using the traditional perturbation method and Adomian Decomposition Method (ADM) together with the diagonal Pade Approximation which is used to determine the thermal criticality values as well as bifurcation conditions. Effects of all – important flow properties on the fluid flow are also presented and discussed. Dr. Haider F Abdul Amir, Universiti Malaysia Sabah, Physics with Electronic, Malaysia Abstract: Space and ground level electronic equipment with semiconductor devices are subjected to the deleterious effects by radiation. This paper is attempted to present the transient and post-irradiation response of optoelectronic devices to gamma (γ) rays utilizing cobalt-60. In situ measurements were made on the devices under test (DUTs) up to a total dose of 60 krad followed by a post-irradiation not in-flux test for eight hours. Current transfer ratio (CTR) with is the vital merit of the optoelectronic system is found to decrease remarkably with the absorbed dose. This degradation is induced by the interaction of the energetic photons from gamma rays via two main mechanisms. The dominant effect is the mechanism by ionization while the secondary is by displacement. This radiation effect is found to arouse either a permanent or temporarily damage in the DUTs depending on their current drives and also the Total Ionizing Dose (TID) absorbed. The TID effects by gamma rays are cumulative and gradually take place throughout the lifecycle of the devices exposed to radiation. The full damage cascade phenomenon in the DUTs is calculated via the simulation. ##### MR Image Intensity Inhomogeneity Correction Punga (Visan) Mirela, Dunarea de Jos University, Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos University of Galati, Romania Simona Moldovanu, Dunarea de Jos University, Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos , Romania Luminita Moraru, Dunarea de Jos University of Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Romania Abstract: MR technology is one of the best and most reliable way to study the brain. Its main drawback is the so-called intensity inhomogeneity or bias field which impairs the visual inspection and the medical proceedings for diagnosis and strongly affects the quantitative image analysis. In order to accurately and effectively restore the original signal, we address here to filtering, bias correction and quantitative analysis of correction. In this report, we used two denoising algorithms; (i) Basis rotation ﬁelds of experts (BRFoE) and (ii) Anisotropic Diffusion (when Gaussian noise, the Perona-Malik and Tukey's biweight functions and the standard deviation of the noise of the input image are considered). Then, the bias field correction is done by using the level set methods. Various metrics, such as Mean Square Error, Peak Signal to Noise Ratio, Normalized Cross-Correlation, Average Difference, Structural Content and Normalized Absolute Error are computed in order to assess the performance of the proposed method. ##### Analytical Models for the Interactions between a Gas Mixture and Quartz Micro Balance Sensor Array Abbas Abdelaziz, Centre de recherche en Soudage et Contrôle (CSC), , Algeria Abstract: The aim of this work is to develop analytical models for the thermodynamic equilibrium at the interfaces (gas mixture / Quarz Micro Balance sensor arrays . Differential equations, which describe the change in the partial sensitivities of the sensor array elements depending on the gas mixture components concentrations, and the sensor array parameters, have been developed. Moreover, the responses of the sensor array as a function of the concentrations of the gas mixture components have been modeled. ##### CFD-Exergy Analysis of the Flow in a Supersonic Steam Ejector Mohamed BOULENOUAR, USTO-MB, Génie Maritime, Algeria Ahmed OUADHA, USTO-MB, Génie Maritime, Algeria Abstract: Owing to the growing price of energy and environmental concerns, it is not surprising that the refrigeration industry is continuously looking for alternative solutions to conventional refrigeration systems. A promising alternative is ejector refrigeration systems using steam water as the working fluid. In an ejector refrigeration system, the mechanical compression is replaced by a thermal compression using an ejector. Ejector simplicity (i.e., it has no moving parts) compared to conventional systems and its low cost make it very attractive. Ejector refrigeration systems have the advantage of being simple, easy to install and require less maintenance. In addition, in an ejector system, the compression can be directly obtained without using mechanical power. They can be driven by thermal energy from solar energy or waste heat from industrial processes. However, because of their low coefficient of performance, ejector refrigeration systems are less dominant as compared to conventional refrigeration systems. Therefore, in order to promote the use of these systems, it is essential to improve their performance. This necessarily requires the understanding and improvement of the entrainment process in the ejector. Understanding the entrainment process and the mechanisms responsible for the losses in an ejector is essential in order to construct more efficient ejector refrigeration systems. Methods used to improve its efficiency present complicated issues for both experimental and numerical investigations, especially those aimed at optimisation of the ejector geometry. Experimental techniques usually do not cover the whole operating parameters range of an ejector. These techniques can be successfully complemented using appropriate numerical simulations. The advances in computational fluids dynamics methods permitted the development and implementation of mathematical models for the simulation of complex phenomena encountered in supersonic steam ejectors used in refrigeration systems. The flow field and the associated heat transfer can be described with less restriction using numerical methods offering possibilities for performance improvements of either components or systems. Numerical simulations of the flow can significantly reduce the time and cost in designing of ejectors before the first prototype is produced. In order to use efficiently and effectively the energy resources, recent analyses join quality to quantity of the energy used to realize a given purpose. In other words, associate the second law of thermodynamics which deals with the quality to the first law of thermodynamics dealing with the quantity of energy. The exergy, defined as the maximum useful work that can be extracted from a system in any process which brings the system into equilibrium with its environment, can be used to assess the quality of energy resource. The exergy concept which is based on the second law of thermodynamics is a powerful tool that identifies the location and the magnitude of irreversibilities in a process. The identification of irreversibilities will help to find and design more efficient processes. Exergy analysis presents also the advantage of evaluating meaningful efficiencies that measure how far the efficiency of a system or process deviates from ideality. Further, this technique permits to identify the causes, locations and magnitudes of exergy losses. Generally, exergy analysis uses thermodynamics-based models. These models are based only on mean values of inlet and outlet parameters. Although, these models are simple and cheap in terms of computation, they fall in predicting the fluid motion features. Fluid motion details can be easily obtained using CFD models. In this case, an exergy analysis can be carried using CFD-based models. These models provide all fluid motion details by solving a set of differential equations representing conservation of mass, momentum and energy and turbulence models. Only few studies on exergy analysis have been found in the open literature to the best of the authors’ knowledge, although there are many studies related to ejectors. The current study aims to carry out a CFD-exergy based analysis to assess the main areas of loss in a supersonic steam ejector encountered in ejector refrigeration systems. The governing equations for a compressible flow are solved using finite volume approach based on SST k- model to handle turbulence effects. Flow rates and the computed mean temperatures and pressures have been used to calculate the rate of exergy at the ejector inlets and outlet as well as the exergy losses within the ejector. Furthermore, the exergy efficiency of the ejector has been calculated. ##### Applying Enhancement Filters in the Pre-processing of Images of Lymphoma Sergio Silva, Federal University of Uberlândia, Faculty of Mechanical Engineering, Brazil Marcelo Zanchetta do Nascimento, Federal University of Uberlândia, FACOM, Brazil Valério Batista, Federal University of ABC, CMCC, Brazil Leandro Neves, São Paulo State University, DCCE, Brazil Abstract: Lymphoma is a type of cancer that affects the immune system, and is classified as Hodgkin or non-Hodgkin. It is one of the ten types of cancer that are the most common on earth. Among all malignant neoplasms diagnosed in the world, lymphoma ranges from three to four percent of them. Our work presents a study of some filters devoted to enhancing images of lymphoma at the pre-processing step. Here the enhancement is useful for removing noise from the digital images. We have analysed the noise caused by different sources, like room vibration, scraps and defocusing, and in the following classes of lymphoma: follicular, mantle cell and B-cell chronic lymphocytic leukemia. The filters Gaussian, Median and Mean-Shift were applied to different colour models (RGB, LAB and HSV). Afterwards, we performed a quantitative analysis of the images by means of the Structural Similarity Index and the Mean Squared Error. This was done in order to evaluate the similarity between the images. In all cases we have obtained a certainty of at least 75%, which rises to 99% if one considers only HSV. Namely, we have concluded that HSV is an important choice of colour model at pre-processing histological images of lymphoma, because in this case the resulting image will get the best enhancement. ##### Ab initio study of the electronic band structure of the valence band of II-VI C(2×2) reconstructed surfaces Alberto Rubio, Universidad Autónoma Metropolitana - Azcapotzalco, Ciencias Básicas, Mexico Daniel Olguín, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Departamento de Física, Mexico Abstract: The structural and electronic properties of the CdTe(001), CdSe(001), and ZnSe(001) C(2×2) reconstructed surfaces have been studied in the framework of the first principles calculations. To simulate the surface, a seventeen atomic layers slab was used, where also we add four atomic layers of vacuum. Using the experimentally determined lattice parameter as input we have relaxed the internal atomic positions of the outer atomic layers. We show that our model reproduces properly the surface structural parameters, as well as known electronic properties found in bulk for these compounds. Then, we discuss our results of the projected bulk bands and the surface and resonance states found for these surfaces. ##### Basic idea of Corbino-type single-electron transistor Akira Suzuki, Tokyo University of Science, Physics, Japan Hisao Taira, Tokyo University of Science, Department of Physics, Japan Abstract: We have formulated the transmission probability of an electron in a Corbino quantum disk by taking into account charging effect. The confining potential of the Corbino disk has a singularity at the centre of the disk. In order to avoid this singularity problem, we have to reformulate the Schroedinger equation in the Riemannian manifold. The Schroedinger equation describing the electron in Corbino disk must be expressed by introducing a momentum operator reformed by the metric tensor since the original momentum operator is not Hermitian. In order to obtain a Hermitian momentum operator, it requires the deformation of the Hilbert space by introducing a new wave function. This deformation leads to the extra effective potential term in the Schroedinger equation, which depends on the metric, i.e. the geometry of the disk. It should be noted that the charging energy due to the confinement of electrons in the Corbino disk strongly depends on the geometry of the disk. Thus, we discuss the quantum tunneling of a particle confined in the Corbino disk to investigate the effect of both the effective and charging energy of the effective confining potential by using the Wentzel-Kramers-Brillouin (WKB) approximation. We will present that the transmission probability strongly depends on the charging energy. This suggests that the formulated transmission probability is applicable to the analysis of the single-electron transistor. ##### A new type of Wavelets and its relation to Gabor analysis Ehud Moshe Baruch, Tecnion, Mathematics, Israel Abstract: We introduce a new type of wavelets. These wavelets interpolate between the classical wavelets frames and a Gabor analysis type frames. We introduce a family of new wavelets which are suitable for localized signals and another family which is suitable for localized frequency. ##### Quantum Magnets and Matrix Lorenz Systems Stam Nicolis, CNRS-LMPT Tours, Physics Department, France Abstract: The Landau–Lifshitz–Gilbert equations for the evolution of the magnetization, in presence of an external torque, can be cast in the form of the Lorenz equations and, thus, can describe chaotic fluctuations. To study quantum effects, we describe the magnetization by matrices, that take values in a Lie algebra. The finite dimensionality of the representation encodes the quantum fluctuations, while the non-linear nature of the equations can describe chaotic fluctuations. We identify a criterion, for the appearance of such non-linear terms. This depends on whether an invariant, symmetric tensor of the algebra can vanish or not. This proposal is studied in detail for the fundamental representation of u(2) = u(1) × su(2). We find a knotted structure for the attractor, a bimodal distribution for the largest Lyapunov exponent and that the dynamics takes place within the Cartan subalgebra, that does not contain only the identity matrix, thereby can describe the quantum fluctuations. ##### Multiscale cross-correlation analysis of Shanghai stock market Dan Li, Wuhan University of Technology, , China Qingju Fan, School of Science, Wuhan University of Technology, Department of Statistics, China Abstract: In this paper, we investigate the correlation and cross-correlation behaviors in Shanghai stock market by combining the traditional detrended fluctuation analysis (DFA) and detrended cross-correlation analysis（DCCA） method with moving fitting windows, respectively. The new method can not only show detailed scale exponent properties of non-stationary time series in small and large scale simultaneously, but also provide a more faithful and more interpretable description of series under investigation. Using the moving fitting windows, we find that the correlations in Shanghai B-share is stronger than Shanghai A-share on the whole, and we also show the dynamic long–range cross-correlations behaviors between Shanghai A-share and B-share index series. ##### High order multi-step variational integrators Dimitrios Vlachos, University of Peloponnese, Department of Informatics and Telecommunications, Greece Abstract: In this work, we present a new approach to the construction of variational integrators. In the general case, the estimation of the action integral in a time interval [qk,qk+1] is used to construct a symplectic map (qk,qk+1) → (qk+1,qk+2). The basic idea here, is that only the partial derivatives of the estimation of the action integral of the Lagrangian are needed in the general theory. The analytic calculation of these derivatives, give raise to a new integral which depends not on the Lagrangian but on the Euler–Lagrange vector, which in the continuous and exact case vanishes. Since this new integral can only be computed through a numerical method based on some internal grid points, we can locally fit the exact curve by demanding the Euler–Lagrange vector to vanish at these grid points. Thus the integral vanishes, and the process dramatically simplifies the calculation of high order approximations. The new technique is tested for high order solutions in the two-body problem with high eccentricity (up to 0.99) and in the outer solar system. ##### On the Integrability and Linearization of the Second Order Differential Equations via First Integrals and Sundman Transformation ÖZLEM, ORHAN, , Turkey Teoman Özer, Istanbul Technical University, Civil Engineering , Turkey Abstract: In this study, we consider the ordinary differential equations of the form x ̈+a2(t,x)x ̇2+a1(t,x)x ̇+ a0(t, x) = 0. The second order ordinary differential equations in this form have first integrals of the form A(t, x)x ̇ +B(t, x), λ-symmetries and integrating factors. The purpose of this study is to characterize the second order differential equations and integrate these equations by using first integrals and λ-symmetries. We use an algorithm to calculate these symmetries. Furthermore, we characterize equations that can be linearized by means of nonlocal transformation which is called Sundman transformation. We can apply these algorithm and transformation to nonlinear fin equation where has thermal conductivity and heat transfer coefficients, which are considered as functions of temperature. We obtain first integrals for different coefficients of fin equation. Finally, we compare the results obtained by different methods. ##### Function projective synchronization of two identical discrete-time hyperchaotic systems Suping Qian, Changsha institute of technology, School of Mathematics and statics, China Abstract: A function projective synchronization is defined in discrete-time dynamical systems, in which the drive and response state vectors evolve in a proportional scaling function matrix. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of two identical discrete-time hyperchaotic systems. Numeric simulations are used to verify the effectiveness of our scheme. ##### Cluster analysis of word frequency dynamics Yulia Maslennikova, Kazan federal university, Institute of Physics, Russian Federation Inna, Kazan Federal University, , Russian Federation Abstract: This paper describes the analysis and modelling of word usage frequency time series. During one of the previous studies, an assumption was put forward that all word usage frequencies have uniform dynamics that is near to a form of a Gaussian function. This assumption can be checked using frequency dictionaries of Google Books Ngram database. Google Books database includes 5.2 million books published between 1500 and 2008. The corpus contains over 500 billion of American English, British English, French, German, Spanish, Russian, Hebrew, and Chinese words. In this research, time series of word usage frequencies were clustered using a Kohonen's neural network. The similarity between input vectors was estimated using both algorithms: the Spearman rank correlation coefficients and the maximum likelihood method. As a result of the neural network training procedure, more than ten different forms of time series were found. They correspond to dynamics of word usage frequencies from the word birth to the word death. Сonsequently, different groups of word forms have different dynamics of word usage frequency variations. ##### Evaluation of outliers in acquired brain MR images Simona Moldovanu, Dunarea de Jos University, Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos , Romania Luminita Moraru, Dunarea de Jos University of Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Romania Punga (Visan) Mirela, Dunarea de Jos University, Galati, Faculty of Sciences and Environment, Department of Chemistry, Physics and Environment, Dunarea de Jos University of Galati, Romania Abstract: Pre-processing is an important stage in the analysis of magnetic resonance images (MRI), because the effect of specific image artefacts, such as intensity inhomogeneity, noise and low contrast can adversely affect quantitative image analysis. Image histogram is a useful tool to analyse MR images as it allows a close relationship with important image features as contrast and noise. The noise and variable contrast are elements that locally modify the quality of images. The key issue of this study derives from the fact that spatial histogram can contain outliers indicating corrupted image information through the disorder of the bins. These aberrant errors should be excluded from the studied data sets. Here, the outliers are evaluated by using rigorous methods based on the probability theory and Chauvenet (CC), Grubbs (GC) and Prices (PC) criteria. In order to check the quality of the MR images, the Minkowsky (MD), Euclidean (ED) and cosine (CD) distance functions were used. They act as similarity scores between histogram of the acquired MRI and processed image. This analysis is necessary because, sometimes, the distance function exceeds the co-domain due to the outliers. In this paper, 32 MRIs are tested and the outliers are removed so that the distance functions generate uncorrupted and real value. ##### Biochemical and histopathological response of liver rats induced by antilipolytic drugs. Nofal, Menoufia university Egypt, Zoology, Egypt Abstract: The present study provides evidence that 1,5-Bis (3,5-Dimethylpyrazol-1-yl)-3-oxapentane-diacetatocopper has an antidiabetic effect, as hypoglycemic agent and as antilipolytic agent, but with many abnormalities. Animals treated with 1,5-Bis (3,5-Dimethylpyrazol-1-yl)-3-oxapentane-diacetatocopper revealed many histopathological, biochemical, histochemical and immunohistochemical alterations on the liver. Sera of animals treated with 1,5-Bis (3,5-Dimethylpyrazol-1-yl)-3-oxapentane-diacetatocopper revealed a significant increase in ALT and AST. The present study revealed many histopathological alterations on the liver; inflammatory infiltration, marked vacuolated cytoplasm in cells, congestion of blood vessels, hemorrhage, pyknotic cells and binucleated cells, as well as, some of the degenerated cells showed karyorhexis, pyknosis and area of necrosis, as well as, significant decrease in proteinic contents on the liver. the present study revealed negative expression of Bcl-2 proteins in all hepatic cells of control rats and positive expression of Bcl-2 proteins in hepatic cells of treated rats with 1,5-Bis(3,5-Dimethylpyrazol-1-yl)-3-oxapentane-diacetatocopper. ##### RELAXED ELASTIC LINES OF SECOND KIND IN SEMI-DUAL SPACE Gülşah Aydın, süleyman demirel university, , Turkey A.Ceylan ÇÖKEN, University of Süleyman Demirel, Department of Mathematics, Turkey Abstract: Theory of elasticity is a topic that keeps improving by using on many fields such as geometry, physics, chemistry and engineering. Energy density is given as some functions of curvature and torsion. If the curve of the α will be an external for the variation problem that minimizes the value of energy density; then this curve is called as relaxed elastic line. The relaxed elastic line on an oriented surface is considered as a model of DNA molecule. In this study, we worked on the second type relaxed elastic lines on the semi-dual spaces which has an important point on kinematic and Einstein’s relativity theory. We also obtained boundary conditions for this type of curves. Moreover, the minimization problem of the energy which occurs with an applied force on an elastic line was discussed. Then, we researched the formed potential energy due to the applied force. Also, during the calculation of the potential energy on the elastic line, the amount of the potential energy for unit length of the elastic line was used. Afterwards, by integrating that amount, total potential energy calculated. So, we study to make a contribute both Einstein’s relativity theory and kinematic. ##### Computer simulation of electron states of the isoelectron substitutional impurities in quantum wire of KCl with edge dislocation Yury K. Timoshenko, Voronezh State University, Department of Mathematical and Applied Analysis, Faculty of Applied Mathematics, Informatics, and Mechanics, Russian Federation Valentina Shunina, Voronezh State Technical University, Department of Information Technologies and Computer Safety, Russian Federation Alexander I. Shashkin, Voronezh State University, Department of Mathematical and Applied Mathematics, Faculty of Applied Mathematics, Informatics, and Mechanics, Russian Federation Abstract: Yury K. Timoshenko, Valentina A. Shunina, Alexander I. Shashkin The electron states of quantum wires KCl, KCl:Br, and KCl:J with an edge dislocations were investigated. The tight-binding semi-empirical band approximation and non-empirical cluster approach were used. Semi-empirical calculations were carried out in framework of model [1, 2]. Besides, the algorithms for electronic levels calculations of polar nanosystems with the partial self-consistency [3] were used. Using results of computer modelling we discuss the problem of localization of electronic states near the line of edge dislocation. References 1. Timoshenko Yu K and Shunina V A 2005 Phys. Stat. Sol. (c) 2 1788 2. Timoshenko Yu K and Shunina V A 2009 Surface Sci. 603 2564 3. Timoshenko Yu K Journal of Physics: Conference Series 490 (2014) 012173 doi:10.1088/1742-6596/490/1/012173 ##### The generalized uncertainty principle as quantum gravitational friction Pedro Bargueno, Universidad de los Andes, Física, Colombia Abstract: The Generalized Uncertainty Principle gives place to deformed commutation relations which are linear or quadratic in particle momenta. In this talk we show that, in the linear case, which corresponds to double special relativity theories, this deformation is equivalent to a gravitationally-induced damping process in an Ohmic environment at zero temperature. Therefore, both minimum length and maximum momentum give place to quantum gravitational friction. ##### Wormholes Threaded by Chiral Fields Theodora Ioannidou, Aristotle University of Thessaloniki, Department of Mathematics, Physics and Computational Sciences, Greece Abstract: We consider Lorentzian wormholes with a phantom field and chiral matter fields. The chiral fields are described by the non-linear sigma model with or without a Skyrme term. When the gravitational coupling of the chiral fields is increased, the wormhole geometry changes. The single throat is replaced by a double throat with a belly inbetween. For a maximal value of the coupling, the radii of both throats reach zero. Then the interior part pinches off, leaving a closed universe and two (asymptotically) flat spaces. A stability analysis shows that all wormholes threaded by chiral fields inherit the instability of the Ellis wormhole. ##### The peculiarities of magnetization processes in layered high-temperature superconductors with ferromagnetic defects under applying of transport current and external magnetic field Vladimir Kashurnikov, National Research Nuclear University MEPhI, Department of Physics of the Solid State and Nanoscaled Systems (№70), Russian Federation Anastasiia Maksimova, National Research Nuclear University MEPhI, Department of Physics of the Solid State and Nanoscaled Systems (№70), Russian Federation Igor Rudnev, National Research Nuclear University MEPhI, Department of Physics of the Solid State and Nanoscaled Systems (№70), Russian Federation Abstract: The Monte-Carlo method was used for study of magnetization processes in 2D high-temperature superconductors with internal ferromagnetic defects under application of transport current and external dc magnetic field. The magnetic part of the pinning force was calculated as an energy of interaction of magnetic dipole of ferromagnetic defect with the field of Abrikosov vortex. The self-consistent interaction between magnetic moments of the particles and the vortex system was taken into account. The current-voltage characteristics (VACH) in presence of external dc magnetic field were calculated. A novel S-type of current-voltage characteristics of the superconductor/ferromagnet system in external magnetic field was demonstrated. It was shown that the S-type nonlinearity is due to the local reversal magnetization of magnetic particles by the field of vortices. The effect of temperature, value of external magnetic field and defect concentration on magnetization processes were analyzed. The H-T phase diagram which demonstrates the region of existence VACH nonlinearity was obtained. Vortex configurations arising during magnetization were obtained. The conditions for electromagnetic generation at the region of nonlinearity were found and the frequency of such a generation was estimated. ##### Sharpening technique to decrease comb passband deviation Gordana Jovanovic Dolecek, Institute INAOE, Electronics, Mexico Abstract: This paper deals with the wideband compensation of the comb decimation filter pass-band droop using the sharpened technique. The sharpening technique is introduced for simultaneous improvements of both the pass-band and stop-band of a linear-phase FIR (Finite Impulse Response) filters. The technique uses the amplitude change function (ACF) which is a polynomial relationship between the amplitudes of the sharpened and the prototype filters. One-stage and two two-stage sharpened-based compensated combs are proposed taking the cascaded narrowband and wideband compensators. The choice among structures offers a trade-off between the complexity and the pass-band improvement. The resulting pass-band characteristic is almost flat for the one-stage decimation comb structure. In the two-stage structures the sharpening is performed only at the second stage and as a result the pass-band deviation is slightly increased but it is less than 0.05db. The proposed structures are compared with the compensated combs introduced in the open literature. ##### COMPTON OPERATOR IN QUANTUM ELECTRODYNAMICS Enrique Ortega Muñoz, Instituto Politécnico Nacional, Ingenieria Quimica, Mexico Abstract: In the frame in the quantum electrodynamics exist four basic operators; the electron self-energy Σ, vacuum polarization Π, vertex correction Λ, and the Compton operator, denoted by C. The first three operators are very important by its relation with renormalized ans Ward identity. However, the Compton operator has equal impotance, but without divergence, and Little attention has been given it. We have calculated the Compton operator and obtained the closed expression for it in the frame of dimensionally continuos integration and hypergeometric functions. ##### Time adaptive phase fitted variational integrators using a space-time geodesic approach Odysseas Kosmas, University of Erlangen-Nuremberg, Mechanical Engineering, Germany Abstract: In this work, we investigate the use of space-time geodesic approach of classical mechanics in order to derive time adaptive phase-fitted variational integrators. The proposed technique is tested in systems with separable Lagrangians. Towards this end, at first we unfold the standard Euler-Lagrange system to its space-time manifold and, then, we recast it as a geodesic problem in which the potential energy part is absent. Preliminary simulated results on the Kepler problem (without optimizing the choice of step sizing) show that, one can use the space-time geodesic formulation to generate an adaptive scheme that still preserves some underlying geometric structure. ##### Study on EP resin modified NANO-SILICA and mechanical properties of composites Ju Chunhua, Harbin Institute of Technology, Material Science, China Abstract: Owing to their light, excellent mechanical properties and a series of other advantages, and obviously advantage of lightweight of polymer composite Liquid Oxygen (LOX) tank, composite materials have been critical and broadly studied in the development of the launch vehicles of next generation, especially in the propelling system. In this present research, prepared polymer matrix of composite was modified, and influence of composite materials interface and mechanical properties at room and low temperature was studied. We want to prepare composite with good properties and wish to the lay a good foundation of this area for the following researchers. Curing kinetics and mechanism of polymer matrix are exmined by means of TG-DSC and FTIR. Using the result of dynamic contact angle, micro-debonding and mechanical properties of composite materials and matrix, influence of modified with nano-silica resin to composite at room and low temperature, and low temperature to matrix, interface, mechanical properties of composite, are exmined. ##### Modeling deformation and fracture of Ni nanofilm Mohammed, Physics department, Faculty of science, Menoufia university, Egypt, Physics , Egypt Abstract: Morse potentials were employed to carry out three dimensional molecular dynamics simulations. A computer experiment is performed at a temperature corresponding to 300K and 1000K. MD simulation used to investigate the effect of cross-sectional area of Ni nanofilm on the nature of deformation and fracture. The engineering stress–time diagrams obtained by the MD simulations of the tensile specimens of these Ni nanofilms show a rapid increase in stress up to a maximum followed by a gradual drop to zero when the specimen fails by ductile fracture. The feature of deformation energy can be divided into four regions: quasi-elastic, plastic, flow and failure. The results showed that breaking position depended on the nanofilm length cross-sectional area. ##### Modeling and simulation of a batch reactor with automatic temperature control applied to fine chemicals. Hachama Kamel, Laboratory valorization on natural substances, Khemis Miliana University, Sciences and Technology, , Algeria BEZZINA MOHAMED, University of Khemis-Miliana, , Algeria ZOUANTI MUSTAPHA, University of Khemis-Miliana, , Algeria Abstract: The approach presented in this work aims to develop a methodology for modeling of a batch chemical reactor, which takes place in these, two consecutive reactions, irreversible, highly exothermic and in a homogeneous liquid phase. We are interested in this study of the thermal stability of the system and the evolution of concentration of the reactants and products as a function of time. This methodology is the first step to develop a comprehensive model that takes into account, the coupling between the equations of material balance, energy balance equations and the system of control and regulation. The results are used to study the operation of the reactor and predict its behavior in various situations, and allow us to optimize its operation to increase efficiency and ensure quality products, while avoiding thermal runaway. ##### Two-Step Syntheses of 3-Methyl-1,2,4-Benzotriazine Hachama Kamel, Laboratory valorization on natural substances, Khemis Miliana University, Sciences and Technology, , Algeria KHODJA MOHAMED, University Blida 1, , Algeria ZOUIKRI MOHAMED, University Blida 1, , Algeria Abstract: The reduction cyclization of nitrophenylhydrazones has been widely used to afford nitrogen-based heterocyclic molecules. To name but a few, there are 4H-pyrazolo-[1,5-a] benzimidazoles, ethyl-(1,2,4-benzotriazine-3-yl) acetate and its derivatives, benzo[1,2-b:5,4-b]bis(1H)-imidazo[1,2-b]pyrazoles. Several pathways for the synthesis of 1,2,4-Benzotriazines have been reported. In continuation of our work on heterocyclic synthesis, we developed short pathways to produce 2-Methyl-1,2,4-benzotriazine compounds and some of its derivatives, were prepared in yields to (50-70%), via a reductive cyclization by a PtO2-catalyzed hydrogenation, of the corresponding 2-nitrophenylhydrazones of the pyrivic acid. The later compounds were obtained in yields higher than 90% by reacting 2-nitrophenylhydrazines with sodium pyruvate salt. ##### High Performance Computing based on the CPU and GPU systems for the Quantum Trajectory Method Joanna Wiśniewska, Military University of Technology, Faculty of Cybernetics, Poland Marek Sawerwain, University of Zielona Góra, Institute of Control and Computation Engineering, Poland Wiesław Leoński, University of Zielona Góra, Quantum Optics and Engineering Division, Institute of Physics, Poland Abstract: Nowadays, the dynamic progress in computational techniques allows for a development of various methods which offer significant speed-up of computations, especially those related to the problems of quantum optics and quantum computing. In this work, we propose computational solutions which re-implement the Quantum Trajectory Method (QTM) algorithm in the modern parallel computation environment where multi-core CPUs and modern many-core GPUs can be used. As the effect, more effective computational routines - than those applied in other commonly used packages, such as Quantum Optics Toolbox for Matlab or QuTIP for Python - are obtained. The QTM algorithm is still widely used method for examination of open quantum systems, but its application requires a special attention at its reimplementation in modern hardware systems, especially those comprising GPUs. The main problem in application of QTM is to focus on a proper definition and use of computational grid (or computational index space), and it is especially important in implementation for CUDA technology discussed here. The proposed implementation of QTM is also a hybrid method, in which power of traditional CPU and modern GPU is combined to obtain highly effective and precise routines for simulation of the dynamics of open quantum systems. It should be pointed out that discussed here solution, based on GPUs, is about 20 or even 50 times faster than other implementations of QTM prepared for traditional serial CPU systems. The calculation speed-up in proposed implementation depends on numerical method chosen for solving ordinary differential equations (Runge-Kutta and Backward Differentiation methods were simultaneously applied in the proposed solution). ##### A new group theoretical approach to ultrahyperbolic general relativity Evangelos Melas, Technological Educational Institution of Patras, Department of Management, Greece Abstract: The Bondi$-$Metzner$-$Sachs (BMS) group $B$ is the common asymptotic group of all asymptotically flat (lorentzian) space$-$times, and is the best candidate for the universal symmetry group of General Relativity (G.R.). $B$ admits generalizations to real space$-$times of any signature, to complex space$-$times, and supersymmetric generalizations for any space$-$time dimension. Generalizations of $B$ are important both for quantum and classical G.R.. %and general relativity. In 1939 Wigner laid the foundations of special relativistic quantum mechanics and relativistic quantum field theory by constructing the Hilbert space strongly continuous unitary irreducible representations (IRs) of the (universal cover) of the Poincare group $P$. In a quantum setting the universal property of $B$ for G.R. make it reasonable to attempt to lay a similarly firm foundation for quantum gravity by following through the analogue of Wigner's programme with $B$ replacing $P$. With this motivation McCarthy constructed the IRs of $B$ some time ago. $B(2,2)$ is the generalization of $B$ appropriate to the to the ultrahyperbolic signature' ($+$,$+$,$-$,$-$) and asymptotic flatness in null directions. Following a historical introduction and some motivating remarks on the correspondence of the IRs of $B$ and its generalisations to the solutions of the Einstein equations in all signatures as well as in complex space$-$times we continue this programme by introducing a new group $\mathcal H \mathcal B$ in the group theoretical study of ultrahyperbolic G.R. which happens to be a proper subgroup of $B(2,2)$. We give the first general results on the representation theory of $\mathcal H \mathcal B$. In particular it is proved that {\it all} little groups of $\mathcal H \mathcal B$ are compact and that the Wigner$-$Mackey's inducing construction is exhaustive despite the fact that $\mathcal H \mathcal B$ is not locally compact in the employed Hilbert topology. The significance of these results for this approach to quantum gravity as well as their repercussions for other approaches to quantum gravity is analysed. Finally relation to other work is outlined. ##### Application of nonlinear methods to the study of ionospheric plasma Alexander Chernyshov, Space Research Institute, , Russian Federation Mikhail Mogilevsky, Space Research Institute, , Russian Federation Boris Kozelov, Polar Geophysical Institute, , Russian Federation Abstract: Most of the processes taking place in the auroral region of Earth's ionosphere are reflected in a variety of dynamic forms of the aurora borealis. In order to study these processes it is necessary to consider temporary and spatial variations of the characteristics of ionospheric plasma. Most traditional methods of classical physics are applicable mainly for stationary or quasi-stationary phenomena, but dynamic regimes, transients, fluctuations, self-similar scaling could be considered using the methods of nonlinear dynamics. Therefore, development of methods for studies of characteristics of nonlinear processes in open dissipative systems is now actual problem, in particular, to study the Earth's ionosphere. Special interest is the development of the methods for describing the spatial structure and the temporal dynamics of auroral ionosphere based on the ideas of percolation theory and fractal geometry. The fractal characteristics (the Hausdorff fractal dimension and the index of connectivity) of Hall and Pedersen conductivities are used to the description of fractal patterns in the ionosphere. To obtain the self-consistent estimates of the parameters the Hausdorff fractal dimension and the index of connectivity in the auroral zone, an additional relation describing universal behavior of the fractal geometry of percolation at the critical threshold is applied. Also, in this work Tsallis statistics is used to study the properties of the auroral ionosphere. ##### Geometry Design of an Electron Dump with Simple Geo Mert Sekerci, Süleyman Demirel University, , Turkey Fatma OZTURK, Istanbul University, Department of Physics, Turkey Nurgul HAFIZOGLU, Istanbul University, Department of Physics, Turkey Suat OZKORUCUKLU, Istanbul University, Department of Physics, Turkey Abstract: The goal of this study is to design a geometry of an electron dump with Simple Geo code which is a freeware product and provides the ability of designing complex geometric systems easily. Also, Simple Geo can output the designed geometry in many different formats. Desired design of the electron dump is to stop the 40 – 42 MeV electron beams. To reach this aim, requested geometric design with the possible material was done with Simple Geo and a FLUKA output format file created to run the simulations in FLUKA code. ##### Residual symmetries and B\"acklund transformations Lou SenYue, Ningbo University , Physics Department, China Abstract: It is known that for a given truncated Painlev\'e expansion of an arbitrary nonlinear Painlev\'e integrable system, the residue with respect to the singularity manifold is a nonlocal symmetry. It is proved that the residual symmetries can be localized to Lie point symmetries for suitable prolonged systems. For the Korteweg-de Vries equation, the $n^{th}$ Binary Darboux transformation is re-obtained by the Lie point symmetry approach companied by the localization of the $n$-fold residual symmetries. ##### Born Oppenheimer Molecular Dynamics calculation of the nuO-H IR spectra for acetic acid cyclic dimers Benmalti Mohamed el Amine, Université abdelhamid ibn badis-mostaganem, Chimie, Algeria Abstract: Both ab initio molecular dynamics simulations based on the Born-Oppenheimer approach calculations and a quantum theoretical model are used in order to study the IR spectrum of the acetic acid dimer in the gas phase. The theoretical model is taking into account the strong anharmonic coupling, Davydov coupling, multiple Fermi resonances between the first harmonics of some bending modes and the rst excited state of the symmetric combination of the two O-H modes and the quantum direct and indirect relaxation. The IR spectra obtained from DFT-based molecular dynamics is compared with our theoretical lineshape and with experiment. Note that in a previous work we have shown that our approach reproduces satisfactorily the main futures of the IR experimental lineshapes of the acetic acid dimer[Mohamed el Amine Benmalti, , Paul Blaise, H. T. Flakus, Olivier Henri- Rousseau, Chem Phys, 320(2006) 267-274.]. ##### KP Predication by Using mixture of MLP-experts Mina Ghoorchian, HIRBODAN ARIANA Professional Engineers Training Institute, , Iran (Islamic Republic of) Abstract: For space weather phenomenon that is searched always,in the paper ,solar activity effects on power system are considered.According research,solar plasma can have destructive effect on power system. such as saturation of the transformer core,extra harmonic that can [switch out of service such quebec blackout of march 13,1989 witch left the whole province without power for over 9 hours].also there are major problems in restoring power after grid collapse such as cold load pick-up,no spare transformer. The solar wind driven magnetosphere is a complex dynamical system with highly nonlinear and chaotic behavior. A large number of studies have been carried out to provide appropriate dynamical models of magnetosphere, and to predict various geomagnetic indices, e.g. Dst storm time index and AE auroral electrojet index. But the most popular indicator of geomagnetic disturbances, the Kp index, which is used mainly in warning and alert systems for power system, has not been considered as much. Kp is used the same as alarm in 5 level, Kp =9,8,7,6 and 5. Kp is predicted and compared with mixture of MLP - experts this method can work similar an alarm intelligent system for power system. ##### FUZZY INTERACTIVE GOAL PROGRAMMING METHOD FOR SUM OF LINEAR FRACTIONAL MULTI-OBJECTIVE PROGRAMMING PROBLEMS Pitam Singh, Motilal Nehru National Institute of Technology Allahabad, Mathematics, India Abstract: This paper is concerned with an efficient algorithm for solving the multi-objective program of sum of linear fractional functions whose constraints are linear. The algorithm proposed here for the solution of sum linear ratios multi-objective programming (SOLR-MOP)is integrate the merits of three approaches , (i) fuzzy approach, (ii) fuzzy goal programming, (iii) Interactive programming. Each membership function of fuzzy objective is approximated into linear function by using first order Taylor theorem about the vertex of the feasible region where the objective function has maximum value. Then the resulted approximated linearized membership function may be used for the formulation of interactive fuzzy goal programming.The efficiency of the method is measured by numerical a example. ##### Some More Solutions of Burgers’ Equation Mukesh Kumar, MNNIT Allahabad, Mathematics, India Abstract: In the present study, one-dimensional Burgers' equation has been studied. An attempt has been made to search Lie symmetries and construction of exact solutions of viscous Burgers' equation through Lie group properties. The symmetry generators are used for constructing Lie group of point symmetries with commuting infinitesimal operators which lead the governing partial differential equation to ordinary differential equation. To the best of author’s knowledge, exact solutions of Burgers' equation obtained in terms of Bessel functions are appearing very first time in the existing literature. Effect of various parameters through graph is shown and discussed physically. ##### Symbolic computations by the Wick's theorem. Igor V Beloussov, Institute of Applied Physics, Academy of Sciences of Moldova, Theoretical Physics, Moldova, Republic of Abstract: The new formulation of Wick's theorem that allows one to present the vacuum or thermal averages of the chronological product of an arbitrary number of field operators as a determinant (permanent) of the matrix is proposed. Each element of the matrix is the average of the chronological product of only two operators. This formulation is extremely convenient for practical calculations in quantum field theory and statistical physics by the methods of symbolic mathematics using computers. ##### Asymptotic solution of natural convection in a uniformly Joule-heating shallow cavity xiaohui zhang, Soochow University, , China Abstract: The steady laminar two-dimensional Joule heating natural convection is investigated using asymptotical analysis, the fluid is in a rectangular cavity, the direct current contributes heat for heating the process medium by a pair of plate electrodes, the top wall is cooled with atmosphere and all the other walls are kept thermally insulated. The asymptotic solution is obtained in the core region in the limit as the aspect ratio, which is defined as the ratio of the vertical dimension of cavity to the horizontal dimension of cavity, goes to zero. The numerical experiments are also carried out to compare with the asymptotic solution of the steady two-dimensional Joule heating convection. The asymptotic results indicate that the expressions of velocity and temperature fields in the core region are valid in the limit of the small aspect ratio. ##### Gravitational radiation as radiation same level of electromagnetic and his generation of pulsed high-current discharge Fisenko, Rusthermosynthesis JSC, , Russian Federation Abstract: The notion of gravitational radiation as a radiation of the same level as the electromagnetic radiation is based on theoretically proved and experimentally confirmed fact of existence of stationary states of an electron in its gravitational field characterized by the gravitational constant K = 10^42G (G is the Newtonian gravitational constant) and unrecoverable space-time curvature Λ. This paper gives an overview of the authors' works [1, 2, 3, 4], which set out the relevant results. Additionally, data is provided on the broadening of the spectra characteristic radiation. The data show that this broadening can be explained only by the presence of excited states of electrons in their gravitational field. What is more, the interpretation of the new line of X-ray emission spectrum according to the results of observation of MOS-camera of XMM-Newton observatory is of interest. The given work contributes into further elaboration of the findings considering their application to dense high-temperature plasma of multiple-charge ions. This is due to quantitative character of electron gravitational radiation spectrum such that amplification of gravitational radiation may take place only in multiple-charge ion high-temperature plasma. ##### The origin of self-focusing effect in terahertz quantum cascade lasers Jian Wang, Beijing Jiaotong University, Department of Physics, China Yanfang Li, Institute of Applied Physics and Computational Mathematics, , China Ning Yang, Institute of Applied Physics and Computational Mathematics, , China Abstract: The terahertz quantum cascade lasers (THz-QCLs) are the compact and coherent terahertz light source based on the inter-subband transition and resonant tunneling of carriers in semiconductor superlattice. In the recent studies on tapered THz-QCLs, it was found that the self-focusing effect in the active region of the devices may cause the abnormal increase of the far-field divergence of the laser beam. By simulating the propagation of optical model in QCL waveguide and considering both the nonlinearity effect and thermal accumulation in the active region, we demonstrate that the refractive index change caused by the third-order nonlinearity of multi-quantum-wells in active region is the key reason for the self-focusing in THz-QCLs. This result indicates that the nonlinear effect has great impact on the beam quality of QCLs which must be carefully considered in applications of THz-QCLs, such as the TH- imaging systems. ##### A simple model of hysteresis behavior using spreadsheet analysis Andrea Ehrmann, Niederrhein University of Applied Sciences, Faculty of Textile and Clothing Technology, Germany Tomasz Blachowicz, Silesian University of Technology, , Poland Abstract: Hysteresis loops occur in many scientific and technical problems, especially as field dependent magnetization of ferromagnetic materials, but also as stress-strain-curves of materials measured by tensile tests including thermal effects, liquid-solid phase transitions, in cell biology or economics. While several mathematical models exist which aim to calculate hysteresis energies and other parameters, here we offer a simple model for a general hysteretic system, showing different hysteresis loops depending on the defined parameters. The calculation which is based on basic spreadsheet analysis plus an easy macro code can be used by students to understand how these systems work and how the parameters influence the reactions of the system on an external field. Importantly, in the step-by-step mode, each change of the system state, compared to the last step, becomes visible. The simple program can be developed further by several changes and additions, enabling the building of a tool which is capable of answering real physical questions in the broad field of magnetism as well as in other scientific areas, in which similar hysteresis loops occur. ##### Anatomy of Demagnetizing and Exchange Fields in Magnetic Nano-Dots Influenced by 3D Shape Modifications Tomasz Blachowicz, Silesian University of Technology, , Poland Andrea Ehrmann, Niederrhein University of Applied Sciences, Faculty of Textile and Clothing Technology, Germany Abstract: Hysteresis loops of 3D ferromagnetic permalloy nano-half-balls (dots) with 100 nm base diameter have been examined by means of LLG micromagnetic simulations and finite element methods. Tests were carried out with two orthogonal directions of the externally applied field at 10 kA/(m.ns) field sweeping speed. The comparison of samples with different 3D modifications at the sub-10nm scale, accessible by nowadays lithographic techniques, enables conclusions about different mechanisms of competition between demagnetizing and exchange fields. Design paradigms provided here can be applied, e.g., in bit-patterned media used as novel magnetic storage systems. ##### Ideal Fluids, the Quark Gluon Plasma, and Hadronic Gases Dr. Nasser S Demir, Kuwait University, Physics, Kuwait Abstract: Ultrarelativistic heavy ion collisions at the Relativistic Heavy Ion Collider (RHIC) and the Large Hadron Collider (LHC) are believed to have created a state of matter known as the Quark Gluon Plasma (QGP), where quarks are thought to be deconfined in a "quark soup." The QGP thought to have been produced at RHIC and LHC has properties resembling those of an ideal fluid. As such, significant interest arose in quantifying the shear viscosity coefficient and the shear viscosity to entropy density ratio of the QGP. A conjecture on the lower bound of the shear viscosity to entropy density ratio of the "most perfect fluid" is that its minimum value should be $\frac{\hbar}{4 \pi k_B}$. However, in order to quantify the shear viscosity of the QGP, it is necessary to quantify the shear viscosity of the hadronic phase of a heavy ion reaction. As the QGP cools and decays, a hadronic gas is formed, which is assumed to be highly viscous. Several calculations of the shear viscosity exist for hadronic systems, but a systematic comparison between two disparate methods is necessary for validation and for testing the limits of any method involved. A systematic comparison between two methods (the Green-Kubo and Chapmann-Enskogg methods) is performed for two sets of hadronic systems. One system involves a system of chiral pions interacting with an energy dependent cross section and the other system involves a pion rho mixture. Differences are highlighted between the results. ##### Persistent Dirac fermion state on Si surface Kehui Wu, Institute of Physics, Chinese Academy of Sciences, , China Abstract: Recently, silicene, a single sheet of Si atoms arranged in honeycomb lattice with sp2 bonding, has been proposed and successfully fabricated on Ag(111) and other substrates in ultrahigh vacuum. The existence of Dirac fermion in silicene on Ag(111) surface with (√3×√3)R30° superstructure has been proven by the observation of linear energy-momentum dispersion and quasiparticle chirality by scanning tunneling microscopy (STM) and spectroscopy (STS). In addition to monolayer silicene sheet, we reported the existence of “multilayer silicene” film on Ag(111), comparable to multilayer graphene. In this talk we will present our new results on silicene, mainly concerning the detailed features of the electronic states, and electronic states on multilayer silicene film. For silicene film with increasing thickness above 30 monolayers (ML), the film always exhibits a (√3×√3)R30° honeycomb superstructure on the surface, which has never been observed on bulk Si(111) surface. More interestingly, we observed persistent Dirac Fermion state on the surface, independent on the film thickness. The origination of this Dirac fermion state is discussed ##### Study of basic structural, sorption and diffusion properties of novel microporous materials based on a combination of molecular simulation methods Stylianos Karozis, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Georgia Charalambopoulou, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Nikolaos Papadimitriou, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Theodore Steriotis, National Center for Scientific Research Demokritos, Institute of Nanoscience and Nanotechnology, Greece Michael Kainourgiakis, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Athanasios Stubos, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Abstract: A new class of microporous materials with extremely interesting properties for a great number of applications is that of Metal Organic Frameworks (MOFs). MOFS are among others extensively investigated for gas and liquid separations and they are typically constructed by connecting metal clusters with organic linkers resulting in crystalline porous materials. In this work we used a combination of stochastic and deterministic molecular simulation techniques, in order to examine structural features as well as thermodynamic and dynamic properties in a MOF/gas system. Focus was placed in well-established MOF structures such as IRMOF-1 and UiO-66(Zr) and gases of technological relevance such as N2, CH4 and CO2. For each MOF/gas system, Monte Carlo simulations were performed in order to calculate e.g. the specific surface area, the percentage of loading, gas adsorption isotherms at various temperatures, etc. In a further step, molecular dynamics simulations were performed in order to calculate the respective self-diffusion coefficient of the gas molecules and examine the mechanism of selective separation due to the atomistic interactions between the the gas molecules and the MOF framework. The simulations were carried out using the parameters of UFF forcefield for a rigid MOF structure, while specialized parameters were taken into account for each gas. All forcefields used in this work, were parameterized according to the Lennard-Jones potential equation. The obtained results show that the combination of Monte Carlo and MD techniques can offer a valuable tool for the study of microporous materials such as MOFs. References 1. Yang, Q., Wiersum, A. D., Jobic, H., Guillerm, V., Serre, C., Llewellyn, P. L., Maurin, G. (2011). The Journal of Physical Chemistry C, 115(28), 13768–13774. 2. Allen, M. P., Tildesley, D. J., Banavar, J. R. (1989). Physics Today, 42(3), 105. 3. Frenkel, D., Smit, B., Ratner, M. a. (1997). Physics Today (Vol. 50, pp. 1–628). 4. Gotzias, A., Heiberg-Andersen, H., Kainourgiakis, M., Steriotis, T. (2010). Applied Surface Science, 256(17), 5226–5231. ##### Passivity-based control of discrete-time SIS epidemics in complex networks Luis Alarcon-Ramos, Universidad Autonoma Metropolitana - Cuajimalpa, Applied Mathematics, Mexico Roberto Bernal-Jaquez, Universidad Autonoma Metropolitana - Cuajimalpa, Matematicas Aplicadas y Sistemas, Mexico Alexander Schaum, Christian-Albrechts-Universität zu Kiel, Institute of Electrical and Information Engineering, , Germany Carlos Rodriguez-Lucatero, Universidad Autonoma Metropolitana - Cuajimalpa, Tecnologias de la Informacion, Mexico Abstract: In this paper, we investigate and analyze the complex dynamics of an epidemic model, in the light of passivity properties for feedback control design. For this purpose, a framework of discrete time Markov process dynamical systems is employed, to propose a control mechanism that allows to bring the system to the extinction state. Considering individual controls at single nodes with relative degree one, an approach is presented to identify the nodes to be controlled in the network, based on the property of feedback equivalence to a passive system. Therefore, taking the set of controlled nodes as degree of freedom, sufficient conditions are derived for an asymptotically stable associated zero dynamics. This implies that it is not necessary to control all nodes, but only a minimal set of nodes for which the associated zero dynamics are asymptotically stable, and the complete network dynamics become passiviable via state-feedback control. Simulation results are presented for large free-scale and regular networks, that corroborate our theoretical findings. ##### Monte Carlo studies of clathrate hydrates for applications that involve energy gases Nikolaos Papadimitriou, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Ioannis Tsimpanogiannis, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Ioannis Economou, Texas A&M University at Qatar, Chemical Engineering Program, Qatar Athanasios Stubos, National Center for Scientific Research Demokritos, Environmental Research Laboratory, Greece Abstract: Clathrate hydrates are ice-like crystalline materials whose crystal lattice contains cavities that can trap gas molecules. Recently, they have attracted strong research interest as materials with potential use in applications that involve the storage, transportation, or separation of energy gases. The present work was motivated by two applications in this field: storage of H2, and CH4/CO2 separation. The concept of our work is to use Grand Canonical Monte Carlo (GCMC) simulations to calculate the number of gas molecules that can be trapped in every cavity of the hydrate (cavity occupancy). In this approach, the gas content of the hydrate at equilibrium is calculated as the result of an adsorption process where the rigid hydrate structure is the adsorbent. The simulations are performed over a wide range of conditions (temperature, pressure, gas mixture composition) and all of the most common hydrate structures (sI, sII, sH) are studied. All simulations were carried out with the MCCCS Towhee code. In the case of H2, the knowledge of cavity occupancies allows the estimation of the amount of gas that can be stored in the hydrate at specified conditions and the evaluation of the hydrogen-storage capacity of each hydrate structure [1]. For reasons of validation, several water models (e.g. SPC/E, TIP4P/Ice, TIP5P) are used along with various sets of interaction parameters for the H2 molecule. The effect of the lattice constant on the H2 content of the hydrate is also studied. H2 is one of the few gases that present the effect of multiple occupancy (i.e. more than one molecules in the same cavity) [2] and this effect is extensively studied. In the case of CH4/CO2 mixtures, the cavity occupancies for each of the gases determine the selectivity of the hydrate for the separation of this mixture. CH4 fills both the small and large cavities of the sI hydrate while CO2 is assumed to fill only the large ones. This different behavior between the two gases is an extra challenge from a computational point of view. To investigate the CH4/CO2 system, first we study the pure gases [3] and then we proceed to binary mixtures of various compositions. References: 1. N. I. Papadimitriou, I. N. Tsimpanogiannis, A. K. Stubos, Colloids. Surf. A 357:67-73 (2010). 2. N. I. Papadimitriou, I. N. Tsimpanogiannis, A. Th. Papapioannou, A. K. Stubos, J. Phys. Chem. C 112:10294–10302 (2008). 3. M. Lasich, A. H. Mohammadi, K. Bolton, J. Vrabec, D. Ramjugernath, Fluid Phase Equilib. 369:47-54 (2014). ##### Influence of Mobility Models in Precision Spray Aided by Wireless Sensor Networks Leandro Bertini Lara Gonçalves, Universidade Estadual Paulista "Júlio de Mesquita Filho", , Brazil Fausto Costa, ICMC-USP, , Brazil Leandro Alves Neves, São Paulo State University (UNESP), Department of Computer Science and Statistics - DCCE, Brazil Geraldo Francisco Donega Zafalon, Sao Paulo State University - UNESP/SJRP, Computer Science and Statistics - DCCE, Brazil Jó Ueyama, ICMC-USP, , Brazil Carlos Montez, Universidade Federal de Santa Catarina - UFSC, , Brazil Alex Sandro Pinto, Universidade Federal de Santa Catarina, Câmpus de Blumenau, Brazil Abstract: Applications of agricultural inputs using Unmanned Aerial Vehicles (UAVs) aided by Wireless Sensor Networks (WSN) is an approach related to the spray problem in precision agriculture. The efficiency of this approach depends of the correct communication between UAV and WSN. This communication might be affected by the method the UAV uses the network. Thus, in this work we perform comparisons among classical mobility models as Random Walk, Random Waypoint, Random Direction, Manhattan Grid, and we analyze how these models act in the the communication performance between UAV and WSN using the IEEE 802.15.4 protocol for random and grid networks. The tests were performed using the OMNeT++ simulator with MiXiM package and BonnMotion for the generation of mobility scenarios. The mobility models were set to be the same conditions for comparisons. In this study were collected and analized in each test: the amount of received frames by UAV; the amount of sent frames; the amount of backoffs from WSN; and the efficiency of network communication. The obtained results show that the network has similar performance both using random and grid implementation. The efficiency decreases as the density of nodes increases, mainly due to the concurrency by the transmission medium and saturation of the received message threshold of the UAV for densities above 3.67 X 10-4 nodes/m2. In the results it possible to check that Random Direction and Manhattan Grid had both similar performance when analyzed the communication efficiency of the mobility models and better results when compared with other models. ##### Frequency comb generation for wave transmission through the nonlinear dimer Sadreev Almas, L.V. Kirensky Institute of Physics, Laboratory of theory of nonlinear processes, Russian Federation Konstantin Pichugin, L.V. Kirensky Institute of Physics, , Russian Federation Abstract: We study dynamical response of the nonlinear dimer relative to monochromatic wave injected via the waveguide. We show existence of a domain in space of frequency and injected amplitude where the stationary solutions of the temporal equations do not exist. We present time dependent solutions which show that scattering waves carry multiple harmonics with frequencies spaced equidistantly. ##### From single- to multi-layer silicene Patrick Vogt, Technische Universität Berlin, Institut für Festkörperphysik, Germany Abstract: Silicene, a novel silicon allotrope, which does not exist in nature, was theoretically conjectured a few years ago [1] as a stand-alone material. However, for the synthesis of silicene a substrate material is essential that prevents the formation of bulk silicon and, at the same time, does not react with the Si-atoms. Recently, silicene mono-layers could be synthesized on different substrates such as Ag(111), Ir(111) or ZrB2 [2]. The successful preparation of single layer silicene rises the question if the multi-layer silicene structure can also be synthesized which might be understood as the Si analogue to graphite. In this talk the epitaxial formation of single layer silicene on a Ag(111) substrate will be briefly summarized. Based on these results the formation of multilayer silicene will be discussed that forms upon further deposition of Si onto the first silicene layer [3]. Atomic structure, stacking order, electronic properties and growth aspects are discussed to demonstrate the differences of theses silicene multi-layer structure to bulk Si(111). The formation of multi-layer silicene could open new possibilities for the technological applicability of silicene. 1) G. G. Guzmán-Verri, L. C. Lew Yan Voon, Phys. Rev. B 76, 075131 (2007); S. Lebègue and O. Eriksson, Phys. Rev. B, 79 115409 (2009); S. Cahangirov et al., Phys. Rev. Lett. 102, 236804 (2009). 2) P. Vogt et al., Phys. Rev. Lett. 108, 55501 (2012); C.-L. Lin et al., Appl. Phys. Exp. 5, 045802 (2012); B. Feng et al., Nano Lett. 11, 3507 (2012); A. Fleurence et al., Phys. Rev. Lett. 108, 245501 (2012); L. Meng et al., Nano Lett. 13, 685 (2013). 3) P. Vogt et al., Appl. Phys. Lett. 104, 021602(2014), A. Resta et al. , Sci. Rep. 3, 2399 (2013), De Padova et al., Appl. Phys. Lett. 102, 163106 (2013). ##### Universal quasi-equilibrium state of self-gravitating systems not depending on dimensions Tohru Tashiro, Ochanomizu University, Department of Physics, Japan Abstract: Universal quasi-equilibrium state not depending on dimensions has been observed in the universe. Globular clusters which consist of about hundreds of thousands of stars are well-known to have a spherically symmetric number density. From a survey of the Herschel space observatory, it has been unveiled that there are about 30 filamentary structures of molecular clouds in IC 5146, and they have a cylindrically symmetric density profile in real space [1]. In both cases, a major factor constructing these structures is the gravity, which means that we can treat the systems as self-gravitating systems: Owing to the symmetries, filamentary structures of molecular clouds and globular clusters can be treated as the two and three dimensional self-gravitating system, respectively. The density profiles of these self-gravitating systems are constant around the center of the system and decrease in a power law at large radius. This is the universal quasi-equilibrium state. Until now, no one can explain the physics behind the universality. In this presentation, we will show that the same density profile as the observations are obtained by N-body simulations of self-gravitating system. Next, we will improve the dimension of our model, which can describe the density profile of three-dimensional self-gravitating system [2], and then we will exhibit that the universal distributions can be derived uniformly by the improved model. [1] D. Arzoumanian, et al. A&A 529 (2011) L6. [2] T. Tashiro and T. Tatekawa, J. Phys. Soc. Jpn. 79 (2010) 063001. Numerical Simulations of Physical and Engineering Processes, Jan Awrejcewicz (Ed.) (INTECH, Croatia) (2011) 301-318. ##### Shubnikov state in a Technetium film JESUS GONZALEZ, UNIVERSIDAD DEL MAGDALENA, DEPARTAMENTO DE FISICA, Colombia Jose Jose Barba Ortega, Universidad Nacional de Colombia, Physics, Colombia Abstract: We numerically investigate the flux quantum configurations and some thermodynamical properties of a Technetium film by using the link variables technique for one shape of circular geometry. The technetium exhibit superconductivity properties indicated by to an extrapolated critical magnetic field value of Hc (T=0)=1410 Oe , and a Ginzburg-Landau parameter of k=0.92, being the magnetic behavior of this material characteristic of a type-II superconductor with a weak-coupling superconductor of the BCS type. The studied sample is a circular sector with angular width surrounded by a dielectric material and submitted to external magnetic field applied perpendicular to its plane. We evaluate the magnetic moment density, Shubnikov state and thermodynamical fields as a function of the external magnetic field. ##### New trace theorems for neutronic function spaces Boulanouar, LMCM-RSA, , France Abstract: Let $X\subset\R^n$ ($n\ge1$) be an open subset with $C^1$ boundary $\partial X$ and let $d\mu$ be a Radon measure on $\R^n$ ($n\ge1$) whose support is $V$. Let $\Gamma_\mp=\left\{(x,v)\in\partial X\times V \; : \; \mp v\cdot n(x)>0\right\}$ where, $n(x)$ is the outer unit normal at $x\in\partial X$. For each $(x,v)\in X\times V$, we set $t(x,v)=\inf\{t,\;\; x-tv\not \in X\}$ and $\theta(x,v)=t(x,v)+t(x,-v).$ Similarly, if $(x,v)\in \Gamma_+$ we set $\tau(x,v)=\inf\{t,\;\; x-tv\not \in X\}.$ Let $$\widetilde{W}^p(X\times V) =\aco{ \varphi\in L^p(X\times V),\;\; v\cdot\nabla_x\varphi\in L^p(X\times V) }$$ whose norm is $\norm{\varphi}_{\widetilde{W}^p(X\times V)}= \left[\norm{\varphi}_p^p+\norm{v\cdot\nabla_x\varphi}_p^p \right]^{\frac{1}{p}}$ and let $L^p(\Gamma_\pm, d\widetilde{\xi}_\pm)$ be the weighted trace spaces whose norm is \begin{equation}\label{} \norm{\varphi}_{L^p(\Gamma_\pm, d\widetilde{\xi}_\pm)}= \left[\int_{\Gamma_{\pm}}\abs{\varphi(x,v)}^pd\widetilde{\xi}_\pm\right]^{\frac{1}{p}} \quad \text{where,}\quad d\widetilde{\xi}_\pm=\min\{\tau(x,\pm v), 1\} \abs{v\cdot n(x)}d\gamma d\mu(v). \end{equation} Finally, let $\gamma_\mp\, :\; \varphi \longrightarrow \varphi\mid_{\Gamma_\mp}$ be the trace mappings whose continuity is given by \begin{Lem}[\cite{Cessenat1}\cite{Cessenat2}] \label{CES} Both trace mappings $\gamma_\mp : \widetilde{W}^p(X\times V) \longrightarrow L^p(\Gamma\!_\mp, d\widetilde{\xi}_\mp)$ are continuous. \end{Lem} \noindent It is well known that Lemma~\ref{CES} is not suitable in practice. Indeed, let $\varphi\in \widetilde{W}^1(X\times V)$ such that $\gamma_+\varphi$ or $\gamma_-\varphi$ exists. Green's formula yields that $$\int_{X\times V} v\cdot\nabla_x\abs{\varphi}dxd\mu(v) =\int_{\Gamma_+}\abs{\gamma_+\varphi(x,v)}d\xi -\int_{\Gamma_-}\abs{\gamma_-\varphi(x,v)}d\xi.$$ One obviously sees that $L^1(\Gamma_\pm, d\xi)$ are natural trace spaces and therefore Lemma~\ref{CES} can not be used because of $d\xi\not=d\widetilde{\xi}$. For instance, let $X\times V=(0,1)\times(0,\infty)$ for which $\Gamma_\pm=(0,\infty)$ and let $\varphi(x,v)=\frac{1}{v^2+1}$ be in $\widetilde{W}^p(X\times V)$. We obviously have $\gamma_\pm\varphi=\varphi\in L^p(\Gamma_\pm, d\widetilde{\xi}_\pm)$ and $\gamma_\pm\varphi\not\in L^p(\Gamma_\pm)$. \par\noindent It is therefore natural to raise the following question : \emph{Does there exist a suitable space $W^p(X\times V)$ $(p \ge 1)$ on which the trace mappings $\gamma_\pm$ are continuous into their natural trace spaces $L^p(\Gamma_\pm)$ ?} A positive answer is given by \begin{The}[\cite{Boulanouar}]\label{THE} Let $W^p(X\times V)$ $(p \ge 1)$ be the following Banach space \begin{equation} W^p(X\times V) = \aco{\varphi\in L^p(X\times V), v\cdot\nabla_x\varphi\in L^p(X\times V), \theta^{-\frac{1}{p}}\varphi\in L^p(X\times V)} \end{equation} whose norm is $$\norm{\varphi}_{W^p(X\times V)}= \left[(p-1)\norm{\varphi}_p^p+\norm{v\cdot\nabla_x\varphi}_p^p +\norm{\theta^{-\frac{1}{p}}\varphi}_p^p\right]^{\frac{1}{p}}.$$ Then, the trace mappings $\gamma_+\, :\; W^p(X\times V) \longrightarrow L^p(\Gamma_+)$ and $\gamma_-\, :\; W^p(X\times V) \longrightarrow L^p(\Gamma_-)$ are continuous. Furthermore $\norm{\gamma_+\varphi}_{L^p(\Gamma_+)} \le \norm{\varphi}_{W^p(X\times V)}$ and $\norm{\gamma_-\varphi}_{L^p(\Gamma_-)} \le\norm{\varphi}_{W^p(X\times V)}.$ \end{The} \begin{thebibliography}{99} \bibitem{Boulanouar} \textsc{M. Boulanouar.} \textsl{New trace theorem for neutronic function spaces.} Trans. Theor. Stat. Phys., 38, 228--242, 2009. \bibitem{Cessenat1} M. Cessenat. \textsl{Th\'eor\emes de trace $L^p$ pour des espaces de fonctions de la neutronique}, C. R. Acad. Sc. Paris, t.299, pp. 831--834, 1984. \bibitem{Cessenat2} M. Cessenat. \textsl{Th\'eor\emes de trace pour des espaces de fonctions de la neutronique}, C. R. Acad. Sc. Paris. t.300, pp. 89--92, 1985. \end{thebibliography} ##### Generation of thrust and lift with airfoils in plunging and pitching motion Manuel Moriche, Universidad Carlos III de Madrid, Bioengineering and Aerospace Department, Spain Abstract: The aerodynamics of flapping wings has been the focus of attention for many researchers for the last decades. Classical unsteady models of Wagner and Theodorsen have been widely used, but they become inadequate at high amplitude/frequency motions and very low Reynolds number, where the flow is massively separated. This is precisely the regime where insects and small birds fly. Improving our understanding of this regime is a key factor to unlock the standardized design of bio-inspired Micro Air Vehicles (MAV), able to achieve high maneuverability and efficiency in their flapping flight. In this talk we present fully resolved Direct Numerical Simulations (DNS) of flow over moving airfoils (2D). The solver used is an in-house code that implements the Immersed Boundary method of Uhlmann1 . A combination of sinusoidal plunging and pitching motions is imposed in rigid airfoils. Starting from a thrust producing case (Reduced frequency, k = 1.41. Plunging amplitude h/c = 1. Mean pitching angle theta_m = 0º. Pitching amplitude theta_0 = 30◦ . Phase shift phi = 90◦ ), we increase the mean pitching angle (in order to produce lift) and vary the phase shift between pitching and plunging (to optimize the direction and magnitude of the net force on the airfoil). These cases will be discussed in terms of their lift coefficient, thrust coefficient and power efficiency. ##### Bistability in self-activating genes regulated by non-coding RNAs Jesus Miro-Bueno, Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, , Czech Republic Abstract: Non-coding RNA molecules are able to regulate gene expression and play an essential role in cells. On the other hand, bistability is an important behaviour of genetic networks. Here, we propose and study an ODE model in order to show how non-coding RNA can produce bistability in a simple way. The model comprises a single gene with positive feedback that is repressed by non-coding RNA molecules. We show how the values of all the reaction rates involved in the model are able to control the transitions between the high and low states. This new model can be interesting to clarify the role of non-coding RNA molecules in genetic networks. As well, these results can be interesting in synthetic biology for developing new genetic memories and biomolecular devices based on non-coding RNAs. ##### An efficient implicit direct forcing immersed boundary method for incompressible flows shanggui, Univiersité de Technologie de Compiègne, , France Abstract: We present a novel efficient implicit direct forcing immersed boundary method for incompressible flows with complex boundaries, based on the work of [M. Uhlmann, An immersed boundary method with direct forcing for the simulation of particulate flows, J. Comput. Phys., 209(2005) 448-476]. In Uhlmann's work, the calculation is performed on the Eulerian grid regardless the immersed object, with a fictitious force to mimic the presence of the physical boundaries. It is also known that Uhlmann's explicit method fails to accurately impose the non-slip boundary condition on the immersed interface. To improve the accuracy, iteration of the whole system is required, which could be extremely time-consuming. In the present work, an implicit treatment of the artificial force is preferred, but with an effective way of system iteration. The Navier-Stokes equation is resolved with the rotational incremental pressure-correction projection method of [J.L. Guermond and J. Shen, An overview of projection methods for incompressible flows, Comput. Methods Appl. Mech. Engrg., 195(2006) 6011-6045], thus a higher precision is reserved. Several numerical simulations are performed to verify the proposed method, which are in good agreement with those in the literature. ##### Evaluation of connectedness between the University courses of Physics and Chemistry basing on the graph model of inter-subject links Tatiana Gnitetskaya, Far Eastern Federal University, School of natural sciences, Russian Federation Elena Ivanova, Far Eastern Federal University, , Russian Federation Abstract: An application of the graph model of inter-subject links to University courses of Physics and Chemistry is presented in this article. A part of inter-subject space with directions of inter-subject links from Physics to Chemistry in the group of physical concepts has been shown. The graph model of inter-subject links includes quantitative indicators. Its numerical values are given in the article. The degree of connectedness between the data of Physics and Chemistry courses is discussed for the courses considered. The effect of the courses placement within a curriculum on the value of their connectedness is shown. The placement of courses within a curriculum can provide the study of the courses at the same time or consecutive study, when one course precedes another. ##### SOLITONIC EFFECTS IN SUPERCONTINNUM GENERATION IN HIGHLY NONLINEAR FIBERS Mário Ferreira, University of Aveiro, Physics, Portugal Abstract: When ultrashort pulses with large enough power are launched into highly nonlinear fibers, soliton fission gives origin to multiple fundamental solitons of different widths and peak powers. Among the host of soliton related effects contributing to supercontinuum generation, there are two which become particularly important: the soliton self-frequency shift and the emission of dispersive radiation in the normal dispersion region. The peculiar dispersive characteristics of highly nonlinear fibers play a key role in these circumstances. If long duration pulses or a continuous wave are used to pump the supercontinuum, the modulation instability becomes the main initial mechanism, breaking the pump wave into multiple fundamental solitons. In this case, both the soliton self-frequency shift and inelastic collisions among such solitons play an important role. In this paper we discuss in detail the solitonic effects in the supercontinuum generation process for different pumping conditions. ##### COMPTON OPERATOR IN QUANTUM ELECTRODYNAMICS Abstract: In the frame in the quantum electrodynamics exist four basic operators; the electron self-energy , vacuum polarization , vertex correction , and the Compton operator, denoted by C. The first three operators are very important by its relation with renormalized and Ward identity. However, the Compton operator has equal importance, but without divergence, and little attention has been given it. We have calculated the Compton operator and obtained the closed expression for it in the frame of dimensionally continuous integration and hypergeometric functions. ##### Representing Structure formation in the Early Universe as a result of non Linear Electrodynamics influencing scale factor size Andrew Beckwith, Chongqing University department of physics( visitor), , China Abstract: We find that having the scale factor close to zero due to a given magnetic field value in, an early universe magnetic field affects how we would interpret Mukhanov’s chapter on ‘self reproduction of the universe’ in in his reference “Physical foundations of cosmology” terms of production of inhomogeneity during inflation and its aftermath. The stronger an early universe magnetic field is, the greater the likelihood of production of about 20 new domains of size 1/ H, with H early universe Hubble’s constant, per Planck time interval in evolution. One final caveat to consider. What may happen is that the Camara (2004) density and Quintessential density (Corda et al.) are both simultaneously satisfied, which would put additional restrictions on the magnetic field which in turn affects structure formation. In time, once Eq.(16) of this paper is refined further, the author hopes that some of the issues raised by Kobayashi and Seto as to allowed inflation models may be addressed, once further refinement of these preliminary results commences ##### Numerical Investigation of Grain Coarsening and Coalescence Model Aliki Muradova, Tecnical University of Crete, Mineral Resources Engineering, Greece Dionisios Hristopulos, Technical University of Crete, Department of Mineral Resources Engineering, Greece Abstract: A kinetic nonlinear model of mass transfer, grain coarsening and coales- cence with potential applications in sintering processes is considered. The model involves nonlinear differential equations that determine the transport of mass between grains. The rate of mass transfer is controlled by the acti- vation energy which depends on the degree of amorphization of the grains, leading to a nonlinear model of mass transfer and grain coarsening. The resulting dynamical system with random initial conditions (grain mass con- guration) is solved by means of the Runge-Kutta method. In order to incorporate coalescence of smaller grains with larger neighbors a computa- tional algorithm is adapted. An analysis of the two-grain system is carried out and the solution of the multi-grain system is studied. Numerical results are presented by examples. ##### Basic idea of Corbino-type single-electron transistor Akira Suzuki, Tokyo University of Science, Physics, Japan Abstract: We have formulated the transmission probability of an electron in a Corbino quantum disk by taking into account charging effect. The geometrical potential of the Corbino disk has a singularity at the centre of the disk. In order to avoid this singularity problem, we have to reformulate the Schroedinger equation in the Riemannian manifold. The Schroedinger equation describing the motion of the electron in the Corbino disk must be expressed by introducing a momentum operator reformed by the metric tensor. In order to obtain a Hermitian momentum operator, we must deform the Hilbert space by introducing a new wave function. This deformation leads to the extra potential term in the Schroedinger equation, which depends on the metric, i.e., the geometry of the disk. It should be noted that the charging energy of confining electrons in the Corbino disk should depend on the geometry of the disk. We discuss the quantum tunneling of an electron confined in the Corbino disk in order to investigate the effect of both geometrical potential and charging energy of confining electrons in the Corbino disk by using the Wentzel-Kramers-Brillouin (WKB) method. It is expected that the charging energy, which depends on the effective confining potential, plays an important role in the transmission probability. This suggests that the formulated transmission probability is applicable to the analysis of the single-electron transistor. ##### Mathematical modeling of a rigid circular membrane in a tri-material transversely isotropic full-space undergoing a prescribed displacement Ladan Mohtati, School of Civil Engineering, College of Engineering, University of Tehran, , Iran (Islamic Republic of) Mohammad Rahimian, School of Civil Engineering, College of Engineering, University of Tehran, , Iran, Islamic Republic Of Morteza Eskandari-Ghadi, School of Civil Engineering, College of Engineering, University of Tehran, , Iran, Islamic Republic Of Abstract: A horizontal layer between two different transversely isotropic half-spaces forms a tri-material full-space, which constitutes the domain for the boundary value problem involved in this paper. The axes of symmetries of all materials are assumed to be parallel to each other and normal to the interface of the middle layer and surrounding half-spaces. A mathematical formulation is presented to determine the response of a rigid circular membrane, which is laid down at an interface of the tri-material transversely isotropic full-space and is considered to be under a prescribed translation, which happens parallel to the plane of membrane. The governing equations are expressed in the cylindrical coordinate system, where the axis of the symmetry of the cylinder and the material are aligned. With the aid of a system of two scalar potential functions, the governing equations of motion can be uncoupled into two separated partial differential equations, which may be transformed to some ordinary differential equations by applying the Hankel integral transforms in the radial direction and Fourier series along the angular coordinate. After determining the unknown functions by imposing the relaxed boundary conditions, they are transformed to a set of four coupled integral equations, which are reduced to two coupled Fredholm-Volterra integral equations of the second kind, from which both displacement and the stress fields are computed. The proposed solutions are applied for a transversely isotropic half-space and the results match with the existing solutions. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for a transversely isotropic half-space. In order to investigate the degree of material anisotropy, some numerical evaluations are given for different combinations of transversely isotropic region. Final results show that the boundary conditions are completely satisfied and the verified numerical method leads to compatible solutions. ##### Quantum Toeplitz Matrix Appearing in Numerical Approximations of Quantum Integrals S.M.Hashemiparast, K.N.Toosi University of Technology, Mathematics and Statistics, Iran (Islamic Republic of) Abstract: Many complex systems in various area of science and technology can be described by supper statistics ,in model building situations the usual procedure is to select a model from a parametric family of distributions or generally the pathway models have been proposed which have connections with quantum integral and quantum fractional integral ,finally numerical approximations of quantum integral. In this paper we present a Quantum Toeplitz matrix for which the numerical q-calculation of the q- integrals based on specified nodes and weights are carried on with minimized error, in this q-calculation we consider the various properties of this Toeplitz matrix and the relations with the ordinary Toeplitz matrix, first the conditions for invetibility of this quantum Toeplitz matrix can be determined, then for having a unique solution, the conditions for the original system of equations (q=1 or ordinary Toeplitz matrix) is compared for the different values of q , so, some numerical examples are given for comparison with the exact solution and alternative numerical solution based on procedures using quantum Gauss -quantum Hermit quadrature rules, and also based on q-variation with iteration method , the related tables of approximations for all methods are presented . ##### Graph Model of Intradisciplinary Connections in Example of General Physics Course Tatiana Gnitetskaya, Far Eastern Federal University, School of natural sciences, Russian Federation Abstract: The model of an intradisciplinary connections was elaborated on the base of the theory of graphs. Every connection which appears in training content may be presented as oriented marked graphs. Each graph is a tree. In this paper we presented definition and model of intradisciplinary connections for example of physics course. The quantitative parameters of model are described in this paper. Quantitative method based on this model could be help to optimize a content of physics course. Furthermore using this model we can distinguish fundamental notions, laws and other elements of knowledge to separate group. This group is very important during the process of creating training course. Method of semantic structure attached to content of physics’ lections and physical problems was described. ##### Characterizing the non-stationary evolution of volume-prices evolution in the New York Stock Market Paulo Rocha, Centro de Matemática e Aplicações Fundamentais, , Portugal Frank Raischel, Instituto Dom Luiz, CGUL, University of Lisbon, 1749-016 Lisbon, Portugal, , Portugal Pedro G. Lind, ForWind and Institute of Physics, University of Oldenburg, DE-26111 Oldenburg, Germany, , Portugal Abstract: We introduce a framework for describing the stochastic evolution of the parameters defining volume-price distributions of the New York stock market. The volume-price data appears to follow a specific statistical pattern, other than the evolution of prices measured in similar studies. We argue that the inverse Gamma distribution fits well the volume-price evolution, with the two corresponding parameters varying in time. Assuming that the evolution of these parameters is governed by coupled Langevin equations, we derive the corresponding drift and diffusion coefficients, which then provide insight for understanding the mechanisms underlying the evolution of the stock market. The data analysed comprises volume-prices distributions extracted from yahoo available data with a sampling frequency of 10 minutes. ##### Multiple Time Series Ising Model for Financial Market Simulations Tetsuya Takaishi, Hiroshima University of Economics, , Japan Abstract: In this paper we propose an Ising model which simulates multiple financial time series. Our model introduces a global spin which couples to spins of other systems. Depending on the value of the global spin, correlations between time series will appear. Simulations from our model show that time series exhibit the volatility clustering that is often observed in real financial markets. We also find non-zero covariance of volatility time series. Thus our model can simulate stock markets where volatilities of stocks are mutually correlated. ##### Effects of Disorder on Critical Behavior of Generalized Conserved Lattice Gas Meesoon Ha, Chosun University, Department of Physics Education, Korea, Republic of ##### Approximate analytical channel potential model of poly-Si thin film transistors operated in the strong inversion region under the high gate and low drain biases Zhen Zhu, Suzhou Vocational University, , China Junhao Chu, East China Normal University, , China Abstract: An approximate analytical channel potential model of polycrystalline silicon thin film transistors operated in the strong inversion region under the high gate and low drain biases is proposed. Thus, the linear relationship between the channel potential and the drain voltage is derived in the strong inversion region under the above bias condition when the polysilicon layer is ultrathin. This model agrees with the two-dimensional-device simulation results under different gate voltages, different drain voltages and different channel lengths. By comparing the relative errors between the model and the simulation results, it presents that this model is more suitable under the higher gate voltage Vg or the lower drain voltage Vd, regardless of the channel length. And this approximate analytical model is helpful in solving the two-dimensional-device problem by one-dimensional Poisson’s equation since the drain bias is taken into account in the channel potential. ##### First-principle studies of phonons and thermal properties of AlN in wurtzite Structure J.Q. Fu, Inner Mongolia University, Physical Science and Technology, China Tie Lei Song, Department of Physics, School of Physical Science and Technology, Inner Mongolia University, , China Xi Xia Liang, Inner Mongolia University, Department of Physics, School of Physical Science and Technology, , China Guo Jun Zhao, Inner Mongolia University, Department of Physics, China Abstract: Group-III nitrides have attracted considerable attention during the past decade due to technological applications in the optoelectronic and electronic devices. Aluminum nitride is one of the important materials among them. It has high thermal conductivity, high melting point, large bulk modulus, and large band gap. In this work, we calculate the band structure, density of states, phonon dispersion and thermodynamic properties of A1N in wurtzite structure based on the first-principle with the software QUANTUMESPRESSO. The local density approximation (LDA) and the generalized gradient approximation (GGA) exchange- correlation potentials are applied in the calculations. The results show that A1N belongs to direct band gap semiconductor. The phonon dispersion characteristics and thermodynamic properties are discussed in detail. The obtained results for the entropy S and the constant-volume specific heat CV as functions of the temperature T based on GGA and LDA are given. CV and S increase with the increasing T. Both the values of S and CV by LDA are slightly lower than those by GGA. The calculated values are in agreement with available experimental data. ##### On Modelling Quantum Potential Flow KUO CHUNG HSUAN, Department of Aeronautics and astronautics, NCKU, , Afghanistan Abstract: In this paper, a new hydrodynamic formulation of complex-valued quantum mechanics is derived to reveal a novel analogy between the probability flow and the potential flow on the complex plane. For a given complex-valued wavefunction , , we first define a complex potential function with and then prove that the streamline lines and the potential lines in the potential flow defined by are equivalent to the constant-probability lines and the constant-phase lines in the probability flow defined by . The discovered analogy is very useful in visualizing the unobservable probability flow on the complex plane by analogy with the 2D potential flow on the real plane, which can be visualized by using dye streaks in a fluid laboratory. ##### THE PROBLEM BY CHOICE OF PRECEDENT WITH EXAMPLE OF DATA ENCRYPTION ALGORITHMS Ayman Iskakova, L.N. Gumilyov Eurasian National University, Department of Mechanical and Mathematics, Kazakhstan Abstract: In this work the process of operational withdrawal of knowledge matrix on precedent described situational vectors realization of computing technique is presented. The new method of withdrawal precedent and its application in data encryption algorithms are presented. ##### Risk management mechanism of payment transactions Ayman Iskakova, L.N. Gumilyov Eurasian National University, Department of Mechanical and Mathematics, Kazakhstan Abstract: The mechanism of protection of smart card software from unauthorized copying based authentication based on symmetric has presented ##### Group theory Analysis of the Magnetic Structures in Rare Earth Iron Garnets revisited Mahieddine LAHOUBI, Badji Mokhtar-Annaba University, Faculty of Sciences , Physics, Laboratory, L.P.S., Algeria Abstract: The rare earth iron garnets with general formula REIG (where RE is a trivalent rare earth ion or the yttrium) discovered by Bertaut and Forrat [1] have been extensively studied during the last decades for the large application as well as fundamental works. Nevertheless, it appears up today that the magnetic and dielectric properties of these ferrimagnets are not achieved as indicated by the large magnetodielectric (MD) effects in low external magnetic fields and at low temperatures revealed by Hur et al. [2] and Song et al. [3] respectively in TbIG and DyIG. The magnetic ions are distributed over the three crystallographic sites of the paramagnetic space group (G) Ia-3d No. 230, RE ions in dodecahedral {24c} sites, and the iron Fe in both octahedral [16a] and tetrahedral (24d) sites respectively. According to the Néel theory of ferrimagnetism [4], the magnetic moments of the RE ions form below the Néel temperature (TN) (which is the same in all REIG (≈ 560 K) [5]) a collinear arrangement antiparallel to the resultant Fe magnetization along the [111] crystallographic direction which is the easy axis of magnetization in a given domain without external magnetic field. At low temperatures, due to the competition between three types of anisotropies (spin-orbit coupling, crystalline field and RE–Fe superexchange interactions) complicated noncollinear arrangement appears with the rhombohedral distortion from the space group cubic G to its highest subgroup (G’) R-3c No. 167. The ''representation analysis'' devised and developed by Bertaut for the determination of magnetic structures [6, 7] and the generalized identification method of Olbrychski [8, 9] of the irreducible representations (irreps) of G and G’ are applied here. These elegant group theoretical techniques are used in the interpretation of our recent neutron powder diffraction studies of the temperature evolution of the ''double umbrella'' magnetic structure observed in TbIG and DyIG [10-12] and the occurrence of the MD effects in these compounds is discussed. According to the concept of the single irrep developed by Izyumov [13] and to the fact that the third power of the three-dimensional irrep of G, (Г4g = T1g)3 contains always the identity representation [14], one can conclude that the magnetic anomaly at the so called low-temperature point of Belov (TB = 54 K) cannot be a second order phase transition, despite the low-T symmetry is a subgroup of the high-T symmetry. [1] E. F. Bertaut, and F. Forrat, C. R. Acad. Sc. Paris, vol. 242 (1956) 382. [2] N. Hur, S. Park, S. Guha, A. Borissov, V. Kiryukhin, and S.-W. Cheong, Appl. Phys. Lett., vol. 87, (2005) 042901. [3] K. M. Song, Y. A. Park, K. D. Lee, B. K. Yun, M. H. Jung, J. Cho, J. H. Jung, and N. Hur, Phys. Rev. B 83 (2011) 012404. [4] L. Néel, Ann. Phys., t. 3 (1948) pp. 137-198. [5] R. Pauthenet, Thesis Grenoble, France, n°. Ordre 81, pp.1-38, 1958. [6] E. F. Bertaut, Acta Cryst. A. 24 (1968) 217. [7] E. F. Bertaut, J. Phys. Colloque C1, suppl. n°. 2-3, vol. 32 (1971) C1- 462. [8] E. F. Bertaut, C. R. Acad. Sc. Paris, vol. 268 (1969) 281. [9] K. Olbrychski, Phys. Stat. Sol., 3, (1963) 2143. [10] M. Lahoubi, “Temperature evolution of the double umbrella magnetic structure in terbium iron garnet”, in Neutron Diffraction, (Ed) I. Khidirov, (2012) Chap. 10, pp. 203-230. [11] M. Lahoubi, Journal of Phys. Conf. Ser., 340 (2012) 012068. [12] M. Lahoubi, W. Younsi, M.-L. Soltani, and B. Ouladdiaf, Journal of Phys. Conf. Ser., 200 (2010) 082018. [13] Yu. A. Izyumov, Physics–Uspekhi, vol. 23, 356−274, 1980 [14] L. D. Landau, and E. M. Lifshitz, Statistical physics, Pergamon Press, 1969. ##### An Axisymmetric Contact Problem for an Elastic Layer Subjected to a Tensile Stress Applied Over an Annular Region Kebli Belkacem, Ecole Nationale Polytechnique, Mechanical Engineering, Algeria Abstract: The study is concerned with an axisymmetric contact problem for an elastic layer on which a tensile uniform stress is applied on the bottom over an annular hole while the lower surface is rigidly clamped. By using the Hankel integral transforms method we reduce the three-part mixed boundary value problem to a system of triple integral equations. With the help of the Gegenbauer formula and some integral representations of the Bessel function, we get an infinite system of algebraic equations for determining the unknown function. The expressions of the stress intensity factors are given analytically. Some quantities of physical interest are shown graphically followed by a discussion of the effect of the radii of the hole as well as the medium thickness on the layer deformation. ##### Precise Approximated Solution for the Bohm Sheath Potential Pablo Martin, Antofagasta University, Physics, Chile Luis Antonio Cortes Vega, Antofagasta University, Mathematics , Chile Abstract: The Poisson equation for the plasma sheath potential near a wall, leads to a non-lineal differential equation, whose analytic solution is not know. The usual approximation taking only the first term does not give good accuracy. Other approximations taken two additional terms gives better accuracy , but it fails to give high accuracy in the intermediate region . Here we present an analytic approximations using quasi-rational multipoint approximation method (MPQA), which leads to new analytic approximate solution with much higher accuracy, and very precise results not only near wall and far away, but also in the transition region, Absolute values of the maximum per cent error as a function of the wall potential will be present. Other several figures showing thess new analytic solutions as a function of the relevant parameters for this problem. The advantages of the present solution compared with those of pervious works will be shown. ##### Reduction Solutions Related to the Residual Symmetry for a (2+1)-Dimensional Burgers Equation Jianping FANG, Lishui University, , China Abstract: The residual symmetry, coming from the standard truncated Painlev\'{e} expansion of a (2+1)-dimensional Burgers equation, is localized in the properly prolonged system with the Lie point symmetry vector. Some different transformation invariance are derived through the obtained symmetries. Further, reduction solution, especially interactive solution is obtained through a generalized tanh function expansion approach. ##### Effective mass Schrödinger equation with Thomas-Fermi potential Gerardo Ovando, Universidad Autonoma Metropolitana, DCBI - Ciencias Básicas , Mexico Jose Juan Peña Gil, Universidad Autonoma Metropoitana Azc., Ciencias Básicas, Mexico Jesús Morales, Universidad Autónoma Metropolitana, DCBI- Ciencias Básicas, Mexico Abstract: The exactly-solvable position-dependent mass Schrödinger equation (PDMSE) for the Thomas-Fermi potential is presented. This model has recent interest because its applications to δ-doped semiconductor structures. To that, the PDMSE is transformed into a standard Schrödinger equation with constant mass (CMSE) with the aim to obtain the transformation that should be used to find the exactly solvable CMSE. In that case, the potential associated to the PDMSE and the potential involved in the CMSE are connected through a Riccati-type relationship which includes a superpotential that determines the position-dependent mass distribution m(x) leading to exactly-solvable PDMSE. To attain the purpose of this work, we assume that the superpotential is constant to find m(x) and consequently an exactly-solvable PDMSE for the Thomas-Fermi potential. Orthogonal eigenfunctions and normalization constants are determined in closed form by developing the particular details involved in the Sturm-Liouville theory for the corresponding CMSE. It is proved that the eigenstates are those of definite parity with eigenvalues expressed through the order of the Bessel functions of the first kind. Beyond the case considered in this work, the approach is general and can be useful in the study of electronic properties of non-uniform materials in which the carrier effective mass depends on the position as well as in the search of new solvable potentials suitable for quantum systems. ##### A Simulation-Based Evaluation of Local Fluxes of Secondary Cosmic Rays at Tehran Zahra bagheri, Research Institute for Astronomy and Astrophysics of Maragha, , Iran (Islamic Republic of) Pantea Davoudifar, Research Institute for Astronomy and Astrophysics of Maragha, Astroparticle Physics, Iran (Islamic Republic of) Abstract: Carrying segments, instruments and small detectors up to the upper atmosphere is a difficult and expensive task. So to evaluate the errors (hard and soft) caused by cosmic rays on onboard parts of a satellite, ordinarily ground-based experiments were being designed to evaluate these errors. In this paper taking the advantage of simulation, the local fluxes of secondary cosmic rays were calculated for Tehran (51°, 35 °). OMERE software were used to get the appropriate fluxes of cosmic rays at the first interaction level of the earth atmosphere with the height of 112.8 kilometers. Considering a flat surface on interaction level, appropriate area and energies were calculated and used to interpret the results of CORSIKA simulations. The local fluxes of secondaries of different types were calculated for Tehran. ##### Scattering of vortex-antivortex pair by single quantum vortex in a Bose-Einstein Condensate. Lev A. Smirnov, Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS), Nonlinear electrodynamics department, Russian Federation Aleksander I. Smirnov, Institute of Applied Physics of the Russian Academy of Sciences (IAP RAS), , Russian Federation Abstract: Dynamics of vortex structures and their interaction with each other in many respects determine key aspects of evolution for the ultracold Bose gas cloud with the repulsing interaction between atoms. Quantum vortices are associated with the breaking of the superfluidity mode and the transition of the Bose-Einstein condensate (BEC) to the turbulent state. Thus, it is important to make a maximal progress in solving the problem of describing different kinds of motion for interacting vortex formations. In the case when the distance between a vortex and an antivortex is substantially smaller than the characteristic scale of the medium inhomogenity the distributions of both the density and the velocities field in vortex pairs are similar to those that take place for the homogeneous flow-free condensate in the correspoding solitary solutions of the Gross-Pitayevsky (GP) equation. In this case one may introduce a concept of the “two-dimensional dark quasisolitons”. Such quasisolitons represent the dips of BEC concentration, propagating in the inhomogeneous Bose gas at subsonic velocities with acceleration and, generally speaking, along the curved paths. We have developed the asymptotic theory describing behaviour of two-dimensional quasisolitons structures in a smoothly inhomogeneous condensate. Using this theory in the case of the quasisolitons motion in the smoothly inhomogeneous small flows of BEC we have succeeded in detailed analizing and explaining peculiarities of scattering for vortex-antivortex pairs on a single vortex. The results of the direct numerical simulation performed within the framework of the GP equation have demonstrated a good agreement with the developed theory. ##### Analytic approximations to the energy eingenvalues of the quadratic Zeeman effect in 2-D for hydrogenlike atoms Pablo Martin, Antofagasta University, Physics, Chile Flavio Citti, Simon Bolivar University, Physics, Venezuela Enrique Castro, Simon Bolivar University, Physics, Venezuela Luis Antonio Cortes Vega, Antofagasta University, Mathematics , Chile Abstract: Analytic energy eigenvalues approximations have been found for the 2-D quadratic Zeeman effect in hydrogenlike atoms. Here a new technique has been used, which is an extension of the two-point quasirational approximation (TPQA) technique, previously used for the same problem . In our previous calculations, two expansions were used, one for small values of the magnetic field and other for large values, that is, expansions around zero and the inﬁnity were determined. Later a bridge between both expansions was built using simple auxiliary functions as well as rational ones. In the present paper expansions around intermediate points were also determined, and used. In this way, the corresponding analytic bridge function is determined, taken care also of these new expansions, so the technique is a multiple point quasirational approximation (MPQA). The calculations are carried out for the ground state 1s and the excited states 2p- and 3d- . These results are now much better than those obtained in previous works . We will also show the advantage of our approximants with respect to other approximations. ##### Bound state solutions of D-dimensional Feynman propagator for the q-deformed Woods–Saxon potential Ahmed Diaf, Laboratory of Energy and Smart Systems, Khemis Miliana University, Sciences and Technology, Algeria Abstract: Using the space-time transformations, approximate analytical solutions of the D-dimensional propagator in the presence of q-deformed Woods–Saxon potential are obtained. The analytical expression of the energy eigenvalues is given for various quantum numbers and the corresponding normalized eigenfunctions are obtained in terms of hypergeometric function. Our results are compared with those given by The Nikivorov-Uvarov method. ##### Designing a Supply Chain Network on the Basis of Variational inequality Abstract: Increasing developments and changes in the field of production and business resulted in rising and development of concepts including supply chain and supply chain management. Supply change management from 190s onward developed increasingly among scientific societies, companies and industries and aimed at establishing cooperation among suppliers, lowering the costs, satisfying the needs of customers, increasing purchasing ability, profits and competitive advantages. The method applied in this study is Modified Image Method that is a common method to solve variational inequality. It assumes that K is a possible space and F is a function that acts in monotonous and Leap Sheets conditions. The method to solve inequality is proved and to apply it generally it was used on different issues with specified capacities. The result of proving the method of solution showed that it is an appropriate and reliable method to solve problems of chain supply management. ##### High Performance Computing of Meshless Time Domain Method on Multi-GPU Cluster Soichiro Ikuno, Tokyo University of Technology, School of Computer Science, Japan Yuta Hirokawa, University of Tsukuba, Graduate School of Systems and Information Engineering, Japan Taku Itoh, Tokyo University of Technology, , Japan Susumu Nakata, Ritsumeikan University, College of Information Science and Engineering, Japan Abstract: High performance computing of Meshless Time Domain Method (MTDM) on Multi-GPU cluster is numerically investigated, and the electromagnetic wave propagation simulation is achieved by using parallelized MTDM on Multi-GPU. Generally, Finite Difference Time Domain (FDTD) Method is adopted for the simulation of the electromagnetic wave propagation phenomena. FDTD has great advantages in terms of parallelization and the scheme of FDTD is a transparent algorithm. However, a numerical domain must be divided in to rectangle meshes, and it is difficult to treat the problem in the complexed shaped domain. On the other hand, a meshless approach does not require meshes of a geometrical structure, and various meshless approaches such as the Radial Point Interpolation Method (RPIM) have been developed. In particular, meshless approaches based on RPIM are applied to time dependent problems, and the method is called Meshless Time Domain Method. The Graphics Processing Unit (GPU) is one of the most progressive device in recent years, and various researches of General Purpose computing on GPU (GPGPU) have been proposed aggressively. The results of computation show that the execution time of the time evolution calculation on GPU with various parallelization techniques is about 54 time faster than that of serial CPU. ##### Organization model for Mobile Wireless Sensor Networks (MWSN) inspired in Artificial Bee Colony (ABC) Guilherme Roberto, São Paulo State University (UNESP), , Brazil Luis Maschi, Federal Institute of São Paulo (IFSP) - Campus Catanduva, Informática, Brazil Daniel Fernando Pigatto, Institute of Mathematics and Computer Sciences (ICMC) / University of São Paulo (USP), , Brazil Carlos Montez, Federal University of Santa Catarina (UFSC), , Brazil Leandro Neves, São Paulo State University, DCCE, Brazil Kalinka Branco, Institute of Mathematics and Computer Sciences (ICMC) / University of São Paulo (USP), , Brazil Alex Sandro Pinto, Universidade Federal de Santa Catarina, Câmpus de Blumenau, Brazil Abstract: Wireless sensor networks (WSN) are a special type of computer networks, which basically aim at monitoring and tracking a specific area, typically with military, environmental or industrial purposes. These networks are considered a type of Ad Hoc network, and are composed of small computational nodes usually with limited processing capacity, capable of environment sensing and messages routing through radio frequency. A major problem in this type of networks is the energy consumption required for nodes operations, usually derived from batteries. The exchange of messages between nodes and data collection stations is the largest energy consumer within a typical WSN. Mobile wireless sensor networks (MWSN) are an interesting alternative to solve the problem of communication range, which usually is subjected to the limitations of a WSN. However, due to the mobility of nodes in a MWSN, these networks require frequent reformulations in route for forwarding messages to the base. Considering all the aspects mentioned above, the purpose of this study is to find a self-organizing model for MWSN based on bee colonies in order to reduce the number of messages transmitted among nodes, and thus reduce the overall consumption energy while maintaining the efficiency of message delivery. The results obtained in this article are originated from simulations carried out with SINALGO software, which demonstrates the effectiveness of the proposed approach. The BeeAODV (Bee Ad-Hoc On Demand Distance Vector) proposed in this paper allows to considerably reduce message exchanges whether compared to AODV (Ad-Hoc On Demand Distance Vector). ##### First-principle studies of lattice and electronic structure of BexZn1-xO X.Lei, Inner Mongolia University, Physical Science and Technology, China Guo Jun Zhao, Inner Mongolia University, Department of Physics, China Xi Xia Liang, Inner Mongolia University, Department of Physics, School of Physical Science and Technology, , China Tie Lei Song, Department of Physics, School of Physical Science and Technology, Inner Mongolia University, , China Abstract: With the development of optoelectronics industry, II-VI wide-gap semiconductor zinc oxide has become a great importance to the photoelectric material, and it was used widely in ultraviolet light photoelectric devices. The causes of study ZnO alloy is due to its easy to doping ternary alloy formation mechanism and it is easy to meet the needs of a variety of optoelectronic devices. In this paper, beryllium doped zinc oxide(BexZn1-xO) ternary alloy was studied based on the density functional theory. After lattice structure and atomic position optimization for different doping concentration BexZn1-xO (x=0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875 and 1, respectively), the lattice parameters for the stable structure and the band gap of BexZn1-xO are obtained. It turned out that the lattice constants a and lattice constants c decrease linearly as Be doping concentration increases, compliance with Vegard's law, the lattice parameters of the BexZn1-xO ternary alloys are consistent with experimental results. Band gap increases with increasing Be content, and the band gap values are fixed. Furthermore, the density of states of BexZn1-xO is calculated, the results shown that the valence band maximum (VBM) occupied by O2p states, and the conduction band minimum (CBM) occupied by Zn4s states. As Be doping, Zn 4s states dominate the conduction band and the conduction band bottom position constantly moving to higher energy region. Density of states strength Zn 4s states with decreasing proportion of Zn is constantly reduced. ##### Mathematical modeling of high-strain-rate deformation, kinetics of alpha-epsilon-phase transition, as well as nucleation, growth and recompaction of spall damage for recovered samples of quenched 30KhGSA steel under explosive loading Natalia Zhilyaeva, Russian Federal Nuclear Center-Zababakhin Russian Science Research Institute of Technical Physics, , Russian Federation Abstract: Advanced models for shear and spall strengths of the quenched 30KhGSA steel (HRc35...40) are described to take into account the reversing solid-state alpha-epsilon-phase transition, as well as the setup and results of earlier experiments with registration under two explosive loading modes of the two-, and three-wave configurations of stress waves in samples having different initial thickness. Consideration is given to the main theoretical predictions and simulation results for explosive experiments wherein wave profiles in the quenched 30KhGSA steel were registered with the help of streak-camera using the optical lever method and with the help of laser-interferometry using the Fabry-Perot and PDV methods. Comparing the calculated wave profiles with the measured ones, as well as comparing the predicted locations of the spall and shear micro-, meso-, and macrodamage zones with those observed on micro-, and macrophotographs of recovered samples cross-sections indicates that our calculations adequately describe wave processes in samples of the quenched 30KhGSA steel taking into account the elastic-plastic properties, direct and reverse alpha-epsilon-phase transition in stress waves, as well as kinetics of nucleation, growth, and recompaction of spall and shear damages. ##### DFT/TDDFT CALCULATIONS OF GROUND AND EXCITED STATES OF CIS AND TRANS 1, 3 INDANEDIOL Moussaoui Yahia, Universite des sciences et de la technologie houari boumediene, Chimie physique, Algeria Souhila Rezzouk, Université des Sciences et de la Technologie Houari Boumediene, Department of Chimie Physique, Algeria Abstract: The system 1, 3-indanediol is presented under two isomers of cis and trans configurations the cis 1, 3-indanediol was used as a building unit in the synthesis of a new aromatic polyester obtained by poly-condensation. The ground state of cis and trans 1,3-indandiol were optimized by using the B3LYP DFT approach in combination with the basis set 6-31G. The cis form have been found more stable than the trans configuration. This observation is in good agreement with experimental results. The excited states of our system were computed using Time dependent-Density Functional Theory (TD-DFT). References: [1] H. Guemmour, F. Carrière, A. Benaboura, Polym. Bull. 1-6 (2001) 46.. [2] E. Runge, E.K.U. Gross, Phys. Rev. Lett. 52, 997–1000 (1984). [3] E.K.U. Gross, C.A. Ullrich, U.J. Gossmann, Density Functional Theory, NATO ASI Series, Plenum, New York, pp. 149–171(1994). [4] R. van Leeuwen, Int. J. Mod. Phys. B 15, 1969 (2001). [5] M.A.L. Marques, E.K.U. Gross, Annu. Rev. Phys. Chem. 55, 427–455 (2004). ##### AB INITIO STUDY OF NEW COMPLEXES OF IMIDAZOLE AND SUBSTITUTED IMIDAZOLE WITH Zn ATOMS Nait Achour Madjid, Universite des Sciences et de la Technologie Houari Boumediene, Chimie Physique, Algeria Abstract: Imidazole and its derivatives are involved in important biological processes where they play a variety of roles [1]. Imidazole is also well known to adsorb and form strong complexes with transition metal ions[2]. Bonding between metal ions and imidazole ligands is very common in nature and many examples of metals in metalloproteins coordinated by imidazole have been reported [3]. Among these metals are found Zn2+ ions which are key structural components in a large number of metalloproteins. In the present work, a series of new compounds formed by imidazole ring and its derivatives with several Zn atoms, in which the first atom of Zn is formally in the +2 oxidation state and the others atoms are in their neutral state, are reported and studied theoretically. Thereby, both Density Functional Theory (DFT) and Moller Plesset (MP2) calculations were performed for these complexes. The elucidation of the structures of these complexes was made using the 6-311++G function basis set. We evaluate the binding energy taking basis set superposition error (BSSE) and zero point vibrational energy (ZPVE) correction into account, as we calculate the IR spectrum, heats of formation and thermodynamic properties for all the obtained complexes. Harmonic vibrational frequencies calculations confirm that these elucidated structures are stable. All the calculations were performed using Gaussian 03 program. [1] (a) H.C. Freeman, in G.L. Eichhom (ed), Inorganic Biochemistry, Elsevier, New York, 1973, Ch.4 (b) R.J.Sundberg and R.B.Martin, Chem. Rev.,74(1974)471. [2]J.Hedin, D.Issaksson, M.Andersson, M.Nyden,J.of Colloid and Intrface Science 336(2009) 388-392. [3]J.M.Guss and H.C.Freeman, J.Mol.Biol.,169 (1983) 521. ##### Arbitrary l state solutions of the Feynman propagator with the Deng-Fan molecular potential Ahmed Diaf, Laboratory of Energy and Smart Systems, Khemis Miliana University, Sciences and Technology, Algeria Abstract: The bound state solutions of the Feynman propagator with the rotating Deng-Fan molecular potential are presented approximately. An approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. The energy spectrum and the normalized eigenfunctions are both obtained for the application of this technique to the Deng-Fan molecular potential. Our results are in very good agreement with those found by using numerical and other methods. ##### Searching for AdS3 waves and Asymptotically Lifshitz black holes in R3-NMG Giorgos Anastasiou, Universidad Andres Bello, Physics Department, Chile Abstract: In this paper we consider the structure of the AdS3 vacua in R3 expansion of New Massive Gravity (R3-NMG). We obtain the degeneracies of the AdS3 vacua at several points of the parametric space. Additionally, following a speci c analysis we show that AdS3 wave solutions are present. Using these wave solutions, we single out two special points of the parametric space for which logarithmic terms appear in the solutions. The rst one is a point at which the e ective mass of the wave pro le, which is interpreted as a scalar mode, completely saturates the Breitenlohner- Freedman bound of the AdS3 space in which the wave is propagating. The second special point is a point at which the central charge of the theory vanishes. Furthermore, we investigate the possibility of asymptotically Lifshitz black hole solutions to be present in the three-dimensional R3-NMG. We derive analytically the Lifshitz vacua considering speci c relations between the mass parameters of R3-NMG. A certain polynomial equation arises at the rst special point where solutions with logarithmic fallo in the AdS3 space appear. Solving this polynomial equation, we obtain the values of the dynamical exponent z which correspond to possible asymptotically Lifshitz black hole solutions. However, it is shown that asymptotically Lifshitz black hole solutions do not exist in the three-dimensional R3-NMG for a speci c ansatz of the black hole metric. ##### Monte-Carlo investigation of proton pencil beam effects in the rectangular target, with using GEANT4 code Seyed Ali Mahdipour, Hakim Sabzevari University, , Iran (Islamic Republic of) Abstract: Radiotherapy with hadron beams like proton have been used for treatment of different cancers for many years. Determination of the particle’s deposited dose in the different tissues of budy is very important in radiotherapy and medical physics. GEANT4 Monte Carlo code reused for considering this effect. Simulation results help us to determine the physical parameters exactly. In this article we have calculate the total depth and lateral dose profiles for the 110 - 220 MeV proton pencil beams in the arbitrary rectangular target made of skin, adipose and tumor tissues. The material of tissues are taken from compositions of the ICRU 46. The results of this Monte Carlo code has a good agreement experiment data. moreover 2D depth dose profiles for the proton beam has been calculated in the phantom. ##### Meteorological time series forecasting based on MLP modeling using heterogeneous transfer functions Voyant Cyril, University of Corsica, , France Abstract: In this paper we propose to study four meteorological and seasonal time series coupled with multi-layer perceptron (MLP) modeling. We choose to combine two transfer functions in one heterogeneous function and to use a temporal indicator (time index as input) in order to take into account the seasonal aspect of the studied time series. The results of the prediction concern two years of never-used data (8 years for the learning step) and show that this methodology can improve the accuracy of meteorological data estimation compared to a classical MLP modeling with homogenous transfer function. The time index is the tool giving the best results for all cases, while in 75% of the cases it is for the use of the heterogeneous transfer function. For the time series with low variation coefficient, the lowest nRMSE is under 10% whereas for the other (solar irradiation and wind speed) the nRMSE is close to 30%. ##### AB INITIO STUDY OF NEW COMPLEXES OF IMIDAZOLE AND SUBSTITUTED IMIDAZOLE WITH Zn ATOMS Nait Achour Madjid, Universite des Sciences et de la Technologie Houari Boumediene, Chimie Physique, Algeria Abstract: Imidazole and its derivatives are involved in important biological processes where they play a variety of roles [1]. Imidazole is also well known to adsorb and form strong complexes with transition metal ions[2]. Bonding between metal ions and imidazole ligands is very common in nature and many examples of metals in metalloproteins coordinated by imidazole have been reported [3]. Among these metals are found Zn2+ ions which are key structural components in a large number of metalloproteins. In the present work, a series of new compounds formed by imidazole ring and its derivatives with several Zn atoms, in which the first atom of Zn is formally in the +2 oxidation state and the others atoms are in their neutral state, are reported and studied theoretically. Thereby, both Density Functional Theory (DFT) and Moller Plesset (MP2) calculations were performed for these complexes. The elucidation of the structures of these complexes was made using the 6-311++G function basis set. We evaluate the binding energy taking basis set superposition error (BSSE) and zero point vibrational energy (ZPVE) correction into account, as we calculate the IR spectrum, heats of formation and thermodynamic properties for all the obtained complexes. Harmonic vibrational frequencies calculations confirm that these elucidated structures are stable. All the calculations were performed using Gaussian 03 program. [1] (a) H.C. Freeman, in G.L. Eichhom (ed), Inorganic Biochemistry, Elsevier, New York, 1973, Ch.4 (b) R.J.Sundberg and R.B.Martin, Chem. Rev.,74(1974)471. [2]J.Hedin, D.Issaksson, M.Andersson, M.Nyden,J.of Colloid and Intrface Science 336(2009) 388-392. [3]J.M.Guss and H.C.Freeman, J.Mol.Biol.,169 (1983) 521. ##### Activation energy of disordering lattices superionic crystals LnF3 (Ln = La, Ce, Pr): experimental results and quantum-chemical calculations Sirojiddin Mirzaev, Instituteof Ionic, Plazma and Lazer Technology, , Uzbekistan Valeriy Krivorotov, Instituteof Ionic, Plazma and Lazer Technology, , Uzbekistan Georgiy Nujdov, Institute of Ionic, Plazma and Lazer Technology , , Uzbekistan Abstract: The lattice disordering in superionic crystal LaF3 investigated by inelastic light scattering spectroscopy and quantum-chemical calculations energy process. Based on analysis of the line widths of Raman scattering in the crystal LaF3 found that the values of the activation energy Ea = 0.18 eV F1 sublattice disordering in the insulating phase and 0.04 eV for the superconductive phase. Quantum-chemical calculations of the potential relief in the LaF3 cluster ions of 1200 proved that the energy Ea of defect vacancy- interstitial fluorine ion equal 0.16 eV when moving to an interstitial single ion F1 ( insulating phase ) and 0.03 eV for the movement of ions in the superionic phase F1 . On the basis of quasi-elastic light scattering in LaF3 shown that potential barriers Ed that impede the movement of ions F1, decrease from 0.28 eV ( insulating phase ) to 0.07 eV in the superionic phase . The results lead to an important conclusion for the physics of superionic conductors : Ed and Ea values obtained for the insulating phase ( T ##### Mathematical Tools for Discovery of Nanoporous Materials for Energy Applications Maciej Haranczyk, Lawrence Berkeley National Laboratory, Computational Research Division, United States Richard Martin, Lawrence Berkeley National Laboratory, Computational Research Division, United States Abstract: Porous materials such as zeolites and metal organic frameworks have been of growing importance as materials for energy-related applications such as CO2 capture, hydrogen and methane storage, and as catalysts. The current state-of-the-art molecular simulations allow for accurate in silico prediction of materials’ properties but the computational cost of such calculations prohibits their application in the characterization of very large sets of structures, which would be required to perform brute-force screening. Our work focuses on the development of novel methodology to harness this complexity of the materials space. In particular, we have been developing algorithms and tools for enumeration and characterization of porous material databases as well as efficient screening approaches. The latter include similarity-based, optimization-based approaches as well as application of structure-property relationships. Our methodology represents a “soup” of mathematical methods. We have used Voronoi tessellation-based techniques to enable high-throughput structure characterization and comparison, PDE-based techniques to predict guest-molecule accessibility, and continues and discrete optimization to design materials. The resulting hybrid material discovery suite requires expensive characterization only for carefully selected and statistically relevant subset of a database, therefore enabling discoveries at a minimal computational cost. Our presentation will give an overview of recent developments as well as highlight few interesting applications. ##### Firewalls: arising from vaccum? Luis Cabarique, Universidad Nacional de Colombia, Departamento de Física, Colombia Robel Arenas, Universidad Nacional de Colombia, Observatorio Astronómico Nacional, Colombia Abstract: The appearance of a firewall near a black hole has caused great controversy. In this paper we discuss the black hole firewall centering in the vaccum properties of each corresponding observer in (1+1)-dimensions. From this properties we found that the horizon appears naturally as a massless radiating Shell, but it no necessarily is the same firewall proposed as a possible solution to an apparent inconsistency in black hole complementarity. ##### Numerical study of the propagation of train of chirped vector solitons in birefringent optical fibers with variable coefficients Siham Aziez , Université Hadj-Lakhdar de Batna, Département de Science de la Matière, Faculté des Sciences, Algeria Derradji Bahloul, Université El Hadj Lakhdar de Batna, Sciences de la Matière, Algeria Abstract: We study numerically in this work the propagation of train of chirped vector solitons in birefringent optical fibers with variable coefficients using the compact split step Padé scheme (CSSPS) [5]. Generally, the propagation of managed vector solitons in birefringent optical fibers is governed by the coupled NLS equations with variable coefficients which are not integrable, but may possess exact solitary-wave solutions (vector solitons) in some particular cases. ##### Generalized Radon Inversion from an Efficient Number of Moment Based Projections Applied on Computerized Tomography Spiros Chountasis, Independent Power Transmission Operator, Department of Systems & Infrastructure, Greece Abstract: This paper presents a new method for image computerized tomography that is based on the usage of a generalized inversion that is rotation-invariant utilizing Radon and time-frequency transforms. The proposed technique employs the Fourier and Haar coefficients for spectral and spatial moment based image analysis, respectively. It provides a new approach to the problem of tomographic image reconstruction where an X-ray image obtained from a set of line projections. The experimental evaluation of the scheme leads to the conclusion that the increased selectivity of the method provides a faster and more robust approach to the problem. The method has been tested by reconstructing a commonly used tomography image at the presence of blur caused by uniform linear motions. The noise during normal transmission process is another issue that is considered in the current work. ##### Keto-enol tautomerism in 5- and 6-azauracils in water solution Nadezhda Markova - Petrova, Institute of Organic Chemistry with Centre of Phytochemistry, Bulgarian Academy of Sciences, , Bulgaria Abstract: Ab initio quantum chemical investigations on the tautomeric equilibrium in 5- and 6-azauracils in water were performed. The solvent effects were considered by explicit inclusion of two pairs of water molecules, which model a first hydration shell around the solute. The effects of the water as solvent were introduced at two different levels - using solute-solvent clusters (four water molecules) and using the same clusters embedded in an external continuum. Full geometry optimizations of these complexes were carried out at MP2/6-31+G(d,p) and C-PCM/MP2/6-31+G(d,p). Single point calculations were performed at CCSD(T)/6-31+G(d,p)//MP2/6-31+G(d,p) computational level to obtain accurate energies. According to our calculations, hydrated azauracils should exist in three forms: mainly dioxo form and two hydroxy forms. The calculated proton transfer activation energies for the tautomeric reactions of 5-azauracil and 6-azauracil show different pictures for these two compounds. According to C-PCM/MP2/6-31+G(d,p) data water-assisted proton transfer in 5-azauracil occurs through two parallel reactions A→B and A→D. Tautomeric equilibrium in 6-azauracil in water could occur by two contiguous reactions, A→D and D→C. The proton transfer investigated reactions in 5- and 6-azauracils involve concerted atomic movement. ##### Stochastic Multiscale Modeling of Physical and Biological Systems George Karniadakis, Brown University, Applied Mathematiacs, United States Abstract: TBA ##### The Enigma of Dark Energy Ofer Lahav, University College London, , United Kingdom Abstract: There is strong observational evidence that our Universe is flat and it consists of three main ingredients: ordinary matter, Dark Matter and Dark Energy. Dark Energy is commonly interpreted as the cause of the observed acceleration of the cosmic expansion. The lecture will review the chequered history of Dark Energy, the current observations and new surveys such as the “Dark Energy Survey”, and mathematical and statistical approaches. ##### Structure and Dynamics of Multi-scale Interacting Diseases Yamir Moreno, Institute BIFI, University of Zaragoza, , Spain Abstract: TBA ##### Hybrid Ab Initio/Molecular Mechanical Simulations of Solutions - Perspectives for Complex Chemistry, Proton Transfer Reactions and Interfaces Thomas Hofer, University of Innsbruck, Institute of General, Inorganic and Theoretical Chemistry, Austria Abstract: Following the continous improvmement of computational resources, theoretical chemistry has proven to be an increasingly valuable approach for investigations of a large number of chemical phenomena, especially in case of liquids and solutions, which are ont one hand the most important but at the same time also one of the most challenging states of matter to describe. Hybrid quantum mechanical/molecular mechanical (QM/MM) simulation techniques are still considered as one of the most promising approaches for investigations of chemical system. These methods separate the system into two regions. While interactions in the chemical most relevant part are accounted for via quantum mechanics, empirical molecular mechanical potentials are sufficiently accurate to describe the remaining part of the system. Especially for the determination of experimentally elusive properties such as ultrafast phenomena or single ion properties QM/MM techniques proved to be particularly useful alternative approaches. Details of advanced QM/MM technqiues are presented and simulation results for various systems ranging from coordination complexes in solution to the description of proton transfer events will be presented. A particularly challenging application is the description of solid interfaces, which is a prerequisite to study of adsorption and related phenomena such as catalysis. The combination of the QM/MM methodology with a periodic quantum mechanical description of the system will presented. Exemplary results of a QM/MM simulation study of the MgO(100)/water interface demonstrate the capabilities of this approach. ##### Geometrodynamics in Cosmology Spyros Basilakos, Academy of Athens, RCAAM, Greece Abstract: In this review talk I will discuss some ideas based on Geometrodynamics towards explaining the accelerated expansion of the Universe. In particular, I will describe some basic modified gravity models namely f(R), Dvali, Gabadadze, and Porrati(DGP) braneworld, Gauss-Bonnet and Finsler, and I will discuss their Cosmological implications. ##### Polarons on nonlinear lattice in the Su–Schrieffer–Heeger approximation: Exact solution and multipeaked polarons. George Vinogradov, Emanuel Institute of Biochemical Physics, Russian Academy of Sciences, Statistical physics, Russian Federation Abstract: We investigate the polaron dynamics on the nonlinear lattice with the cubic nonlinearity. The electron-phonon interaction is accounted in the Su-Schrieffer-Heeger approximation. An exact analytical solution is obtained in the continuum approximation. The numerical simulation agrees with analytics very well. Moreover, colliding polarons recover their shapes and velocities after the elastic collision suggesting that the solution belongs to the exactly integrable system. When the continuum approximation is invalid (parameters of nonlinearity and electron-phonon interaction are not small), a new family of stable multipeaked polarons is found. These polarons are formed by the coupled solitons hold together by the electron-phonone interaction. #### International Conference on Mathematical Modeling in Physical Sciences August 28-31, 2014	2014-10-02 12:25:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5009106397628784, "perplexity": 1537.5772669918729}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663754.0/warc/CC-MAIN-20140930004103-00477-ip-10-234-18-248.ec2.internal.warc.gz"}
https://online-vwl.de/english/macro/dynvwlengse21.html	### 21.1 Basic principles and assumptions At the core of the Mundell-Fleming model is the balance of payments (BoP) equilibrium, i.e. the ex post equilibrium according to which every international transaction of goods is paid for. If goods or services are exported or imported, it is recorded in the current account. Payments are recorded in the capital account. The sum of the two is called the balance of payments and must be even (apart from balancing items, see below), as each transaction is recorded on both sides "delivery" and "payment" (this can also be a debt or credit). With flexible exchange rates, the balance of trade is kind of automatically balanced. On the foreign exchange market, if there is a trade balance surplus, the supply of foreign currency is greater than the demand. The domestic currency appreciates. As the external value of the domestic currency increases, domestic goods become more expensive abroad. Exports fall and domestic growth is impaired. At the same time, however, imports become cheaper. Falling import prices have a moderating effect on the domestic rate of price increase and thus support economic development. Since the early 1990s, the USA has had a substantial current account deficit. Despite flexible exchange rates, the compensation that takes places via the foreign exchange market is apparently not sufficient. Contrary to the textbooks, the dollar has not depreciated in the long run. Obviously, other factors influencing the exchange rate have been more significant, but they did not bring about the compensation of the current account deficit. In the Mundell-Fleming model, the relationship between exchange rate and BoP equilibrium is controlled by the reactions of the international capital market and the real competitive position of a country. The responsiveness (interest rate elasticity) of international investors is finite, i.e. interest rate differences lead to limited capital transfers. The exchange rate adjusts so that the value of foreign currency inflows multiplied by the exchange rate equals the value of outflows. Export surpluses thus represent an increased demand for the domestic currency and thus lead to appreciation pressure. ##### Current account, capital account, balance of payments The balance of payments consists of four sub-balance-sheets: the current account (LB), the capital account (KB), the capital transfers account (BV) 1 and the statistical residual item (sR). Within the framework of the MF-model, we will restrict ourselves to the current and capital account. Because on the one hand, the other two items are generally relatively small and, on the other hand, we assume that they are exogenous with regard to the dynamics of the MF-model, i.e. they can be treated as constants. Since the statistical residual item (also the balance of unrecorded transactions) is defined as an adjustment item, ex post the following identity is always valid: $\mathit{LB}+\mathit{KB}+\mathit{BV}+\mathit{sR}=0$ The current account2 consists of the trade and services balance, which contains all exports and imports of goods and services including additional and transport costs, the acquisition and capital account (primary income)3 and the current transfers balance (secondary income)4. $\text{LB=}\underset{\text{Handelsbilanz}}{\underbrace{\text{Warenhandel}}}+\underset{\text{Dienstleistungsbilanz}}{\underbrace{\text{Dienstleistungen}}}\text{+Primäreinkommen+Sekundäreinkommen}$ The capital account records the inflows and outflows of payments from exports, imports and capital transfers (usually for investment purposes at home or abroad) and changes in foreign exchange holdings in the foreign exchange balance. $\text{KB=Direktinvestitionen+Wertpapieranlagen+Finanzderivate+ÜbrigerKapitalverkehr+Währungsreserven}$ For the Mundell-Fleming model, we will concentrate on the illustration of the trade and services balance within the current account and will not differentiate the capital account in most cases, but only use the overall effect. $\mathit{LB}+\mathit{KB}=0$ A positive value of the current account indicates an export surplus. A positive value of the capital account indicates a net capital import. The above identity – which is generally always valid, independently of any model – shows a particularly important and often ignored fact: Being the export world champion therefore also means being the world champion in exporting capital. This can be easily illustrated with an example: 1. A car is sold to the USA (=export of goods) 2. Payment is made in US$to an account or cash. This corresponds to a claim on the USA, which means it is capital that belongs to D but is located in the USA. (= export of capital) 3. In order to bring back the capital to D, either something must be bought from the USA with the$ (= import of goods) or the \$ must be exchanged for , i.e. set off against a claim on D which originates from a previous import (US goods against ). Hence, politicians who first (sometimes even in one and the same speech) celebrate German exports and then demonize capital exports show that they either have no idea what they are talking about or that they want to deceive the citizens. ##### Current account imbalances since the 1990s At the beginning of the 1990s, individual countries developed large and persistent current account imbalances and this trend has worsened since the end of the 1990s. While some countries have persistent current account surpluses, others have almost permanent current account deficits. These structural and permanent trade imbalances are seen as one of the causes of the global economic and financial crisis as well as the European crisis. Although the EU as a whole shows a nearly balanced external trade, there are strong imbalances within the EU. In the last three years, for example, Germany annually exported 250 billion more in goods than it imported. In order to limit these imbalances, the EU has introduced the MIP (macroeconomic imbalance procedure), under which macroeconomic imbalances are monitored and assessed. If required, the states must work to reduce these imbalances. Outside the eurozone, in particular the USA, with current account deficits of up to 6% of GDP, and China and Japan, with permanent high surpluses, stood out. Current account imbalances are not bad per se. If they arise in free markets without being induced by political or exogenous shocks, they are the result of different savings, investment and consumption preferences of countries. However, they do become a problem, 1. if the market processes are massively distorted by policy measures, for example in the case of exchange rate manipulation or unilateral export promotion, e.g. through the tax and customs system, subsidies or trade barriers. 2. if the deficits are permanent, so that there is a risk of over-indebtedness. 3. if competitive differences within a monetary union are no longer balanced. This is where the failure of politics within the EU is particularly evident. Even after the start of the monetary union, many countries acted as if they still had their own currencies as a compensatory instrument. While in Germany - mainly due to the Hartz-laws - unit labor costs fell by 6%, in Greece they rose by almost 10%. Thus, the relative competitive advantage for Germany increased by 15%, resulting in an increase in both the current account surplus of Germany and the current account deficit of Greece. Since no real depreciation can take place within the monetary union, the only remaining option to solve this structural problem are rising wages in Germany or falling wages in Greece. 1The capital transfers account includes mainly gifts such as debt relief and payments on intangible non-produced goods like royalties. 2see German Central Bank: https://www.bundesbank.de/Redaktion/DE/Dossier/Statistik/zahlungsbilanz.html?notFirst=true&docId=172974 3These include, in particular, cross-border income from employment and interest- and dividend-payments. 4This includes, primarily, payments by the state to international organizations and development aid, as well as remittances by foreign workers to their home country which are not matched by any direct output. (c) by Christian Bauer Prof. Dr. Christian Bauer Chair of monetary economics Trier University D-54296 Trier Tel.: +49 (0)651/201-2743 E-mail: Bauer@uni-trier.de URL: https://www.cbauer.de	2021-10-20 15:54:54	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 4, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33423882722854614, "perplexity": 2709.082924096937}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585322.63/warc/CC-MAIN-20211020152307-20211020182307-00671.warc.gz"}
http://www.musicgearreview.com/reviews.php?man=Fender&cat=Electric_Guitars&mod=Tom%20Delonge%20Strat	# Fender Tom Delonge Strat Reviews Bought online from Drumcityguitarland on closeout about a month ago. $380 Everything. Simple, streamlined, one humbucker, one knob, fast neck, great tone. [quote]For all you dumb people out there: this is a PUNK guitar. [/quote] For the guy who said this: you're the dumb person. I NEVER play punk, but this guitar works for a ton of different styles. Hard rock/metal it does VERY well. The Invader is an amazing pickup. Nothing really...oh, the "tom delonge" neckplate. replaced Solid-feeling, great mexican fender. When I got it, the setup on it was PERFECT and still is. I'm in love. For the money, it's one of the best guitars I've owned, and easily the best value. IF YOU FIND ONE OF THESE, BUY IT! If you can find one at a retailer, they're probably still on closeout for under$400. If you see someone on ebay selling it for over $600, they're dumb, but it's still worth it. Have fun, guys. Davetheguitarhero rated this unit on 2005-04-08. I bought it from a friend for 250 bucks because he wanted to get rid of it. I figured out why. hmmm... highly flammable laquer. easily breaks when ran over by a car or thrown against a wall. well lets see, I would say there are only 2 other ways to get a better sound than with this guitar: 1. play any other guitar ever made. 2. listen to yourself taking a shit.when i first played this guitar, I listened to it's sound, and I would say it is compareable to that of a goat being slaughtered. As triumph would say, the tonal diversity is very good..... for me to poop on. it has 1 pickup, one knob, NO tone knobs, No tremelo. There is one sound! N/A this thing was put together by a 3 year old in korea or whatever. Tom Delonge is a stupid sack of crap that sucks at playing, just like his guitar. he is a moron for using it. MY friend who owns the guitar thinks it is cool. He is blind and deaf, and is on multiple prescription drugs, and is mildy retarded. Tom Delonge rated this unit on 2004-06-27. Ordered the guitar through fender corp. online. I payed a total of$600.00 which included shipping. I thought the design of the guitar was awesome, and the most unique i've seen in a while! CHARLES B. DOESN'T KNOW WHAT THE HELL HE'S TALKING ABOUT!!! It's simple... everything. This unit was built to pump out it's clean high notes and it's fat&beffy bass notes. With just one volume knob and one humbucker pick-up, it blows your head off and your mind away. The guitar only comes in a few colors, unless you special order one. Very well built, smooth and def. fun to play. I love the no nonsense approach to making of this awesome guitar. Just shows that you don't need to be all complicated to get good sound... look how famous blink 182 is now(2004) jeremiah puentes rated this unit on 2004-06-25. I picked this guitar up from guitar center for $402 with tax. I also got a "free" deluxe fender gig bag. I really like the sound of this guitar. Its has a punchy, but heavy sound to it. I always leave the tone knobs cranked, so I like how the tone pot has been nixed. A simple guitar that's great for playing power\bar chords. It is not very heavy, but enough so that you know it's there. The vintage tuners are not that great, I'm suprised they stuck them on this guitar. They don't keep the guitar tuned up as long as grovers or other higher end ones. I'm probably going to nix them and install some grovers. This guitar has the fender strat name, so you know its built well. The neck is straight and the innotation is great. The paint job is super shiny and thick, the way a strat should be.(I hate sunburst paint jobs.) If you want to play obscene 20 minute solos (like metallica) DON'T buy this guitar. The neck isn't that fast because of the high frets and factory action. If you want to play rythm and have a mean sound then this guitar is for you. It's great for guitar driven music like Green Day and Blink 182(of course). I hate Tom Delonge and his little band rated this unit on 2004-01-07. I bought it from a yard sale that some old guy had. I thought it would be fun to start a guitar collection after my 13 years of playing guitar. I paid about$300 for it. It was pretty much brand new. Just a few scratches on the pickgaurd. The only thing I like about this hunk of garbage is that it is lighter than any of my other guitars. The tone is horrible! Way too simple of machine. Sounds like a rubber-band strechted over a tin can with a bobcat inside! Only one Invader humbucker(no offense Seymor Duncan), no tone variations at all. The neck is so slow that my grandma can walk a mile before I can even get half way through a major scale. The color is so girly that it makes me want to gag! (Surf Green) BPOC Big Piece Of Crap! It is acually put together pretty nice in Mexico! Yea baby. No whammy-bar makes it imposible to take dives or do any tremolo whats so ever. Do not get this guitar! Even if you are completely stupid, there is no reason for this chunk of cheap wood to even be in anyones home, let alone acually use it. Way too simple. Even too simple for a beginner. I put in the attick under some old clothes locked in a trunk so I never have to see or hear it ever again! Lyle Seversen rated this unit on 2003-12-08. I haven't bought it yet. I'm really holding out to get a black one. They tend to be more expensive because most places don't carry them any more. I got to play one at a Guitar Center. It cost 450 Unlike other tight wads, I LIKE the single humbucker/volume nob. I also like the high powered, overdriven sound of the Detonator humbucker. The guitar is heavier than most Strats. I'm 6'3 and pretty strong for my weight. I'd rather have a heavier guitar. Some one said the neck was slow. They're full of it. The guitar does have a thick neck, but people with long fingers like me (and presumably Tom DeLonge) find that more comfortable. It looks cool as well, but if you've seen one strat, you've seen 'em all. I don't like the fact that Fender didn't release this guitar before Tom could make it his signature model. Then, it would be cheaper than Standard Strats and be available in more colors. I also hate the fact that Musicians Friend, Guitar Center, and basically every other music store stopped carrying the black ones. The other irratating thing is I'm in a band, so I'll get a lot of flak for playing a signature model. It looks great. THe bdy is well made and well painted. It uses a Detonator, my favorite humbucker. It also has the seventies head stock. It's a great guitar, but don't just run out and buy it. It's my idea of the perfect guitar, but a lot of people either don't like it or they have rich parents who spend 500 dollars on them to have a Blink-182 guitar that they don't even know how to play. Juston Bondora rated this unit on 2003-08-07. I wanted the Tom Delonge Start so bad and I purchased it off of Musician's Friend for $500 I think the sound of the guitar is great. It is very easy to play. I also like the look of the guitar it is different from any other strat. There is nothing I don't like about the Tom Delonge Strat The construction and quality of this is excellent! If you are a beginner and want to cool nice looking guitar. Buy the Tom Delonge start it is fun and easy to play. Trisha rated this unit on 2003-06-09. I was stopping by Guitar Center at least twice a week searching for a guitar that would fit my playing style. I played them all. After 2 months I bough a TD Strat. I fell in love with the look and sound. I like it's looks, the big headstock, the classic shape of the body, the dark rosewood fretboard, the meaty frets, and that killer looking invader pick up. The sound works for me. Some people complain about it having only one tone. That's O.K. with me. I'm not a virtiouso, I'm not one of those players who constanly fiddle with the tone and volume knobs while there playing to find that "just right tone". I want to plug n play. And I want a wall of distortion! The quality on these guitars can be spoty. Look at it real close. Have one of the guitar guys look at it too. Guitar Center had 3 on the rack. The first 2 had some visible flaws, they also sounded bad. The third one was the charm. One of the bad ones had ripples on the pick guard. And the bridge was crooked. Shop carefully. Great! After passing on two others. Solid, fits me like a glove. Mine has everything put together well, worth the$500.00 I payed for it. Don't buy this gitar if you like to constanly mess with the 4 or more tone and volume knobs found on most guitars in search of that elusive perfect tone. It's a one size fits all guys. By the way, Tom is not the first to play a Strat with one pick up, volume knob. In the mid 70's another young guitarist put together a "homemade" Strat with the neck and body of diferent vintiges. He took out all three sigle coils, and put in a humbucker in the bridge position. He eventually became a guitar icon. His name is Eddie Van Halen. This particular guitar can be heard on Van Halens first album (now a classic). Final conclusion? If you are a down picker, like that hard sound, and want to keep things simple, then this is your axe. KAIROS rated this unit on 2002-12-19. I picked this baby at my local Guitar center.I got this strat for around 400 dollars on sale. It's around 450 dollars not on sale. I need a new guitar because my old Fender Squier was getting old and I was getting better. I found it was a great choice. I got this guitar because I heard a ton of great things about it. And I loved the great sound it came with. I also like it because it only has two pick ups which are right next to each other. It also has one voluem nob. I find that it really doesn't matter about thoes little things. The only thing I don't like about this guitar is that it's pretty hard to change the strings. This might be because my old Squier was really easy to change the strings. This guitar is constructed great. The neck is really nice wood and also very smooth. It surpising that this is a Mexican made guitar. All around it is very well construced. You don't have to be a real punk rocker (even tho I'm)to use this guitar. I love it I play it every day. Steve Olander (Steve o) rated this unit on 2002-11-30. About two years ago i was looking for a new guitar and i saw Tom Delonge playing a fender Strat with only one humbucker and i called every store in town and not one store had heard of it.. during that summer i finally saw one in a "Tom Lee music" store and tried it out. i LOVED it. so when i got back hom I called "Long&McQuade" (a local music store) and purchased one for about $700 (canadian funds) I really like the simple design of the guitar. you dont have to know about what kind of tone you want becase there is only one volume knob. i love the "Invader" Humbucker because it is the perfect pickup for punk. it gives you a Loud hard punchy sound and it is also great for clean So far i havent had any problems with this guitar This guitar is extremely good quality (it has falen over many times and has no damage) i love the vintage neck and large 70's head stock The bottom line is that if you love to play punk this is the guitar for you.. Simple yet powerful Mike rated this unit on 2002-11-13. The Tom Delonge strat caught my attention after I discovered Blink 182 which I still listen to older cds of, and I wanted it ever since I saw it. The Seymour Duncan Invader pickup grabbed my eye also. My parents gave it to me for my birthday, they bought it for five hundred dollars in northwest Indiana. -Seymour Duncan Invader -pearloid pickguard -finish -high quality neck the tuning machines were a big disapointment because they are a hassle to put the strings on. I plan on buying standard or Spurzel tuning machines shortly. The plastic cover over the pickguard (not the peely one) was chipping off a bit but it's not a big problem. The construction and quality is great, except maybe for the pickguard. The bottom line is I got exactly what I expected and this guitar is perfect for the type of music I was playing at the time. I wouldn't take it back if I had the chance. Andy rated this unit on 2002-09-18. I purchased the guitar at my local Guitar Center for around$450. It did not come with the gig bag that Fender advertises with it but I had a hard case to put it in, so no big deal. I bought this guitar as a back-up for my Fender Fat Strat that just happens to have a Seymour Duncan Invader in the bridge position as well (total coincidence!) I like it a lot because it's got the warmth and crunch of a humbucker, yet still maintains the bright tone of a Strat. The neck feels great and it's nice and light because of the minimal hardware. I've read a lot of reviews of people complaining about the guitar only having one pickup and one volume knob. I don't really need a lot of bells and whistles for the type of music I play. Plus, I figure if Eddie Van Halen, Steve Vai and George Lynch could play guitars with 1 pickup and 1 knob...then it's probably good enough for me as well. The only thing I don't really like about the guitar is the vintage tuners. They make changing strings a hassle. But I don't really have a problem with them staying in tune. I recommend Ernie Ball strings. The construction is very good for a Mexican guitar. It took some tweeking to set it up the way I like it. But the guitar seems very sturdy and reliable. You don't have to be a Blink 182 or Tom Delonge fan to like this guitar. Bobby Q. Ribb rated this unit on 2002-09-12. To tell you the truth, i didn't even buy it. It was in the store for like $500 and when i played it, i found out that you pay 50 bucks for the guitar and 450 for the name I did no like anything except that it was a guitar and thats better than not having one Somebody at my skool(i wont mention who he is,(glen) but hes an asshole)told me to check this out. In the discription it says "stripped down and ready to rock!"I want to personally find the guy who wrote that and punch him in the face. The thing's a piece of fuckin shit! thers only one humbucker and one volume nob, so theres no tone adjusting and the humbucker only provides a cruchy sound.The neck is smooth and ruogh in different places. Neck is very slow. Inlays stick out. The tuners are ok, but its no reason to buy because ofnice tuners. its a little on the heavy side. And i hate the hi-gloss finish. Probably durable so tom doesn't ruin it cuz he cant play. he's funny but he only plays power chords. Shit. a big flaming pile of shit. if i could give it a lower rating i would. if youlike being ripped off, or like exspensive firewood, by all means, go get it turd fergeson rated this unit on 2002-09-11. I didn't buy it, I played it several times at a local music store. Its got a good punk sound, its got a strat feel (not a very good one though) Soundwise it sucks, one sound, no tonal changes at all, No Tremelo because they said it was to complicated (your an idiot if you can't work one), I guess people can't bend a bar anymore. The headstock is ugly. I hate the jumbo frets on it. The fretboard overall feels like crap. Its built like a tank (which won't make a good strat). Its a crap job IMHO by fender just a get quick rich scheme it looks like. Don't buy it, buy a standard strat please. I mean if you are starting out and you wanna a cool guitar, you MAY want to get this guitar. DONT. You'll quickly relieze that the limited capabilities of this "instrument" are mind boggiling. And you'll kick yourself in the pants because of it. Kevin Kelly rated this unit on 2002-09-05. I got this guitar from musicians friend for about$500. The quality of the guitar is good. All the frets are dressed and it feels comfortable. The setup was a little out of wack when i got it (string hieght, intonation, etc.) but that was expected. After i adjusted it it was better. It played well and sounded good unamplified. When i plugged it in it sounded just as well. The clean sound was very good and trebly and distortion was all pretty good. Its a good guitar for playin straight ahead rock but not much else. The tuners frequently got out of tune even which was a hassle but there was no reason to change the tuners to any kind of locking tuners because theres no tremolo. Just sealed tuners will do. You are also limited to one sound out of your amp unless you dial in different settings for every song unless you have 3 or 4 equalizers. There isnt much too this guitar. Its almost too simple and you are stuck in one sound which isnt always a good thing though it can be sometimes. Good quality. This is the quality expected of the pricerange. It would be better if they threw in some good sealed tuners instead of the being stingy and throwing those crap vintage tuners around but hey that's the established industries for you. Not a good guitar for the kids and the blink-182 poseurs. I mean come on, in a few years ur tastes are definately gonna change and ur gonna be stuck with this one tone which is a good tone but still. You wont be able to experience the other great things about the electric guitar like a tremolo or a bridge pickup. I highly recommend this as a secondary guitar to a jackson or a les paul. Good guitar but too unreasonable for the beginner. I'd save my pennies for another year and get a jackson neck thru. its not that much more money anyway. Matt rated this unit on 2002-07-11. I got mine at Guitar center for 450, but they don't include a gig bag with it. Slight haggling got me a gig bag for 20 bucks, so 470 for the whole thing. The Delong strat sounds great and is extremely comfortable. I haven't been playing for that long so I didn't want somehting with a lot of switches and knobs, so I fell in love with it's simplicity. All you can do with this is plug it in and play it. You should know what kind of sound you're looking for and play it before you buy it. The one and only thing I don't like about it is that it comes out of tune really often. but how long does it take to tune a guitar? 2 minutes at the most? It's pretty much a non-issue. Look it over before you buy it. The first one I bought had an issue with the high e string poppinng out of the nut and getting stuck on the side of the neck. I broght it back and had it filed and that didn't help it at all. So Guitar center offered to give me a new one which I immediately took. The one I have no has no problems at all. Just look it over before you buy it and you shouldn't have any problems. Based on my experience with it, I would't order this from any mail order or internet site cause if you get a ba done, it could be a hassle to send it back. Get it from a local store. This is the guitar I'm learning to play on. It's perfect if you want to learn to play and don't want to learn on a piece of crap. There isn't much more I can say about it except 1. buy it from a store and not throguh the mail, and 2. look it over really well and play it before you buy it to avoid any issues. Super Modes rated this unit on 2002-05-03. After Blink 182's Tom Delonge hurt his back and cancelled their european tour, I was bummed. We were walking around Zuerich (Switzerland, you hick) and my girl caught sight of the guitar in the window of a shop. I paid one thousand swiss franks ($600). I was all cheered up then. I replaced the machines with Sperzel locking tuners and haven't been disappointed since. After replacing the tuners, it did exactly what it was built to do. No disappointments at all. I was bummed about the show being cancelled, though. The stooges who bought it only to be disappointed should have seen the componants and known exactly what they were in for. They should have played the silly thing first. I paid a bit more because it's imported to Switzerland, but only the tuners were a bit cheap. That's where Fender saves its money often. That's not a reason to take away points. That's why there's Sperzel and Schaller. Just fine. I play it. I don't play tennis with it, so I can't comment on its durability. If something's not right, it's probably adjustable (string height, bridge, etc). Fender didn't break any promises. It does what it's supposed to do. I'm getting a second one. That'll cheer me up even more. G. Galbraith rated this unit on 2002-03-18. i bought this at a local dealership. it cost me about$490 it is a very simple design which offers fat, meaty tone and sutain for punk rock. the hardtail bridge allows for making a sound unlike a standard fat strat. the only thing i can really think of is that it comes out of tune fairly often i really like mine in its grafitti yellow color. the vintage neck and headstock also gives it a nice vintage feel that i really like very good guitar, but for punk and pop punk only Drew rated this unit on 2002-03-03. This is a piece of crap that goes for arounf \$500. I didn't like everything else. This should be called the Tom Delonge Piece of Crap. 1 Seymor Duncan Invader humbucker, 1 volume nob and thats it. The Invader didnt impress me that much(I expected better from Seymor Duncan.) There hardly any tonal range. You 1 sound (and not a very good one. I got better sounds and a wider range of tone out of a Squire Strat(which is a better guitar). The action was too high and the sound had shrill highs. I personaly didnt like the giand frets, but maybe some people do. I dont know what that idiot was thinkin when he made this guitar. Thats Blink 182(and all those other stupid new bands), they cant play guitar for crap and dont know a thing about how good guitar should be. The construction quality was good over all except for the high action and those giant frets which I dont really like. Its a strat so its very comfortable(one of the few good things about this guitar). DONT BUY THIS GUITAR! IT SUCKS! Charles B. rated this unit on 2001-12-14. ## More Fender Electric_Guitars ### Fender Stratocaster Mexican \| Fender 97 Fender American Strat \| Fender Tom DeLonge Signature Model Stratocaster \| Fender Jagmaster \| Fender Super-Sonic \| Other Reviews & Articles Related to Electric_Guitars � Gear Review Network / MusicGearReview.com - 2000	2015-04-01 10:37:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1944756805896759, "perplexity": 2749.9556160079765}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-14/segments/1427131304444.86/warc/CC-MAIN-20150323172144-00140-ip-10-168-14-71.ec2.internal.warc.gz"}
http://sciencewise.info/	• #### On the Late-Time Behavior of Virasoro Blocks and a Classification of Semiclassical Saddles Recent work has demonstrated that black hole thermodynamics and information loss/restoration in AdS$_3$/CFT$_2$ can be derived almost entirely from the behavior of the Virasoro conformal blocks at large central charge, with relatively little dependence on the precise details of the CFT spectrum or OPE coefficients. Here, we elaborate on the non-perturbative behavior of Virasoro blocks by classifying all `saddles' that can contribute for arbitrary values of external and internal operator dimensions in the semiclassical large central charge limit. The leading saddles, which determine the naive semiclassical behavior of the Virasoro blocks, all decay exponentially at late times, and at a rate that is independent of internal operator dimensions. Consequently, the semiclassical contribution of high-energy states does not resolve a well-known version of the information loss problem in AdS$_3$. However, we identify two infinite classes of sub-leading saddles, and one of these classes does not decay at late times. Virasoro blocksMonodromyConformal field theoryOperator product expansionAnti de Sitter spaceCentral chargeClassificationInstantonBlack holeUnitarity... • #### A Geometric Formulation of Supersymmetry The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example, we introduce modified supersymmetry variations and redefined auxiliary fields that transform covariantly under reparametrizations. The resulting action and transformation laws are manifestly covariant and highlight the geometric structure of the supersymmetric theory. The covariant methods are developed first for general theories (not necessarily supersymmetric) whose scalar fields are coordinates of a Riemannian target space. SupersymmetryAuxiliary fieldCovariant transformationScalar fieldManifoldSupergravityCovariant derivativeCurvatureDiffeomorphismSuperpotential... • #### What galaxy masses perturb the local cosmic expansion? We use 12 cosmological $N$-body simulations of Local Group systems (the Apostle models; Sawala et al. 2016) to inspect the relation between the virial mass of the main haloes ($M_{\rm vir,1}$ and $M_{\rm vir,2}$), the mass derived from the relative motion of the halo pair ($M_{\rm tim}$), and that inferred from the local Hubble flow ($M_{\rm lhf}$). We show that within the Spherical Collapse Model (SCM), which provides an idealized description of structure formation in an expanding Universe, the correspondence between the three mass estimates is exact, i.e. $M_{\rm lhf}=M_{\rm tim}=M_{\rm vir,1}+M_{\rm vir,2}$. However, comparison with Apostle simulations reveals that, contrary to what the SCM states, a relatively large fraction of the mass that perturbs the local Hubble flow and drives the relative trajectory of the main galaxies is not contained within $R_{\rm vir}$, and that the amount of "extra-virial" mass tends to increase in galaxies with a slow accretion rate. In addition, we find that modelling the peculiar velocities around the Local Group returns an unbiased constraint on the virial mass ratio of the main galaxy pair ($f_m\equiv M_1/M_2\approx M_{\rm vir,1}/M_{\rm vir,2}$), as well as the individual masses of the main galaxies ($M_1$ and $M_2$) without a priori assumptions on the matter distribution nor the equilibrium state of these systems. Adopting Diemer \& Kravtsov (2014) outer halo profile, which scales as $\rho\sim R^{-4}$ at $R\gtrsim R_{\rm vir}$, indicates that $M_1$ and $M_2$ roughly correspond to the asymptotically-convergent (total) masses of the individual haloes. In contrast, we find that estimates of $M_{\rm vir}$ based on the dynamics of tracers at $R\gg R_{\rm vir}$ require a priori information on the internal matter distribution and the growth rate of the main galaxies, both of which are typically difficult to quantify. Virial massLocal groupHubble flowGalaxy massMilky WayExpansion of the UniverseKinematicsSpherical collapse modelNavarro-Frenk-White profileAccretion... • #### On Gravitational Chirality as the Genesis of Astrophysical Jets It has been suggested that single and double jets observed emanating from certain astrophysical objects may have a purely gravitational origin. We discuss new classes of plane-fronted and pulsed gravitational wave solutions to the equation for perturbations of Ricci-flat spacetimes around Minkowski metrics, as models for the genesis of such phenomena. These solutions are classified in terms of their chirality and generate a family of non-stationary spacetime metrics. Particular members of these families are used as backgrounds in analysing time-like solutions to the geodesic equation for test particles. They are found numerically to exhibit both single and double jet-like features with dimensionless aspect ratios suggesting that it may be profitable to include such backgrounds in simulations of astrophysical jet dynamics from rotating accretion discs involving electromagnetic fields. GeodesicAstrophysical jetGravitational waveChiralityHelicityGenesisCoframeAccretion diskProper timeGravitational fields... • #### Energy spectra of 3He-rich solar energetic particles associated with coronal waves In addition to their anomalous abundances, 3He-rich solar energetic particles (SEPs) show puzzling energy spectral shapes varying from rounded forms to power laws where the later are characteristics of shock acceleration. Solar sources of these particles have been often associated with jets and narrow CMEs, which are the signatures of magnetic reconnection involving open field. Recent reports on new associations with large-scale EUV waves bring new insights on acceleration and transport of 3He-rich SEPs in the corona. We examined energy spectra for 32 3He-rich SEP events observed by ACE at L1 near solar minimum in 2007-2010 and compared the spectral shapes with solar flare signatures obtained from STEREO EUV images. We found the events with jets or brightenings tend to be associated with rounded spectra and the events with coronal waves with power laws. This suggests that coronal waves may be related to the unknown second stage mechanism commonly used to interpret spectral forms of 3He-rich SEPs. Helium-3Solar energetic particlesSolar Terrestrial Relations ObservatoryAbundanceRadio burstsSolar minimumMagnetic reconnectionCoronaLarge Angle and Spectrometric CoronagraphSolar flare... • #### Programming quantum computers using 3-D puzzles, coffee cups, and doughnuts The task of programming a quantum computer is just as strange as quantum mechanics itself. But it now looks like a simple 3D puzzle may be the future tool of quantum software engineers. QubitOptimizationQuantum circuitQuantum computationQuantum technologyQuantum algorithmsQuantum programmingQuantum mechanicsArchitectureComputational modelling... • #### Twitter-Network Topic Model: A Full Bayesian Treatment for Social Network and Text Modeling Twitter data is extremely noisy -- each tweet is short, unstructured and with informal language, a challenge for current topic modeling. On the other hand, tweets are accompanied by extra information such as authorship, hashtags and the user-follower network. Exploiting this additional information, we propose the Twitter-Network (TN) topic model to jointly model the text and the social network in a full Bayesian nonparametric way. The TN topic model employs the hierarchical Poisson-Dirichlet processes (PDP) for text modeling and a Gaussian process random function model for social network modeling. We show that the TN topic model significantly outperforms several existing nonparametric models due to its flexibility. Moreover, the TN topic model enables additional informative inference such as authors' interests, hashtag analysis, as well as leading to further applications such as author recommendation, automatic topic labeling and hashtag suggestion. Note our general inference framework can readily be applied to other topic models with embedded PDP nodes. Topic modelTwitterSocial networkInferenceNetwork modelLatent Dirichlet allocationBayesianDirichlet processGaussian processCosine similarity... • #### Is the deconvolution layer the same as a convolutional layer? In this note, we want to focus on aspects related to two questions most people asked us at CVPR about the network we presented. Firstly, What is the relationship between our proposed layer and the deconvolution layer? And secondly, why are convolutions in low-resolution (LR) space a better choice? These are key questions we tried to answer in the paper, but we were not able to go into as much depth and clarity as we would have liked in the space allowance. To better answer these questions in this note, we first discuss the relationships between the deconvolution layer in the forms of the transposed convolution layer, the sub-pixel convolutional layer and our efficient sub-pixel convolutional layer. We will refer to our efficient sub-pixel convolutional layer as a convolutional layer in LR space to distinguish it from the common sub-pixel convolutional layer. We will then show that for a fixed computational budget and complexity, a network with convolutions exclusively in LR space has more representation power at the same speed than a network that first upsamples the input in high resolution space. TransposeNetworksResolution • #### A Panchromatic View of Relativistic Jets in Narrow-Line Seyfert 1 Galaxies The discovery by the Large Area Telescope on board Fermi of variable gamma-ray emission from radio-loud narrow-line Seyfert 1 (NLSy1) galaxies revealed the presence of a possible third class of Active Galactic Nuclei (AGN) with relativistic jets in addition to blazars and radio galaxies. Considering that NLSy1 are usually hosted in spiral galaxies, this finding poses intriguing questions about the nature of these objects and the formation of relativistic jets. We report on a systematic investigation of the gamma-ray properties of a sample of radio-loud NLSy1, including the detection of new objects, using 7 years of Fermi-LAT data with the new Pass 8 event-level analysis. In addition we discuss the radio-to-very-high-energy properties of the gamma-ray emitting NLSy1, their host galaxy, and black hole mass in the context of the blazar scenario and the unification of relativistic jets at different scales. Relativistic jetBlazarAstrophysical jetSingle background subtractionActive Galactic NucleiBlack holeFlat spectrum radio quasarSpectral energy distributionHost galaxyTest statistic... • #### Complete Reionization Constraints from Planck 2015 Polarization We conduct an analysis of the Planck 2015 data that is complete in reionization observables from the large angle polarization $E$-mode spectrum in the redshift range $6 < z < 30$. Based on 5 principal components, all of which are constrained by the data, this single analysis can be used to infer constraints on any model for reionization in the same range; we develop an effective likelihood approach for applying these constraints to models. By allowing for an arbitrary ionization history, this technique tests the robustness of inferences on the total optical depth from the usual step-like transition assumption, which is important for the interpretation of many other cosmological parameters such as the dark energy and neutrino mass. The Planck 2015 data not only allow a high redshift $z>15$ component to the optical depth but prefer it at the $2\sigma$ level. This preference is associated with excess power in the multipole range $10 \lesssim \ell \lesssim 20$ and may indicate high redshift ionization sources or unaccounted for systematics and foregrounds in the 2015 data. Principal componentIonizationReionizationPlanck missionCosmological parametersMonte Carlo Markov chainCosmic microwave backgroundBayesian posterior probabilityGravitational lensingMaximum likelihood... • #### Chiral medium produced by parallel electric and magnetic fields We compute (pseudo)critical temperature, $T_c$, of chiral symmetry restoration for quark matter in the background of parallel electric and magnetic fields. This field configuration leads to the production of a chiral medium on a time scale $\tau$, characterized by a nonvanishing value of the chiral density that equilibrates due to microscopic processes in the thermal bath. We estimate the relaxation time $\tau$ to be about $\approx 0.1-1$ fm/c around the chiral crossover; then we compute the effect of the fields and of the chiral medium on~$T_c$. We find $T_c$ to be lowered by the external fields in the chiral medium. Relaxation timeNambu-Jona-Lasinio modelChiralityQuantum chromodynamicsCritical temperatureQuark massQuark matterChiral anomalyChiral symmetryChiral symmetry breaking... • #### Direct Search for keV Sterile Neutrino Dark Matter with a Stable Dysprosium Target We investigate a new method to search for keV-scale sterile neutrinos that could account for Dark Matter. Neutrinos trapped in our galaxy could be captured on stable $^{163}$Dy if their mass is greater than 2.83~keV. Two experimental realizations are studied, an integral counting of $^{163}$Ho atoms in dysprosium-rich ores and a real-time measurement of the emerging electron spectrum in a dysprosium-based detector. The capture rates are compared to the solar neutrino and radioactive backgrounds. An integral counting experiment using several kilograms of $^{163}$Dy could reach a sensitivity for the sterile-to-active mixing angle $\sin^2\theta_{e4}$ of $10^{-5}$ significantly exceeding current laboratory limits. Mixing angles as low as $\sin^2\theta_{e4} \sim 10^{-7}$ / $\rm m_{^{163}\rm Dy}\rm{(ton)}$ could possibly be explored with a real-time experiment. Dark matterKeV sterile neutrinosCountingNeutrinoMixing angleSterile neutrinoElectron captureSolar neutrinoSterile neutrino DMNuisance parameter... • #### Lectures on the Quantum Hall Effectver. 2 The purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective Chern-Simons theories, and the modes which live on the boundary. The notes are aimed at graduate students in any discipline where $\hbar=1$. A working knowledge of quantum field theory is assumed. Contents: 1. The Basics (Landau levels and Berry phase). 2. The Integer Quantum Hall Effect. 3. The Fractional Quantum Hall Effect. 4. Non-Abelian Quantum Hall States. 5. Chern-Simons Theories. 6. Edge Modes. WavefunctionAnyonHamiltonianLandau levelQuantum Hall EffectLaughlin wavefunctionChern-Simons termGauge fieldChern-Simons theoryBerry phase... • #### EPR before EPR: a 1930 Einstein-Bohr thought experiment revisitedver. 4 In 1930 Einstein argued against consistency of the time-energy uncertainty relation by discussing a thought experiment involving a measurement of mass of the box which emitted a photon. Bohr seemingly triumphed over Einstein by arguing that the Einstein's own general theory of relativity saves the consistency of quantum mechanics. We revisit this thought experiment from a modern point of view at a level suitable for undergraduate readership and find that neither Einstein nor Bohr was right. Instead, this thought experiment should be thought of as an early example of a system demonstrating nonlocal "EPR" quantum correlations, five years before the famous Einstein-Podolsky-Rosen paper. Quantum mechanicsQuantum nonlocalityGeneral relativityQuantum correlationEntanglementHamiltonianEarthExperimental verificationEPR paradoxDegree of freedom... • #### Einstein's Boxesver. 2 At the 1927 Solvay conference, Einstein presented a thought experiment intended to demonstrate the incompleteness of the quantum mechanical description of reality. In the following years, the thought experiment was picked up and modified by Einstein, de Broglie, and several other commentators into a simple scenario involving the splitting in half of the wave function of a single particle in a box. In this paper we collect together several formulations of this thought experiment from the existing literature; analyze and assess it from the point of view of the Einstein-Bohr debates, the EPR dilemma, and Bell's theorem; and generally lobby for Einstein's Boxes taking its rightful place alongside similar but historically better-known quantum mechanical thought experiments such as EPR and Schroedinger's Cat. • #### EPR and Bell Localityver. 3 A new formulation of the EPR argument is presented, one which uses John Bell's mathematically precise local causality condition in place of the looser locality assumption which was used in the original EPR paper and on which Niels Bohr seems to have based his objection to the EPR argument. The new formulation of EPR bears a striking resemblance to Bell's derivation of his famous inequalities. The relation between these two arguments -- in particular, the role of EPR as part one of Bell's two-part argument for nonlocality -- is also discussed in detail. EPR paradoxQuantum mechanicsBell's theoremCompletenessHidden variable theoryRelativityCausalityQuantum theoryLight conesLocality principle... • #### Statistics of fractionalized excitations through threshold spectroscopy We show that the anyonic statistics of fractionalized excitations display characteristic signatures in threshold spectroscopic measurements. Drawing motivation from topologically ordered phases such as gapped quantum spin liquids and fractional chern insulators which possess fractionalized excitations, we consider gapped systems with abelian anyonic excitations. The low energy onset of associated correlation functions near the threshold show universal behaviour depending on the statistics of the anyons. This explains some recent theoretical results in spin systems and also provides a route towards detecting statistics in experiments such as neutron scattering and tunneling spectroscopy. StatisticsAnyonSpin liquidTwo-point correlation functionHamiltonianDynamic structure factorInsulatorsTunneling spectroscopyNeutron scatteringHarmonic oscillator... • #### Matrix product states and equivariant topological field theories for bosonic symmetry-protected topological phases in (1+1) dimensions Matrix Product States (MPSs) provide a powerful framework to study and classify gapped quantum phases --symmetry-protected topological (SPT) phases in particular--defined in one dimensional lattices. On the other hand, it is natural to expect that gapped quantum phases in the limit of zero correlation length are described by topological quantum field theories (TFTs or TQFTs). In this paper, for (1+1)-dimensional bosonic SPT phases protected by symmetry $G$, we bridge their descriptions in terms of MPSs, and those in terms of $G$-equivariant TFTs. In particular, for various topological invariants (SPT invariants) constructed previously using MPSs, we provide derivations from the point of view of (1+1) TFTs. We also discuss the connection between boundary degrees of freedom, which appear when one introduces a physical boundary in SPT phases, and "open" TFTs, which are TFTs defined on spacetimes with boundaries. Topological field theoryMatrix product statesSymmetry protected topological orderTopological invariantPartition functionOrientationTime-reversal symmetryDegree of freedomGroup cohomologyTorus... • #### Topological Field Theory and Matrix Product States It is believed that most (perhaps all) gapped phases of matter can be described at long distances by Topological Quantum Field Theory (TQFT). On the other hand, it has been rigorously established that in 1+1d ground states of gapped Hamiltonians can be approximated by Matrix Product States (MPS). We show that the state-sum construction of 2d TQFT naturally leads to MPS in their standard form. In the case of systems with a global symmetry G, this leads to a classification of gapped phases in 1+1d in terms of Morita-equivalence classes of G-equivariant algebras. Non-uniqueness of the MPS representation is traced to the freedom of choosing an algebra in a particular Morita class. In the case of Short-Range Entangled phases, we recover the group cohomology classification of SPT phases. Topological field theoryMatrix product statesHamiltonianProjective representationPartition functionClassificationHolonomyRenormalization groupManifoldGauge field... • #### Strictification of weakly equivariant Hopf algebrasver. 3 A weakly equivariant Hopf algebra is a Hopf algebra A with an action of a finite group G up to inner automorphisms. We show that each weakly equivariant Hopf algebra can be replaced by a Morita equivalent algebra B with a strict action of G and with a coalgebra structure that leads to a tensor equivalent representation category. However, the coproduct of this strictification cannot, in general, be chosen to be unital, so that a strictification of the G-action can only be found on a weak Hopf algebra B. Hopf algebraInner automorphismTensor productTopological field theoryOrbifoldAutomorphismIsomorphismDualityConformal field theoryVector space... • #### Surprises with Nonrelativistic Naturalness We explore the landscape of technical naturalness for nonrelativistic systems, finding surprises which challenge and enrich our relativistic intuition already in the simplest case of a single scalar field. While the immediate applications are expected in condensed matter and perhaps in cosmology, the study is motivated by the leading puzzles of fundamental physics involving gravity: The cosmological constant problem and the Higgs mass hierarchy problem. PhononShift symmetryTechnical NaturalnessNaturalnessScalar fieldClassificationGraph theoryHiggs boson massSuperconductivityCosmology... • #### Holographic Renormalization of Einstein-Maxwell-Dilaton Theoriesver. 2 We generalize the boundary value problem with a mixed boundary condition that involves the gauge and scalar fields in the context of Einstein-Maxwell-Dilaton theories. In particular, the expectation value of the dual scalar operator can be a function of the expectation value of the current operator. The properties are prevalent in a fixed charge ensemble because the conserved charge is shared by both fields through the dilaton coupling, which is also responsible for non-Fermi liquid properties. We study the on-shell action and the stress energy tensor to note practical importances of the boundary value problem. In the presence of the scalar fields, physical quantities are not fully fixed due to the finite boundary terms that manifest in the massless scalar or the scalar with mass saturating the Breitenlohner-Freedman bound. Expectation ValueGauge fieldField theoryScalar fieldAnti de Sitter spaceDilatonRenormalizationMixed boundary conditionQuantizationRadiative correction... • #### SpaceTime from Hilbert Space: Decompositions of Hilbert Space as Instances of Timever. 2 There has been recent interest in identifying entanglement as the fundamental concept from which space may emerge. We note that the particular way that a Hilbert space is decomposed into tensor factors is important in what the resulting geometry looks like. We then propose that time may be regarded as a variable that parameterizes a family of such decompositions, thus giving rise to a family of spatial geometries. As a proof of concept, this idea is demonstrated in two toy models based on Kitaev's toric code, which feature a dynamical change of dimension and topology. Mutual informationEmbeddingGraphToric codeStarTorusEntanglementHamiltonianEntropyManifold... • #### Classically stable non-singular cosmological bouncesver. 2 One of the fundamental questions of theoretical cosmology is whether the universe can undergo a non-singular bounce, i.e., smoothly transit from a period of contraction to a period of expansion through violation of the null energy condition (NEC) at energies well below the Planck scale and at finite values of the scale factor such that the entire evolution remains classical. A common claim has been that a non-singular bounce either leads to ghost or gradient instabilities or a cosmological singularity. In this letter, we examine cubic Galileon theories and present a procedure for explicitly constructing examples of a non-singular cosmological bounce without encountering any pathologies and maintaining a sub-luminal sound speed for co-moving curvature modes throughout the NEC violating phase. We also discuss the relation between our procedure and earlier work. Null energy conditionInstabilityCurvature perturbationScalar fieldSpeed of soundFriedmann Robertson WalkerGalileon modelPlanck scaleScale factorFriedmann equations... • #### Absolute Stability and Spatiotemporal Long-Range Order in Floquet systemsver. 3 Recent work has shown that a variety of novel phases of matter arise in periodically driven Floquet systems. Among these are many-body localized phases which spontaneously break global symmetries and exhibit novel multiplets of Floquet eigenstates separated by quantized quasienergies. Here we show that these properties are stable to all weak local deformations of the underlying Floquet drives -- including those that explicitly break the defining symmetries -- and that the models considered until now occupy sub-manifolds within these larger "absolutely stable" phases. While these absolutely stable phases have no explicit global symmetries, they spontaneously break Hamiltonian dependent emergent symmetries, and thus continue to exhibit the novel multiplet structure. The multiplet structure in turn encodes characteristic oscillations of the emergent order parameter at multiples of the fundamental period. Altogether these phases exhibit a form of simultaneous long-range order in space and time which is new to quantum systems. We describe how this spatiotemporal order can be detected in experiments involving quenches from a broad class of initial states. HamiltonianGlobal symmetrySymmetry protected topological orderCat stateQuenchingDomain wallTopological orderWeak localizationSpin glassIncommensurate... • #### Holographic Wilson Loopsver. 3 We show that all half-BPS Wilson loop operators in N=4 SYM -- which are labeled by Young tableaus -- have a gravitational dual description in terms of D5-branes or alternatively in terms of D3-branes in AdS_5xS^5. We prove that the insertion of a half-BPS Wilson loop operator in the cal N=4 SYM path integral is achieved by integrating out the degrees of freedom on a configuration of bulk D5-branes or alternatively on a configuration of bulk D3-branes. The bulk D5-brane and D3-brane descriptions are related by bosonization. • #### An advanced Study on Cryptography Mechanisms for Wireless Sensor Networks Wireless Sensor Network (WSN) is consisting of independent and distributed sensors to monitor physical or environmental conditions, such as temperature, sound, pressure, etc. The most crucial and fundamental challenge facing WSN is security. Due to minimum capacity in-term of memory cost, processing and physical accessibility to sensors devices the security attacks are problematic. They are mostly deployed in open area, which expose them to different kinds of attacks. In this paper, we present an illustration of different attacks and vulnerabilities in WSN. Then we describe and analyze security requirement, countermeasures based on cryptography mechanisms in literature. Finally, we present possible directions in future research. Sensor networkCryptographySecurityTemperaturePressure... • #### Abundances of Suprathermal Heavy Ions in CIRs during the Minimum of Solar Cycle 23 In this paper we examine the elemental composition of the 0.1-1 MeV/nucleon interplanetary heavy ions from H to Fe in corotating interaction regions (CIRs) measured by the SIT (Suprathermal Ion Telescope) instrument. We use observations taken on board the STEREO spacecraft from January 2007 through December 2010, which included the unusually long solar minimum following solar cycle 23. During this period instruments on STEREO observed more than 50 CIR events making it possible to investigate CIR ion abundances during solar minimum conditions with unprecedented high statistics. The observations reveal annual variations of relative ion abundances in the CIRs during the 2007-2008 period as indicated by the He/H, He/O and Fe/O elemental ratios. We discuss possible causes of the variability in terms of the helium focusing cone passage and heliolatitude dependence. The year 2009 was very quiet in CIR event activity. In 2010 the elemental composition in CIRs were influenced by sporadic solar energetic particle (SEP) events. The 2010 He/H and He/O abundance ratios in CIRs show large event to event variations with values resembling the SEP-like composition. This finding points out that the suprathermal SEPs could be the source population for CIR acceleration. Solar cycle 23South ecliptic poleSolar Terrestrial Relations ObservatorySolar minimumTelescopesAbundance ratioStatisticsSolar energetic particlesHelium Focusing ConeIon... • #### Simulation of a Time-Of-Flight Telescope for Suprathermal Ions in the Heliosphere A Monte Carlo code based on Geant 3.21 has been used for simulations of energy losses and angular scattering in a time-of-flight Suprathermal Ion Telescope (SIT) on the Solar-Terrestrial Relations Observatory (STEREO). A hemispherical isotropic particle distribution, a monoenergetic or power law in energy is used in these simulations. The impact of scattering, energy losses and system noise on the instrument mass resolution is discussed. TelescopesTime-of-flightHeliosphereSolar Terrestrial Relations ObservatoryMonte Carlo methodIonEnergyScatteringResolutionParticles... • #### Abundances of Suprathermal Heavy Ions in CIRs on STEREO during the Minimum of Solar Cycle 23 We examine the composition of the 0.1 - 1 MeV/n interplanetary heavy ions from H to Fe in corotating interaction regions (CIRs) measured by the SIT (Suprathermal Ion Telescope) instrument. We use observations taken on board the two STEREO spacecraft during the unusually long minimum of Solar Cycle 23 from January 2007 through December 2010. During this period instruments on STEREO observed more than 50 CIR events making it possible to investigate CIR ion abundances during solar minimum conditions with unprecedentedly high statistics. The observations reveal annual variations of relative ion abundances in the CIRs during the 2007 - 2008 period. In 2010 the elemental composition in CIRs were influenced by solar energetic particle events. Solar Terrestrial Relations ObservatorySouth ecliptic poleSolar cycle 23Pickup ionsAbundance ratioIntensityChemical abundanceSolar minimumTelescopesSolar wind... • #### Recurring 3He-rich Solar Energetic Particle Events Using the SIT instrument aboard STEREO we have examined the abundance of the 3He during the ascending phase of solar cycle 24 from January 2010 through December 2012. We report on several cases when 3He-rich solar energetic particle events were successively observed on ACE and STEREO-A with delays consistent with the Carrington rotation rate. In the investigated period ACE and STEREO-A were significantly separated in the heliolongitude corresponding to solar rotation times of 5 to 10 days. We inspect STEREO-A EUV images and use the potential-field source-surface extrapolations together with in-situ magnetic field data to identify responsible solar sources. We find the 3He/4He ratio highly variable in these events and correlated between the spacecraft for the cases with the same connection region on the Sun. South ecliptic poleSolar energetic particlesEclipticParker spiralAbundanceX-ray flaresHelium-3EarthSunSolar Terrestrial Relations Observatory... • #### Case studies of multi-day 3He-rich solar energetic particle periods Context. Impulsive solar energetic particle events in the inner heliosphere show the long-lasting enrichment of 3He. Aims. We study the source regions of long-lasting 3He-rich solar energetic particle (SEP) events Methods. We located the responsible open magnetic field regions, we combined potential field source surface extrapolations (PFSS) with the Parker spiral, and compared the magnetic field of the identified source regions with in situ magnetic fields. The candidate open field regions are active region plages. The activity was examined by using extreme ultraviolet (EUV) images from the Solar Dynamics Observatory (SDO) and STEREO together with radio observations from STEREO and WIND. Results. Multi-day periods of 3He-rich SEP events are associated with ion production in single active region. Small flares or coronal jets are their responsible solar sources. We also find that the 3He enrichment may depend on the occurrence rate of coronal jets. Solar energetic particlesSouth ecliptic poleHelium-3Solar Terrestrial Relations ObservatorySolar Dynamics ObservatoryWINDPlageParker spiralHeliospherePeriodate... • #### Long-lived energetic particle source regions on the Sun Discovered more than 40 years ago, impulsive solar energetic particle (SEP) events are still poorly understood. The enormous abundance enhancement of the rare 3He isotope is the most striking feature of these events, though large enhancements in heavy and ultra-heavy nuclei are also observed. Recurrent 3He-rich SEPs in impulsive events have only been observed for limited time periods, up to a few days which is typically the time that a single stationary spacecraft is magnetically connected to the source active regions on the Sun. With the launch of the two STEREO spacecraft we now have the possibility of longer connection time to solar active regions. We examined the evolution of source regions showing repeated 3He-rich SEP emissions for relatively long time periods. We found that recurrent 3He-rich SEPs in these long-lived sources occur after the emergence of magnetic flux. South ecliptic poleSunAbundanceEarthSolar Terrestrial Relations ObservatorySolar energetic particlesSolar activityInterplanetary magnetic fieldIsotopeHelium-3... • #### Observations of EUV Waves in 3He-Rich Solar Energetic Particle Events Small 3He-rich solar energetic particle (SEP) events with their anomalous abundances, markedly different from solar system, provide evidence for a unique acceleration mechanism that operates routinely near solar active regions. Although the events are sometimes accompanied by coronal mass ejections (CMEs) it is believed that mass and isotopic fractionation is produced directly in the flare sites on the Sun. We report on a large-scale extreme ultraviolet (EUV) coronal wave observed in association with 3He-rich SEP events. In the two examples discussed, the observed waves were triggered by minor flares and appeared concurrently with EUV jets and type III radio bursts but without CMEs. The energy spectra from one event are consistent with so-called class-1 (characterized by power laws) while the other with class-2 (characterized by rounded 3He and Fe spectra) 3He-rich SEP events, suggesting different acceleration mechanisms in the two. The observation of EUV waves suggests that large-scale disturbances, in addition to more commonly associated jets, may be responsible for the production of 3He-rich SEP events. South ecliptic poleCoronal mass ejectionRadio burstsSolar energetic particlesSolar activityIntensitySunTurbulenceAbundanceMeridian... • #### Observations of solar X-ray and EUV jets and their related phenomenaver. 2 Solar jets are fast-moving, elongated brightenings related to ejections seen in both images and spectra on all scales from barely visible chromospheric jets to coronal jets extending up to a few solar radii. The largest, most powerful jets are the source of type III radio bursts, energetic electrons and ions with greatly enhanced $^3$He and heavy element abundances. The frequent coronal jets from polar and equatorial coronal holes may contribute to the solar wind. The primary acceleration mechanism for all jets is believed to be release of magnetic stress via reconnection; however the energy buildup depends on the jets' source environment. In this review, we discuss how certain features of X-ray and EUV jets, such as their repetition rate and association with radio emission, depends on their underlying photospheric field configurations (active regions, polar and equatorial coronal holes, and quiet Sun). Coronal holeSunspotGalaxy filamentPlageQuiet sunRadio burstsSouth ecliptic polePhotosphereChromospherePenumbra... • #### Association of 3He-Rich Solar Energetic Particles with Large-Scale Coronal Waves Small 3He-rich solar energetic particle (SEP) events have been commonly associated with extreme-ultraviolet (EUV) jets and narrow coronal mass ejections (CMEs) which are believed to be the signatures of magnetic reconnection involving field lines open to interplanetary space. The elemental and isotopic fractionation in these events are thought to be caused by processes confined to the flare sites. In this study we identify 32 3He-rich SEP events observed by the Advanced Composition Explorer near the Earth during the solar minimum period 2007-2010 and examine their solar sources with the high resolution Solar Terrestrial Relations Observatory (STEREO) EUV images. Leading the Earth, STEREO-A provided for the first time a direct view on 3He-rich flares, which are generally located on the Sun's western hemisphere. Surprisingly, we find that about half of the 3He-rich SEP events in this survey are associated with large-scale EUV coronal waves. An examination of the wave front propagation, the source-flare distribution and the coronal magnetic field connections suggests that the EUV waves may affect the injection of 3He-rich SEPs into interplanetary space. Coronal mass ejectionRadio burstsHelium-3EarthSunSolar energetic particlesIntensityX-ray flaresInterplanetary magnetic fieldMagnetic reconnection... • #### On conservation laws in quantum mechanics We raise fundamental questions about the very meaning of conservation laws in quantum mechanics and we argue that the standard way of defining conservation laws, while perfectly valid as far as it goes, misses essential features of nature and has to be revisited and extended. HamiltonianQuantum mechanicsCausalityPlane waveConserved quantitiesRelativityFree propagatorWave packetPast light conesStatistical ensemble... • #### A new view on quantum electrodynamics We analyze the equations of quantum electrodynamics and establish that the electron must be described by two bispinors that satisfy two mutually connected Dirac equations. The equations of the electronic and electromagnetic fields are reformulated in terms of c-numbers, which enables one to elucidate the structure of the electron. Although the equations obtained allow only for numerical solution, some characteristics of the electron, in particular its size, can be found at this stage. It is shown also that the Dirac equation should, instead of the mass of the electron, contain a combination involving the electron Compton wavelength. In this case the equations obtained can be used not only for the description of the electron but also for the description of other leptons, which will allow one to find the mass spectrum of leptons. Quantum electrodynamicsBispinorMass spectrumCompton wavelengthElectronLeptonsDirac equationMassElectromagnetic field... • #### A new interpretation of quantum mechanics The present paper is based upon equations obtained in an earlier paper by the author devoted to a new formulation of quantum electrodynamics. The equations describe the structure of the electron as well as its motion in external fields, interaction with a measuring apparatus inclusive, in a deterministic manner without any jumps. Quantum mechanics is an approximate theory because its equations follow from the above equations upon neglecting the self-field of the electron itself. Just this leads to paradoxes, seeming contradictions and jumps in quantum mechanics. The quantum mechanical wavefunction has a dual interpretation. In some problems the square of its modulus represents a real distribution of the electronic density while in others the same square determines the probability distribution of coordinates. It is shown why, given the different interpretations of the wavefunction, it satisfies one and the same Dirac or Schr\"odinger equation. Description of many-electron systems is also considered in the starting approach as well as in quantum mechanics. Neutrinos are discussed in brief. Quantum mechanicsInterpretations of quantum mechanicsWavefunctionSelf fieldElectronic densityQuantum electrodynamicsNeutrinoElectronContradictionProbability... • #### Collision geometry fluctuations and triangular flow in heavy-ion collisionsver. 3 We introduce the concepts of participant triangularity and triangular flow in heavy-ion collisions, analogous to the definitions of participant eccentricity and elliptic flow. The participant triangularity characterizes the triangular anisotropy of the initial nuclear overlap geometry and arises from event-by-event fluctuations in the participant-nucleon collision points. In studies using a multi-phase transport model (AMPT), a triangular flow signal is observed that is proportional to the participant triangularity and corresponds to a large third Fourier coefficient in two-particle azimuthal correlation functions. Using two-particle azimuthal correlations at large pseudorapidity separations measured by the PHOBOS and STAR experiments, we show that this Fourier component is also present in data. Ratios of the second and third Fourier coefficients in data exhibit similar trends as a function of centrality and transverse momentum as in AMPT calculations. These findings suggest a significant contribution of triangular flow to the ridge and broad away-side features observed in data. Triangular flow provides a new handle on the initial collision geometry and collective expansion dynamics in heavy-ion collisions. Triangular flowElliptic flowEccentricityHeavy ion collisionTransverse momentumTwo-particle azimuthal correlationsReaction planeCentrality of collisionTwo-point correlation functionAzimuthal correlation... • #### Principal component analysis of event-by-event fluctuationsver. 2 We apply principal component analysis to the study of event-by-event fluctuations in relativistic heavy-ion collisions. This method brings out all the information contained in two-particle correlations in a physically transparent way. We present a guide to the method, and apply it to multiplicity fluctuations and anisotropic flow, using ALICE data and simulated events. In particular, we study elliptic and triangular flow fluctuations as a function of transverse momentum and rapidity. This method reveals previously unknown subleading modes in both rapidity and transverse momentum for the momentum distribution as well as elliptic and triangular flows. RapidityAnisotropic flowPrincipal componentTransverse momentumTriangular flowPrincipal component analysisEvent-by-event fluctuationsALICE experimentAzimuthHeavy ion collision... • #### Why does deep and cheap learning work so well? We show how the success of deep learning depends not only on mathematics but also on physics: although well-known mathematical theorems guarantee that neural networks can approximate arbitrary functions well, the class of functions of practical interest can be approximated through "cheap learning" with exponentially fewer parameters than generic ones, because they have simplifying properties tracing back to the laws of physics. The exceptional simplicity of physics-based functions hinges on properties such as symmetry, locality, compositionality and polynomial log-probability, and we explore how these properties translate into exceptionally simple neural networks approximating both natural phenomena such as images and abstract representations thereof such as drawings. We further argue that when the statistical process generating the data is of a certain hierarchical form prevalent in physics and machine-learning, a deep neural network can be more efficient than a shallow one. We formalize these claims using information theory and discuss the relation to renormalization group procedures. Various "no-flattening theorems" show when these efficient deep networks cannot be accurately approximated by shallow ones without efficiency loss - even for linear networks. Neural networkEllipticityHamiltonianDeep learningStatisticsMachine learningRenormalizationClassificationDeep Neural NetworksActivation function... • #### Deep Networks with Stochastic Depthver. 3 Very deep convolutional networks with hundreds of layers have led to significant reductions in error on competitive benchmarks. Although the unmatched expressiveness of the many layers can be highly desirable at test time, training very deep networks comes with its own set of challenges. The gradients can vanish, the forward flow often diminishes, and the training time can be painfully slow. To address these problems, we propose stochastic depth, a training procedure that enables the seemingly contradictory setup to train short networks and use deep networks at test time. We start with very deep networks but during training, for each mini-batch, randomly drop a subset of layers and bypass them with the identity function. This simple approach complements the recent success of residual networks. It reduces training time substantially and improves the test error significantly on almost all data sets that we used for evaluation. With stochastic depth we can increase the depth of residual networks even beyond 1200 layers and still yield meaningful improvements in test error (4.91% on CIFAR-10). ArchitectureSurvival probabilityHyperparameterConvolutional neural networkTraining setOverfittingNeural networkCOCO simulationInformation flowHidden layer... • #### Total Variation Applications in Computer Vision The objectives of this chapter are: (i) to introduce a concise overview of regularization; (ii) to define and to explain the role of a particular type of regularization called total variation norm (TV-norm) in computer vision tasks; (iii) to set up a brief discussion on the mathematical background of TV methods; and (iv) to establish a relationship between models and a few existing methods to solve problems cast as TV-norm. For the most part, image-processing algorithms blur the edges of the estimated images, however TV regularization preserves the edges with no prior information on the observed and the original images. The regularization scalar parameter {\lambda} controls the amount of regularization allowed and it is an essential to obtain a high-quality regularized output. A wide-ranging review of several ways to put into practice TV regularization as well as its advantages and limitations are discussed. RegularizationImage ProcessingAlgorithmsObjectiveScalar... • #### Improving Initial Conditions for Cosmological $N$-Body Simulationsver. 3 In cosmological $N$-body simulations, the representation of dark matter as discrete "macroparticles" suppresses the growth of structure, such that simulations no longer reproduce linear theory on small scales near $k_{\rm Nyquist}$. Marcos et al. demonstrate that this is due to sparse sampling of modes near $k_{\rm Nyquist}$ and that the often-assumed continuum growing modes are not proper growing modes of the particle system. We develop initial conditions that respect the particle linear theory growing modes and then rescale the mode amplitudes to account for growth suppression. These ICs also allow us to take advantage of our very accurate $N$-body code Abacus to implement 2LPT in configuration space. The combination of 2LPT and rescaling improves the accuracy of the late-time power spectra, halo mass functions, and halo clustering. In particular, we achieve 1% accuracy in the power spectrum down to $k_{\rm Nyquist}$, versus $k_{\rm Nyquist}/4$ without rescaling or $k_{\rm Nyquist}/13$ without 2LPT, relative to an oversampled reference simulation. We anticipate that our 2LPT will be useful for large simulations where FFTs are expensive and that rescaling will be useful for suites of medium-resolution simulations used in cosmic emulators and galaxy survey mock catalogs. Code to generate initial conditions is available at https://github.com/lgarrison/zeldovich-PLT Second order lagrangian perturbation theoryZeldovich approximationInitial conditions for cosmological simulationsGlassTwo-point correlation functionRankSpherical OverdensityFast Fourier transformFriends of friends algorithmHalo mass function... • #### Stellar clusterings around "Isolated" Massive YSOs in the LMC Observations suggest that there is a significant fraction of O-stars in the field of the Milky Way that appear to have formed in isolation or in low mass clusters ($<$100 $M_\odot$). The existence of these high-mass stars that apparently formed in the field challenges the generally accepted paradigm, which requires star formation to occur in clustered environments. In order to understand the physical conditions for the formation of these stars, it is necessary to observe isolated high-mass stars while they are still forming. With the $Hubble$ $Space$ $Telescope$, we observe the seven most isolated massive ($>$8 $M_\odot$) young stellar objects (MYSOs) in the Large Magellanic Cloud (LMC). The observations show that while these MYSOs are remote from other MYSOs, OB associations, and even from known giant molecular clouds, they are actually not isolated at all. Imaging reveals $\sim$100 to several hundred pre--main-sequence (PMS) stars in the vicinity of each MYSO. These previously undetected PMS stars form prominent compact clusters around the MYSOs, and in most cases they are also distributed sparsely across the observed regions. Contrary to what previous high-mass field star studies show, these observations suggest that high-mass stars may not be able to form in clusters with masses less than 100 $M_\odot$. If these MYSOs are indeed the best candidates for isolated high-mass star formation, then the lack of isolation is at odds with random sampling of the IMF. Moreover, while isolated MYSOs may not exist, we find evidence that isolated clusters containing O-stars can exist, which in itself is rare. Large Magellanic CloudHigh mass starYoung stellar objectStar formationStarO starPre-main-sequence starHigh massTelescopesOB associations... • #### Planck 2015 results. XIX. Constraints on primordial magnetic fieldsver. 2 We compute and investigate four types of imprint of a stochastic background of primordial magnetic fields (PMFs) on the cosmic microwave background (CMB) anisotropies: the impact of PMFs on the CMB spectra; the effect on CMB polarization induced by Faraday rotation; the impact of PMFs on the ionization history; magnetically-induced non-Gaussianities; and the magnetically-induced breaking of statistical isotropy. Overall, Planck data constrain the amplitude of PMFs to less than a few nanogauss. In particular, individual limits coming from the analysis of the CMB angular power spectra, using the Planck likelihood, are $B_{1\,\mathrm{Mpc}}< 4.4$ nG (where $B_{1\,\mathrm{Mpc}}$ is the comoving field amplitude at a scale of 1 Mpc) at 95% confidence level, assuming zero helicity, and $B_{1\,\mathrm{Mpc}}< 5.6$ nG for a maximally helical field.For nearly scale-invariant PMFs we obtain $B_{1\,\mathrm{Mpc}}<2.0$ nG and $B_{1\,\mathrm{Mpc}}<0.9$ nG if the impact of PMFs on the ionization history of the Universe is included. From the analysis of magnetically-induced non-Gaussianity we obtain three different values, corresponding to three applied methods, all below 5 nG. The constraint from the magnetically-induced passive-tensor bispectrum is $B_{1\,\mathrm{Mpc}}< 2.8$ nG. A search for preferred directions in the magnetically-induced passive bispectrum yields $B_{1\,\mathrm{Mpc}}< 4.5$ nG, whereas the the compensated-scalar bispectrum gives $B_{1\,\mathrm{Mpc}}< 3$ nG. The analysis of the Faraday rotation of CMB polarization by PMFs uses the Planck power spectra in $EE$ and $BB$ at 70 GHz and gives $B_{1\,\mathrm{Mpc}}< 1380$ nG. In our final analysis, we consider the harmonic-space correlations produced by Alfv\'en waves, finding no significant evidence for the presence of these waves. Together, these results comprise a comprehensive set of constraints on possible PMFs with Planck data. Cosmological magnetic fieldBispectrumCosmic microwave backgroundFaraday rotationHelicityNon-GaussianityScale invarianceAlfvén waveCMB temperature anisotropyAnisotropy...	2016-09-26 17:17:48	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6206566691398621, "perplexity": 2004.9662671726996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-40/segments/1474738660871.1/warc/CC-MAIN-20160924173740-00081-ip-10-143-35-109.ec2.internal.warc.gz"}
https://math.gatech.edu/seminars-colloquia/series/geometry-topology-seminar/subhadip-dey-20220131	## Stein property of complex-hyperbolic Kleinian groups Series Geometry Topology Seminar Time Monday, January 31, 2022 - 2:00pm for 1 hour (actually 50 minutes) Location Online Speaker Let M be a complex-hyperbolic n-manifold, i.e. a quotient of the complex-hyperbolic n-space $\mathbb{H}^n_\mathbb{C}$ by a torsion-free discrete group of isometries, $\Gamma = \pi_1(M)$. Suppose that M is convex-cocompact, i.e. the convex core of M is a nonempty compact subset. In this talk, we will discuss a sufficient condition on $\Gamma$ in terms of the growth-rate of its orbits in $\mathbb{H}^n_\mathbb{C}$ for which M is a Stein manifold. We will also talk about some interesting questions related to this result. This is a joint work with Misha Kapovich.	2022-08-08 03:48:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6843546628952026, "perplexity": 968.7347796407053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882570765.6/warc/CC-MAIN-20220808031623-20220808061623-00206.warc.gz"}
https://www.omnicalculator.com/statistics/dice	# Dice Probability Calculator Created by Wojciech Sas, PhD Reviewed by Bogna Szyk and Jack Bowater Last updated: Feb 05, 2023 The dice probability calculator is a great tool if you want to estimate the dice roll probability over numerous variants. There are many different polyhedral dice included, so you can explore the likelihood of a 20-sided die as well as that of a regular cubic die. So, just evaluate the odds, and play a game! You'll also find short descriptions of each option in the text. 🔎 Don't you have any physical dice? No problem - try our dice roller calculator! ## Polyhedral dice Everybody knows what a regular 6-sided die is, and, most likely, many of you have already played thousands of games where t used one (or more) But, did you know that there are different types of die? Out of the countless possibilities, the most popular dice are included in the Dungeons & Dragons dice set, which contains seven different polyhedral dice: • 4 sided dice, also known as a tetrahedron — each face is an equilateral triangle; • 6 sided dice, a classic cube — each face is a square; • 8 sided dice, also known as an octahedron — each face is an equilateral triangle; • 10 sided dice, also known as a pentagonal trapezohedron — each face is a kite; • 12 sided dice, also known as a dodecahedron — each face is a regular pentagon; and • 20 sided dice, also known as an icosahedron — each face is an equilateral triangle. 💡 You can master your D&D strategy using Omni's point buy calculator 5e. Don't worry, we take each of these dice into account in our dice probability calculator. You can choose whichever you like, and e.g., pretend to roll five 20-sided dice at once! ## How to calculate dice roll probability? Well, the question is more complex than it seems at first glance, but you'll soon see that the answer isn't that scary! It's all about maths and statistics. First of all, we have to determine what kind of dice roll probability we want to find. We can distinguish a few, which you can see in this dice probability calculator. Before we make any calculations, let's define some variables which we'll use in the formulas. n - the number of dice, s - the number of individual die faces, p - the probability of rolling any value from a die, and P - the overall probability for the problem. There is a simple relationship - p = 1/s, so the probability of getting 7 on a 10-sided die is twice that of a 20-sided die. 1. The probability of rolling the same value on each die - while the chance of getting a particular value on a single die is p, we only need to multiply this probability by itself as many times as the number of dice. In other words, the probability P equals p to the power n, or P = pⁿ = (1/s)ⁿ. If we consider three 20-sided dice, the chance of rolling 15 on each of them is: P = (1/20)³ = 0.000125 (or P = 1.25·10⁻⁴ in scientific notation). And if you are interested in rolling the set of any identical values, simply multiply the result by the total die faces: P = 0.000125 · 20 = 0.0025. 2. The probability of rolling all the values equal to or higher than y - the problem is similar to the previous one, but this time p is 1/s multiplied by all the possibilities which satisfy the initial condition. For example, let's say we have a regular die and y = 3. We want to rolled value to be either 6, 5, 4, or 3. The variable p is then 4 · 1/6 = 2/3, and the final probability is P = (2/3)ⁿ. 3. The probability of rolling all the values equal to or lower than y - this option is almost the same as the previous one, but this time we are interested only in numbers that are equal to or lower than our target. If we take identical conditions (s=6, y=3) and apply them in this example, we can see that the values 1, 2, & 3 satisfy the rules, and the probability is: P = (3 · 1/6)ⁿ = (1/2)ⁿ. 4. The probability of rolling exactly X same values (equal to y) out of the set - imagine you have a set of seven 12-sided dice, and you want to know the chance of getting exactly two 9s. It's somehow different than previously because only a part of the whole set has to match the conditions. This is where the binomial probability comes in handy. The binomial probability formula is: P(X=r) = nCr · pʳ · (1-p)ⁿ⁻ʳ, where r is the number of successes, and nCr is the number of combinations (also known as "n choose r"). In our example we have n = 7, p = 1/12, r = 2, nCr = 21, so the final result is: P(X=2) = 21 · (1/12)² · (11/12)⁵ = 0.09439, or P(X=2) = 9.439% as a percentage. 1. The probability of rolling at least X same values (equal to y) out of the set - the problem is very similar to the prior one, but this time the outcome is the sum of the probabilities for X=2,3,4,5,6,7. Moving to the numbers, we have: P = P(X=2) + P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) = 0.11006 = 11.006%. As you may expect, the result is a little higher. Sometimes the precise wording of the problem will increase your chances of success. 2. The probability of rolling an exact sum r out of the set of n s-sided dice - the general formula is pretty complex: $\scriptsize \qquad P(r,n,s) = \frac{1}{s^n} \sum^{\lfloor(r-n)/s\rfloor}_{k=0}(-1)^k\binom{n}{k}\binom{r\!-s\!\cdot\!k\!-\!1}{n\!-\!1}$ However, we can also try to evaluate this problem by hand. One approach is to find the total number of possible sums. With a pair of regular dice, we can have 2,3,4,5,6,7,8,9,10,11,12, but these results are not equivalent! Take a look; there is only one way you can obtain 2: 1+1, but for 4, there are three different possibilities: 1+3, 2+2, 3+1, and for 12 there is, once again, only one variant: 6+6. It turns out that 7 is the most likely result with six possibilities: 1+6, 2+5, 3+4, 4+3, 5+2, and 6+1. The number of permutations with repetitions in this set is 36. Our permutation calculator may be handy for finding permutations for other dice types. We can estimate the probabilities as the ratio of favorable outcomes to all possible outcomes: P(2) = 1/36, P(4) = 3/36 = 1/12, P(12) = 1/36, P(7) = 6/36 = 1/6. The higher the number of dice, the closer the distribution function of sums gets to the normal distribution. As you may expect, as the number of dice and faces increases, more time is consumed evaluating the outcome on a sheet of paper. Luckily, this isn't the case for our dice probability calculator! 1. The probability of rolling a sum out of the set, not lower than X - like the previous problem, we have to find all results which match the initial condition and divide them by the number of all possibilities. Taking into account a set of three 10-sided dice, we want to obtain a sum at least equal to 27. As we can see, we have to add all permutations for 27, 28, 29, and 30, which are 10, 6, 3, and 1, respectively. In total, there are 20 good outcomes in 1,000 possibilities, so the final probability is: P(X ≥ 27) = 20 / 1,000 = 0.02. 2. The probability of rolling a sum out of the set, not higher than X - the procedure is precisely the same as for the prior task, but we have to add only sums below or equal to the target. Having the same set of dice as above, what is the chance of rolling at most 26? If you were to do it step by step, it would take ages to obtain the result (to sum all 26 sums). But, if you think about it, we have just worked out the complementary event in the previous problem. The total probability of complementary events is exactly 1, so the probability here is: P(X ≤ 26) = 1 - 0.02 = 0.98. ## When to use dice probability calculator? There are a lot of board games where you take turns to roll a die (or dice), and the results may be used in numerous contexts. Let's say you're playing Dungeons & Dragons and attacking. Your opponent's armor class is 17. You roll a 20-sided dice, hoping for a result of at least 15 - with your modifier of +2. That should be enough. With these conditions, the probability of a successful attack is 0.30. If you know the odds of a successful attack, you can choose whether you want to attack this target or pick another with better odds. Or maybe you're playing The Settlers of Catan, and you hope to roll the sum of exactly 8 with two 6-sided dice, as this result will yield you precious resources. Just use our dice probability calculator, and you'll see the chance is around 0.14 - you'd better get lucky this turn! ## Should I play or should I pass? - Let's play a game! There are various types of games, like lotteries, where your task is to make a bet depending on the odds. Rolling dice is one of them. Although taking some risks is inevitable, you can choose the most favorable option and maximize your chances of a win. Take a look at this example. Imagine you are playing a game where you have one of three options to choose from, which are: • The sum of five 10-sided dice is at least 30; • The sum of five 12-sided dice is at most 28; • The sum of five 20-sided dice is at least 59. You only win if the option you pick comes up. You can also pass if you feel none of these will happen. Intuitively, it's difficult to estimate the most likely success, but with our dice probability calculator, it takes only a blink of an eye to evaluate all the probabilities. The resulting values are: • P₁ = 0.38125 for 10-sided dice; • P₂ = 0.3072 for 12-sided dice; and • P₃ = 0.3256 for 20-sided dice. The probability for a pass to be successful is the product of the complementary events of the remaining options: • P₄ = (1-P₁) · (1-P₂) · (1-P₃) = 0.61875 · 0.6928 · 0.6744 = 0.2891. We can see that the most favorable option is the first one, while passing is the least likely event to happen. We cannot assure you'll win all the time, but we strongly recommend that you pick the 10-sided dice set to play. ## FAQ ### What is a probability? Probability determines how likely certain events are to occur. The simple formula for probability is the number of desired outcomes/number of possible outcomes. In board games or gambling, dice probability is used to determine the chance of throwing a certain number, e.g., what is the possibility of getting a specific number with one die? ### How many possible outcomes are there from rolling two dice? There are 36 outcomes when you throw two dice. For a single die, there are six faces, and for any roll, there are six possible outcomes. For two dice, you should multiply the number of possible outcomes together to get 6 × 6 = 36. With subsequent dice, simply multiply the result by 6. If you use dice of a different shape, enter the number of their sides instead of 6. ### When rolling 2 dice, what is the probability of 7? It's 1/6 or 0.1666667. Let's assume that a total of 7 occurs at least once. For 2 dice, there are 6 ways to throw the sum of 7 - (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). The total number of combinations for a pair of cube dice is 36. So the probability of summing up to 7 is 6/36 = 1/6 = 0.1666667. ### How many times do I throw 5 on a pair of dice? 20. Let's assume that a pair of dice is rolled 180 times. You have 4 ways to get a sum of 5 - (1,4), (2,3), (3,2), and (4,1). The probability of throwing a sum of 5 is 4/36 = 1/9. The expected number in 180 throws is 180 × (1/9) = 20. You will throw a sum of 5 at least 20 times. ### Can I always roll a 6 on a dice? No, it is always a matter of luck, but you can increase your chances by using some tricks: 1. Place your index finger and thumb on the numbers that are on opposite sides revealing 1 and 6. 2. Throw the dice slowly and hope the dice rolls straight. The trick is that you let the dice roll with the remaining numbers, creating a higher probability of landing on the number 6. Wojciech Sas, PhD Choose the type and the number of dice Dice type Cube (6 faces) Total number of dice Choose the conditions - Game rules I want to get: All dice with the same face/side value The dice value I want to get: ...which results in... The probability of getting any value from the dice People also viewed… ### Car crash force With this car crash calculator, you can find out how dangerous car crashes are. ### Exponential regression The exponential regression calculator helps you find the exponential curve that best models your dataset. ### Process capability index Our process capability index calculator helps you calculate whether the variation of your process is within specification limits and whether your process can produce the intended output. ### Social Media Time Alternatives Check what you could have accomplished if you get out of your social media bubble.	2023-02-05 23:02:59	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6314517855644226, "perplexity": 394.5679786512289}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500294.64/warc/CC-MAIN-20230205224620-20230206014620-00217.warc.gz"}
https://mailman.ntg.nl/pipermail/ntg-context/2015/082068.html	# [NTG-context] alternative numerical \cite command Csikos Bela bcsikos425 at freemail.hu Tue May 5 18:19:26 CEST 2015 Alan BRASLAU írta: >On Tue, 5 May 2015 12:52:41 +0200 >Csikos Bela wrote: > >> Thanks. But there's no any indication in the log file of using mkII, >> unless mkiv uses the same code. All \cite[alternative][key] variants >> work for me except the \cite[textnum][key] variant. See the attached >> example tex file with its pdf output and log file. > >\setupbibtex and \setuppublications pull-in the "MKII" code. > I am puzzled a little bit. I also tried to use \setuppublicationlist[pagenumber=yes], which had no effect on the output. I found related to this the followings: http://tex.stackexchange.com/questions/94023/context-how-to-set-up-interaction-mode-to-emulate-hyperref http://www.ntg.nl/pipermail/ntg-context/2011/061528.html Based on these, in my understanding the bug affects mkiv and mkii should work. So, if I "use" mkii code (pulled by \setuppublications), why pagenumber=yes doesn't work for me? Or it doesn't work in mkii either? Thanks, bcsikos More information about the ntg-context mailing list	2022-05-20 00:32:32	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9254779815673828, "perplexity": 11663.973141855078}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662530553.34/warc/CC-MAIN-20220519235259-20220520025259-00685.warc.gz"}
https://answers.ros.org/questions/222474/revisions/	# Revision history [back] ### setUpdatePeriod() in gmapping? Hi all, I'm tracing the code of gmapping and try to find out the parameter "temporalUpdate" usage https://svn.openslam.org/data/svn/gmapping In slam_gmapping.cpp(https://github.com/ros-perception/slam_gmapping/blob/hydro-devel/gmapping/src/slam_gmapping.cpp), it looks like the parameter is used in line#508 line#508: gsp_->setUpdatePeriod(temporalUpdate_); but I can not find the setUpdatePeriod() method in gridslamprocessor.cpp or gridslamprocessor.h. https://svn.openslam.org/data/svn/gmapping/trunk/gridfastslam/gridslamprocessor.cpp Anybody find it?? ps. I'm using ROS distribution "indigo". ### setUpdatePeriod() in gmapping? Hi all, I'm tracing the code of gmapping and try to find out the parameter "temporalUpdate" usage usage in: https://svn.openslam.org/data/svn/gmapping In slam_gmapping.cpp(https://github.com/ros-perception/slam_gmapping/blob/hydro-devel/gmapping/src/slam_gmapping.cpp), it looks like the parameter is used in line#508 line#508: gsp_->setUpdatePeriod(temporalUpdate_); but I can not find the setUpdatePeriod() method in gridslamprocessor.cpp or gridslamprocessor.h. https://svn.openslam.org/data/svn/gmapping/trunk/gridfastslam/gridslamprocessor.cpp Anybody find it?? ps. I'm using ROS distribution "indigo".	2021-06-18 18:52:12	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34555870294570923, "perplexity": 11875.66570178892}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487640324.35/warc/CC-MAIN-20210618165643-20210618195643-00025.warc.gz"}
https://www.physicsforums.com/threads/diff-eq-please-help-me.263937/	# Diff eq please help me! 1. Oct 13, 2008 ### mathgirl2007 Find the value of the constant c so that solutions of the equation 4u"+cu'+6u=0 tend to zero as fast as possible. I think that c must be positive in order for this to tend towards zero but I cannot figure out what c has to be. Thanks for your help! 2. Oct 13, 2008 ### gabbagabbahey What is the characteristic polynomial of this ODE? What are the solutions (in terms of c) of that polynomial? What does that make the general solution for u? 3. Oct 13, 2008 ### mathgirl2007 this is all i was given. would it be that m=4 lambda=c and k=6? 4. Oct 13, 2008 ### gabbagabbahey Have you studied ODE's yet?? Are you familiar with the term characteristic polynomial? For example, the characteristic polynomial of $2u''+5u'-3=0$ is $2 \lambda^2+5\lambda-3=0$ which has roots $\lambda_1= -3$ and $\lambda_2=\frac{1}{2}$ and a general solution of $u(x)=c_1e^{\lambda_1 x} +c_2e^{\lambda_2 x}$ So, what is the characteristic polynomial of 4u" + cu'+6u=0? 5. Oct 13, 2008 ### mathgirl2007 So the equation would be $4\lambda^2+C\lambda+6=0$ 6. Oct 13, 2008 ### mathgirl2007 and the roots would be (-C+/- the square root(c^2 - 96))/8 7. Oct 13, 2008 ### gabbagabbahey Yes, so what is the general solution u(x) then? 8. Oct 13, 2008 ### mathgirl2007 u(x) = c1e^(-C + the square root(c^2 - 96))/8)x + C2e^(-C - the square root(c^2 - 96))/8 9. Oct 13, 2008 ### gabbagabbahey Good, now what does it mean for a function to tend to zero? (in terms of the derivative of the function) 10. Oct 13, 2008 ### mathgirl2007 its going to have to be getting infinitely smaller 11. Oct 13, 2008 ### gabbagabbahey Yes, it gets smaller as x-gets larger and so du/dx is negative correct? What is du/dx of your function? 12. Oct 13, 2008 ### mathgirl2007 im not sure how to find that here. is that the derivative in regards to x? 13. Oct 13, 2008 ### mathgirl2007 im really stuck. would it be that C must b be 1 to tend towards zero? 14. Oct 13, 2008 ### gabbagabbahey Yes, du/dx is the derivative with regard to x...You know what u(x) is, so calculate u'. Last edited: Oct 13, 2008 15. Oct 13, 2008 ### mathgirl2007 okay i did that. now where in there can i find what c is? 16. Oct 13, 2008 ### gabbagabbahey Well u' should be as large of a negative number as possible if u tends to zero as fast as possible correct? In other words you want to find the minumum value of u'(x) with respect to c. The derivative of u'(x) with respect to c should be zero at its minimum, so solve the equation $$\frac{d u'}{dc}=0$$ for c. 17. Oct 13, 2008 ### klondike "(the solution) tends to zero as fast as possible" My interpretation is that the transient response is "as short as possible". given a second order system $$ay''+by'+cy=dx'+ex$$ under zero input excitation or $$ay''+by'+cy=0$$, the response is due to non-zero initial condition(s). In order for the solution to converge (stable system and non oscillating), it requires either 1) a>0,b>0, and c>0, OR 2) a<0, b<0, and c<0 such that all poles are on the left half of s-plane (excluding $$j \omega$$) axis. In the other word, the fourier transform must exist. since the OP mentioned m, c, and k, I'm assuming she is dealing with a spring-mass-damper system ($$my''+cy'+ky=0$$ with non-equilibrium initial displacement ), I bet the answer is when $$\zeta=1$$ or critically damped. Note that when system is critically damped (double real roots), the solution doesn't take the form as other poster mentioned. Last edited: Oct 13, 2008 18. Oct 13, 2008 ### gabbagabbahey Yes, that makes more sense :0) Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook	2017-10-17 07:24:42	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.768983006477356, "perplexity": 1960.8132693148223}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187820927.48/warc/CC-MAIN-20171017052945-20171017072945-00573.warc.gz"}
https://researchportal.bath.ac.uk/en/publications/analysis-of-charm-pair-production-at-the-lhc	# Analysis of Charm Pair Production at the LHC D P De Souza, N. H. Brook Research output: Contribution to journalArticle ### Abstract The DGLAP and CCFM approaches to perturbative QCD evolution have been investigated by examining correlations of charmed hadron pairs in $pp$ collisions at $\sqrt{s}=7$ TeV. The theoretical models are compared to the data taken by the LHCb experiment. Differences in the parton kinematics between the two approaches are discussed. In general a model incorporating NLO diagrams matched to parton showers describes the data best. Original language English 9 Journal of Physics G:Nuclear and Particle Physics G34 1 https://doi.org/10.1088/0954-3899/43/1/015001 Published - 8 Dec 2015 • hep-ph • ## Profiles ### Nick Brook Person: Research & Teaching	2020-09-20 15:24:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42942777276039124, "perplexity": 6266.3549149253095}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400198213.25/warc/CC-MAIN-20200920125718-20200920155718-00416.warc.gz"}
https://zenodo.org/record/4081237/export/csl	Journal article Open Access # Coherence Time Extension by Large-Scale Optical Spin Polarization in a Rare-Earth Doped Crystal Welinski, Sacha; Tiranov, Alexey; Businger, Moritz; Ferrier, Alban; Afzelius, Mikael; Goldner, Philippe ### Citation Style Language JSON Export { "DOI": "10.1103/PhysRevX.10.031060", "author": [ { "family": "Welinski, Sacha" }, { "family": "Tiranov, Alexey" }, { "family": "Businger, Moritz" }, { "family": "Ferrier, Alban" }, { "family": "Afzelius, Mikael" }, { "family": "Goldner, Philippe" } ], "issued": { "date-parts": [ [ 2020, 9, 16 ] ] }, "abstract": "<p>Optically addressable spins are actively investigated in quantum communication, processing, and sensing. Optical and spin coherence lifetimes, which determine quantum operation fidelity and storage time, are often limited by spin-spin interactions, which can be decreased by polarizing spins. Spin polarization can be achieved using optical pumping, large magnetic fields, or mK-range temperatures. Here, we show that optical pumping of a small fraction of ions with a fixed-frequency laser, coupled with spin-spin interactions and spin diffusion, leads to substantial spin polarization in a paramagnetic rare-earth doped crystal, 171Yb3+\u2236Y2SiO5. Indeed, more than 90% spin polarization has been achieved at 2 K and zero magnetic field. Using this spin polarization mechanism, we further demonstrate an increase in optical coherence lifetime from 0.3 ms to 0.8 ms, due to a strong decrease in spin-spin interactions. This effect opens the way to new schemes for obtaining long optical and spin coherence lifetimes in various solid-state systems such as ensembles of rare-earth ions or color centers in diamond, which are of interest for a broad range of quantum technologies.</p>", "title": "Coherence Time Extension by Large-Scale Optical Spin Polarization in a Rare-Earth Doped Crystal", "version": "1", "type": "article-journal", "id": "4081237" } 77 17 views	2023-03-23 13:54:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24663566052913666, "perplexity": 9598.68285892388}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296945168.36/warc/CC-MAIN-20230323132026-20230323162026-00667.warc.gz"}
https://thehumanasia.com/0054kh/11-letter-word-that-begins-and-ends-with-und-e018d8	Piute Lake Campground, Family Systems Theory Pdf, 7-ingredient Vegan Recipes, Tender Is The Night Synopsis, In A Failed Crucial Conversation The Biggest Issue Is Often:, " />Piute Lake Campground, Family Systems Theory Pdf, 7-ingredient Vegan Recipes, Tender Is The Night Synopsis, In A Failed Crucial Conversation The Biggest Issue Is Often:, ">11 letter word that begins and ends with und Human Asia # 11 letter word that begins and ends with und If we want to create a pyridine that is as basic as possible, we want $+I$ effects, i.e. Journal of the American Chemical Society 1986, 108 (20) , 6250-6254. This is because the cation resulting from oxygen protonation is resonance stabilized. explain why amines are more basic than amides, and better nucleophiles. Its basicity and nucleophilicity may be modified by steric hindrance, as in the case of 2,6-dimethylpyridine (pK a =6.7), or resonance stabilization, as in the case of 4-dimethylaminopyridine (pK a =9.7). Basicity of common amines (pKa of the conjugate ammonium ions). We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. The two immiscible liquids are then easily separated using a separatory funnel. Instead, in terms of its reactivity, pyridine more closely resembles nitrobenzene. But why is pyrimidine less basic than pyridine? Electrophilic Aromatic Substitution 5. Pyridine is more basic as compared to pyridazine, pyrimidine and pyrazine because pyridazine, pyrimidine and pyrazine containing two nitrogen atoms which are exerted inductive effect to each other so availability of lone pair for donation is less. Answer to: Rank the following compounds in order of basicity: pyridine, 4-methoxypyridine, 5-methoxyindole, and 3-methoxypyridine. The lone pair of electrons on the nitrogen atom of amines makes these compounds not only basic, but also good nucleophiles. ... Pyridine is an aromatic amine, but in a very different sense from aniline. As we all know that nitrogen containing compounds basicity depends on its ability to donate the lone pair of nitrogen. The two immiscible liquids used in an extraction process are (1) the solvent in which the solids are dissolved, and (2) the extracting solvent. Heterocycles:Heterocycles: PyridinePyridine Dr. Taj Khan Dept. Finally, the two amide bases see widespread use in generating enolate bases from carbonyl compounds and other weak carbon acids. Pyrimidine has two $\mathrm{sp^2}$ -hybridised lone pairs available for protonation, compared with pyridine's one. Because alkyl groups donate electrons to the more electronegative nitrogen. Have questions or comments? I would've considered D, since chlorine is the most electronegative, and would therefore have the largest partial negative charge, making it more basic than the nitrogen substituent. Although pyrrole is an amine, it is not basic. 4-dimethylaminopyridine is, of course, strongly activated: the $+M$ effect strongly outweighs the $-I$ effect. In a pyridine ring, for example, the nitrogen lone pair occupies an sp 2-hybrid orbital, and is not part of the aromatic sextet - it is essentially an imine nitrogen. Whilst basic centers are attractive features to have in drug molecules because they offer the ability to create water soluble, crystalline, high melting salts, usually without the plasma protein binding associated with carboxylic acids.They can cause problems with HERG, CYP450 2D6.. Instead of inductive effects, let's consider the resonance structures of our molecules: A positive charge on a nitrogen is always more favorable than a positive charge on a chlorine. Barton's base is a strong, poorly-nucleophilic, neutral base that serves in cases where electrophilic substitution of DBU or other amine bases is a problem. Dr. Dietmar Kennepohl FCIC (Professor of Chemistry, Athabasca University), Prof. Steven Farmer (Sonoma State University), William Reusch, Professor Emeritus (Michigan State U. describe how an amine can be extracted from a mixture that also contains neutral compounds illustrating the reactions which take place with appropriate equations. if the molecule $\ce{B}$ was already partially negatively charged before the proton came in. The aniline, pyridine, and pyrrole examples are good models for predicting the reactivity of nitrogen atoms in more complex ring systems (a huge diversity of which are found in nature). Pyridine is more basic than aniline and pyrrol because is lone pair of nitrogen is does not involved in pi cloud formation that means it is localised while pryrrol is less basic than aniline because is lone pair involved in pi cloud formation of pyrrol ring Hence correct basic order is (iV) > (iii)> (I)> (ii) The inductive effect makes the electron density on the alkylamine's nitrogen greater than the nitrogen of ammonium. Photomodulation of Lewis basicity in a pyridine-functionalized 1,2-dithienylcyclopentene H. D. Samachetty and N. R. Branda, Chem. To learn more, see our tips on writing great answers. 2 & \ce{C5H5N} & 5.2 & \text{Bordwell}\\ Correspondingly, primary, secondary, and tertiary alkyl amines are more basic than ammonia. 2,6-lutidine is closest in terms of basicity (proton "scavenging"), 4-N,N-dimethylaminopyridine is both basic and assists in many acylations. Click to comment To Top	2021-06-13 17:10:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4713698625564575, "perplexity": 6915.165066442117}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487610196.46/warc/CC-MAIN-20210613161945-20210613191945-00489.warc.gz"}
https://www.physicsforums.com/threads/electric-fields-and-rods.87643/	# Electric Fields and rods Here's my problem: Three 10-cm-long rods form an equilateral triangle. Two of the rods are charged to + 10 nC, the third to -10 nC. What is the electric field strength at the center of the triangle? Answer in back of book: 1.08 * 10^5 N/C By looking at the corresponding section, it gives the formula for the electric field strength in the plane that bisects a charged rod as: Q/(4pie_0rsqrt(r^2 + (L/2)^2)), where e_0 is given to be 8.85*10^-12. I thought that you would add the vertical and horizontal components of the 3 electric fields in the center due to each rod to get the net electric field. After some calculations, I get that the final answer should be 2 times the formula I gave above, but this does not give me the correct answer. What am I doing wrong? Please respond, thanks!	2020-11-23 19:56:26	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8223670721054077, "perplexity": 225.25612379882594}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141164142.1/warc/CC-MAIN-20201123182720-20201123212720-00529.warc.gz"}
https://mlbaker.net/2011/02/28/recurrences-and-rational-generating-series/	## Recurrences and rational generating series sips tea Alright, so it’s 4:00 AM and I can’t sleep yet again, so I’m here to ramble on about rational generating functions and the recurrences they give rise to. Example. Consider the generating function given by $F(x) = \frac{5-x}{1-2x-x^2+2x^3}$. This is a rational function and we are asked the question: How do we extract its coefficients? We denote by $\langle x^n, F(x) \rangle$ the coefficient of $x^n$ in $F(x)$. We will also denote $f_n = \langle x^n, F(x) \rangle$ for brevity. First off, we note that $(1-2x-x^2+2x^3)F(x) = 5-x$ and so surely their coefficients must agree, that is, $\langle x^n, (1-2x-x^2+2x^3)F(x) \rangle = \langle x^n, 5-x \rangle$. The right-hand side is obviously zero if $n \geq 2$, so keeping this in mind, let us manipulate the equation a bit. It should be fairly obvious that $\langle x^n, x^kF(x) \rangle = \langle x^{n-k}, F(x) \rangle$. Also, the operator $\langle \cdot, \cdot \rangle$ turns out to be linear in its second argument (this is also not difficult to show). So our previous equation suddenly becomes $\langle x^n, F(x) \rangle - 2 \langle x^n, xF(x) \rangle - \langle x^n, x^2F(x) \rangle + 2 \langle x^n, x^3F(x) \rangle = 0$ for all $n \geq 2$, but now we apply our previous remark; this gives $\langle x^n, F(x) \rangle - 2 \langle x^{n-1}, F(x) \rangle - \langle x^{n-2}, F(x) \rangle + 2 \langle x^{n-3}, F(x) \rangle = 0$ for all $n \geq 3$. Applying the definition of $f_n$ this gives the nice recurrence $f_n - 2f_{n-1} - f_{n-2} + 2f_{n-3} = 0$. This is called a homogeneous recurrence because the constant is zero. OK, but this doesn’t uniquely determine the function $F(x)$. We have a recurrence satisfied whenever $n \geq 3$, but what about when $n$ is 0, 1, or 2? We have to specify these alongside the recurrence in order to get rid of the ambiguity. First, we find $f_0 = 5$, by evaluating $F(0)$. As for the other two, they can be determined from the equation $\langle x^n, (1-2x-x^2+2x^3)F(x) \rangle = \langle x^n, 5-x \rangle$, by splitting it up as before (we obtain, for example, $f_1 - 2f_0 = -1$ and hence $f_1 = 9$). General result: (it is a routine exercise to prove this) Let $(f_n)_{n \geq 0}$ and $(g_n)_{n \geq 0}$ be sequences with generating series $F(x)$ and $G(x)$ respectively, and suppose there exist constants $a_1, \ldots, a_k$ such that $f_n + a_1f_{n-1} + \ldots + a_kf_{n-k} = g_n$ for all $n \geq k$. Then there are polynomials $a(x)$ and $b(x)$ such that $a(x)$ is invertible as a power series and $a(x)F(x) = G(x) + b(x)$. Information loss. As I said previously, we should note that in passing to the recurrence $f_n - 2f_{n-1} - f_{n-2} + 2f_{n-3} = 0$ we have lost information about the generating function, which can not be recovered unless we are supplied with initial conditions $f_0, f_1, f_2$. So suppose we are given $f_0, f_1, f_2$. We can try to reassemble it: $\langle x^n, F(x) \rangle - 2 \langle x^{n-1}, F(x) \rangle - \langle x^{n-2}, F(x) \rangle + 2 \langle x^{n-3}, F(x) \rangle = 0$ for all $n \geq 3$ and hence $\langle x^n, (1 - 2x - x^2 + 2x^3)F(x) \rangle = 0$ for all $n \geq 3$ Hmm. So obviously from this we can conclude that the right-hand side must have been a polynomial $p(x)$ of degree at most 2. Say $p(x) = a + bx + cx^2$. We get $\langle x^n, (1-2x-x^2+2x^3)F(x) \rangle = \langle x^n, a+bx+cx^2 \rangle$ (for all $n$). working with the equation some more and using common sense to guide us, we get $f_0 = a$, $f_1 - 2f_0 = b$, etc. In this way, plugging back in the initial conditions, we can solve for the right-hand side, and hence reform the rational generating function $F(x)$.	2017-09-22 06:07:05	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 49, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9656499624252319, "perplexity": 114.91097205691442}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688671.43/warc/CC-MAIN-20170922055805-20170922075805-00661.warc.gz"}
https://math.stackexchange.com/questions/4193908/kolmogorovs-extension-theorem-and-consistent-probability-measure	# kolmogorov's extension theorem and consistent probability measure In Durrett's probability theory, Kolmogorov extension theorem is given as below: Theorem 2.1.21 (Kolmogorov's extension theorem) Suppose we are given probability measure $$\mu_n$$ on $$(\mathbf{R}^n, \mathcal{R}^n)$$ that are consistent, that is, $$\mu_{n+1}((a_1, b_1] \times \cdots \times (a_n, b_n] \times \mathbf{R}) = \mu_n((a_1, b_1] \times \cdots \times (a_n, b_n])$$ then there is a unique probability measure $$P$$ on $$(\mathbf{R}^\mathbf{N}, \mathcal{R}^\mathbf{N})$$ with $$P(\omega: \omega_i \in (a_i, b_i], 1 \le i \le n) = \mu_n((a_1, b_1] \times \cdots \times (a_n, b_n])$$ where $$\mathbf{N}$$ stands for natural numbers. My questions are: (1) are all probability measures consistent (by the above definition)? I'm assuming they're not but in the above condition, we can write $$\mu_{n+1}$$ as $$\mu_n((a_1, b_1] \times \cdots \times (a_n, b_n]) \mu_1(\mathbf{R}) = \mu_n((a_1, b_1] \times \cdots \times (a_n, b_n])$$. This is always going to hold for any probability measure since $$\mu_1(\mathbf{R}) = 1$$ for any probability measure on a real line. (2) What are some examples of non-consistent probability measure? (3) the consistency condition is slightly different from the ones shown in Wikipedia where there are two consistency conditions, especially the permutation part: For all $$t_1, \cdots , t_k \in T$$, $$k \in \mathbb{N}$$ let $$\nu_{t_1,\cdots,t_k}$$ be probability measures on $$\mathbb{R}^{nk}$$ s.t. $$\nu_{t_{\pi(1)},\cdots,t_{\pi(k)}} (F_1 \times \cdots \times F_k) = \nu_{t_1,\cdots,t_k} (F_{\pi(1)} \times \cdots \times F_{\pi(k)})$$ for all permutations $$\pi$$ on $$\{1,2, \cdots,k\}$$ and $$\nu_{t_1,\cdots,t_k}(F_1\times \cdots \times F_k) = \nu_{t_1,\cdots,t_k, t_{k+1}, \cdots, t_{k+m}}(F_1\times \cdots \times F_k\times \mathbb{R}^n \times \cdots \times\mathbb{R}^n )$$ for all $$m \in \mathbb{N}$$ Is Durrett's condition of consistency weaker? How are they different? Let $$f(x)$$ be the PDF of a continuous random variable $$X$$. Based on $$f(x)$$, we can build three different measures $$\mu_n$$, $$\gamma_n$$, $$\beta_n$$ to use as examples. For each positive integer $$n$$ and for each Borel measurable set $$A \subseteq \mathbb{R}^n$$ define \begin{align} \mu_n(A) &= \int_{(x_1, ..., x_n) \in A} \left(\prod_{i=1}^n f(x_i)\right) dx_1...dx_n\\ \gamma_n(A) &=\int_{(x_1, ..., x_n) \in A} \left(\prod_{i=1}^n f(x_i-i)\right) dx_1...dx_n\\ \beta_n(A) &= \int_{(x_1, ..., x_n) \in A} \left(\prod_{i=1}^n f(x_i-n)\right) dx_1...dx_n\\ \end{align} Then: • $$\mu_n$$ satisfies the consistency property of Durrett and treats all dimensions in the same way. It could be used to model i.i.d. random variables $$\{X_i\}_{i=1}^{\infty}$$. • $$\gamma_n$$ satisfies the consistency property of Durrett but treats different dimensions differently. It could be used to model mutually independent random variables $$\{X_i\}_{i=1}^{\infty}$$ where the variables have different distributions (where $$X_i$$ has PDF $$f(x-i)$$). • $$\beta_n$$ does not satisfy the consistency property of Durrett. It cannot be used to model random variables $$\{X_i\}_{i=1}^{\infty}$$. This is because the marginal distribution of $$X_1$$, when grouped with the first five variables $$(X_1, ..., X_5)$$, would be different from the marginal distribution of $$X_1$$ when grouped with the first six variables $$(X_1, ..., X_6)$$. I observe that Durrett seems to be stating a theorem about probability measures on $$\mathbb{R}^{\mathbb{N}}$$. This can be viewed as a theorem about discrete time stochastic processes. The Wikipedia article seems to be stating a theorem in more generality, one which could apply to either continuous time or discrete time stochastic processes. So it uses more complex notation that is not needed when only discrete time stochastic processes are considered. Note that the permutation notation in the Wikipedia description is similar to observing that if we have three different random variables $$X_1, X_2, X_3$$, we can write a CDF using any ordering we want: $$F_{X_1, X_2, X_3}(x_1, x_2, x_3) = F_{X_2, X_3, X_1}(x_2, x_3, x_1) = P[X_1\leq x_1, X_2\leq x_2, X_3 \leq x_3]$$ It is useful to allow different orderings if we want to isolate $$k+m$$ points in time and group $$k$$ of them first and the remaining $$m$$ of them last, regardless of their actual ordering on the timeline. This ordering issue is not required for discrete time because we would always list the dimensions in order. For example we would always write $$F_{X_1, X_2, X_3}(x_1, x_2, x_3)$$ and we would never write it as $$F_{X_2, X_3, X_1}(x_2, x_3, x_1)$$. So we could even simplify the indexing notation (as Durrett does) via: $$F_3(x_1, x_2, x_3) \equiv F_{X_1, X_2, X_3}(x_1, x_2, x_3)$$ since there is no ambiguity about ordering the first three random variables of the discrete time process $$\{X_1, X_2, X_3, X_4, ...\}$$. • Thank you for the detailed answer! Jul 16 at 0:29	2021-10-26 22:36:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 50, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9871945977210999, "perplexity": 136.55144427556144}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587926.9/warc/CC-MAIN-20211026200738-20211026230738-00671.warc.gz"}
https://earthscience.stackexchange.com/questions/13592/stream-function-on-a-periodic-domain	# Stream function on a periodic domain? Part 1 In this paper the authors calculate the barotropic stream function from an output of a numerical model as: $$\psi(x,y)=\int_0^y\int_{-H}^0u(x,y',z)~dz~dy'$$ over a global domain and this is the result: In the caption, they specify that the value at the African continent was subtracted from the result of the integral. If I interpret correctly, this is necessary because the domain is periodic and we need to ensure that the integral over the globe (excluded the Southern Ocean) is zero. Is this correct? If yes, what is the rationale for choosing the values at the African coast? wouldn't the value at Cape Horn be more natural? Part 2 Another aspect of this calculation that I do not understand is the fact that the values of $\psi$ near the coasts are not zero. I would expect the values of the stream function to be zero near the coast in order to ensure a zero transport across the coast. Why is this not an issue?	2020-01-28 10:37:20	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.721160352230072, "perplexity": 380.9829434725965}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251778168.77/warc/CC-MAIN-20200128091916-20200128121916-00318.warc.gz"}
https://chemistry.stackexchange.com/questions/73603/tagging-functional-group	# Tagging functional group Is it a standard practice to name functional group by the greek alphabet of the carbon it is attached to? Recently read a question in which the order of translation (protein synthesis) was asked and there were a couple of options with the $\ce{NH2}$ was labelled as $\ce{\alpha-NH2}$ and $\ce{COOH}$ as $\ce{\alpha-COOH}$. I read wiki, it says H atoms are labeled in that way but are functional groups too labeled in the same way? • As you can see, they are. – Mithoron Apr 29 '17 at 15:50 • Definitely not standard though. Standard is nothing but the IUPAC name. These are simply useful notations chemists use in certain chemicals as they have useful properties being that way. – Pritt Balagopal Apr 29 '17 at 16:39	2019-10-22 16:43:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5529998540878296, "perplexity": 834.4604576692129}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987822458.91/warc/CC-MAIN-20191022155241-20191022182741-00524.warc.gz"}
https://mtosmt.org/issues/mto.96.2.3/mto.96.2.3.willner.html	# More on Handel and the Hemiola: Overlapping Hemiolas ## Channan Willner KEYWORDS: hemiola, sarabande, courante, musette, expansion, contraction, Handel, J.S. Bach, Mozart ABSTRACT: To the three categories of hemiolas I identified in an earlier study I add a fourth, overlapping hemiolas. Particularly in the Baroque repertoire, and especially in the works of Handel, there are frequent instances of two successive two-bar hemiolas that overlap because they are collapsed onto three bars. I examine the larger context in which their preparation, elaboration, and peroration may represent central compositional issues, especially in light of the brevity of most Baroque compositions. Volume 2, Number 3, March 1996 [1] In my article, “The Two-Length Bar Revisited: Handel and the Hemiola” (Göttinger Händel-Beiträge, Vol. 4 [1991], pages 208–31), I attempted to identify several categories of Handelian hemiolas—cadential, expansion, and contraction hemiolas—in the hope that their establishment would help us sort out some of the complexities of Handel’s phrase rhythm (and that of other composers, for that matter). I also pointed to several types of hemiola that could not be readily stratified. If nothing else, the article demonstrated that the hemiola could assume a great variety of contextually defined senses. The present update is designed to complement my earlier study by pointing to an additional category—overlapping hemiolas—and by assessing its impact on the surrounding elements of the design. After establishing this new category in the first part, I shall seek to revise two of my earlier readings in the second part and, in closing, point to several relatively recent studies that illuminate this complex and elusive subject.(1) [2] Among the difficulties of observing the hemiola and approaching it from a theoretical or analytical perspective is the high degree of uncertainty (not to say ambiguity) that surrounds its articulation. The compositional environment will often suggest hemiolas by emphasizing the third beat of a measure (or the second beat in the following measure) through thematic, textural, harmonic, or registral stresses of varying impact, but it will not necessarily follow it up with an explicitly marked hemiola formation. In other words, it will stop just short of defining three contiguous long, hemiolic beats (each divided into two short internal beats, one strong, the other weak) over the span of two measures in triple meter. Compounding the consequent uncertainty is the well-established absence of a requirement for the hemiola to be articulated by both outer voices: The bass may not necessarily support the suggestion of a hemiola by the upper voice, and the upper voice will not necessarily corroborate its realization by the bass. Especially in such cases, the emphases articulating the hemiola will accrue largely through a series of design stresses—rhythmic accents that (as just intimated) are due to melodic, textural, harmonic, or registral intensification of purely local origin, at the very surface. In borderline instances, it is up to such design accents to try and supplant the metrical accents of the notated meter, whose supporting grid extends to deeper levels of durational structure. And indeed, there are many cases where it is in fact the notated meter that wins out. (On the other hand, the presence of several hemiolas may foster parallelisms that will reinforce the design stresses in potentially ambiguous passages.) Since not all voices necessarily participate in the hemiolic activity, the hemiola’s effect on the composition’s harmonic rhythm and other underlying paces will vary considerably from one hemiola to another. Example 1. Overlapping Hemiolas (click to enlarge) [3] The formation I call overlapping hemiolas, which may be defined as a set of two hemiolas collapsed onto three measures, makes use of just this possibility of articulating the hemiola incompletely; see Example 1, which also depicts the possibility of a third overlapping hemiola, sometimes found in Bach and occasionally in Handel. The formation often begins, somewhat unexpectedly and perhaps furtively, at a distance of three, rather than two, bars from the closing cadential progression of a phrase or subphrase, namely at the beginning of the group. Its location lends it a thematic weight different in nature, if not in emphasis or impact, from that of hemiolas that appear closer to the cadential chords of the group in question; its length allows it to shape the entire group in a way no single hemiola could. (Single hemiolas may, of course, also appear at the beginning of a group without being followed by an overlapping hemiola.) [4] In the first bar of the formation, two-beat patterns in the soprano or bass (or in both) briefly contradict the notated meter and establish the first hemiola. In the second bar, the hemiola’s articulation becomes uncertain, as the broken stems in Example 1 show. On the one hand, the metrical accent on the first beat is not attenuated to the same degree it usually is in hemiola formations; on the other, the expected stress on the second beat is elided or contradicted by adjacent stresses. The first two beats of the second measure may be regarded as a grey area, a durational “pivot zone,” that plays host to two events: the premature peroration of the first hemiola, and the sly entrance of the second hemiola. For the second hemiola enters, however surreptitiously, at the downbeat of this second measure; it now begins to make its presence known. As a result, the first hemiola’s division of long hemiolic beats into strong and weak internal beats undergoes metrical reinterpretation, as the diagram of accentual conflicts at the bottom of Example 1 demonstrates. The first hemiola’s conclusion thus assumes a jagged and unsettled quality, a sense of tentative and incomplete realization that may have significant repercussions for the metrical design in the phrases and sections that follow. Once the third measure has been reached, the outline of the second hemiola emerges quite clearly. Because it is usually the second hemiola that enlists the cadential support of the bass, it brings the formation to a decisive close and at the same time sends out the signal that it has neutralized and absorbed the first hemiola. Example 2. Handel, Suite in G minor (1720), Sarabande, mm. 1–4 (click to enlarge and listen) Example 3. Handel, Suite in G minor (1720), Sarabande, mm. 5–8 (click to enlarge and listen) [5] To illustrate the foregoing explanation and its more extended ramifications, I should like to offer several observations on the appearance of overlapping hemiolas in the Sarabande from Handel’s G-minor Suite of 1720. The Sarabande opens with a four-bar subphrase that strikes an immediately memorable impression by replacing the expected, largely stepwise outlines of the typical sarabande melody with a series of bold leaps; see the braces in Example 2. While these help underscore the Sarabande’s four-bar grouping they also prevent it from assuming the predictable melodic contours of the genre. The overlapping hemiolas occupy bars 5–7, much of the second four-bar subphrase (Example 3). [6] The two-chord patterns in bars 5–6 begin to establish a hemiola and continue through to the downbeat of bar 6 (see the brackets atop Example 3). The melodic line’s two pairs of descending thirds, F5–D5 and E5–C5, are supported by rising fourths in the bass, D3–G3 and C3–F3. Together, melody and bass articulate an S–W, S–W formation that reaches into the beginning of bar 6. The progression stands out—and can superimpose a hemiolic interpretation over the notated meter—because it comprises the Sarabande’s first genuinely harmonic progressions spanning only two internal beats each, and because it suggests a durational contraction (as well as a harmonic realization) of the longer, contrapuntally conceived progressions that straddle the barline at the turn of bars 2, 3, and 4. [7] At the downbeat of bar 6, then, two events overlap: The statement of the hemiola’s fourth, weak internal beat, and the beginning of an unexpectedly sustained F-major chord, whose continuation through the second beat of the measure supports the notated meter as established in bars 1–4 and generates what Joel Lester called a “durational accent.”(2) Not only is the fifth, strong internal beat of the hemiola elided—it is subsequently contradicted by the third beat of bar 6, which initiates a faster melodic pace of quarter notes. The group of quarter notes, supported by a strong cadential progression in the bass, straddles the downbeat of bar 7 and describes a typical cadential hemiola (Example 3). The gradual realization of this second hemiola, then, overlaps the equally gradual peroration of the first hemiola; both realization and peroration are the subject matter of bar 6, whose first two beats emerge as the “pivot zone” referred to earlier. Note how the movement in parallel tenths, F5–E5–D5 (upper voice) and D3–C3–B3 (bass), established by the first hemiola, is completed not on the second beat of bar 6 but on the third, lending further weight to the emerging second hemiola. [8] Because the overlapping hemiolas span three bars and occupy the greater part of a four-bar subphrase, the temporary metrical uncertainty they portray in their central measure has the potential for creating a genuine disturbance in the rhythmic flux of the piece. To foster a compositional and rhetorical milieu in which such disturbance will realize its assigned effect without appearing out of line, Handel often prepares the onset of overlapping hemiolas in some way during the preceding passages and then only gradually allows them to dissipate in the phrase or phrases that follow. By the time their peroration is completed, then, their very presence in the piece, as such, will likely have promoted additional rhythmic dialectics, and these might have in turn become intimately linked to the compositional essence of the piece. [9] The two-chord patterns that launch the first hemiola in bars 5–6 are prepared by the falling third F4–D4 in bar 4. Their movement forward begins with the quasi-improvisatory reappearance of this falling third in the two-line octave, F5 conspicuously replacing F5 at the turn of bar 5. The transfer of F to the high register and its alteration to F represents yet another way of sidestepping excessive thematic predictability within the Sarabande’s periodic framework. Example 4. Handel, Suite in G-minor (1720), Sarabande, mm. 9–16 (click to enlarge and listen) [10] Let us look now at several later allusions to the overlapping hemiolas; these, too, help prevent the remaining three eight-bar phrases from outlining an excessively mechanical profile. Although the four-bar group that follows the double bar brings back the rhythmic outlines of bars 1–4, the unexpected entrance of a two-beat G major chord on the second beat of bar 12, at the close of the group (and in the manner of a written-out sforzato), nearly usurps the cadential status of F, the subtonic that entered on the downbeat of the measure (see the arrow in Example 4). It is as if Handel insisted on affirming, following the upheaval of bars 5–7, that we are indeed listening to a Sarabande, but that further upheaval is in store for us as well.(3) The resulting metrical imbalance makes it possible for the new thematic material that enters in bar 13 to chart a more flexible course than the opening of a foursquare group would normally allow. The mysterious quarter-note rests on the third beat of bar 13 and the second beat of bar 14 represent suppressed accents: On account of their proximity they seem jointly to allude to a hemiola, if not to express one explicitly (see the asterisks in Example 4; the rest in bar 13, though a reference to the rest in bar 1, is dramatized by its contradiction of the two-beat G-major chord in bar 12). As in bar 6, earlier, their more decisive continuation—namely, at the third beat of bar 14—establishes a typical cadential hemiola (bars 14–15). Like the cadential hemiola of bars 6–7, this new hemiola absorbs the uncertainties of bars 13–14. One could, then, view the events in bars 13–15 as a partly silent, hidden reminiscence of those in bars 5–7. Given the relative surface regularity of bars 9–12, which recalls that of bars 1–4, one could take the correspondence one step further and regard the route followed by the Sarabande’s second phrase as parallel to that followed by its first phrase.(4) [11] The uncertainties and tensions of the Sarabande’s overlapping hemiolas find their complete peroration only in its remaining two phrases (bars 17–24 and 25–32). The subphrase in bars 17–20 restores the outlines of bars 1–4 but forgoes the striking leaps of the first subphrase in favor of a more traditionally cantabile, conjunct setting of the characteristic incipit. The following subphrase, in bars 21–24, shows a comparatively mechanical quality (a quality underscored by the repetition of the same subphrase in bars 29–32). The literal transposition of bars 21 and 29 in bars 22 and 30 (a third higher) underscores the insistence of the subphrase’s repeated notes (A4, C5), as well as the closing impulse of its plainly cadential hemiolas (bars 22– 23, 30–31). This is Handel’s response to the accentual irregularities occasioned by the overlapping hemiolas: Though they play their role well, the two subphrases in question count among the less inspired passages in the 1720 collection of suites (the Sarabande dates from about 1703–06, but it was revised for the 1720 publication). Their slight awkwardness exemplifies the difficulties Baroque composers faced when, in the course of very short pieces, they felt need to resolve complex issues they had raised moments earlier but did not quite have the needed durational space in which to work out the resolution. Example 5. Handel, Suite in G minor (1720), Sarabande, mm. 25–28 (click to enlarge and listen) [12] It is only in the course of bars 25–28, the first subphrase of the closing phrase, that a vestige of genuine tension reemerges. At bar 26, Handel sidesteps the opportunity to present generic repeated-chord patterns (in imitation of bars 17ff. and bar 25) and sustains the second-beat D chord through the end of the measure instead. Handel can thereby suggest a “hidden hemiola” in bars 25–26 without fully realizing it. The seventh chord on G, sustained in different positions through the second and third beats of bar 25, militates against the realization of the hemiola (Example 5). Along the same lines, by beginning bar 27 with two quarter notes, Handel evokes the preceding cadential hemiola (that of bars 22–23) without really articulating it (cf. the brackets in Example 5). As a group, bars 25–27 thus portray an attenuated rhythmic reference to the Sarabande’s temporal peculiarities (the suggestion of hemiolic closure in bars 26 and 27 not being matched by that of hemiolic opening in bars 25 or 26), but at the same time they steer clear of the peculiarities’ actual portrayal—a signal indication that the turbulence of the Sarabande’s temporality has finally reached the point of complete peroration.(5) Though not as elegant as its introduction, Handel’s resolution of the Sarabande’s durational dialectic is emblematic of the dynamic, improvisatory nature of Baroque style, and it embodies a measure of compositional freedom missing perhaps from his later, more closely integrated compositions. [13] I should like to take the opportunity of writing again about the hemiola to modify my account of the hemiola formations in two of the pieces I presented in “The Two-Length Bar Revisited”: Those in the Courante from Handel’s F minor Suite, and those in the Musette from the G minor Concerto Grosso, Op. 6 No. 6 (Examples 3 and 4 in that article). Even though the hemiolas in each piece appear at the close of a phrase, one could make a plausible case for reading them as constellations of overlapping hemiolas.(6) Example 6. Handel, Suite in F minor (1720), Courante, mm. 14–20 (click to enlarge and listen) [14] In bars 17–19 of the Courante (Example 6 in the present essay), the upper voice’s first hemiola (bars 17–18) is self-evident; that an additional, overlapping hemiola spans bars 18–19 in the upper voice is suggested by the entrance of the bass G at the turn of bar 18, which underscores the downbeat of the measure, by the subsequent emphasis on the supertonic chord on the third beat of bar 18, and by the articulation of the dominant’s resolution on the first two beats of bar 19, which places substantial motivic weight on the second beat of that measure. The succession of these events suggests a metric reinterpretation similar to that displayed in the present Example 1. [15] Though it is the second, rather than the first, hemiola that is relatively tentative here—its interpretation is supported by the grouping of the upper voice but contradicted by the return of the bass tone G at the beginning of bar 19—the durationally angular setting of the three-bar segment and its collection of conflicting accents does evoke the thematic and rhythmic contraction typical of overlapping hemiolas and as such assumes growing significance in the course of the piece. First introduced as the climax to a set of imitative entrances of the Courante’s short theme over the dominant (bars 10– 14–17), it reappears in the form of seemingly incidental allusions to the tentative hemiola of bars 18–19 during the cadential progression of bars 27–29 and, more concretely, in the progression of bars 30–32 (and, transposed but complete, in bars 41–43). Example 7. Handel, Concerto Grosso in G minor, Op. 6, No. 6, Musette, mm. 1–15 (click to enlarge and listen) Example 8. Handel, Concerto Grosso in G minor, Op. 6, No. 6, Musette, mm. 11–13 (click to enlarge) Example 9. Handel, Concerto Grosso in G minor, Op. 6, No. 6, Musette, mm. 1–7 (click to enlarge and listen) Example 10. Handel, Concerto Grosso in G minor, Op. 6, No. 6, Musette, mm. 11–14, 49–53, 81–82 (click to enlarge and listen) [16] The overlapping hemiolas in the Musette from the G minor Concerto Grosso (bars 11–13) stand, by contrast, on nearly equal footing (bars 1–15 are quoted in Example 7 of the present article; my new analytical observations are illustrated in Examples 8–10). The first hemiola is outlined by three pairs of chords whose articulation of strong and weak internal beats—SW, SW, SW—supports their contrapuntal and harmonic priorities. The first chord of each pair acts as an accented appoggiatura to the second. The metrical reinterpretation that takes place in the course of bar 12 is made possible by this contrapuntal and harmonic function: As bar 12 unfolds, the second chord of each pair is reinterpreted accentually as the principal chord of the pair. The primacy of the rising fourths in the bass in bars 11–12 is gradually replaced by that of the falling thirds in bars 12–13, which are supported by the melody’s movement in parallel tenths with the bass beginning at the downbeat of bar 12.(7) The reinterpretation is possible, indeed necessary, because at a deeper level the bass tone A, introduced by the first chordal pair in bar 11, is retained across bar 12 through to the downbeat of bar 13; its retention possesses substantial harmonic significance in that Asupports the first-inversion supertonic of the Musette theme’s closing cadential progression (Example 8 of the present article). Both the B and C of the bass in bar 12 gain in accentual importance because they help extend A through an ascent to the supertonic’s inner-voice tone C, a third above, and in so doing gradually define the contour of the expanded cadential progression that spans bars 11–13 (closing in bar 14). By the time the Bdominant enters on the second beat of bar 13, it has gained its requisite hemiolic strong accent.(8) [17] The effect of a hemiola depends in large measure on its relation to the prevailing rhythmic and thematic design. From this perspective, the Musette’s overlapping hemiolas are particularly noteworthy for they introduce the third change in design within the six- and eight-bar groups in which they occur (bars 1–6 and 7–14; the hemiolas are first suggested, in germinal form, by the chordal pairs in bars 5–6). The Musette’s incipit, which moves in quarter notes (bars 1–2, 7–8), is followed by an extraordinary rising slide to a sustained E (bars 3, 7) and a responding, falling slide to a sustained B; the slides represent displaced contractions of the quarter-note incipit (Example 9). The hemiolas (incipiently in bars 5–6, fully in bars 11–13) reintroduce the movement in quarter notes but contradict their earlier grouping in threes through the hemiolas’ characteristic articulation in pairs. The expansive nature of the dialogue between the concertino and ripieno groups that follows—and many of the ensuing tonal and durational enlargements—throughout the movement arise from the need to work out and then dissipate the tensions resulting from this uncommonly close succession of changes in design and, in particular, from the effects of contraction occasioned by the slides and the chordal pairs. [18] To my original remarks regarding the influence the passage exerts on the rest of the Musette I should like to add also the observation that durational groupings in the Musette’s extended developmental passages are remarkably regular. Like the brief spurt of periodicity that follows the double bar in the F-minor Courante and the growing accentual conformity of the G-minor Sarabande, they mitigate the accentual uncertainties of the earlier, thematic hemiolas. More important, later allusions to the chordal pairs that originally introduced the overlapping hemiolas present them in an expanded state, their ascending bass fourths altered to ascending fifths (bars 49– 53, Example 10 in the present article). The bass line carrying the ascending fifths rises, like the bass line that carried the hemiolas’ original ascending fourths, from E to F and G; instead of continuing up to A, though, it quickly falls back to F and E. By allowing each chord to occupy a full measure rather than just a quarter note, Handel sidesteps the questions that marked the original progression and paves the way for the introduction of altogether new tensions in the stormy C minor section that is to follow. It is perhaps a mere coincidence—but what a wonderful coincidence—that the C minor section (bars 81ff.) opens, as well, with a rising fifth in the bass, which ascends from tonic to dominant; however common and, in this instance, isolated from a sequential setting, the progression nonetheless carries a recollection of the earlier sequence (Example 10). [19] The hemiola, to be sure, occupies a special place in the Handelian repertoire, but its cultivation as a durational and tonal resource with consequences ranging well beyond its immediate appearance was hardly within Handel’s exclusive compositional domain. Overlapping hemiolas, in particular, appear with great frequency in the music of J.S. Bach, and especially in Bach’s Courantes, Sarabandes, and Minuets. Particularly worthy of study are such pieces as the Sarabande from the G-major Partita for Clavier, in which almost every four-bar group contains overlapping hemiolas that are expressed in different ways by different constellations of inner and outer voices. [20] Although the literature on the hemiola remains modest in scope, several important studies that shed considerable light on its durational properties (and offer some intriguing further references) have appeared in the recent and relatively recent past; I should like to close by calling them to the reader’s attention. Channan Willner The New York Public Library for the Performing Arts Music Division 40 Lincoln Center Plaza New York, NY 10023–7498 cwillner@nypl.org ### Works Cited Cohn, Richard. 1992. “Metric and Hypermetric Dissonance in the Menuetto of Mozart’s Symphony in G minor, K. 550,” Integral 6: 1–33. Cohn, Richard. 1992. “Metric and Hypermetric Dissonance in the Menuetto of Mozart’s Symphony in G minor, K. 550,” Integral 6: 1–33. Corrigan, Vincent. 1992. “Hemiola in the Eighteenth Century.” In Johann Sebastian: A Tercentenary Celebration, ed. Seymour L. Benstock. 23–32. Westport, CT: Greenwood Press. Corrigan, Vincent. 1992. “Hemiola in the Eighteenth Century.” In Johann Sebastian: A Tercentenary Celebration, ed. Seymour L. Benstock. 23–32. Westport, CT: Greenwood Press. Grave, Floyd K. 1995. “Metrical Dissonance in Haydn.” Journal of Musicology 13, no. 2, 168–202. Grave, Floyd K. 1995. “Metrical Dissonance in Haydn.” Journal of Musicology 13, no. 2, 168–202. Hlawicka, Karl. 1971. “Musikalischer Rhythmus und Metrum.” Die Musikforschung 24, no. 4: 385–406. Hlawicka, Karl. 1971. “Musikalischer Rhythmus und Metrum.” Die Musikforschung 24, no. 4: 385–406. Hlawicka, Karl. 1958. “Die rhythmische Verwechslung.” Die Musikforschung 11, no. 1: 33–49. —————. 1958. “Die rhythmische Verwechslung.” Die Musikforschung 11, no. 1: 33–49. Jackson, Timothy L. 1989. “Mozart’s ‘Little Gigue’ in G major K. 574: A Study in Rhythmic Shift—A Reminiscence of the Competition with Haessler.” Mitteilungen der Internationalen Stiftung Mozarteum 37, nos. 1–4: 70–80. Jackson, Timothy L. 1989. “Mozart’s ‘Little Gigue’ in G major K. 574: A Study in Rhythmic Shift—A Reminiscence of the Competition with Haessler.” Mitteilungen der Internationalen Stiftung Mozarteum 37, nos. 1–4: 70–80. Krebs, Harald. 1987. “Some Extensions of the Concepts of Metrical Consonance and Dissonance.” Journal of Music Theory 31, no. 1: 99–120. Krebs, Harald. 1987. “Some Extensions of the Concepts of Metrical Consonance and Dissonance.” Journal of Music Theory 31, no. 1: 99–120. Little, Meredith Ellis, and Natalie Jenne. 1992. Dance and the Music of J. S.Bach. Bloomington: Indiana University Press. Little, Meredith Ellis, and Natalie Jenne. 1992. Dance and the Music of J. S.Bach. Bloomington: Indiana University Press. Schneider, Herbert. 1992. “Structure metriques du menuet au XVIIe et au debut du XVIIIe siecle.” Revue de Musicologie 78, no. 1: 27–65. Schneider, Herbert. 1992. “Structure metriques du menuet au XVIIe et au debut du XVIIIe siecle.” Revue de Musicologie 78, no. 1: 27–65. Sutton, Julia. 1985. “The Minuet: An Elegant Phoenix.” Dance Chronicle 8, nos. 3–4: 119–52. Sutton, Julia. 1985. “The Minuet: An Elegant Phoenix.” Dance Chronicle 8, nos. 3–4: 119–52. ### Footnotes 1. I wish to thank Floyd K. Grave for reading both articles and offering illuminating comments on the intricacies of Handel’s G-minor Sarabande, which I discuss in the course of this study. 2. Joel Lester, The Rhythms of Tonal Music (Carbondale and Edwardsville, Ill.: Southern Illinois University Press, 1986), 3–4 and 18–21. This durational accent is considerably intensified by the trill embellishing C5, but the trill, which appears in brackets or parentheses in the most reliable editions, is implicit in Handel’s melodic outline (note the two eighths by which it is followed) rather than explicit in his text. 3. It is possible to find several hemiolic implications in bars 9–12, especially across bars 10–11 and 11–12. These, I believe, represent an allusion to bars 5–7 that is superseded by the more obvious parallelisms among the second-beat emphases throughout the passage. The emphases win out (as we shall presently see) on account of the stronger need to evoke the durational design of bars 1–4. 4. Floyd K. Grave (private communication) has suggested that the Sarabande rhythm’s second-beat emphasis comes into its own in bars 13–15 and persists as an unnotated expression of ${\text{}}_{4}^{2}$ time through the second beat of bar 15 (the tied E5 standing for a quarter-note rest at the beginning of bar 15); and that the sense of an event is underscored by the entrance of A5 in bar 13. The melodic peak of the Sarabande, it also contradicts the inner-voice A4 of bar 12 in much the same way that the F5 of bar 5 contradicted the F4 of bar 4. These wonderful observations are by no means incompatible with mine and reflect the extraordinary richness of meaning with which Handel invests the surface—particularly remarkable in view of the substantial rests and static F-minor harmony (also pointed out by Grave) that pervade the passage. 5. The hemiolic implications of bars 25–27 echo those of bars 10–12 (see footnote 3, above) but they are more explicitly articulated owing to the intensified activity on the third beat of bar 25. 6. Like most of Handel’s Courantes, the piece under discussion is really a Corrente, but Handelians—unlike Bach scholars—persist in using the French term even when the Italian is clearly preferable. To maintain Handelian consistency, I retain the French form here. 7. Bar 12 includes the overlapping hemiolas’ grey area, their “pivot zone,” spanning beats 1 and 2. Our retrospective interpretation of the area’s metrical disposition allows the chords on B and C (beats 1 and 3) to assert their accentual primacy over the appoggiatura-like chords by which they are preceded. The parallel tenths between the outer voices in bars 12–13 allow both performers and listeners to absorb the accentual reinterpretation in a fluent, unforced way. Paradoxically, both appearances of the underlying A (bar 11, beat 2; bar 13, beat 1) are metrically weaker than those of B and C, which prolong A; but the metrical weakness of structural chords following their introduction by sequential appoggiatura chords and preceding the appearance of still more structural chords (such as the dominant on beats 2 and 3 of bar 13) is quite common. 8. Similar pairs of hemiolic chords appear as an idiom under more straightforward circumstances throughout the Classical era. In their later formation, they extend for four—rather than three—bars, and therefore divide into two sets of complete hemiolas. See, for instance, the second movement from Haydn’s Keyboard Sonata in D, No. 61 [Hoboken XVI: 51], bars 31–34, for a particularly dramatic example; or the Menuet from Haydn’s Symphony No. 99 in E, bars 52–55. Though they don’t occur very frequently, such groups of successive hemiolas are by no means uncommon in the Classical style (see also Mozart’s Little Gigue in G, K. 574, which incorporates successive hemiolas in its principal thematic material as a well-known borrowing of similar hemiolas from the Gigue of Handel’s F-minor Suite). For a set of genuine late 18th-century overlapping hemiolas see Mozart’s Piano Concerto in B, K. 595, third movement, bars 51–52; the hemiolas appear in the bass line, extending from the middle of bar 51 through the end of bar 52 (the movement is in ${\text{}}_{8}^{6}$ time, and the hemiolas span the duration of what would be three bars in ${\text{}}_{8}^{3}$ time). Canonic hemiolas in the Menuetto from Mozart’s G-minor Symphony, K. 550, that in some ways resemble overlapping hemiolas are discussed by Richard Cohn (1992), pages 22–26, Example 7 (bars 28–36). Canonic hemiolas occur in different voices; overlapping hemiolas are usually collapsed onto a single voice or onto several voices moving simultaneously. I wish to thank Floyd K. Grave for reading both articles and offering illuminating comments on the intricacies of Handel’s G-minor Sarabande, which I discuss in the course of this study. Joel Lester, The Rhythms of Tonal Music (Carbondale and Edwardsville, Ill.: Southern Illinois University Press, 1986), 3–4 and 18–21. This durational accent is considerably intensified by the trill embellishing C5, but the trill, which appears in brackets or parentheses in the most reliable editions, is implicit in Handel’s melodic outline (note the two eighths by which it is followed) rather than explicit in his text. It is possible to find several hemiolic implications in bars 9–12, especially across bars 10–11 and 11–12. These, I believe, represent an allusion to bars 5–7 that is superseded by the more obvious parallelisms among the second-beat emphases throughout the passage. The emphases win out (as we shall presently see) on account of the stronger need to evoke the durational design of bars 1–4. Floyd K. Grave (private communication) has suggested that the Sarabande rhythm’s second-beat emphasis comes into its own in bars 13–15 and persists as an unnotated expression of ${\text{}}_{4}^{2}$ time through the second beat of bar 15 (the tied E5 standing for a quarter-note rest at the beginning of bar 15); and that the sense of an event is underscored by the entrance of A5 in bar 13. The melodic peak of the Sarabande, it also contradicts the inner-voice A4 of bar 12 in much the same way that the F5 of bar 5 contradicted the F4 of bar 4. These wonderful observations are by no means incompatible with mine and reflect the extraordinary richness of meaning with which Handel invests the surface—particularly remarkable in view of the substantial rests and static F-minor harmony (also pointed out by Grave) that pervade the passage. The hemiolic implications of bars 25–27 echo those of bars 10–12 (see footnote 3, above) but they are more explicitly articulated owing to the intensified activity on the third beat of bar 25. Like most of Handel’s Courantes, the piece under discussion is really a Corrente, but Handelians—unlike Bach scholars—persist in using the French term even when the Italian is clearly preferable. To maintain Handelian consistency, I retain the French form here. Bar 12 includes the overlapping hemiolas’ grey area, their “pivot zone,” spanning beats 1 and 2. Our retrospective interpretation of the area’s metrical disposition allows the chords on B and C (beats 1 and 3) to assert their accentual primacy over the appoggiatura-like chords by which they are preceded. The parallel tenths between the outer voices in bars 12–13 allow both performers and listeners to absorb the accentual reinterpretation in a fluent, unforced way. Paradoxically, both appearances of the underlying A (bar 11, beat 2; bar 13, beat 1) are metrically weaker than those of B and C, which prolong A; but the metrical weakness of structural chords following their introduction by sequential appoggiatura chords and preceding the appearance of still more structural chords (such as the dominant on beats 2 and 3 of bar 13) is quite common. Similar pairs of hemiolic chords appear as an idiom under more straightforward circumstances throughout the Classical era. In their later formation, they extend for four—rather than three—bars, and therefore divide into two sets of complete hemiolas. See, for instance, the second movement from Haydn’s Keyboard Sonata in D, No. 61 [Hoboken XVI: 51], bars 31–34, for a particularly dramatic example; or the Menuet from Haydn’s Symphony No. 99 in E, bars 52–55. Though they don’t occur very frequently, such groups of successive hemiolas are by no means uncommon in the Classical style (see also Mozart’s Little Gigue in G, K. 574, which incorporates successive hemiolas in its principal thematic material as a well-known borrowing of similar hemiolas from the Gigue of Handel’s F-minor Suite). For a set of genuine late 18th-century overlapping hemiolas see Mozart’s Piano Concerto in B, K. 595, third movement, bars 51–52; the hemiolas appear in the bass line, extending from the middle of bar 51 through the end of bar 52 (the movement is in ${\text{}}_{8}^{6}$ time, and the hemiolas span the duration of what would be three bars in ${\text{}}_{8}^{3}$ time). Canonic hemiolas in the Menuetto from Mozart’s G-minor Symphony, K. 550, that in some ways resemble overlapping hemiolas are discussed by Richard Cohn (1992), pages 22–26, Example 7 (bars 28–36). Canonic hemiolas occur in different voices; overlapping hemiolas are usually collapsed onto a single voice or onto several voices moving simultaneously. [1] Copyrights for individual items published in Music Theory Online (MTO) are held by their authors. 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Rothfarb, General Editor and Tahirih Motazedian, Editorial Assistant	2020-01-22 23:55:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 6, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46214884519577026, "perplexity": 5749.146981374541}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250607596.34/warc/CC-MAIN-20200122221541-20200123010541-00173.warc.gz"}
https://nwrickert.wordpress.com/2018/03/	March 29, 2018 ## Morality and Quantum Mechanics Quick editorial comment: the connection that I make between morality and quantum mechanics is entirely metaphorical. I am not proposing that quantum physicists work on moral philosophy. This post is mostly a response to Dan Kaufman’s post at The Electric Agora: I am posting it here, because my response is a bit long for a comment on Dan’s post. I have usually avoided moral theories, because it has seemed obvious that they could not work. In his post, Dan is pretty much arguing that. He is arguing that moral theories don’t work and probably cannot work. This is refreshing, given that we are so often bombarded with arguments that propose moral theories. ### Description Dan is discussing the difficulties of a rules based approach to moral issues. We have, with science, a pretty good rules based approach to description. And that’s where my metaphor arises. So I’ll start with a rough overview of science as description. March 28, 2018 ## Saying true things about the world This continues my series of posts on truth. Up to now, my discussion has mainly been technical. But truth matters to us because we want to be able to say true things. We use natural language statements about the world (where “world” is understood broadly) in order to say those true things. Linguistics is not my area, but I cannot avoid it completely. Chomsky’s linguistics is based on the idea that language is a syntactic structure. Presumably the semantics are an add-on to that underlying syntactic structure, although Chomsky doesn’t say much about how semantics makes it into language. I very much disagree with Chomsky’s view of language. As I see it, language is primarily semantic. I see the rules of syntax as mostly an ad hoc protocol used for disambiguation. So today’s post will be mainly about semantics or meanings. This has to do with how words can refer to things in the world, or how words can be about something. This is related to the philosophical problem of intentionality (or aboutness) of language statements. Here I will be presenting only a broad overview. I expect to get into more details in future posts. ### Carving up the world I hinted at the idea when I presented my modest theory of truth. There, I said: Similarly, if I were to say “the cat is on the mat”, you would see that as true provided that I had followed the standards of the linguistic community in the way that I used the words “cat”, “on” and “mat”. According to my theory of truth, we need standards for the use of words such as “cat”, “on” and “mat”, and we judge the truth of a statement based on whether it conforms to those standards. Tags: , March 21, 2018 ## Truth and pragmatics We make decisions. That’s a good part of what we do. For example, I have just decided to compose a post about decision making. But how do we make decisions? How do we decide? Generally speaking, we make some decisions on the basis of what is true. And we make other decisions on the basis of what works best for us. That latter kind of decision is usually said to be a pragmatic choice. ### Examples If I am solving a mathematical problem such as balancing my checkbook, then I am making decisions based on truth. If I am working on a logic problem, again that is going to be making decisions based on truth. I walk into a restaurant, look at the menu, and decide what to order. That’s normally a pragmatic choice. It need not be. Perhaps I have created a rule for myself that if it is Sunday I should order the first item on the menu, if it is Monday I should order the second item, etc. If I am exactly following those rules, then I am making a decision based on truth. But that isn’t what we normally do when ordering a meal at a restaurant. Tags: , March 14, 2018 ## Does consciousness exist? To answer the title question, of course consciousness exists. Galen Strawson has an article in the New York Review of Books (h/t Brian Leiter): I doubt that I am on Strawson’s list of deniers, but perhaps only because he doesn’t know who I am. What is the silliest claim ever made? The competition is fierce, but I think the answer is easy. Some people have denied the existence of consciousness: conscious experience, the subjective character of experience, the “what-it-is-like” of experience. Given that introduction, I would probably fit right in with Strawson’s deniers. March 11, 2018 ## Odds and ends about truth In my previous post, I proposed a somewhat limited theory of truth. Here I’ll discuss some of the issues that might arise out of that theory. ### What if there are no relevant standards? According to my theory, we assess the truth of a statement based on accepted standards for evaluating that truth. So what will happen if there are no applicable standards? The simple answer, is that we cannot assess the truth of that statement. This is not really a new situation. When Gödel proved his incompleteness theorem, he showed that there are mathematical statements (arithmetic statements) cannot be proved true or false. Such statements are often said to be undecidable. If you use my suggested theory of truth, then there will be undecidable statements in ordinary life, and not just in mathematics. The existence of undecidable statement has not been any kind of calamity in mathematics. And it is unlikely to pose a serious problem in ordinary life. ### What about the law of the excluded middle? According the the law of the excluded middle (or LEM), a statement is either true or false. However, LEM is usually considered a law or reasoning, rather than part of a theory of truth. Mathematicians still use LEM in their reasoning, following Gödel’s incompleteness theorem. And it does appear to cause any problems. I would expect the same to be true in ordinary life. If you use my suggested theory of truth, you will not have to give up LEM as part of your reasoning strategy. ### Changing standards What happens if we change standards? March 5, 2018 ## A modest theory of truth I have previously discussed some of the problems that I have with the so-called correspondence theory of truth. In this post, I shall suggest my own theory. I am describing it as modest, because it does not attempt to settle all truth questions. The use of “true” in ordinary language is a mess, and my theory will not attempt to address all such use. Rather, it is intended only for technical uses, such as in mathematics and science. In my last post, I made a distinction between ordinary mathematical statements such as $3+5=8$ and the axiom systems (such as the Peano axioms) that we use to prove those ordinary statements. There is widespread agreement on truth questions about those ordinary mathematical questions. But there is less agreement about whether axioms are true. Mathematics can be done, without settling questions on the truth of the axioms used. Coming up with axiom systems is also part of mathematics. But when a new axiom system is offered, the main concern is on whether that axiom system is useful. Whether the axioms are true is often not asked, perhaps because there isn’t a good way to decide. Axiom systems are usually adopted on a pragmatic basis. That is, they are adopted for their usefulness. Something similar happens in science. The ideal gas laws of physics are a good example. Those laws are true only for an imagined ideal gas. They are false for any real gas. But although technically false, they provide a pretty good approximation of the behavior of real gases. And that makes them very useful. So, with the gas laws, we see important scientific laws that are adopted on a pragmatic basis, even though they might be technically false.	2019-12-15 05:13:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 1, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5071914196014404, "perplexity": 1169.6104989973653}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541301598.62/warc/CC-MAIN-20191215042926-20191215070926-00116.warc.gz"}
https://github.com/Khan/khan-exercises/blob/khan_people/exercises/angles_of_a_polygon.html	# Khan/khan-exercises ### Subversion checkout URL You can clone with HTTPS or Subversion. Fetching contributors… Cannot retrieve contributors at this time 95 lines (92 sloc) 4.472 kb Angles of a polygon randRange( 5, 7 ) 180 * ( SIDES - 2 ) {} What is the sum of this polygon's interior angles? init({ range: [ [ -5, 5 ], [ -1, 5 ] ], scale: [ 40, 40 ] }); graph.polygon = new Polygon( SIDES ); graph.polygon.draw(); CLONE = graph.polygon.clone(); There are a couple ways to approach this problem. Does it help to remember that there are 180 degrees in a triangle? Since this polygon has SIDES sides, we can draw SIDES triangles that all meet in the center. We can combine all the triangles' angles, and then we must subtract 360 degrees because the circle in the middle is extra. \begin{align}&SIDES \times 180^{\circ} - 360^{\circ} \\ &= SIDES 180^{\circ} - 360^{\circ} \\ &= ANSWER^{\circ}\end{align*} An alternative approach is shown below. We can use four of the cardinal( SIDES ) sides to make 2 triangles, as shown in orange. init({ range: [ [ -5, 5 ], [ -1, 5 ] ] }); graph.polygon = CLONE; graph.polygon.draw(); graph.polygon.drawDiagonals( randRange( 0, SIDES - 1 ) ); There plural( "is", SIDES - 4 ) plural( SIDES - 4, "side" ) between the orange triangles, to make SIDES - 4 additional plural( "triangle", SIDES - 4 ). We chopped this polygon into SIDES - 2 triangles, and each triangle's angles sum to 180 degrees. SIDES - 2 \times 180^{\circ} = ANSWER^{\circ} The sum of the polygon's interior angles is ANSWER degrees. What is the sum of this polygon's exterior angles? init({ range: [ [ -6, 6 ], [ -2, 7 ] ] }); graph.polygon = new Polygon( SIDES ); graph.polygon.draw(); 360 degrees The exterior angles are shown above. graph.polygon.drawExteriorAngles(); graph.polygon.animateExteriorAngles( randRange( 0, SIDES - 1 ) ); The exterior angles fit together to form a circle Therefore, the sum of the exterior angles is 360 degrees. Something went wrong with that request. Please try again.	2015-03-02 15:44:43	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9827455282211304, "perplexity": 3285.36749675368}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936462839.81/warc/CC-MAIN-20150226074102-00032-ip-10-28-5-156.ec2.internal.warc.gz"}
https://www.thejournal.club/c/paper/103391/	#### Efficient L1-Norm Principal-Component Analysis via Bit Flipping It was shown recently that the $K$ L1-norm principal components (L1-PCs) of a real-valued data matrix $\mathbf X \in \mathbb R^{D \times N}$ ($N$ data samples of $D$ dimensions) can be exactly calculated with cost $\mathcal{O}(2^{NK})$ or, when advantageous, $\mathcal{O}(N^{dK - K + 1})$ where $d=\mathrm{rank}(\mathbf X)$, \$K	2021-11-30 06:33:11	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8369210362434387, "perplexity": 4122.597279264617}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358953.29/warc/CC-MAIN-20211130050047-20211130080047-00145.warc.gz"}
http://mathhelpforum.com/algebra/19218-equation-set-up.html	Math Help - equation set up 1. equation set up The product of 2 numbers is 800. The difference is 7. annndddddd. The sum of 3 numbers is 47. the second number is 5 time bigger than the smallestt.the third number is 5 times larger than the second number. 2. Originally Posted by Buttnessa The product of 2 numbers is 800. The difference is 7. ? $xy = 880$ $x-y=7$ 3. Originally Posted by Buttnessa The sum of 3 numbers is 47. the second number is 5 time bigger than the smallestt.the third number is 5 times larger than the second number. Let the smallest number be $x$, so the median number is $5x$, and the largest number is $5(5x) = 25x$ there sum is 47, so we have: $x + 5x + 25x = 47$ now continue	2015-08-04 00:39:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6032521724700928, "perplexity": 477.52234401925523}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042990123.20/warc/CC-MAIN-20150728002310-00013-ip-10-236-191-2.ec2.internal.warc.gz"}
http://mathoverflow.net/feeds/question/56892	Entropy of nested compact invariant sets - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-26T05:55:26Z http://mathoverflow.net/feeds/question/56892 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56892/entropy-of-nested-compact-invariant-sets Entropy of nested compact invariant sets Peng Sun 2011-02-28T12:55:24Z 2011-11-24T15:15:40Z <p>Let $f$ be a homeomorphism on a compact metric space $X$. $K_1\supset K_2\supset\cdots \supset K$ are compact subsets of $X$ such that $f(K_n)=K_n$ and $K=\bigcap K_n$. If $h(f, K_1)<\infty$, do we always have $h(f,K)=\lim h(f,K_n)$?</p> <p>I can show that this is true for $C^\infty$ diffeomorphisms where the entropy map of invariant measures is upper semi-continuous.</p> <p>OK. I see the point. This is definitely false for the most general case. For example, take the union of countable hyperbolic toral automorphisms of shrinking size and add one point with Identity map on it.</p> <p>However, what if $f$ is a diffeomorphism on a compact manifold? I still expect negative answer.</p> http://mathoverflow.net/questions/56892/entropy-of-nested-compact-invariant-sets/56906#56906 Answer by Benoît Kloeckner for Entropy of nested compact invariant sets Benoît Kloeckner 2011-02-28T15:46:19Z 2011-02-28T15:46:19Z <p>The answer is negative: consider the map $\varphi:z\mapsto z^2$ acting on the unit disc $D(1)$ of $\mathbb{C}$. We know that this map has entropy $\log 2$ in restriction to every circle centered at $0$, and in fact since the dynamics is trivial transversally to this circle we have $h(\varphi,D(1))=\log 2$. Now, consider $K_n=D(1/n)$: we still have $h(\varphi,K_n)=\log 2$ since $\varphi_{\|K_n}$ is conjugated to $\varphi$. But then <code>$K=\{0\}$</code> and <code>$h(\varphi,\{0\})=0$</code>!</p> <p>Ok, I cheated: $\varphi$ is not a homeomorphism. But there is an obvious way to extend the above example to an homeomorphism. First take $\psi:Y\to Y$ a positive entropy one, then construct $c\psi : cY\to cY$ its cone as follows. First, $cY$ is the topological cone over $Y$, that is $cY=(Y\times[0,1])/((x,0)\~ (y,O))$. Then $c\psi$ is the map induced on this quotient by $(x,t)\mapsto (\psi(x),t)$. Then $c\psi$ is a homeomorphism, and has the same entropy as $\psi$. But taking $K_n$ the trace on the quotient of $Y\times[0,1/n]$ you get a sequence of compacts on which the dynamics is the same than for the full map, but whose intersection is reduced to a point.</p> http://mathoverflow.net/questions/56892/entropy-of-nested-compact-invariant-sets/81809#81809 Answer by lbdl for Entropy of nested compact invariant sets lbdl 2011-11-24T15:15:40Z 2011-11-24T15:15:40Z <p>The strategy of Benoît Kloeckner fails for differentiable maps. Indeed if $K$ is a single point and $K_n$ invariant balls around $K$ it implies that $K$ is an attracting fixed point. Therefore the log of the differential of the diffeo $f$ should be close to zero near $K$ and so does the entropy.</p> <p>However conter-examples in any finite smoothness ($C^r$ maps with $1\leq r<+\infty$) were given by Misisurewicz in the early seventies :</p> <p>Diffeomorphism without any measure with maximal entropy, Bull. Acad. Pol. Sci., Ser. sci. math., astr. et phys. 21 (1973), 903--910 </p>	2013-05-26 05:55:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9480530619621277, "perplexity": 300.4445987124616}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706631378/warc/CC-MAIN-20130516121711-00074-ip-10-60-113-184.ec2.internal.warc.gz"}
https://www.openfoam.com/documentation/guides/latest/api/solverFieldSelection_8H_source.html	The open source CFD toolbox solverFieldSelection.H Go to the documentation of this file. 1/---------------------------------------------------------------------------\ 2 ========= \| 3 \\ / F ield \| OpenFOAM: The Open Source CFD Toolbox 4 \\ / O peration \| 5 \\ / A nd \| www.openfoam.com 6 \\/ M anipulation \| 7------------------------------------------------------------------------------- 8 Copyright (C) 2017-2019 OpenCFD Ltd. 9------------------------------------------------------------------------------- 11 This file is part of OpenFOAM. 12 13 OpenFOAM is free software: you can redistribute it and/or modify it 15 the Free Software Foundation, either version 3 of the License, or 16 (at your option) any later version. 17 18 OpenFOAM is distributed in the hope that it will be useful, but WITHOUT 19 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or 20 FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License 21 for more details. 22 23 You should have received a copy of the GNU General Public License 24 along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>. 25 26Class 27 Foam::functionObjects::volFieldSelection 28 29Description 30 Helper class to manage solver field selections 31 32SourceFiles 33 solverFieldSelection.C 34 35\---------------------------------------------------------------------------/ 36 37#ifndef functionObjects_solverFieldSelection_H 38#define functionObjects_solverFieldSelection_H 39 40#include "fieldSelection.H" 41 42// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // 43 44namespace Foam 45{ 46namespace functionObjects 47{ 48 49/---------------------------------------------------------------------------\ 50 Class solverFieldSelection Declaration 51\---------------------------------------------------------------------------/ 54: 55 public fieldSelection 56{ 57private: 58 59 // Private Member Functions 60 61 //- No copy construct 63 64 65public: 66 67 //- Construct from object registry 69 ( 70 const objectRegistry& obr, 71 const bool includeComponents = false 72 ); 73 74 75 //- Destructor 76 virtual ~solverFieldSelection() = default; 77 78 79 // Member Functions 80 81 //- Update the selection using current contents of obr_ 83}; 84 85 86// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // 87 88} // End namespace functionObjects 89} // End namespace Foam 90 91// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * // 92 93#endif 94 95// ************************************************************************* // Helper class to manage field selections.	2023-04-02 08:31:13	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8579015731811523, "perplexity": 1004.6472348953669}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950422.77/warc/CC-MAIN-20230402074255-20230402104255-00345.warc.gz"}
http://git.kamailio.org/gitlist/index.php/sip-router/blame/vseva/mod_fix_pvar_3/modules/p_usrloc/utime.c	modules/p_usrloc/utime.c 71a26065 /* * Usrloc time related functions * * Copyright (C) 2001-2003 FhG Fokus * * This file is part of Kamailio, a free SIP server. * * Kamailio is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2 of the License, or * (at your option) any later version * * Kamailio 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, write to the Free Software 9e1ff448 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA 71a26065 / /! \file * \brief USRLOC - time related functions * \ingroup usrloc * * - Module \ref usrloc */ #include "utime.h" time_t act_time; void get_act_time(void) { act_time = time(0); }	2020-06-06 08:30:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8447498679161072, "perplexity": 3238.2766748087097}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348511950.89/warc/CC-MAIN-20200606062649-20200606092649-00060.warc.gz"}
https://en.wikipedia.org/wiki/Antiperovskite_(structure)	# Antiperovskite (structure) Antiperovskites (or inverse perovskites) is a type of crystal structure similar to the perovskite structure that is common in nature.[1] The key difference is that the positions of the cation and anion constituents are reversed in the unit cell structure. In contrast to perovskite, antiperovskite compounds consist of two types of anions coordinated with one type of cation. Antiperovskite compounds are an important class of materials because they exhibit interesting and useful physical properties not found in perovskite materials. ## Structure The crystal lattice of an antiperovskite structure is the same as that of the perovskite structure, but the anion and cation positions are switched. The typical perovskite structure is represented by the general formula ABX3, where A and B are cations and X is an anion. When the anion is the (divalent) oxide ion, A and B cations can have charges 1 and 5, resepectively, 2 and 4, respectively, or 3 and 3, respectively. In antiperovskite compounds, the general formula is reversed, so that the X sites are occupied by an electropositive ion, i.e., cation (such as an alkali metal), while A and B sites are occupied by different types of anion. In the ideal cubic cell, the A anion is at the corners of the cube, the B anion at the octahedral center, and the X cation is at the faces of the cube. Thus the A anion has a coordination number of 12, while the B anion sits at the center of an octahedron with a coordination number of 6. Similar to the perovskite structure, most antiperovskite compounds are known to deviate from the ideal cubic structure, forming orthorhombic or tetragonal phases depending on temperature and pressure. Whether a compound will form an antiperovskite structure depends not only on its chemical formula, but also the relative sizes of the ionic radii of the constituent atoms. This constraint is expressed in terms of the Goldschmidt tolerance factor, which is determined by the radii, ra, rb and rx, of the A, B, and X ions. Tolerance factor = ${\displaystyle {\frac {(r_{a}+r_{x})}{{\sqrt {2}}(r_{b}+r_{x})}}}$ For the antiperovskite structure to be structurally stable, the tolerance factor must be between 0.71 and 1. If between 0.71 and 0.9, the crystal will be orthorhombic or tetragonal. If between 0.9 and 1, it will be cubic. By mixing the B anions with another element of the same valence but different size, the tolerance factor can be altered. Different combinations of elements result in different compounds with different regions of thermodynamic stability for a given crystal symmetry. ## Occurrence Antiperovskites naturally occur in sulphohalite, galeite, schairerite, kogarkoite, nacaphite, arctite, polyphite, and hatrurite.[1] It is also demonstrated in superconductive compounds such as CuNNi3 and ZnNNi3. ## Material Properties ### Synthesized Antiperovskites Man-made antiperovskites exhibit interesting properties. The physical properties of antiperovskite compounds can be manipulated by altering the stoichiometry, element substitution, and synthesis conditions. #### Lithium Rich Antiperovskites (LiRAP) Recently synthesized antiperovskites with chemical formula Li3OBr and Li3OCl have demonstrated high lithium-ion conductivity. Known as LiRAPs, these are being investigated for use in solid-state batteries and fuel cells. In addition, other alkali-rich antiperovskites such as Na3OCl are also being investigated for their superionic conductivity. #### Metallic Antiperovskite Discovered in 1930, these crystals have the formula M3AB where M represents a magnetic element, Mn, Ni, or Fe; A represents a transition or main group element, Ga, Cu, Sn, and Zn; and B represents N, C, or B. These materials exhibit superconductivity, giant magnetoresistance, and other unusual properties. #### Antiperovskite manganese nitrides Antiperovskite manganese nitrides have been shown to exhibit zero thermal expansion. ## References 1. ^ a b Krivovichev, Sergey (2008-01-01). "Minerals with antiperovskite structure: A review". Zeitschrift Fur Kristallographie - Z KRISTALLOGR. 223 (1–02): 109–113. Bibcode:2008ZK....223..109K. doi:10.1524/zkri.2008.0008.	2019-03-24 03:22:36	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7311573028564453, "perplexity": 2968.4538927552762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912203168.70/warc/CC-MAIN-20190324022143-20190324044143-00135.warc.gz"}
http://www.dcs.kcl.ac.uk/?search=au:Linus%20au:Wulff	Found 1 result(s) ### 09.02.2017 (Thursday) #### Generalized type II supergravity from kappa symmetry Regular Seminar Linus Wulff (Imperial) at: 14:00 QMWroom G.O. Jones 610 abstract: It has been known since the 80's that the Green-Schwarz superstring possesses the fermionic kappa symmetry, required for the consistency of the formulation, if the target space is a solution of the supergravity equations of motion. However, contrary to the standard lore and previous claims in the literature, it was recently shown that the converse is not true. Kappa symmetry of the Green-Schwarz superstring implies only a weaker set of equations for the target space fields, which we refer to as generalized supergravity equations. I will describe these equations for the type II case and contrast them with the standard type II supergravity equations which arise as a special case.	2018-02-19 11:39:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6925909519195557, "perplexity": 742.3911293298269}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812584.40/warc/CC-MAIN-20180219111908-20180219131908-00675.warc.gz"}
http://jprm.sms.edu.pk/page/13/	# Journal of Prime Research in Mathematics Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing two issues in June and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year. Latest Published Articles ### Combined effect of slip and radiation on MHD flow past a constantly moving vertical plate with variable temperature JPRM-Vol. 1 (2016), Issue 1, pp. 130 – 144 Open Access Full-Text PDF M. A. Imran, Shakila Sarwar, M. Imran, Maryam Aleem. Abstract: The unsteady free convection of an MHD flow of a viscous fluid passing a vertical plate which is constantly moving with variable temperature is analyzed by taking slip and radiation into consideration. The dimensionless governing equations for temperature and velocity fields are solved using Laplace transform technique. The radiative and slip effects are taken into consideration and the whole system is rotating as a rigid body with a constant angular velocity about the z-axis. Exact solutions are obtained for the two components of velocity. Some known solutions from the literature are obtained as a limiting case. The obtained solutions satisfy the initial and boundary conditions. Some physical aspects of flow parameters on the fluid motion are graphically presented. ### Cartesian product of interval-valued fuzzy ideals in ordered semigroup JPRM-Vol. 1 (2016), Issue 1, pp. 120 – 129 Open Access Full-Text PDF Hidayat Ullah Khan, Asghar Khan, Nor Haniza Sarmin Abstract: Interval-valued fuzzy set theory is a more generalized theory that can deal with real world problems more precisely than ordinary fuzzy set theory. In this paper, the concepts of interval-valued fuzzy (prime, semiprime) ideal and the Cartesian product of interval-valued fuzzy subsets have been introduced. Some interesting results about Cartesian product of interval-valued fuzzy ideals, interval-valued fuzzy prime ideals, intervalvalued fuzzy semiprime ideals, interval-valued fuzzy bi-ideals and intervalvalued fuzzy interior ideals in ordered semigroups are obtained. The purport of this paper is to link ordinary ideals with interval-valued fuzzy ideals by means of level subset of Cartesian product of interval-valued fuzzy subsets. ### A novel approach to approximate unsteady squeezing flow through porous medium JPRM-Vol. 1 (2016), Issue 1, pp. 91 – 109 Open Access Full-Text PDF Mubashir Qayyum, Hamid Khan, M.T. Rahim Abstract: In this article, a new alteration of the Homotopy Perturbation Method (HPM) is proposed to approximate the solution of unsteady axisymmetric flow of Newtonian fluid. The flow is squeezed between two circular plates and passes through a porous medium channel. The alteration extends the Homotopy Perturbation with a Laplace transform, which is referred to as the Laplace Transform Homotopy Perturbation Method (LTHPM) in this manuscript. A single fourth order non-linear ordinary differential equation is obtained using similarity transformations. The resulting boundary value problem is then solved through LTHPM, HPM and fourth order Implicit Runge Kutta Method (IRK4). Convergence of the proposed scheme is checked by finding absolute residual errors of various order solutions. Also, the validity is confirmed by comparing numerical and analytical (LTHPM) solutions. The comparison of obtained residual errors shows that LTHPM is an effective scheme that can be applied to various initial and boundary value problems in science and engineering ### Reciprocal product degree distance of strong product of graphs JPRM-Vol. 1 (2016), Issue 1, pp. 79 – 90 Open Access Full-Text PDF K. Pattabiraman, A. Arivalagan, V.S.A. Subramanian Abstract: In this paper, the exact formula for the reciprocal product degree distance of strong product of a connected graph and the complete multipartite graph with partite sets of sizes $$m_0, m_1, . . . , m_{r−1}$$ is obtained. Using the results obtained here, the formula for the reciprocal degree distance of the closed fence graph is computed. ### Hardy-type inequalities involving generalized fractional integrals via superquadratic functions JPRM-Vol. 1 (2016), Issue 1, pp. 60 – 78 Open Access Full-Text PDF Sajid Iqbal, Josip Pecaric, Muhammad Samraiz ### Vertex-to-clique detour distance in graphs JPRM-Vol. 1 (2016), Issue 1, pp. 45 – 59 Open Access Full-Text PDF I. Keerthi Asir, S. Athisayanathan Abstract: Let $$v$$ be a vertex and $$C$$ a clique in a connected graph $$G$$. A vertex-to-clique $$u − C$$ path P is a $$u − v$$ path, where v is a vertex in $$C$$ such that $$P$$ contains no vertices of $$C$$ other than $$v$$. The vertex-to-clique distance, $$d(u, C)$$ is the length of a smallest $$u−C$$ path in $$G$$. A $$u−C$$ path of length $$d(u, C)$$ is called a $$u − C$$ geodesic. The vertex-to-clique eccentricity $$e_1(u)$$ of a vertex $$u$$ in $$G$$ is the maximum vertex-to-clique distance from $$u$$ to a clique $$C ∈ ζ$$, where $$ζ$$ is the set of all cliques in $$G$$. The vertex-to-clique radius $$r_1$$ of $$G$$ is the minimum vertex-to-clique eccentricity among the vertices of $$G$$, while the vertex-to-clique diameter $$d_1$$ of $$G$$ is the maximum vertex-to-clique eccentricity among the vertices of $$G$$. Also the vertex toclique detour distance, $$D(u, C)$$ is the length of a longest $$u−C$$ path in $$G$$. A $$u−C$$ path of length $$D(u, C)$$ is called a $$u−C$$ detour. The vertex-to-clique detour eccentricity $$e_{D1}(u)$$ of a vertex $$u$$ in $$G$$ is the maximum vertex-toclique detour distance from u to a clique $$C ∈ ζ$$ in $$G$$. The vertex-to-clique detour radius $$R_1$$ of $$G$$ is the minimum vertex-to-clique detour eccentricity among the vertices of $$G$$, while the vertex-to-clique detour diameter $$D_1$$ of $$G$$ is the maximum vertex-to-clique detour eccentricity among the vertices of $$G$$. It is shown that $$R_1 ≤ D_1$$ for every connected graph $$G$$ and that every two positive integers a and b with $$2 ≤ a ≤ b$$ are realizable as the vertex-to-clique detour radius and the vertex-to-clique detour diameter, respectively, of some connected graph. Also it is shown that for any three positive integers $$a$$, $$b$$, $$c$$ with $$2 ≤ a ≤ b < c$$, there exists a connected graph G such that $$r_1 = a$$, $$R_1 = b$$, $$R = c$$ and for any three positive integers $$a$$, $$b$$, $$c$$ with $$2 ≤ a ≤ b < c$$ and $$a + c ≤ 2b$$, there exists a connected graph $$G$$ such that $$d_1 = a$$, $$D_1 = b$$, $$D = c$$.	2022-10-02 08:56:23	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5354400873184204, "perplexity": 675.7435179169482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337307.81/warc/CC-MAIN-20221002083954-20221002113954-00728.warc.gz"}
https://tradingkhaso.netlify.app/hannibal15741fow/future-value-formula-financial-calculator-ku.html	## Future value formula financial calculator Answer to Complete the following using the future value formula or financial calculator. (Do not round intermediate calculations. Understanding the calculation of present value can help you set your calculator app, or any other financial calculator app that you can download to your When using a Microsoft Excel spreadsheet you can use a PV formula to do the The Excel FV function is a financial function that returns the future value of an investment. You can use Excel formula: Compare effect of compounding periods. Calculate the Inflation-Adjusted, After-Tax Future Value of a Single Deposit or Savings accounts at a financial institution may pay as little as 0.25% or less but That formula will give you the future value of an investment in nominal terms, 23 Feb 2018 This is called calculating the future value of your goal. There are mutual fund · excel · financial goals · Future Value · Inflation · present value Length of time, in years, that you plan to save. Step 3: Interest Rate. Estimated Interest Rate. Your estimated annual interest rate. The future value (FV) calculation allows investors to predict, with a very high degree using a financial calculator or manually by using the future value formula. Present value calculator, formula, real world and practice problems to It is an online a financial tool requires three positive real numbers, future value ## All financial calculators have five financial keys, and Excel's basic time value Never type a number directly into any formulas or Excel functions (unless that 20 Dec 2019 Put simply, FV is the future value of an asset adjusted for interest over time. It's a useful tool for investors and financial planners to estimate how Future value is the value of an asset at a specific date. It measures the nominal future sum of The financial compensation for saving it (and not spending it) is that the money value will accrue through the interests that he will This formula gives the future value (FV) of an ordinary annuity (assuming compound interest):. Among other places, it's used in the theory of stock valuation. See How Finance Works for the present value formula. You can also sometimes estimate present Deposit, No. of interest payments, Calculation, Accumulated amount. Year 1, $$\ text{R}\,\text{500}$$ Write down the given information and the future value formula. All financial calculators have five financial keys, and Excel's basic time value Never type a number directly into any formulas or Excel functions (unless that Future Value (FV) Formula is a financial terminology used to calculate the value of cash flow at a futuristic date as compared to the original receipt. The objective of ### 9 Mar 2020 NPV (Net present value) is the difference between the present value of cash inflows and outflows discounted at a specific rate. Read about the 20 Dec 2019 Put simply, FV is the future value of an asset adjusted for interest over time. It's a useful tool for investors and financial planners to estimate how ### All financial calculators have five financial keys, and Excel's basic time value Never type a number directly into any formulas or Excel functions (unless that Calculation of Future Value. The values which are described below are very essential when calculating the future value of an investment. Present Value: The 20 Jun 2019 the number of time periods involved algebra, financial calculator, or Excel NPER function. The exact formula that we can use depends on whether we are dealing We can use the expression for future value in case of simple interest to arrive Find out the number of periods in both financial instruments. ## Understanding the calculation of present value can help you set your calculator app, or any other financial calculator app that you can download to your When using a Microsoft Excel spreadsheet you can use a PV formula to do the Calculate the Inflation-Adjusted, After-Tax Future Value of a Single Deposit or Savings accounts at a financial institution may pay as little as 0.25% or less but That formula will give you the future value of an investment in nominal terms, 23 Feb 2018 This is called calculating the future value of your goal. There are mutual fund · excel · financial goals · Future Value · Inflation · present value Length of time, in years, that you plan to save. Step 3: Interest Rate. Estimated Interest Rate. Your estimated annual interest rate. The future value (FV) calculation allows investors to predict, with a very high degree using a financial calculator or manually by using the future value formula. Present value calculator, formula, real world and practice problems to It is an online a financial tool requires three positive real numbers, future value The future value (FV) calculation allows investors to predict, with a very high degree using a financial calculator or manually by using the future value formula. Present value calculator, formula, real world and practice problems to It is an online a financial tool requires three positive real numbers, future value The calculator is also a quick method of double checking your formula PV – present value (the amount of money at the beginning of the transaction.). Present Value Worth Equations Calculator. Finance Investment Analysis Formulas. Solving for present value or worth. present value or worth. note: If interest rate is	2022-08-18 07:53:06	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.24392065405845642, "perplexity": 1499.0437292694355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573172.64/warc/CC-MAIN-20220818063910-20220818093910-00559.warc.gz"}
http://energyeducation.ca/encyclopedia/Brake	# Braking The thermal energy generated during friction braking can be seen in this friction brake/rotor set-up during stress testing. Braking is the process of controlling the velocity of an object by inhibiting its motion. An object in motion possesses kinetic energy and to bring the object to a stop this kinetic energy must be removed. Removing the kinetic energy can be accomplished by dissipating the energy to the atmosphere through friction or by converting it into another form of energy. The most common type of braking is a mechanical brake which inhibits motion through friction brake pads. A mechanical brake applies a friction force to convert the kinetic energy of the vehicle into thermal energy which then dissipates into the atmosphere.[1] Braking systems which don't use friction are referred to as regenerative braking systems (RBSs). In RBSs, the kinetic energy is converted into other forms of useful energy, which can be stored for later use, increasing fuel efficiency. ## Background As with any system, the process of braking must follow the principal of conservation of energy. Energy cannot be created or destroyed but only converted from one form to another, $\Sigma E_{in}=\Sigma E_{out}$ The energy present in an object in motion is given by the following equation: $E_{kinetic}=\frac{(mv^2)}{2}$ where, $m$ is the mass of the object in kilograms (kg). $v$ is the velocity of the object in meters per second (m/s). $E_{kinetic}$ is the kinetic energy in joules (J) From this equation, and assuming the mass of the object is constant, it is clear the in order to remove the kinetic energy from the system, the velocity must be brought to zero. ## Friction braking Friction braking is the most commonly used braking method in modern vehicles. It involves the conversion of kinetic energy to thermal energy by applying friction to the moving parts of a system. The friction force resists motion and in turn generates heat, eventually bringing the velocity to zero. The energy taken from the system is given by the following equation: $E_{thermal}=F_f \times d$ where, $F_f$ is the force of friction in newtons (N). $d$ is the stopping distance in meters (m). $E_{thermal}$ is the thermal energy produced by the brakes in Joules. Applying conservation of energy to the above two equations, the thermal energy produced must equal the kinetic energy dissipated: $E_{kinetic}=E_{thermal}$; $\frac{(mv^2)}{2}=F_f \times d$; $F_f=\frac{(mv^2)}{2d}$ From this equation it can be seen that increasing the velocity or mass of an object means the applied friction force must be increased to bring the object to a stop in the same distance. ## Braking in motor vehicles ### Mechanical braking The most common method of braking in motor vehicles is mechanical or friction braking. In this method, some or all of the vehicles wheels are fitted with brake pads which apply a friction force that inhibits the motion of the wheels. Frictional braking results in a conversion of the kinetic energy gained from fuel consumption to thermal energy. This thermal energy then dissipates to the atmosphere in the form of waste heat. Large friction forces can be needed to inhibit a vehicle's motion, particularly in large machines and trucks which have a high mass and therefore high kinetic energy. The brake pads, which are responsible for applying the friction force, experience wear over the course of their life due to this friction force. The brake pad wear causes the brakes to become less effective over the course of their life and need regular replacement. ### Regenerative braking main article Regenerative braking system involves the removal of the kinetic energy of a moving object by converting it into another form of useful energy, such as electric, pneumatic, or stored kinetic energy. The use of regenerative braking can increase the overall efficiency of a motor vehicle by conserving some of its kinetic energy which can then be used to bring the vehicle back up to speed. ## References 1. How the braking system works \| How a Car Works. (n.d.). Retrieved from http://www.howacarworks.com/basics/how-the-braking-system-works	2017-06-26 01:49:24	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 12, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4855346977710724, "perplexity": 449.36068327182284}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320666.34/warc/CC-MAIN-20170626013946-20170626033946-00606.warc.gz"}
https://en.wikibooks.org/wiki/Digital_Signal_Processing/Continuous-Time_Fourier_Transform	# Digital Signal Processing/Continuous-Time Fourier Transform The Continuous-Time Fourier Transform (CTFT) is the version of the fourier transform that is most common, and is the only fourier transform so far discussed in EE wikibooks such as Signals and Systems, or Communication Systems. This transform is mentioned here as a stepping stone for further discussions of the Discrete-Time Fourier Transform (DTFT), and the Discrete Fourier Transform (DFT). The CTFT itself is not useful in digital signal processing applications, so it will not appear much in the rest of this book ## CTFT Definition The CTFT is defined as such: [CTFT] ${\displaystyle {\mathcal {F}}(\omega )=\int f(t)e^{-j\omega t}dt}$ ## Convolution Theorem Multiplication in the time domain becomes convolution in the frequency domain. Convolution in the time domain becomes multiplication in the frequency domain. This is an example of the property of duality. The convolution theorem is a very important theorem, and every transform has a version of it, so it is a good idea to become familiar with it now (if you aren't previously familiar with it).	2017-03-27 05:00:55	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8779706358909607, "perplexity": 291.3420212523706}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189403.13/warc/CC-MAIN-20170322212949-00309-ip-10-233-31-227.ec2.internal.warc.gz"}
https://scholars.unh.edu/dissertation/1852/	## Doctoral Dissertations Spring 1995 Dissertation Chemistry #### Degree Name Doctor of Philosophy The reactions of the dimolybdenum cage complex Mo(CO)$\sb4$-$\rm \lbrack\sp{i}Pr\sb2NPO\rbrack\sb4Mo(CO)\sb4\sp{}$ with phosphorus and nitrogen nucleophiles were studied. This dimolybdenum cage complex reacted with tertiary phosphines of the type PPh$\sb2$R (R = Ph, Me, H) in refluxing toluene. In each case, incorporation of a single phosphine led to the loss of three carbonyls to form orange complexes of the type $\rm Mo(CO)\sb3\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4Mo(CO)\sb2PPh\sb2R$(2, 3, 4). The X-ray molecular structure of 2 has been determined. This revealed that a cage P-O-P bond has been cleaved near the substitution site with the resulting phosphinito oxygen replacing a second CO. Additionally, the phosphido group generated displaced a third CO at the other Mo center to bridge the two metals which are now within bonding distance of each other. Under milder conditions, reactions using phosphite yielded both mono- and disubstituted products $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack\sb4Mo(CO)\sb3P(OMe)\sb3$ or $\rm Mo(CO)\sb3P(OMe)\sb3$-$\rm \lbrack \sp{i}Pr\sb2NPO\rbrack \sb4Mo(CO)\sb3P(OMe)\sb3$ with the original core structure intact. Both products were mixtures of diastereomers and can be transformed to orange $\rm Mo(CO)\sb3\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4Mo(CO)\sb2P(OMe)\sb3$. Treatment of the mixed-valent $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4Mo(CO)\sb2I\sb2$ cage complex with sodium dimethyldithiocarbamate selectively removed the divalent molybdenum vertex to give the metalla-ligand $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4$ (14) via an orange intermediate $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack\sb4$-$\rm Mo(CO)\sb2(S\sb2CNMe\sb2)\sb2$. The metalla-ligand has been characterized spectrally and by X-ray crystallography. It has been used as a precursor to assemble novel heterobimetallic cage complexes of the type $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4ML\sb{n}$ where ML$\sb{\rm n}$ can be $\rm Cr(CO)\sb4, Fe(CO)\sb3, Cu(MeCN)\sb2BF\sb4, AgNO\sb3, PtCl\sb2, NiBr\sb2$ and PdBr$\sb2$, or the type $\rm Mo(CO)\sb3\lbrack \sp{i}Pr\sb2NPO\rbrack \sb5ML\sb{n}$ where ML$\sb{\rm n}$ can be PdCl$\sb2$, PdBr$\sb2$. All these heterobimetallic cage complexes have been characterized by elemental analyses and spectral data. In addition, X-ray structures of the heterobimetallic cage complexes $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4MBr2$ (M = Ni(21), Pd(25)) have been determined. Comparison of the well-resolved Al carbonyl stretching frequency and the $\sp{13}$C NMR chemical shift of the cis-Mo(CO)$\sb4$ moiety in $\rm Mo(CO)\sb4\lbrack \sp{i}Pr\sb2NPO\rbrack \sb4ML\sb{n}$ and also the X-ray structures of 14, 21, 25 suggest a transmission of the increasing electron demand of the second cage metal to the molybdenum vertex. ftnSee Appendix A for the structure.	2020-10-24 06:08:57	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5542068481445312, "perplexity": 5810.327165881974}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107882102.31/warc/CC-MAIN-20201024051926-20201024081926-00056.warc.gz"}
https://nrich.maths.org/12182	### Pent The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus. ### Tuning and Ratio Why is the modern piano tuned using an equal tempered scale and what has this got to do with logarithms? ### Rarity Show that it is rare for a ratio of ratios to be rational. # Another Triangle in a Triangle ##### Age 16 to 18 Challenge Level: You may wish to look at Triangle in a Triangle and Areas and Ratios before exploring this problem. In the diagram below, points have been chosen that are one third of the way along each side. Each of these points is then joined to the opposite vertex. What fraction of the area of the whole triangle is the area of the green triangle? If you are not sure how to get started, click below to read some thoughts, hints and suggestions that might be helpful. Before moving onto the next hint, do as much as you can with the information you have already worked out. The base of triangle $a+f+e$ is $\tfrac{1}{3}$ of the base of the whole triangle. Can you use this to work out the area of $a+f+e$ as a fraction of the whole triangle? What about $a+b+c$ and $c+d+e$? We have three triangles, each with an area of $\tfrac{1}{3}$ of the whole triangle. But none of these tell us anything about $g$. But we do know that $a$, $b$, $c$, $d$, $e$, $f$ and $g$ together make the whole triangle! Can we combine all this to find an expression for $g$ in terms of other areas? It would be useful to know the areas of the little blue triangles... We know that: • $a$ has the same height as triangle $ECB$. • Triangle $ECB$ is $\tfrac{1}{3}$ of the whole triangle If we can find the length $EH$ as a fraction of $HB$, we could work out the area of the blue triangle... Sometimes it helps to add in an extra line... Can you find some similar triangles in this diagram? How does $EJ$ compare with $AF$? How does $EJ$ compare with $BF$ How does $EH$ compare with $HB$? How does $EH$ compare with $EB$? An alternative method for solving this problem is to use vectors.	2019-09-20 05:56:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5543908476829529, "perplexity": 253.9933147967939}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573832.23/warc/CC-MAIN-20190920050858-20190920072858-00456.warc.gz"}
http://openstudy.com/updates/4f57b86ae4b0c9fd2d4b6089	wowbriana 3 years ago how would i solve (7/8)-(1/x)=3/4 ? i got x=8 but i know for a fact thats not right. can someone please show me? 1. campbell_st it becomes -1/x = -1/8 (subtract 7/8 from both sides) equating denominators x = 8 2. wowbriana so i am right? 3. krypton yeah u are right honey :) got the same nswer 4. wowbriana lol thanks. i must have done the checking stage wrong then 5. krypton anytime :) just be a little bit careful,is math 6. phi Check $\frac{7}{8}-\frac{1}{8}= \frac{6}{8}= \frac{3}{4}$	2015-05-26 10:03:39	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.773621678352356, "perplexity": 6422.036138717008}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207928817.87/warc/CC-MAIN-20150521113208-00280-ip-10-180-206-219.ec2.internal.warc.gz"}
https://brilliant.org/problems/ajiteshs-function/	# Ajitesh's function Algebra Level 4 Consider a function $$f$$ from the real numbers to the real numbers, such that $$2f(xy) = [{f(x)}]^y + [{f(y)}]^x$$ for all real values $$x,y$$, and $$f(1) =2$$. If $$\sum_{i=1}^{100} f(i)$$ can be written as $$2^a-2$$, what is $$a$$? This problem is posed by Ajitesh M. ×	2017-05-22 17:42:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8763299584388733, "perplexity": 202.67344328835006}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463605485.49/warc/CC-MAIN-20170522171016-20170522191016-00360.warc.gz"}
http://kea-monad.blogspot.com/2007/08/blogrolling-on-ii.html	# Arcadian Functor occasional meanderings in physics' brave new world Name: Location: New Zealand Marni D. Sheppeard ## Sunday, August 05, 2007 ### Blogrolling On II Recall that binary trees satisfied the Catalan relation $T = 1 + T^{2}$, whereas Schroeder numbers, or Motzkin numbers, satisfy the substitution rule $X = 1 + X + X^{2}$. In this paper, Cossali studies a generalisation of the generating function for the Catalan numbers $C_{n}$. Let $L(x,z) = \sum_n \sum_m C_{m} B(2m + n, n) x^m z^n = J(x, z/x)$ where $B(i,j)$ is the binomial coefficient. The substitution rules above are all united by the function $J(x,y)$ which satisfies the rule $xJ^{2} + xy J + 1 = J$ When $x = 1$ and $y = 0$ this reduces to $J = 1 + J^{2}$, the rule for counting the number of vertices on an associahedron, but when $x = y = 1$ it reduces to the rule $J^{2} + J + 1 = J$. In general, the generating function takes the form $J(x,y) = \frac{1}{2x} [(1 - yx) \pm \sqrt{(1 - yx)^{2} - 4x}]$ Note that the coefficients $g(m,n) = C_{m} B(2m + n, n)$ of the double series $L(x,z)$ could only give the Schroeder numbers when $x = z$, so by summing the diagonals of the table on page 4 (that is, summing the $g(m,n)$ of weight $i$, starting with $g(0,0) = 1$ for $i = 0$) the Schroeder numbers are obtained. This proves that the Schroeder numbers $S_{i}$ are given by $S_{i} = \sum_{m + n = i} C_m B(2m + n, n)$ which is a little nicer than the hypergeometric expression $2F1 (1 - i, 2 + i ; 2;-1)$. By setting $y = -1$ the coefficients are alternating sums of the $g(m,n)$ and this leads to the sequence $1,0,0,0,0,0,...$ The Motzkin rule follows from setting $y = \sqrt{x}^{-1}$ and then working with $z = \sqrt{x}$, which one may verify by looking at the generating function. Can we generate more cute Abel sums using $J(x,y)$?	2018-09-23 00:36:03	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9368950128555298, "perplexity": 348.34714966083254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267158766.65/warc/CC-MAIN-20180923000827-20180923021227-00276.warc.gz"}
https://convex.indigits.com/la/matrices_3.html	# 4.8. Matrices III# ## 4.8.1. Orthogonal Matrices# Definition 4.109 A real square matrix $$\bU$$ is called orthogonal if the columns of $$\bU$$ form an orthonormal set. In other words, let $\bU = \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix}$ with $$\bu_i \in \RR^n$$. Then we have $\bu_i \cdot \bu_j = \delta_{i , j}.$ Lemma 4.44 An orthogonal matrix $$\bU$$ is invertible with $$\bU^T = \bU^{-1}$$. Proof. Let $\bU = \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix}$ be orthogonal with $\begin{split} \bU^T = \begin{bmatrix} \bu_1^T \\ \bu_2^T \\ \vdots \\ \bu_n^T \end{bmatrix}. \end{split}$ Then $\begin{split} \bU^T \bU = \begin{bmatrix} \bu_1^T \\ \bu_2^T \\ \vdots \\ \bu_n^T \end{bmatrix} \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix} = \begin{bmatrix} \bu_i \cdot \bu_j \end{bmatrix} = \bI. \end{split}$ Since columns of $$\bU$$ are linearly independent and span $$\RR^n$$, hence $$\bU$$ is invertible. Thus $\bU^T = \bU^{-1}.$ Lemma 4.45 (Determinant of an orthogonal matrix) Determinant of an orthogonal matrix is $$\pm 1$$. Proof. Let $$\bU$$ be an orthogonal matrix. Then $\det (\bU^T \bU) = \det (\bI) \implies \left ( \det (\bU) \right )^2 = 1.$ Thus we have $\det(\bU) = \pm 1.$ ## 4.8.2. Unitary Matrices# Definition 4.110 (Unitary matrix) A complex square matrix $$\bU$$ is called unitary if the columns of $$\bU$$ form an orthonormal set. In other words, let $\bU = \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix}$ with $$u_i \in \CC^n$$. Then we have $\bu_i \cdot \bu_j = \langle \bu_i , \bu_j \rangle = \bu_j^H \bu_i = \delta_{i , j}.$ Lemma 4.46 A unitary matrix $$\bU$$ is invertible with $$\bU^H = \bU^{-1}$$. Proof. Let $\bU = \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix}$ be unitary with $\begin{split} \bU^H = \begin{bmatrix} \bu_1^H \\ \bu_2^H \\ \vdots \\ \bu_n^H \end{bmatrix}. \end{split}$ Then $\begin{split} \bU^H \bU = \begin{bmatrix} \bu_1^H \\ \bu_2^H \\ \vdots \\ \bu_n^H \end{bmatrix} \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix} = \begin{bmatrix} \bu_i^H \bu_j \end{bmatrix} = \bI. \end{split}$ Since columns of $$\bU$$ are linearly independent and span $$\CC^n$$, hence $$\bU$$ is invertible. Thus $\bU^H = \bU^{-1}.$ Lemma 4.47 (Determinant of unitary matrices) The magnitude of determinant of a unitary matrix is $$1$$. Proof. Let $$\bU$$ be a unitary matrix. Then $\det (\bU^H \bU) = \det (\bI) \implies \det(\bU^H) \det(\bU) = 1 \implies \overline{\det(\bU)}{\det(\bU)} = 1.$ Thus we have $\|\det(\bU) \|^2 = 1 \implies \|\det(\bU) \| = 1.$ ## 4.8.3. F Unitary Matrices# We provide a common definition for unitary matrices over any field $$\FF$$. This definition applies to both real and complex matrices. Definition 4.111 A square matrix $$\bU \in \FF^{n \times n}$$ is called $$\FF$$ unitary if the columns of $$\bU$$ form an orthonormal set. In other words, let $\bU = \begin{bmatrix} \bu_1 & \bu_2 & \dots & \bu_n \end{bmatrix}$ with $$\bu_i \in \FF^n$$. Then we have $\langle \bu_i , \bu_j \rangle = \bu_j^H \bu_i = \delta_{i , j}.$ We note that a suitable definition of inner product transports the definition appropriately into orthogonal matrices over $$\RR$$ and unitary matrices over $$\CC$$. When we are talking about $$\FF$$ unitary matrices, then we will use the symbol $$\bU^H$$ to mean its inverse. In the complex case, it will map to its conjugate transpose, while in real case it will map to simple transpose. This definition helps us simplify some of the discussions in the sequel (like singular value decomposition). Following results apply equally to orthogonal matrices for real case and unitary matrices for complex case. Lemma 4.48 (Norm preservation) $$\FF$$-unitary matrices preserve norm. i.e. $\\| \bU \bx \\|_2 = \\| \bx \\|_2.$ Proof. We have $\\| \bU \bx \\|_2^2 = (\bU \bx)^H (\bU \bx) = \bx^H \bU^H \bU \bx = \bx^H \bI \bx = \\| \bx \\|_2^2.$ Remark 4.11 For the real case we have $\\| \bU \bx \\|_2^2 = (\bU \bx)^T (\bU \bx) = \bx^T \bU^T \bU \bx = \bx^T \bI \bx = \\| \bx\\|_2^2.$ Lemma 4.49 (Preservation of inner products) $$\FF$$-unitary matrices preserve inner product. i.e. $\langle \bU \bx, \bU \by \rangle = \langle \bx, \by \rangle.$ Proof. We have $\langle \bU \bx, \bU \by \rangle = (\bU \by)^H \bU \bx = \by^H \bU^H \bU \bx = \by^H \bx.$ Remark 4.12 For the real case we have $\langle \bU \bx, \bU \by \rangle = (\bU \by)^T \bU \bx = \by^T \bU^T \bU \bx = \by^T \bx.$	2023-01-31 14:12:29	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9501035809516907, "perplexity": 550.1864216935056}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499871.68/warc/CC-MAIN-20230131122916-20230131152916-00555.warc.gz"}
http://jbrd.github.io/2017/01/17/aperiodic-improved-perlin-noise.html	In this post, I will show how the reference implementation of Improved Perlin Noise can be rewritten to yield an aperiodic noise function. The reference implementation for Improved Perlin Noise (which can be found on Ken Perlin’s website here), is given (in Java) as: The reference implementation makes use of a permutation table (omitted for brevity) to build an 8-bit hash for eight corners of the unit cube surrounding the given input coordinate. The permutation table is a fixed size of 256 but actually repeated to conveniently avoid buffer overflow errors. To ensure that we don’t overflow this table, the modulus operator is first applied to the input coordinates. We can think of this as an initial hashing function: A consequence of this is that the reference implementation repeats for every 256 units. The first step in removing this repetition is to apply a better initial hashing function, that makes use of the full precision range of the input value. For example, we could choose to reuse the permutation table to perform a Pearson Hash of the input value: We could then change the first three lines of the noise function to apply this better hashing scheme instead: However, this isn’t enough. The following lines that make use of the X,Y and Z values make a very important assumption on the initial hashing function used to generate them: Whilst the modulus operator has this property, our new hashing function doesn’t. We can see how this affects the computation of the gradient hashes by expanding one of them out: For the positive corners of the unit grid we are adding 1 to the X, Y, and Z terms but these terms are the results of the initial hashing function, and will therefore only work if our initial hashing function maintains the assumption stated above. In breaking this assumption, we must rewrite these terms as well. We’ll start by computing the hash of the positive corners too: Then we can rewrite these these terms such that, for example, the expression: p[ p[ p[ X + 1 ] + Y + 1 ] + Z + 1 ] becomes: p[ p[ p[ XX ] + YY ] + ZZ ] After some factorisation, here is the resultant function (in C++): The full source listing can be found here: https://gist.github.com/jbrd/290bcef984b3e2e0224da6acc76e7489 Whilst this is more expensive than the original implementation, this should go to demonstrate a technique that can be used to remove the 256 unit repetition in the reference implementation.	2017-08-17 13:29:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7091341018676758, "perplexity": 556.553156145819}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886103316.46/warc/CC-MAIN-20170817131910-20170817151910-00429.warc.gz"}
https://gmatclub.com/forum/is-the-product-of-j-k-l-and-m-or-jklm-an-odd-number-142196.html	Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack It is currently 26 May 2017, 23:00 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # Events & Promotions ###### Events & Promotions in June Open Detailed Calendar # Is the product of j, k, l and m, or jklm, an odd number? Author Message TAGS: ### Hide Tags Manager Joined: 25 Jun 2012 Posts: 65 Followers: 0 Kudos [?]: 55 [1] , given: 21 Is the product of j, k, l and m, or jklm, an odd number? [#permalink] ### Show Tags 10 Nov 2012, 04:54 1 KUDOS 1 This post was BOOKMARKED 00:00 Difficulty: 45% (medium) Question Stats: 64% (02:04) correct 36% (01:57) wrong based on 44 sessions ### HideShow timer Statistics Is the product of j, k, l and m, or jklm, an odd number? (1) j^4 + k^4 + l^2 + m^2 = 0 (2) -j = k = -l = m [Reveal] Spoiler: OA Last edited by Bunuel on 10 Nov 2012, 04:57, edited 1 time in total. Edited the question. Math Expert Joined: 02 Sep 2009 Posts: 38908 Followers: 7740 Kudos [?]: 106265 [0], given: 11618 Re: Is the product of j, k, l and m, or jklm, an odd number? [#permalink] ### Show Tags 10 Nov 2012, 05:01 Is the product of j, k, l and m, or jklm, an odd number? (1) j^4 + k^4 + l^2 + m^2 = 0 --> j^4, k^4, l^2, and m^2 are all non-negative numbers. The sum of non-negative numbers is zero only when all of them equal to zero, thus j=k=l=m=0 --> jklm=0=even. Sufficient. (2) -j = k = -l = m. If all variables equal to zero, then the answer is NO but if k=m=1 and j=l=-1, then the answer is YES. Not sufficient. Hope it's clear. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 15474 Followers: 649 Kudos [?]: 209 [0], given: 0 Re: Is the product of j, k, l and m, or jklm, an odd number? [#permalink] ### Show Tags 29 Mar 2017, 05:50 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: Is the product of j, k, l and m, or jklm, an odd number? [#permalink] 29 Mar 2017, 05:50 Similar topics Replies Last post Similar Topics: 6 Is the range of the set of numbers {j, k, l, m,n, p} greater than 5? 1 15 Jan 2017, 08:41 8 Is J + K > L + M ? 4 26 Sep 2014, 10:51 1 In a set of positive integers {j,k,l,m,n,o} in which j<k<l<m 4 16 Aug 2014, 13:41 If j and k are positive integers and j + k is odd 3 06 Mar 2017, 20:18 7 A certain expressway has Exits J, K, L, and M, in that order 8 22 Jul 2016, 11:57 Display posts from previous: Sort by	2017-05-27 06:00:52	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8174024224281311, "perplexity": 4701.4127926074725}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608773.42/warc/CC-MAIN-20170527040600-20170527060600-00083.warc.gz"}
https://proofwiki.org/wiki/Summation_over_Cartesian_Product_as_Double_Summation	# Summation over Cartesian Product as Double Summation It has been suggested that this page or section be merged into General Distributivity Theorem. (Discuss) ## Theorem Let $\mathbb A$ be one of the standard number systems $\N, \Z, \Q, \R, \C$. Let $S, T$ be finite sets. Let $S \times T$ be their cartesian product. Then we have an equality of summations over finite sets: $\displaystyle \sum_{s \mathop \in S} \sum_{t \mathop \in T} f \left({s, t}\right) = \sum_{\left({s, t}\right) \mathop \in S \times T} f \left({s, t}\right)$ ## Outline of proof We use induction on the cardinality of $T$. In the induction step, we use Sum over Disjoint Union of Finite Sets and Summation of Sum of Mappings on Finite Set.	2019-09-17 02:59:58	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9923694729804993, "perplexity": 304.0955500496834}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514573011.59/warc/CC-MAIN-20190917020816-20190917042816-00422.warc.gz"}
https://eng.libretexts.org/Bookshelves/Computer_Science/Programming_and_Computation_Fundamentals/Book%3A_An_Introduction_to_Ontology_Engineering_(Keet)/zz%3A_Back_Matter/02%3A_Complexity_Recap	# Complexity Recap This appendix is expected to be relevant only to those who have no idea of, or too little recollection of, computational complexity, or who have come across it many years ago and may like a brief refresher. Theory of computation concerns itself with, among other things, languages and its dual, problems. A problem is the question of deciding whether a given string is a member of some particular language; more precisely: if $$\Sigma$$ is an alphabet, $$L$$ is a language over $$\Sigma$$, then the problem $$L$$is “given a string $$w\in\Sigma^{*}$$ , decide whether or not $$w$$ is in $$L$$”. The usage of ‘problem’ and ‘language’ is interchangeable. When we focus on strings for their own sake (e.g., in the set $$\{o^{n}1^{n} \| n\geq 1\}$$), then we tend to think of the set of strings as a language. When we focus on the ‘thing’ that is encoded as a string (e.g., a particular graph, a logical expression, how satisfiable a class is), we tend to think of the set of strings as a problem. Within the context of ontologies, we typically talk of the representation languages and reasoning problems. There are several classes of languages; see Figure 13.1. The regular free languages have their counterpart with finite automata; the context-free languages with push-down automata; the recursive languages is the class of languages accepted by a Turing machine (TM) that always halts; the recursively enumerable languages is the class of languages defined by a TM; the non-recursively enumerable languages is the class of languages for which there is no TM (e.g., the diagonalization language). The recursive languages, and, to a lesser extent, the recursively enumerable languages, are by far the most interesting ones for ontologies. Turing machines are used as a convenient abstraction of actual computers for the notion of computation. A TM that always halts = algorithm, i.e., the TM halts on all inputs in finite time, either accepting or rejecting; hence, the recursive languages are decidable problems/languages. Problems/languages that are not recursive are called undecidable, and they do not have an algorithm; if they are in the class of recursively enumerable languages (but not recursive), then they have a procedure that runs on an arbitrary TM that may give you an answer but may very well never Figure 13.1: Graphical depiction of the main categories of languages. halt; see also Figure 13.2. First order predicate logic in its full glory is undecidable. Description logics are decidable fragments of first order predicate logic1, i.e., they are recursive languages and (can) have algorithms for the usual problems (standard reasoning services). Figure 13.2: Graphical depiction of the main categories of languages; the rectangle denotes a Turing Machine; $$w$$ is a string and $$L$$ is a language. Not all algorithms are alike, however, and some take up more time (by the CPU) or space (in the form of memory size) to compute the answer than others. So, we want to know for a given problem, the answer to “how much time [/space] does it take to compute the answer, as a function of the size of the input?”. If the computation takes many years with the top-of-the-range hardware, then it is still not particularly interesting to implement (from a computer science viewpoint, that is). To structure these matters, we use the notion of a complexity class. There are very many of them, but we only refer to a few in the context of ontologies. For instance, it may take a polynomial amount of time to compute class subsumption for an OWL 2 EL-formalized ontology and exponential time to compute how satisfiable an EER diagram (represented in the DL $$\mathcal{DLR}_{\texttt{ifd}}$$) is and the bigger the diagram (more precisely: the logical theory), correspondingly the longer it takes. The intuition is depicted in Figure 13.3: for small ontologies, there is but a minor difference in performance, but one really starts to notice it with larger logical theories. Figure 13.3: General idea of time complexity of an algorithm, as function of the size of the input. e.g.: All basic arithmetic operations can be computed in polynomial time; evaluating a position in generalized chess and checkers on an $$n\times n$$ board costs exponential time. Looking ahead at the complexity classes relevant for OWL, we list here a description of the meaning of them (copied from the OWL 2 Profiles Standard page [MGH+09]): - Decidability open means that it is not known whether this reasoning problem is decidable at all. - Decidable, but complexity open means that decidability of this reasoning problem is known, but not its exact computational complexity. If available, known lower bounds are given in parenthesis; for example, (NP-Hard) means that this problem is at least as hard as any other problem in NP. - X-complete for X one of the complexity classes explained below indicates that tight complexity bounds are known—that is, the problem is known to be both in the complexity class X (i.e., an algorithm is known that only uses time/space in X) and hard for X (i.e., it is at least as hard as any other problem in X). The following is a brief sketch of the classes used in Table 4.2.3, from the most complex one down to the simplest ones. - 2NEXPTIME is the class of problems solvable by a nondeterministic algorithm in time that is at most double exponential in the size of the input (i.e., roughly $$2^{2^{n}}$$ , for $$n$$ the size of the input). - NEXPTIME is the class of problems solvable by a nondeterministic algorithm in time that is at most exponential in the size of the input (i.e., roughly $$2^{n}$$ , for $$n$$ the size of the input). - PSPACE is the class of problems solvable by a deterministic algorithm using space that is at most polynomial in the size of the input (i.e., roughly $$n^{c}$$ , for $$n$$ the size of the input and $$c$$ a constant). - NP is the class of problems solvable by a nondeterministic algorithm using time that is at most polynomial in the size of the input (i.e., roughly $$n^{c}$$ , for $$n$$ the size of the input and $$c$$ a constant). - PTIME is the class of problems solvable by a deterministic algorithm using time that is at most polynomial in the size of the input (i.e., roughly $$n^{c}$$ , for $$n$$ the size of the input and $$c$$ a constant). PTIME is often referred to as tractable, whereas the problems in the classes above are often referred to as intractable. - LOGSPACE is the class of problems solvable by a deterministic algorithm using space that is at most logarithmic in the size of the input (i.e., roughly $$log(n)$$, for $$n$$ the size of the input and $$c$$ a constant). NLOGSPACE is the nondeterministic version of this class. - AC0 is a proper subclass of LOGSPACE and defined not via Turing Machines, but via circuits: AC0 is the class of problems definable using a family of circuits of constant depth and polynomial size, which can be generated by a deterministic Turing machine in logarithmic time (in the size of the input). Intuitively, AC0 allows us to use polynomially many processors but the run-time must be constant. A typical example of an AC0 problem is the evaluation of first-order queries over databases (or model checking of first-order sentences over finite models), where only the database (first-order model) is regarded as the input and the query (first-order sentence) is assumed to be fixed. The undirected graph reachability problem is known to be in LogSpace, but not in AC0 . ## Footnotes 1More precisely: there is at least one that turned out to be undecidable ($$\mathcal{DLR_{US}}$$ ), but this is an exception to the rule.	2021-10-22 14:07:22	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8068411350250244, "perplexity": 336.41803031895495}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585507.26/warc/CC-MAIN-20211022114748-20211022144748-00030.warc.gz"}
http://thetravelingcheetah.com/human-intervention-rccoqlq/oxidation-state-of-nitrogen-b8144c	# oxidation state of nitrogen The above table can be used to conclude that boron (a Group III element) will typically have an oxidation state of +3, and nitrogen (a group V element) an oxidation state of -3. +6 What is the oxidation state of an individual nitrogen atom in HNO_3? 5 years ago. Nitrogen displays a considerable number of oxidation states, from -3 to +5. How is it +5 then? What is the oxidation state of an individual nitrogen atom in HNO3? Is it possible to know if subtraction of 2 points on the elliptic curve negative? 3. what is the oxidation state of nitrogen in KNO2? # Hydrogen has an oxidation state of +1 except when bonded to more electropositive elements such as sodium, aluminium, and boron, as in NaH, NaBH4, LiAlH4, where each H has an oxidation state of -1.\ So here, N2H4 means nitrogen is the more electropositive, so H is … Can I assign any static IP address to a device on my network? Transition metals are not included, as they tend to exhibit a variety of oxidation states. Share Tweet Send Chromium [Wikimedia] Chromium is an element of the 4ᵗʰ period of the 6ᵗʰ group (it is located in the side subgroup). It only takes a minute to sign up. 2 Answers. O. How can I quickly grab items from a chest to my inventory? A. Compounds in the -3 oxidation state are weak reducing agents. Identifying an Oxidation Number Given a particular compound with an unknown oxidation number on one species, we have to: Hence, the oxidation state of N is, (+5) 4. answers left. What is the oxidation state of bromine in BrO3? Trending Questions. Asking for help, clarification, or responding to other answers. Still have questions? Why was there a "point of no return" in the Chernobyl series that ended in the meltdown? PROOF: Quantum Mechanics basics. So, while determining oxidation state from the structure : References: These include ammonia, ammonium, amide and nitrides. Count electrons. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. If oxygen has a negative 2 oxidation state, hydrogen has a positive 1 oxidation state. Join. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. We know, nitrogen can show oxidation numbers from -3 to +5. Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. The sum of the oxidation numbers is the charge on the ion or molecule. https://en.wikipedia.org/wiki/Dinitrogen_pentoxide. Û0ñ¢æÊ:õ�Äèç�”ãhÈí�Öf—ë�«§Ç¿5ªQÓ³ªL¿›6Éié¼œ‹™q¶MwKÂæ�HQàH±:Ó–’jé†¶$É&yÓi?V#/òÄ‹Š°ûÕÈKW!X‹“ S is a theoretical concept. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The sum of the oxidation numbers in a polyatomic ion is equal to the charge of the ion. 1 + X + (-2) 3 = 0. Or does it have to be within the DHCP servers (or routers) defined subnet? That means all five valence electrons are considered lost from nitrogen in the oxidation state calculation. e‚.–Ãl0BT¿�èêEñÄ,.FpH �Yc.AÃ]U>°Õ5´u«ó\|U™µ©ÉànÍ½�ÊèÔi Typesetting oxidation state and charge simultaneously. @AbirPal Throw that book away. What causes dough made from coconut flour to not stick together? Ask Question + 100. Two things come in handy here. Answer Save. Showing that the language L={⟨M,w⟩ \| M moves its head in every step while computing w} is decidable or undecidable, Sensitivity vs. Limit of Detection of rapid antigen tests. Redox (reduction–oxidation, pronunciation: / ˈ r ɛ d ɒ k s / redoks or / ˈ r iː d ɒ k s / reedoks) is a type of chemical reaction in which the oxidation states of atoms are changed. Why do electrons jump back after absorbing energy and moving to a higher energy level? Hydrazine, a compound in the -2 oxidation state… +4 NO2Nitrogen dioxide, a brown gas usually produced by the reaction of … Nitrogen compounds, on the other hand, encompass oxidation states of nitrogen ranging from -3, as in ammonia and amines, to +5, as in nitric acid. This is because oxygen always has an oxidation number of -2. Oxidation number of nitrogen in NO 2 is +4. Relevance. In compounds, the H atom bears an oxidation state of +1. for Nitrogen it ranges from 0 to 1. Jan. Lv 7. endstream endobj 10 0 obj << /Type /ExtGState /SA false /SM 0.02 /TR /Identity >> endobj 1 0 obj << /Type /Pages /Kids [ 5 0 R ] /Count 1 >> endobj 2 0 obj << /CreationDate (D:20030106122008) /Producer (Acrobat Distiller 4.05 for Windows) /ModDate (D:20030106122010-08'00') >> endobj xref 0 3 0000000000 65535 f +4 In an ion, the sum of the oxidation states is equal to the overall tonic charge. 0000002585 00000 n Éß(�Gêä,¹<>Z\|š]:ÈßI According to the formula it should be +5 but according to its structure shouldn't it be +4? Oh, I always advocate properly assigning formal charges to all atoms that need them, which is why I wouldn’t have upvoted your answer if only the first structure were shown ;). Compounds with an oxidation state of nitrogen of -3. To learn more, see our tips on writing great answers. The oxidation number for NO3, or nitrate, is -1. ‰"SÌ'¤TÀ\|g0mr…„Fc�ÿGA4†í„A:¸ÓõH ‹¬ëÚ¶îÈœ‘ 3. Synthetic chemists customarily tune the redox characteristics of π-conjugated molecules by introducing electron-donating or electron-withdrawing substituents onto the molecular core, or by modifying the length of the π-conjugated pathway. Making statements based on opinion; back them up with references or personal experience. The typically-used oxidation state of nitrogen in N 2 O is +1, which also obtains for both nitrogens by a molecular orbital approach. E. What is the oxidation state … Don't count bonds. Nitrogen cannot exhibit a +5 oxidation state due to the absence of d-orbitals. But then you have two of them. + color(red)(5) xx (-2) = 0# Hence by the basic principle of quantum mechanics we can say that in N2O5 nitrogen has +4 oxidation state. Thus +5. (rÓ‘Ï8E§üóÿSÑbœ0TØ g:‹cîâÃdÄŠ$æ‹¶x½„$Óî Ê(×íö�Dä†eÀâ$ÃT¸pg-üI÷EO¿[ló3MÉC Ş—»]Y ¤7e[t�b+×A�ÕÚ¢SÍ£Á^Iu[šbT³Gƒ¯k�PQ$9Z”EvFÖK¢5 £ÅêjvHÜhÊ÷ù,µ�b1Ú(_6ÈîÕÅ’2Z\í³ªü¹ÏõÎn"?ı�&şè4›jjÿ°'†n±MÊÊK6‘İ´«Ïå'ùÍÊFÑùôzåÈĞ?Ú\M But they have some limitations But in order to overcome those limitations one must use the basics of the subject. P A.2 (pg 2 of 3) Oxidation Numbers ANSWERS Note: While elements in their standard state are always assigned an oxidation state of zero, it is allowable for an atom to have an oxidation number of zero even if it is part of a molecule. In nature it is only found in the form of compounds – for example chromite or crocoite. Aspects for choosing a bike to ride across Europe, Signora or Signorina when marriage status unknown. to find the oxidation number of N , we need to use the rule ' that the sum of the oxidation number of the each element of a compound is equal to the o if the compound is neutral or the net charge of it if the compound has a net charge.So, in HNO3 lets say that the Nitrogen charge is x. The 2 most common types of compounds in which the oxidation state of nitrogen is -3 is ammonium and ammonium salt (or ammonium hydroxide NH₄OH). Typical oxidation states of the most common elements by group. Nitrogen cannot exhibit a +5 oxidation state due to the absence of d-orbitals. Nitrogen comes in with five valence electrons but all five are used to form bonds with more electronegative atoms (oxygen). To begin, we assign the oxidation state of H before the N atom. The given compound is, Let the oxidation state of 'N' be, 'x'. D. Determine the oxidation state of arsenic in sodium arsenate. Amino acids and proteins contain nitrogen in this oxidation state. X = +5 The following table lists some of the known organic compounds of nitrogen, having different oxidation states of that element. As Nitrogen is in 2nd period in the modern periodic table, principal quantum number being n=2, the Azimuthual Quantum numbers = 0 to n-1 The formal charges on the right comply with electronegativities, and this implies an added ionic bonding contribution. 1+ x+ (-6) = 0. x -5 = 0. The three oxygen atoms have a combined oxidation of -6, corresponding to their electromagnetic charge and the lone nitrogen has a charge, or oxidation number, of +5. Each hydroxide part of this molecule is going to have a net oxidation state of negative 1. #color(blue)(2) xx ? Sorry ,I think you don't even know a basic difference between covalency and oxidation state.It may sound same but they are entirely different. https://en.wikipedia.org/wiki/Dinitrogen_pentoxide, Oxidation State in Tetraaquadichlorochromium(III) chloride. As an example, in the reaction of nitrogen dioxide and water reaction, nitrogen atom is oxidized to +5 oxidation state (nitric acid). 5 years ago. So the net oxidation for this part of the molecule or the compound is going to be negative 2 nets out with the positive 2 from magnesium. In a C-H bond, the H is treated as if it has an oxidation state of +1. Each of those oxidation states has its set of compounds. NOTE: Formulae are made to simplify the things. Determine the oxidation state of nitrogen in nitrogen gas. Help modelling silicone baby fork (lumpy surfaces, lose of details, adjusting measurements of pins), Dog likes walks, but is terrified of walk preparation. Express the oxidation state numerically (e.g., +1). Oxidation States of Nitrogen Oxidation HNO3 N2O +1 +5 -3 NO +2 NH3-1/3 HN3 Reduction It is the standard textbook for 12 grade in India. Because ammonia is neutral, the individual oxidation numbers must sum to zero. rev 2021.1.8.38287, The best answers are voted up and rise to the top, Chemistry Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, But according to the structure it should be + 4, A coordinate bond gives a formal charge of +1 to N, implying that it effectively gets a raise in oxidation state by +2. how to fix a non-existent executable path causing "ubuntu internal error"? Electrons shared between two unlike atoms are counted towards more electronegative element. Evidently, I picked it up for representation purpose. MathJax reference. This means that every C-H bond will decrease the oxidation state of carbon by 1.; For carbon bonded to a more electronegative non-metal X, such as nitrogen, oxygen, sulfur or the halogens, each C-X bond will increase the oxidation state of the carbon by 1. What are the oxidation states of galium and arsenic in GaAs semiconductor? C. Determine the oxidation state of oxygen in hydrogen peroxide. Determine the oxidation state of chlorine in the perchlorate ion. 3 0. ¼×xÎ€A�M…G^–ãTpÈùI�auóe±ır%zÀBã³‰¹+i è„L1Öx‹W´�¬-¥Â£èœä ¥PBŠ L—#æä^0øÕ•—UnêÚéñœ»jPàq®›^g�ğ2‹4˜òŞ¦÷ä¨è…’ág�‘Ÿ›C�¨"Õ…�i[�ÙrÌÉx0�ØuÚjP(Î‚8Ëù�B…Ìwá! What is the oxidation state of an individual sulfur atom in BaSO_4? Thanks for contributing an answer to Chemistry Stack Exchange! Determine the oxidation number of nitrogen in {eq}NH_4^+ {/eq}. Notice that it is a resonance structure of: Now one of the bonds are coordinate bonds where nitrogen donates BOTH its electrons to oxygen (otherwise, oxygen cannot have a single bond without a negative charge and no peroxy type linkage). site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. As Nitrogen is in 2nd period in the modern … state Species +5 NO3 -Nitrate ion, oxidizing agent in acidic solution. Oxidation states of nitrogen Ox. 8ÆÂ±w5³ïŞœd&qü�„œİb«²Ôeå¶R{¬a/ÚnÎq†p\ÁãêGkhüâ5ã?šğš†‚Õ$’»¶LvÕ•© Şah×ÑP³Í°Öê¾Ğ%Ñ7Ûeˆ ŸÙÒç,"ƒdØ8W7Ö¾.è¿Ùî Öy3Ü¿ú¡œ¤ÜoÃz¸Î{ /Â¿ ùM)� How is the oxidation number related to the group number? B. 0 0. 0000002649 00000 n Other articles where Nitrogen oxide is discussed: oxide: Oxides of nitrogen: …2HNO3 + NO Nitrogen (N) forms oxides in which nitrogen exhibits each of its positive oxidation numbers from +1 to +5. @Martin A lot many people, myself included would have to throw that book out! But don't worry, I checked it and it clearly says that the covalency is limited to 4, not oxidation state! Your second image is better since it shows formal charges. trailer << /Size 3 /ID[<728e021b9c5f5af6fc70a6301ad7ee54><728e021b9c5f5af6fc70a6301ad7ee54>] >> startxref 173 %%EOF. Use MathJax to format equations. Get your answers by asking now. The sum of the oxidation numbers of all of the atoms in a neutral compound is zero. Join Yahoo Answers and get 100 points today. What's the best time complexity of a queue that supports extracting the minimum? NH3, Ammonia is a neutral compound as the individual oxidation numbers elements that make up the compound NH3 are Nitrogen (N) and Hydrogen (H) sum to zero. What is the oxidation state of nitrogen in N2O5? If they make such a bold and painfully obvious wrong statement, nothing, absolutely nothing in it is trustworthy. µ”–EŠØ)©ÌÑKÎ¸%²AJÃt(+x²Í=ìt±‡�it^3øÔÜ�©ì3ê²)aSV;X‘—CB Where the sum of the oxidation states of N and H must equate to +1. There are 2 different nitrogen atoms in $\ce{NH4NO3}$, one having oxidation number -3 and one with +5.They are different, having separate oxidation numbers independently of each other. 0 (zero) represents an s orbital and 1 represents p orbital hence no D orbitals are there. How is there a McDonalds in Weathering with You? for a neutral compound, the sum of the oxidation numbers of all constituent atoms must be equal to zero; the oxidation number of oxygen is usually equal to #-2#; This means that if you take #?# to be the oxidation number of nitrogen in dinitrogen pentoxide, #"N"_color(blue)(2)"O"_color(red)(5)#, you can say that. N = + 3. Oxidation states of chromium How many oxidation states does chromium have? Note that the sign of the oxidation states and the number of atoms associated with each oxidation state must be considered. True, but that's not much of an improvement. Although this is a really crappy answer, it's an attempt at answering the question and thus I would downvote, not flag. Adnan. Therefore, nitrogen atom in nitrogen dioxide has the capability of oxidizing and reducing. When a microwave oven stops, why are unpopped kernels very hot and popped kernels not hot? Nitrogen compounds, on the other hand, encompass oxidation states of nitrogen ranging from -3, as in ammonia and amines, to +5, as in nitric acid. Give the oxidation number of the nitrogen … Various laboratory reactions that yield nitrogen include heating ammonium nitrite (NH 4 NO 2) solutions, oxidation of ammonia by bromine water, and oxidation of ammonia by hot cupric oxide. ... which clearly tells us that due to absence of d orbitals, nitrogen cannot expand its oxidation state greater than 4. Abir probably conflated them both. 1 + N - 4 = 0.	2021-06-13 14:56:17	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.46500611305236816, "perplexity": 2622.5915051788365}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487608856.6/warc/CC-MAIN-20210613131257-20210613161257-00379.warc.gz"}
http://www.math.cmu.edu/CCF/ccfseminar.php?SeminarSelect=956	Faculty in Mathematical Finance Math Finance Home Conferences Seminars People Open Positions Contact CCF Seminar Zsolt Pajor-Gyulai University of Maryland Title: From averaging to homogenization in cellular flows - an exact description of the transition Abstract: We consider a two-parameter averaging-homogenization type elliptic problem together with the stochastic representation of the solution. A limit theorem is derived for the corresponding diffusion process and a precise description of the two-parameter limit behavior for the solution of the PDE is obtained. Joint work with M. Hairer and L. Koralov. Date: Monday, January 26, 2015Time: 4:30 pmLocation: Wean Hall 6423Submitted by: Shreve	2018-03-17 04:37:42	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8230586647987366, "perplexity": 2679.208837874269}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257644271.19/warc/CC-MAIN-20180317035630-20180317055630-00707.warc.gz"}
https://www.physicsforums.com/threads/calculate-flux-in-a-ferrite-bead-on-a-wire.827427/	Calculate flux in a ferrite bead on a wire Tags: 1. Aug 12, 2015 EmilyRuck Suppose that a ferrite bead is put around a cable where a constant current $I$ flows, just like in this image. The coordinate system has the $z$ axis along the cable. Let's evaluate the current through the $(x,y)$ plane: according to the Ampère's law, the only magnetic field component generated by that current is $H_{\phi} = \displaystyle \frac{I}{2 \pi r}$ where $r$ is the distance from the origin. In order to calculate the inductance of the wire with the ferrite bead, the magnetic flux through the ferrite should be calculated first. The ferrite bead has $a$ as internal radius and $b$ as external radius, so it is present in the $(x,y)$ plane only for $a \leq r \leq b$. It surrounds the conductor (which has of course a section diameter less than $2a$) and the flux of the magnetic field through the ferrite bead should be: $\Phi = \mu_0 \mu_r \displaystyle \frac{I}{2 \pi} \int_a^b \displaystyle \frac{1}{r} dr = \displaystyle \frac{\mu_0 \mu_r I}{2 \pi} \ln \left( \displaystyle \frac{b}{a} \right)$ Then the inductance is $L = \Phi / I$ as usual. My question is: why is the flux calculated in such a way?? Should not be considered all the surface surrounded by the circuit or something similar? (I know, it is a linear cable and I didn't specify that area) 2. Aug 12, 2015 marcusl It makes sense to speak of the inductance of the wire/bead combination because the ferrite has a high permeability so its inductance dominates over that of the rest of the wire. Does that address your question? 3. Aug 13, 2015 athosanian Thant means the thickness of the ferrite bead is unity 4. Aug 13, 2015 EmilyRuck Thanks to both of you. And for @marcusl yes, sure, your observations address my question. 5. Aug 13, 2015 Philip Wood I think there's a small slip. You need to integrate the flux through an area at right angles to the flux, so you need to multiply by the axial length of the bead. Alternatively you must interpret your Phi as flux per unit axial length of bead.	2017-10-18 05:08:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8196688294410706, "perplexity": 659.0475082100438}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822739.16/warc/CC-MAIN-20171018032625-20171018052625-00710.warc.gz"}
https://www.physicsforums.com/threads/how-do-we-get-the-n-th-term-of-the-sequence.771173/	# How do we get the n th term of the sequence? 1. Sep 16, 2014 ### basheer uddin 1. The problem statement, all variables and given/known data how do we get the n th term of a sequence if it is given in form of $x_{ n+1 }=f({ x }_{ n })$ and the p th term is given 2. Relevant equations I figured we may get it if we get it in the form of $x_{ n+1 }-{ x }_{ n }$ but how?can we even get it?if yes,under what conditions? 3. The attempt at a solution example: n th term of sequence where $x_{ n+1 }=\frac { { x }_{ n }+\frac { 2 }{ { x }_{ n } } }{ 2 }$ where ${ x }_{ 0 }=1$ Last edited: Sep 16, 2014 2. Sep 16, 2014 ### pasmith Non-linear recurrences are unlikely to have solutions in closed form. Iteration is generally the only way to find $x_n$ given $x_0$.	2018-01-23 00:18:40	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8893650770187378, "perplexity": 1029.1726322441032}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891546.92/warc/CC-MAIN-20180122232843-20180123012843-00212.warc.gz"}
http://mybiasedcoin.blogspot.com/2020/06/algorithms-with-predictions-survey-and.html	## Wednesday, June 17, 2020 ### Algorithms with Predictions: Survey and Workshop There's a whole new, interesting theory trend -- Algorithms with Predictions. The idea, spurred by advances in machine learning, is that you assume you have predictor that tells you something about your input. For example, in caching, you might have a prediction of when the item you are currently accessing will be next accessed. Of course, machine learning predictions aren't perfect. Still, you'd like to use this prediction to improve your caching algorithm, but from the theory side, we'd like provable statements. For example, you could say, if my prediction is THIS good (e.g., the error is bounded under some metric), then my caching performance will correspondingly be at least THIS good (e.g., performance bounded in some way). If you haven't seen the burgeoning spread of this line of work and are interested, you're in luck. First, Sergei Vassilvitskii and I have written a brief survey that's now on the arxiv. We had written it for a collection Tim Roughgarden is organizing on Beyond Worst-Case Analysis (that we thought we be out by now, and should be out from the publisher soon-ish), but we've gone ahead and put a version on the arxiv to make it available. The area is moving fast, so there are already many new results -- we hope to update the "survey" with new material as the area grows. Second, one of the STOC'20 Workshops will be on Algorithms with Predictions. It will be on Friday from 1-4pm, with speakers Tim Roughgarden, Edith Cohen, Ravi Kumar, and me. I'll be talking about some of my recent work (in submission) on queues with predictions, and partitioned learned Bloom filters. (Arxiv papers are here, here, and here, but maybe you want to see the talk first.) I'll also do a blog post on partitioned learned Bloom filters in the near future. #### 1 comment: td said... Predicted variables (https://arxiv.org/abs/1810.00619v1) seem like a good interface for many such methods	2021-01-25 11:38:56	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.801369845867157, "perplexity": 2102.286648280518}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703565541.79/warc/CC-MAIN-20210125092143-20210125122143-00584.warc.gz"}
https://gamedev.stackexchange.com/questions/101260/bouncing-projectile-off-of-sprite-the-sides-work-but-top-and-bottom-do-not/101284	# Bouncing projectile off of sprite, the sides work but top and bottom do not I'm having a problem bouncing a projectile off a sprite, we've been asked to move the projectile using the equations of motions which makes things a little more difficult but as far as I can see what I have should work. What I'm trying to do is change the angle of the collided projectile depending on which direction it is coming from. Here is a video that is hopefully not too laggy for you to see what is happening: When the projectile collides with the left or right hand side of the sprite everything works as expected, it just switches X direction. When it hit's the top or bottom of the sprite however it doesn't change, it just sort of rolls along the top and the shoots off. Here is the movement code: float nX = get_x() + cos(nGetAngle() * 3.14 / 180) * getU() * getT(); float nY = get_y() - sin(nGetAngle() * 3.14 / 180) * getU() * getT() + 0.5 * 9.8 * getT() * getT(); set_world_position(nX, nY); Where U is initial velocity, T is time and nGetAngle() is the angle in degrees (which is set to radians whenever the angle is set). Here is my collision for the top of the player: //if the projectile is colliding in any way with the player sprite if (projectiles[currProj]->get_y() < player->get_y()) // top of player { float vx = cos(projectiles[currProj]->nGetAngle()); float vy = sin(projectiles[currProj]->nGetAngle()); float newAngle = atan2(-vy, vx) * 180 / 3.14; projectiles[currProj]->nSetAngle(newAngle); projectiles[currProj]->set_world_position_y(player->get_y() - projectiles[currProj]->get_height() - 1); } and here is my collision for the left of the player: else if (projectiles[currProj]->get_x() < player->get_x()) // left of player { projectiles[currProj]->set_world_position_x(player->get_x() - projectiles[currProj]->get_width()); float vx = cos(projectiles[currProj]->nGetAngle()); float vy = sin(projectiles[currProj]->nGetAngle()); float newAngle = atan2(vy, -vx) * 180 / 3.14; projectiles[currProj]->nSetAngle(newAngle); } The left side collision works, the top does not and I have no idea why. If necessary I can post the entire project somewhere. Let me put this simply. (Or I will try to) First of all, you should read up on Vectors, find out what these are: Vector Magnitude; Vector X,Y coordinates; Normalised Vector; After this, you should read up a bit on physics, especially Newtons three laws; kinetics; momentum; and collisions. After a week or so you should start to understand these things. You will need to assign a velocity vector to the "ball"(upon shooting it), on every frame you will add the Gravity vector to this "ball". Then you will set up a collision detection function, that will return the collision normal, and the collision point. Using this data, you will remove both objects from penetration. Then you will need to calculate the relative velocity of both objects = vA - vB = vAB. you will then use the dotProduct to project the Relative Velocity Vector onto the collision Normal. This will Give you the Impulse scalar. You will Scale this by -(elasticity (value between 0-1) + 1). You will then Scale the collision normal vector by the scaled Impulse * 2 (because you just want the ball to move). After doing all this. You will have learned a lot about physics, expanded your knowledge of many usefull things, (that will be very usefull to you in game programming and many other programming fields). best of luck!!	2021-04-23 09:02:19	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33254706859588623, "perplexity": 1355.3299420227308}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039568689.89/warc/CC-MAIN-20210423070953-20210423100953-00302.warc.gz"}
https://math.stackexchange.com/questions/522186/is-there-an-elementary-introduction-to-higher-order-functions	# Is there an elementary introduction to higher order functions? I am teaching a pre-calculus course (using the textbook by Michael Sullivan if it helps), and I realized that higher order functions seem to show up in with some frequency in pre-calculus and calculus. Since these students are particularly good (high school students taking college classes), I introduced this concept to them. Without being too rigorous, let me make some definitions. A first order function will be a function of the form, $f:A\to B$ such that $A$, and $B$ are (nice enough) subsets of $\mathbb{R}$. $\phantom{}$ An n-th order functions will be a function of the form, $f:A\to B$ such that either $A$ or $B$ are (perhaps sufficiently nice) sets of functions of order at most $n-1$. $\phantom{}$ The plethora of all the $n$-th order functions will be collectively known as higher order functions. The examples that they have seen are families of functions such as, $$a\mapsto (x\mapsto f(ax))$$ $$r\mapsto (x\mapsto x^r).$$ (in fact they have seen animations of these and others in mathematica in fact I used their experience with this program to help illustrate the concept). Some other examples that they have seen that are of the form $$PFun(\mathbb{R},\mathbb{R})\to PFun(\mathbb{R},\mathbb{R}),$$ where $PFun(\mathbb{R},\mathbb{R})$ is the set of partially defined functions on $\mathbb{R}$ (I made them partially defined so that I do not have to be too careful with the exact domain, as that can change from problem to problem), given by $$f\mapsto (x\mapsto f(x-a))\\f\mapsto (x\mapsto f(mx))\\f\mapsto (x\mapsto f(x)+b)\\f\mapsto (x\mapsto mf(x)),$$ as well as composites of these, so as to be able to talk about the affine transformations that we made to the graph. Another example of this is the difference quotient, $$(h,f)\mapsto \frac{f(x+h)-f(x)}{h},$$ and in calculus, they will also see the derivative. It seems that this notion is a fairly simple one, and one that will prove useful later in life as well as now. A student asked for a place to read about this, and I said that I did not know an appropriate place for this. I know that I can find some good treatments of this if I look up the lambda calculus or Cartesian closed categories, but I would not want them to learn the notions of category theory or the notation of the lambda calculus. I also know that this notion is described in books about programming languages like Haskell or LISP, but this seems like they would have to learn a certain amount of code to fully understand this. So my question: Is there a treatment of higher order functions that is not a computer science book and is reasonably elementary (say at the level of elementary set theory)? • What is the order of a function? – copper.hat Oct 11 '13 at 3:40 • I messes up the indexing in the inductive definition. It is fixed. – Baby Dragon Oct 11 '13 at 3:42 • @BabyDragon : I am having trouble understanding your question. Can you please give a specific example of a higher order function that occurs in pre-calc and calc? – Stefan Smith Oct 12 '13 at 2:22 • @StefanSmith In particular, a second order function (let's call it an operator) is a map such that either the domain or codomain is a collection (partially defined) functions from the reals to the reals. The canonical example in calculus is the map, $f\mapsto \frac{df}{dx}$. This takes the set of differentiable functions to functions. Another example that we see often enough is $f\mapsto f(x-a)$ ( used the notation $f\mapsto(x\mapsto f(x-a))$ in the question). Another example would be the difference quotient. – Baby Dragon Oct 12 '13 at 4:06 • We could also write the difference quotient as $$f\mapsto(h\mapsto \frac{f(x+h)-f(x)}{h})$$ or $$h\mapsto (f\mapsto\frac{f(x+h)-f(x)}{h})$$. – Baby Dragon Oct 12 '13 at 4:11	2020-01-27 03:03:07	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7591190338134766, "perplexity": 175.62617533734098}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579251694176.67/warc/CC-MAIN-20200127020458-20200127050458-00286.warc.gz"}
https://apboardsolutions.com/ap-board-9th-class-maths-solutions-chapter-13-intext-questions/	# AP Board 9th Class Maths Solutions Chapter 13 Geometrical Constructions InText Questions AP State Syllabus AP Board 9th Class Maths Solutions Chapter 13 Geometrical Constructions InText Questions and Answers. ## AP State Syllabus 9th Class Maths Solutions 13th Lesson Geometrical Constructions InText Questions Try These Question Observe the sides, angles and diagonals of quadrilateral BEFD. Name the figures given below and write properties of figures. [Page No. 283] Solution: In fig. (1) $$\overrightarrow{\mathrm{BF}}$$ is the bisector of ∠B and ∠F. BE = BD = DF = EF It is a rhombus In fig. (2) BD = BE FD = FE ∴ BEFD is a kite. BF is bisector of ∠B and ∠F. Try This Question Draw a circle, identify a point on it. Cut arcs on the circle with the length of the radius in succession. How many parts can the circle be divided into ? Give reasons. [Page No. 284] Solution: Let P be the centre of the circle. A is any point on its circumference. It can be divided into 2π parts ∴ $$\frac{\text { Circumference }}{\text { Radius }}=\frac{2 \pi r}{r}=2 \pi$$ Think, Discuss and Write Question Can you construct a triangle ABC with BC = 6 cm, ∠B = 60° and AB + AC = 5 cm? If , not, give reasons. (Page No. 286) Solution: We can’t construct a triangle with measures ∠B = 60°; BC = 6 cm and AB + AC = 5 cm. ∵ AB + AC < BC Sum of any two sides of a triangle must be greater than the third side. Think, Discuss and Write Question Can you construct the triangle ABC with the same measures by changing the base angle ∠C instead of ∠B ? Draw a rough sketch and construct it. BC = 4.2cm. ∠C = 30°, AB – AC = 1.6 cm (Page No. 287) Solution: Steps of construction: 1. Construct ΔBCD where BC = 4.2 cm and ∠C = 30° and AC – AB = 1.6 cm. 2. Draw perpendicular bisector of BD which meets $$\overline{\mathrm{CD}}$$ produced at A. 3. Join B, D. 4. ΔABC is the required triangle. Try These Can you draw the triangle with the same measurements as shown in the figure in alternate way ? (Page No. 289) [Measurements : ∠B = 6Q°, ∠C = 45° and AB + BC + CA =11 cm] [Hint: Take ∠YXL = 60°/2 = 30° and ∠XYM = 45°/2 = 22 $$\frac { 1 }{ 2 }$$ ] Solution: → Draw XY = 11 cm [AB + BC + CA = 11 cm] Construct ∠YXP = 30° at X $$\left[\frac{B}{2}=\frac{60^{\circ}}{2}=30^{\circ}\right]$$ Construct ∠XYQ = 22$$\frac { 1 }{ 2 }$$ at Y $$\left[\frac{\mathrm{C}}{2}=\frac{45^{\circ}}{2}=22 \frac{1}{2}^{\circ}\right]$$ → $$\overrightarrow{\mathrm{XP}}$$ and $$\overrightarrow{\mathrm{YQ}}$$ meet at A. → At A, draw $$\overrightarrow{\mathrm{AB}}$$ such that ∠XAB = 30° where B is a point on XY. → Also draw $$\overrightarrow{\mathrm{AC}}$$ such that ∠YAC = 22$$\frac{1}{2}^{\circ}$$ where C is a point on XY. → Δ ABC is the required triangle. Try These Question What happens if the angle in the. circle segment is right angle ? What kind of segment do you obtain ? Draw the figure and give reason. [Page No. 290] Solution: If the angle in the circle segment is right angle i.e., 90°, then the angle subtended by it at the centre is 2 x 90° = 180° Thus the line segment becomes the diameter and the circle segment becomes the semi-circle.	2023-02-05 23:13:46	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6147653460502625, "perplexity": 2889.7498281457138}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500294.64/warc/CC-MAIN-20230205224620-20230206014620-00296.warc.gz"}
http://mathhelpforum.com/advanced-statistics/57920-mean-variance-joint-marginal-pdfs.html	Math Help - Mean and Variance of joint marginal pdfs? 1. Mean and Variance of joint marginal pdfs? 1. Let X1, X2, X3, X4 be four mutually independent random variables, having the same pdf, f(x) = 2x, 0 < x < 1, zero elsewhere. Find the mean and variance of The sum Y, of these four random variables. I don't even know how to start this problem. I'm trying to understand it in the book and am completely lost. All we learned how to do is turn X1 and X2 into functions of f(X1) and f(X2). Any help? 2. Originally Posted by wolverine21 1. Let X1, X2, X3, X4 be four mutually independent random variables, having the same pdf, f(x) = 2x, 0 < x < 1, zero elsewhere. Find the mean and variance of The sum Y, of these four random variables. I don't even know how to start this problem. I'm trying to understand it in the book and am completely lost. All we learned how to do is turn X1 and X2 into functions of f(X1) and f(X2). Any help? $E(Y) = E(X_1) + E(X_2) + E(X_3) + E(X_4) = 4 E(X_1)$. And you should know that $E(X_1) = \int_0^1 (x) (2x) \, dx$. Since the $X_i$ are independent, $Var(Y) = Var(X_1) + Var(X_2) + Var(X_3) + Var(X_4) = 4 Var(X_1)$. And you should know that: $Var(X_1) = E(X_1^2) - [E(X_1)]^2$. $E(X_1^2) = \int_0^1 (x^2) (2x) \, dx$.	2015-11-26 20:15:51	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7902570366859436, "perplexity": 224.87301302172636}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398447773.21/warc/CC-MAIN-20151124205407-00020-ip-10-71-132-137.ec2.internal.warc.gz"}
http://mathhelpforum.com/calculus/182590-need-help-integration-problem.html	# Math Help - Need help with an integration problem 1. ## Need help with an integration problem Here's what I'm working with: $\int e^xcos(x)dx$ This does not appear to be a trivial problem, and I'm having trouble figuring out how to approach this. If I try integrating it by parts, I just end up with another integral that's very similar. Tossing this into WolframAlpha shows a really complicated u-sub. I've run into situations where WolframAlpha makes things a lot more complicated than they need to be. I'm hoping this is one of those times. Can anyone give me a hand? 2. Define it with its corresponding integral and integrate both by parts: \begin{aligned} & I : = \int e^x\cos{x}\;{dx}, ~~ J := \int e^x \sin{x}\;{dx} \\& I = \int e^x \left(\sin{x}\right)'\;{dx} = e^x\sin{x}-\int e^x\sin{x}\;{dx} = e^x\sin{x}-J. \\& J = -\int e^x \left(\cos{x}\right)'\;{dx} = -e^x\cos{x}+\int e^x\cos{x}\;{dx} = -e^x\cos{x}+I. \end{aligned} Now by abstracting these two integrals from each other, we have: \begin{aligned} & I-J = e^x\sin{x}-J+e^x\cos{x}-I \\& \Rightarrow 2I = e^x\sin{x}+e^x\cos{x} \\& \Rightarrow I = \frac{1}{2}e^x \left(\sin{x}+\cos{x}\right). \end{aligned} 3. Definitely not a technique I'm familiar with. I'm going to have to stare at this for a while in order to comprehend it fully. Thank you for the insight! 4. Originally Posted by Lancet Here's what I'm working with: $\int e^xcos(x)dx$ This does not appear to be a trivial problem, and I'm having trouble figuring out how to approach this. If I try integrating it by parts, I just end up with another integral that's very similar. Tossing this into WolframAlpha shows a really complicated u-sub. I've run into situations where WolframAlpha makes things a lot more complicated than they need to be. I'm hoping this is one of those times. Can anyone give me a hand? A 'suggestive' solution is based on the 'identity'... $e^{x}\ \cos x = \frac{e^{(1+i) x} + e^{(1-i) x}}{2}$ (1) ... and You can integrate both terms of (1) using the standard rule... $\int e^{a x} dx = \frac{e^{a x}}{a} + c$ (2) Kind regards $\chi$ $\sigma$ 5. Originally Posted by Lancet Definitely not a technique I'm familiar with. I'm going to have to stare at this for a while in order to comprehend it fully. Thank you for the insight! Just in case a picture helps (helps me by mapping out the relationships implied by combinations of relative pronouns, integral of, derivative of) ... Key: Spoiler: ... is the product rule: straight continuous lines differentiate downwards with respect to x. ... as lazy integration by parts, doing without u and v and du and dv (as does THC, too, to an extent) ... then you want 'integration by parts twice' i.e. filling the blanks here... ... and then solving the top row for I. Larger __________________________________________________ __________ Don't integrate - balloontegrate! Balloon Calculus; standard integrals, derivatives and methods Balloon Calculus Drawing with LaTeX and Asymptote! 6. I believe I understand it now. Thanks for helping, everyone!	2015-04-19 16:28:31	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9777721762657166, "perplexity": 988.0753929634402}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246639191.8/warc/CC-MAIN-20150417045719-00178-ip-10-235-10-82.ec2.internal.warc.gz"}
http://ima.ucv.cl/pre-prints/on-the-local-global-divisibility-over-gl2-type-varieties/	Síguenos en las redes sociales: # On the local-global divisibility over GL2-type varieties ## Resumen Let k be a number field and let A be a GL2-type variety defined over k of dimension d. We show that for every prime number p satisfying certain conditions (see Theorem 2), if the local-global divisibility principle by a power of p does not hold for A over k, then there exists a cyclic extension k˜ of k of degree bounded by a constant depending on d such that A is k˜-isogenous to a GL2-type variety defined over k˜ that admits a k˜-rational point of order p. Moreover, we explain how our result is related to a question of Cassels on the divisibility of the Tate-Shafarevich group, studied by Ciperiani and Stix and Creutz Autores: Florence Gillibert, Gabriele Ranieri, URL de la publicación: https://arxiv.org/pdf/1703.06235.pdf Compartir esta información en: Compartir	2021-02-27 04:39:36	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8764296770095825, "perplexity": 1334.5417199503793}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358064.34/warc/CC-MAIN-20210227024823-20210227054823-00442.warc.gz"}
https://www.dur.ac.uk/physics/staff/profiles/?mode=pdetail&id=3357&pdetail=112281	We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue. Department of Physics # Staff profile ## Publication details for Dr Russell Smith Beifiori, Alessandra, Mendel, J. Trevor, Chan, Jeffrey C. C., Saglia, Roberto P., Bender, Ralf, Cappellari, Michele, Davies, Roger L., Galametz, Audrey, Houghton, Ryan C. W., Prichard, Laura J., Smith, Russell, Stott, John P., Wilman, David J., Lewis, Ian J., Sharples, Ray & Wegner, Michael (2017). The KMOS Cluster Survey (KCS). I. The Fundamental Plane and the Formation Ages of Cluster Galaxies at Redshift 1.4 < Z < 1.6. The Astrophysical Journal 846(2): 120. ### Abstract We present the analysis of the fundamental plane (FP) for a sample of 19 massive red-sequence galaxies (${M}_{\star }\gt 4\times {10}^{10}$ ${M}_{\odot }$) in three known overdensities at $1.39\lt z\lt 1.61$ from the K-band Multi-object Spectrograph (KMOS) Cluster Survey, a guaranteed-time program with spectroscopy from the KMOS at the VLT and imaging from the Hubble Space Telescope. As expected, we find that the FP zero-point in B band evolves with redshift, from the value 0.443 of Coma to −0.10 ± 0.09, −0.19 ± 0.05, and −0.29 ± 0.12 for our clusters at z = 1.39, z = 1.46, and z = 1.61, respectively. For the most massive galaxies ($\mathrm{log}{M}_{\star }/{M}_{\odot }\gt 11$) in our sample, we translate the FP zero-point evolution into a mass-to-light-ratio M/L evolution, finding ${\rm{\Delta }}\mathrm{log}M/{L}_{B}=(-0.46\pm 0.10)z$, ${\rm{\Delta }}\mathrm{log}M/{L}_{B}=(-0.52\pm 0.07)z$, to ${\rm{\Delta }}\mathrm{log}M/{L}_{B}=(-0.55\pm 0.10)z$, respectively. We assess the potential contribution of the galaxy structural and stellar velocity dispersion evolution to the evolution of the FP zero-point and find it to be ~6%–35% of the FP zero-point evolution. The rate of M/L evolution is consistent with galaxies evolving passively. Using single stellar population models, we find an average age of ${2.33}_{-0.51}^{+0.86}$ Gyr for the $\mathrm{log}{M}_{\star }/{M}_{\odot }\gt 11$ galaxies in our massive and virialized cluster at z = 1.39, ${1.59}_{-0.62}^{+1.40}$ Gyr in a massive but not virialized cluster at z = 1.46, and ${1.20}_{-0.47}^{+1.03}$ Gyr in a protocluster at z = 1.61. After accounting for the difference in the age of the universe between redshifts, the ages of the galaxies in the three overdensities are consistent within the errors, with possibly a weak suggestion that galaxies in the most evolved structure are older.	2019-12-12 07:02:26	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4820106625556946, "perplexity": 4599.407731234695}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540537212.96/warc/CC-MAIN-20191212051311-20191212075311-00116.warc.gz"}
https://dsp.stackexchange.com/questions/58941/integration-property-of-fourier-series	# integration property of fourier series The integration property in Fourier series is as follows: So, for proving the above property, i took this approach: This is where my doubt is. Some books and websites just put upper limit (ignoring the lower limit) and compare with (1) to conclude that However, when the lower integral limit is substituted, we get This value cannot be evaluated. Though some websites say that this corresponds to the "initial value"(?) and that is zero... etc., how does one justify this mathematically? Any help is appreciated. Thank you. • just a friendly suggestion: in the future, please learn to use $\LaTeX$ and express your equations with source code rather than screenshots. i want to just be able to copy them without re-expression (in $\LaTeX$). make it easier for people to help you rather than harder for them to help. – robert bristow-johnson Jun 17 '19 at 8:14 • Hil, using a reverse argument (what would the resulting Fourier series have to be if you differentiated it?) you could come up with all of the Fourier coefficients except for the DC coefficient. That would be undetermined unless the bottom limit of the integral was known and set to a finite value. – robert bristow-johnson Jun 17 '19 at 8:22 • BTW, the notation for a definite integral from whatever the book that was screen shot is horrible: $$\int\limits_{-\infty}^{t} x(t) \, dt$$ the dummy variable of integration should not be the same as the upper limit of the integral in an definite integral. this notation is legit: $$\int\limits_{-\infty}^{t} x(u) \, du$$ – robert bristow-johnson Jun 17 '19 at 8:26 • @robert bristow Johnson, I m extremely sorry for the inconvenience sir. I will make sure that I will source the equations from next post onwards. Thank you so much for your suggestion. – Nishanth Rao Jun 17 '19 at 8:57 • so Nish, have you seen how to render equations with $\LaTeX$? – robert bristow-johnson Jun 17 '19 at 18:41 Note that the antiderivative of a function is only defined up to a constant. Furthermore, note that if you integrate a periodic function, the result is not necessarily periodic. Let $$x(t)=\sum_{k=-\infty}^{\infty}a_ke^{jk\omega_0t}\tag{1}$$ Now we integrate $$(1)$$ with an arbitrary lower integration limit $$t_0$$. I'll say more about that later. \begin{align}y(t)&=\int_{t_0}^tx(\tau)d\tau\\&=\sum_{k=-\infty}^{\infty}a_k\int_{t_0}^te^{jk\omega_0\tau}d\tau\\&=a_0(t-t_0)+\sum_{k=-\infty\\k\neq 0}^{\infty}\frac{a_k}{jk\omega_0}e^{jk\omega_0t}-\sum_{k=-\infty\\k\neq 0}^{\infty}\frac{a_k}{jk\omega_0}e^{jk\omega_0t_0}\tag{2}\end{align} Clearly, if $$a_0\neq 0$$, $$y(t)$$ isn't periodic, so we can't hope to obtain a formula for its Fourier coefficients. So in order to end up with a periodic function $$y(t)$$, we require that $$a_0=0$$. If $$a_0=0$$, we get from $$(2)$$ $$y(t)=\sum_{k=-\infty}^{\infty}b_ke^{jk\omega_0t}\tag{3}$$ with $$b_k=\begin{cases}\displaystyle\frac{a_k}{jk\omega_0},&k\neq 0\\\displaystyle-\sum_{l=-\infty\\l\neq 0}^{\infty}\frac{a_l}{jl\omega_0}e^{jl\omega_0t_0},&k=0\end{cases}\tag{4}$$ So in general the antiderivative $$y(t)$$ has a non-zero DC component, which depends on the choice of the lower integration limit $$t_0$$. The antiderivative $$\tilde{y}(t)=\sum_{k=-\infty\\k\neq 0}^{\infty}\frac{a_k}{jk\omega_0}e^{jk\omega_0t}\tag{5}$$ is the specific antiderivative of $$x(t)$$ that has a zero DC Fourier coefficient, and this is the one that is meant by the formula that is usually given in textbooks. Consequently, the expression $$y(t)=\int_{-\infty}^tx(\tau)d\tau\tag{6}$$ for the antiderivative of $$x(t)$$ with Fourier coefficients $$b_k=a_k/(jk\omega_0)$$, $$k\neq 0$$, and $$b_0=0$$, is at least inaccurate; it is in fact a sloppy way of expressing the specific antiderivative $$\tilde{y}(t)$$ given by $$(5)$$, i.e., the one with a zero DC coefficient. • i like Eq. (4). – robert bristow-johnson Jun 17 '19 at 19:51 • @MattL. Thank you very much for your insight sir. However, this doesn't answer one of the queries i have asked in the post i.e, what happens when $$t_{o} = \infty ?$$ The complex exponential in equation 4 still doesn't converge to any value right? – Nishanth Rao Jul 6 '19 at 16:09 • @NishanthARao: As you've already noticed, that limit doesn't exist. – Matt L. Jul 6 '19 at 18:19 • @MattL. I am very grateful for your detailed answer. However with due respect, my main question was what happens to the complex exponential at $t_{o} = - \infty$ ? In both your approach and my approach, we dont come to an exact conclusion on what happens when $t_{o} \to \infty$ or in my case, $e^{-jkw_{o} \infty}$. I just wanted to know how to get the answer from our approach, and conceptually where is it going wrong. I am, totally thankful for robertbristow-johnson and you, for clearing my doubt. – Nishanth Rao Jul 23 '19 at 10:40 • @Jarvis: The answer is given in my previous comment. That limit doesn't exist. – Matt L. Jul 23 '19 at 10:44 It appears to me that the "initial value" issue would affect only the DC value, $$a_0$$, of the Fourier series. In my opinion, the author should have left the integrals as indefinite integrals (which are the same as the "anti-derivative") or have expressed this relationship only in terms of differentiation, and not integration. Actually, now that I think of it, the original $$x(t)$$ would have to have $$a_0 = 0$$ in order for the integration theorem to make any sense. And the resulting Fourier series can have any finite DC value you want. You would have to determine the resulting DC value by other means. To do this theorem properly, you must first do it for the derivative of $$x(t)$$ first and then apply the results in reverse. I dunno what book you're using but there are both some notational and even mathematical problems with the expression of this problem. • i'm gonna let someone else (maybe @MattL. ) make the appropriate and rigorous answer to this question. as it is posed, it's sorta a flawed problem in definition. (and i do not blame the OP for this, it could be the fault of the book.) – robert bristow-johnson Jun 17 '19 at 8:34 Oh, hell... Let's say you have two periodic functions, $$x(t)$$ and $$y(t)$$ having exactly the same period (and fundamental frequency): $$x(t) \triangleq \sum\limits_{k=-\infty}^{\infty} a_k \, e^{j k \omega_0 t}$$ $$y(t) \triangleq \sum\limits_{k=-\infty}^{\infty} b_k \, e^{j k \omega_0 t}$$ where the period common to both is $$\frac{2 \pi}{\omega_0}$$. Suppose you were to differentiate $$y(t)$$: $$y'(t) = \sum\limits_{k=-\infty}^{\infty} j k \omega_0 b_k \, e^{j k \omega_0 t}$$ you can see right away that the DC term of $$y'(t)$$ is zero (as it should be): $$j k \omega_0 b_k \bigg\|_{k=0} = 0$$ Now let's say that you set that differentiated periodic function to $$x(t)$$: $$x(t) = y'(t)$$ That means $$y(t)$$ is the indefinite integral of $$x(t)$$. Then you see that all of the coefficients of $$y(t)$$ are well-defined in terms of the coefficients of $$x(t)$$ except for the DC coefficient, $$b_0$$, which could be any finite value. $$a_k = j k \omega_0 b_k$$ or $$b_k = \frac{a_k}{j k \omega_0} \qquad \qquad \forall k \in \mathbb{Z} \ne 0$$. That is, in my opinion, the only legit way to look at the integration of a Fourier series. • This is a wonderful way to look at the property. Extremely thankful for your insight sir. With due respect however, I just want to know where I am going wrong, and if at all, why? I am pretty sure there must be some way to continue from that step. – Nishanth Rao Jun 17 '19 at 8:59 • @NishanthARao: rbj's answer is probably the most straightforward way to look at the problem. If you're interested in how to figure out the solution by integration, have a look at my answer. – Matt L. Jun 17 '19 at 10:58	2020-07-14 04:03:08	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 45, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8994536399841309, "perplexity": 341.352705541545}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657147917.99/warc/CC-MAIN-20200714020904-20200714050904-00167.warc.gz"}
https://plainmath.net/83517/how-does-the-refractive-index-of-air-rel	# How does the refractive index of air rely on the temperature? Is there a theoretical derivation of it? How does the refractive index of air rely on the temperature? Is there a theoretical derivation of it? You can still ask an expert for help • Questions are typically answered in as fast as 30 minutes Solve your problem for the price of one coffee • Math expert for every subject • Pay only if we can solve it Killaninl2 The refractive index of air is easy, because air is a dilute gas with a very small refractive index, which is given by: $n=1-\sum {n}_{i}{\delta }_{i}\left(k\right)$ for small wavenumbers k. The ${n}_{i}$ are the number density for each species of molecule, and ${\delta }_{i}$ is the contribution to the index from this molecular species. You can just use N2 and O2 to get a good enough fit, and include CO2 and H2O for a better fit. In the ideal gas limit, which is nearly perfect for air, $n=\frac{P}{kT}$. If you double the pressure, you double the deviation from 1. If you double the temperature, you halve the deviation from one, because all the components go with the same ideal gas law: So the formula for the long-wavelength index of air is $\overline{)n\left(P,T\right)=1+.000293×\frac{P}{{P}_{0}}\frac{{T}_{0}}{T}}$ Where ${P}_{0}$ is atmospheric pressure, and ${T}_{0}$ is the standard temperature of 300K. and this is essentially exact for all practical purposes, the corrections are negligible away from oxygen/nitrogen/water/CO2 resonances, and any deviation from the formula will be due to varying humidity. The actual contributions ${\delta }_{i}$ requires the forward scattering amplitude for light on a diatomic molecule. This is just beyond what you can do with pencil and paper, but it is within the reach of simulations.	2022-08-12 08:18:09	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 17, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8549802303314209, "perplexity": 314.2046824098811}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571597.73/warc/CC-MAIN-20220812075544-20220812105544-00765.warc.gz"}
https://gamasutra.com/blogs/FabricePiquet/20180621/320400/True_First_Person_Camera_in_Unreal_Engine_4.php	February 19, 2019 February 19, 2019 Press Releases February 19, 2019 Games Press If you enjoy reading this site, you might also want to check out these UBM Tech sites: # True First Person Camera in Unreal Engine 4 by Fabrice Piquet on 06/21/18 05:56:00 am The following blog post, unless otherwise noted, was written by a member of Gamasutra’s community. The thoughts and opinions expressed are those of the writer and not Gamasutra or its parent company. I decided to share the method I use in my current project to handle my true first person camera. There is little to no documentation on this specific type of first person view, so after looking into the subject for a while I wanted to write about it. Especially since I had a few issues which took me a bit of time to resolve. The end result looks something like that : ## True First Person ? What do we call "True First Person" (or TFP) ? It can also be called "Body Awareness" in some occasions. It's basically a camera that when used in a First Person point of view is attached to a an animated body to simulate realistic body movements of the played character, contrary to a simple floating camera. Here are a few examples of games having this kind of camera : (The Chronicles of Riddick: Assault on Dark Athena) (Syndicate) (Mirror's Edge) (Mirror's Edge) ## What I'm not doing : separate body and arms In a separate system, the two arms of the character are independent and attached directly to the camera. This allows to directly animate the arms in any situations while being sure it follows the camera rotation and position at all time. The rest of the body is usually an independent mesh that has its own set of animations. One of the problem of this setup is performing full body animations (like a fall reception) as it requires to synchronize properly the two separate animations (both when authoring the animation and playing them in-engine). Sometimes games use a body mesh that is only visible to the player, while a full body version is used for drawing the shadows on the ground (and visible to other players in multiplayer, this is the cas in recent Call of Duty games). This can be appropriate in order to optimize further, however if fidelity is the goal I wouldn't recommend it. I won't go in details about this method as it wasn't what I was looking for. Also there is already tons of tutorials on this kind of setup out there. ## Full-body mesh setup As a full-body mesh suggests we use only one mesh to represent the character. The camera is attached to the head, which means the body animation drives it. We never modify the camera position or rotation directly. The class hierarchy can be seen as this : PlayerControler -> Character -> Mesh -> AnimBlueprint -> Camera The PlayerController can always be seen on top of the Character (or Pawn) in Unreal, so this is nothing new here. The Character has a mesh, here a skeletal mesh of the body, which has an AnimBlueprint to manage the various animations and blending. Finally we have the camera, which is attached to the mesh in the constructor. So the Camera is attached to the mesh, are we done ? Of course not. Since the camera is driven by the mesh, we have to modify/animate the mesh to simulate the usual camera movements : looking up/down and left/right. This is done by creating additive animation (1 frame animation) that will be used as offsets from a base animation (1 frame as well). In total I use 10 animations. You can add more poses if you want the character to look behind itself but I found it wasn't necessary in the end. In my case I rotate the body when the player camera look at his left or right (like in the Mirror's Edge gif above). There is an additional animation for the idle as well, which is applied on top of all these poses. For me it looks like this : Once those animations are imported into Unreal we have to setup a few things. Be sure sure to name the base pose animation properly to find it back easily later. In my case I named it "anim_idle_additive_base". Then for the other poses I opened the animation and changed a few properties under the "Additive Settings" section. I set the parameter "Additive Anim Type" to "Mesh space" and the parameter "Base Pose Type" to "Selected Animation". Finally in the asset slot underneath I loaded my base pose animation. Repeat this process for every pose. Now that the animations are ready, it is time to create an "Aim Offset". An Aim Offset is an asset that store references to multiple animations and allow to easily blend between them based on input parameters. The resulting animation is then added on top of existing animation in the Animation graph (such as running, walking, etc). For more more details take a look at the documentation : Aim Offset. Once combined, here is what the animation blending looks like : My Aim Offset takes two parameters as input : the Pitch and the Yaw. These values are driven by variables updated in the game code. See below for the details ## Updating the animation blending To update the animation, you have to convert the inputs made the player into a value that is understandable by the Aim Offset. I do it in three specific steps : 1. Converting the input into a rotation value in the PlayerController class 2. Converting the rotation which is world based into a local rotation amount in the Character class. 3. Updating the AnimBlueprint based on the local rotation values. #### Step 1 : PlayerController input When the player move its mouse or gamepad control I take the input into account in the PlayerController class and update the Controller rotation (by overriding the UpdateRotation() function : void AExedrePlayerController::UpdateRotation(float DeltaTime) { if( !IsCameraInputEnabled() ) return; float Time = DeltaTime * (1 / GetActorTimeDilation()); FRotator DeltaRot(0,0,0); DeltaRot.Yaw = GetPlayerCameraInput().X * (ViewYawSpeed * Time); DeltaRot.Pitch = GetPlayerCameraInput().Y * (ViewPitchSpeed * Time); DeltaRot.Roll = 0.0f; RotationInput = DeltaRot; Super::UpdateRotation(DeltaTime); } Notes : UpdateRotation() is called every Tick by the PlayerController class. I take into account the GetActorTimeDilation() so that the camera rotation is not slowed down when using the "slomo" console command. #### Step 2 : Camera local rotation in Character My Character class has a function named "PreUpdateCamera()" which mostly do the following : void AExedreCharacter::PreUpdateCamera( float DeltaTime ) { if( !FirstPersonCameraComponent \|\| !EPC \|\| !EMC ) return; //------------------------------------------------------- // Compute rotation for Mesh AIM Offset //------------------------------------------------------- FRotator ControllerRotation = EPC->GetControlRotation(); FRotator NewRotation = ControllerRotation; // Get current controller rotation and process it to match the Character NewRotation.Yaw = CameraProcessYaw( ControllerRotation.Yaw ); NewRotation.Pitch = CameraProcessPitch( ControllerRotation.Pitch + RecoilOffset ); NewRotation.Normalize(); // Clamp new rotation NewRotation.Pitch = FMath::Clamp( NewRotation.Pitch, -90.0f + CameraTreshold, 90.0f - CameraTreshold); NewRotation.Yaw = FMath::Clamp( NewRotation.Yaw, -91.0f, 91.0f); //Update loca variable, will be retrived by AnimBlueprint CameraLocalRotation = NewRotation; } The functions CameraProcessYaw() and CameraProcessPitch() convert the Controller rotation into local rotation values (since the controller rotation is not normalized and in World Space by default). Here is what these functions look like : float AExedreCharacter::CameraProcessPitch( float Input ) { //Recenter value if( Input > 269.99f ) { Input -= 270.0f; Input = 90.0f - Input; Input = -1.0f; } return Input; } float AExedreCharacter::CameraProcessYaw( float Input ) { //Get direction vector from Controller and Character FVector Direction1 = GetActorRotation().Vector(); FVector Direction2 = FRotator(0.0f, Input, 0.0f).Vector(); //Compute the Angle difference between the two dirrection float Angle = FMath::Acos( FVector::DotProduct(Direction1, Direction2) ); //Find on which side is the angle difference (left or right) FRotator Temp = GetActorRotation() - FRotator(0.0f, 90.0f, 0.0f); FVector Direction3 = Temp.Vector(); float Dot = FVector::DotProduct( Direction3, Direction2 ); //Invert angle to switch side if( Dot > 0.0f ) { Angle = -1; } return Angle; } #### Step 3 : AnimBlueprint update The last step is the easiest. I retrieve the local rotation variable (with the "Event Blueprint Update Animation" node) and feed it to the AnimBlueprint which has the Aim Offset : ## Avoiding frame lag I didn't mention it yet but an issue may appear. If you follow my guidelines and are not familiar with how Tick() functions operate in Unreal Engine, you will encounter a specific problem : a 1 frame delay. It is quite ugly and very annoying to play with, potentially creating strong discomfort. Basically the camera update will always be done with data from the previous frame (so late from the player point of view). It means that if you move your point of view quickly and then suddenly stop, you will stop only during the next frame. It will create discontinuities, no matter the framerate in your game, and will always be visible (more or less consciously). It took me a while to figure out but there is a solution. To solve the issue you have to understand the order in which the Tick() function or each class is called. By default it is in the following order : _____ UpdateTimeAndHandleMaxTickRate (Engine function) _____ Tick_PlayerController _____ Tick_SkeletalMeshComponent _____ Tick_AnimInstance _____ Tick_GameMode _____ Tick_Character _____ Tick_Camera So what happens here ? As you can see the Character class updates after the AnimInstance (which is basically the AnimBlueprint). This means the local camera rotation will only be taken into account at the next global Tick, so the AnimBlueprint use old values. To solve that I don't call my function "PreUpdateCamera()" mentioned before into the Character Tick() but instead at the end of the PlayerController Tick(). This way I ensure that my rotation is up to date before the Mesh and its Animation are updated. ## Playing montages The base of the system should work now. The next step is to be able to play specific animations that can be applied over the whole body. AnimMontages are great for that. The idea is to play an animation that override the current AnimBlueprint. So in my case I wanted to play a fall reception animation when hitting the ground after falling a certain amount of time. Here is the animation I want to play : The code is relatively simple (and probably even easier in Blueprint) : void AExedreCharacter::PlayAnimLanding() { if( MeshBody != nullptr ) { if( EPC != nullptr ) { EPC->SetMovementInputEnabled( false ); EPC->SetCameraInputEnabled( false ); EPC->ResetFallingTime(); } //Snap mesh FRotator TargetRotation = FRotator::ZeroRotator; if( EPC != nullptr ) { TargetRotation.Yaw = EPC->GetControlRotation().Yaw; } else { TargetRotation.Yaw = GetActorRotation().Yaw; } SetActorRotation( TargetRotation ); //Start anim SetPerformingMontage(true); TotalMontageDuration = MeshBody->AnimScriptInstance->Montage_Play(AnmMtgLandingFall, 1.0f); LatestMontageDuration = TotalMontageDuration; //Set Timer to the end of the duration FTimerHandle TimeHandler; this->GetWorldTimerManager().SetTimer(TimeHandler, this, &AExedreCharacter::PlayAnimLandingExit, TotalMontageDuration - 0.01f, false); } } The idea here is to block the inputs of the player (EPC is my PlayerController) and then play the AnimMontage. I set a Timer to re-enable the inputs at the end of the animation. If you just do that, here is the result : No exactly what I wanted. What happens here is that my anim slot is setup before the Aim Offset node in my AnimBlueprint. Therefor when the full body animation is played the anim Offset is added after on top. So if I look at the ground and then play an animation where the head of the character look down as well, it doubles the amount of rotation applied to the head... which makes the character look between her legs in a strange way. Why doing the aim offset after ? Simply because it allows me to blend in and out very nicely the camera rotation. If I applied the animation after, the blend in time of the Montage would have been too harsh. It would have been very hard to balance between quickly blending the body movement and doing a smooth fade on the head to not make the player sick. So the trick here is to also reset the camera rotation in the code while a Montage is being played. We can do that because the montage is disabling the player inputs. So it is safe to override the camera rotation. To do so I added few lines of code in the function "PreUpdateCamera()" that I mentioned earlier : //------------------------------------------------------- // Blend Pitch to 0.0 if we are performing a montage (input are disabled) //------------------------------------------------------- if( IsPerformingMontage() ) { //Reset camera rotation to 0 for when the Montage finish FRotator TargetControl = EPC->GetControlRotation(); TargetControl.Pitch = 0.0f; float BlenSpeed = 300.0f; TargetControl = FMath::RInterpConstantTo( EPC->GetControlRotation(), TargetControl, DeltaTime, BlenSpeed); EPC->SetControlRotation( TargetControl ); } These lines are called at the beginning of the function, before the local camera rotation is computed from the PlayerController rotation. What it does is that it simply resets the pitch to 0 over time with the "RInterpConstantTo()" function. If you do that, here is the result : Much better ! :) It should be easy to also save the initial pitch value and blend it back at the end of the montage animation to set back the original player camera angle. However in my case it wasn't necessary for this animation. ## Animation tip to avoid motion sickness Last thing to mention. When authoring fullbody animations it is important to be careful with the movements that happen to the head. Head bobbing, quick turns and other kind of fast animations can make people sick when playing. So running, walking animations should be as steady as possible. Even if in real-life people move, looking at a screen is different. This si similar to the kind of motion sickness that can arise with Virtual Reality. It is usually related to the dissonance between what the human body feel versus what we see. A little trick I use in my animations, mostly for my looping animation like running, is to apply a constraint on the character head to always look at a specific point very far away. This way the head focus on a point that doesn't move and, being far away, stabilize the camera. (I used an Aim constraint on the head controller in Maya) You can then apply additional rotations on top to simulate a bit the body motion. The advantage is that it's easier to go back and tweak in case people become sick. You can even imaging adding these rotations in-game via code instead, so it can become an option that people disable. That's all ! ### Related Jobs IllFonic — Tacoma, Washington, United States [02.19.19] Senior AI Engineer IllFonic — Golden, Colorado, United States [02.18.19] Backend Engineer IllFonic — Tacoma, Washington, United States [02.18.19]	2019-02-19 23:29:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17365431785583496, "perplexity": 2308.6106683708567}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247493803.26/warc/CC-MAIN-20190219223509-20190220005509-00350.warc.gz"}
http://mathhelpforum.com/calculus/23016-problem-diffing-rational-expression-print.html	# Problem with Diff'ing a rational expression • Nov 18th 2007, 07:17 AM BClary Problem with Diff'ing a rational expression Keep getting all twisted up in the algebra in finding the first and second derivative of the following x(third)-4x(squared)/(x-2)(squared) F’(x) (x(third)-4x(squared))’(x-2)(squared)-(x(third)-4x(squared))((x-2)(squared))’/(x-2)(fourth) than (3x(squared)-8x)(x-2)(squared)-(x(third)-4x(squared)(2)(x-2)(1)/(x-2)(fourth) than (x-2)[(3x(squared)-8x)(x-2)-2x(third)+8x(squared)]/(x-2)(fourth) now stuck any help on further factoring would be appreciated • Nov 18th 2007, 07:45 AM topsquark Quote: Originally Posted by BClary Keep getting all twisted up in the algebra in finding the first and second derivative of the following x(third)-4x(squared)/(x-2)(squared) F’(x) (x(third)-4x(squared))’(x-2)(squared)-(x(third)-4x(squared))((x-2)(squared))’/(x-2)(fourth) than (3x(squared)-8x)(x-2)(squared)-(x(third)-4x(squared)(2)(x-2)(1)/(x-2)(fourth) than (x-2)[(3x(squared)-8x)(x-2)-2x(third)+8x(squared)]/(x-2)(fourth) now stuck any help on further factoring would be appreciated $F(x) = \frac{x^3 - 4x^2}{(x - 2)^2}$ So $F^{\prime}(x) = \frac{(3x^2 - 8x)(x - 2)^2 - (x^3 - 4x^2)(2(x - 2))}{(x - 2)^4}$ $F^{\prime}(x) = \frac{(x - 2)[(3x^2 - 8x)(x - 2) - 2(x^3 - 4x^2)]}{(x - 2)^4}$ This is about where you got to. Now divide through by the common x - 2: $F^{\prime}(x) = \frac{(3x^2 - 8x)(x - 2) - 2(x^3 - 4x^2)}{(x - 2)^3}$ Expand: $F^{\prime}(x) = \frac{3x^3 - 8x^2 - 6x^2 + 16x - 2x^3 + 8x^2)}{(x - 2)^3}$ And simplify: $F^{\prime}(x) = \frac{x^3 - 6x + 16}{(x - 2)^3}$ -Dan • Nov 18th 2007, 08:05 AM Soroban Hello, BClary! You seem to be doing fine . . . Quote: Find the first and second derivatives: . $F(x) \;=\;\frac{x^3-4x^2}{(x-2)^2}$ Quotient Rule: . $F'(x) \;=\;\frac{(x-2)^2\cdot(3x^2-8x) - (x^3-4x^2)\cdot2(x-2)}{(x-2)^4}$ . . . . . . . . . . . $F'(x) \;=\;\frac{x(x-2)^2(3x-8) - 2x^2(x-4)(x-2)} {(x-2)^4}$ Factor/reduce: . $F'(x) \;=\;\frac{x(x-2)\cdot\left[(x-2)(3x-8) - 2x(x-4)\right]}{(x-2)^4} \;=$ . $\frac{x\cdot\left[(x-2)(3x-8) - 2x(x-4)\right]}{(x-2)^3}$ Simplify: . . . . $F'(x) \;=\;\frac{x\left[3x^2 - 8x - 6x + 16 - 2x^2 + 8x\right]}{(x-2)^3}$ Therefore: . . . $\boxed{F'(x) \;=\;\frac{x\left(x^2-6x+16\right)}{(x-2)^3}}$ Now try the second derivative . . . • Nov 18th 2007, 08:09 AM BClary Thanks to all, off doing second now Thanks for all your help, lets see where I end up at thanks • Nov 18th 2007, 08:57 AM BClary 2nd derivative should be after a little algrebra (haha) (-8x-32)/((x-2)(fourth)) Right? • Nov 18th 2007, 08:59 AM topsquark Quote: Originally Posted by BClary after a little algrebra (haha) (-8x-32)/((x-2)(fourth)) Right? Yup! :) -Dan • Nov 18th 2007, 09:00 AM BClary Thanks so much TY Ty Ty Ty ty TY	2017-10-17 17:39:27	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9403252601623535, "perplexity": 2986.574002239537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822145.14/warc/CC-MAIN-20171017163022-20171017183022-00765.warc.gz"}