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Edexcel A Level Further Maths: Core Pure:复习笔记3.2.2 Method of Differences

Method of Differences

What is the Method of Differences?

• The Method of Differences is a way of turning longer and more complicated sums into shorter and simpler ones
• Sometimes when summing series, you will notice that many of the terms (or parts of the terms) simply “cancel out” or eliminate each other
• This can turn a very long series summation, into a much simpler shorter one
• In the case of
• (and so on, until…)
• This is the penultimate term
• This is the last term
• You can see that when these are summed, most of the terms will cancel out
• This leaves just
• We can say that

How can I use partial fractions along with the method of differences?

• You will often need to use partial fractions to change the general term into a sum of two or three terms, rather than a single fraction
• For example,  can be rewritten as
• This may lead to a more interesting pattern of cancellations than was seen for
• For example,  can be written as , where , and the terms can then be listed as:
• (and so on, until…)
• When these are summed, it will just leave
• You can then evaluate this expression with  to get to your final answer
• It is helpful to use  notation to spot the pattern, rather than substituting  into the expression every time, especially with more complicated expressions
• You need to consider carefully which term to make  and then how the other terms in the expression relate to it
• If this is difficult for a particular expression, it may be more straightforward to substitute  into each term in the series and spot any patterns that way
• This is essentially writing the series out in full until you spot which terms will cancel
• In your working, however, you should still write out the last two or three terms in terms of , etc.

How can I use the method of differences for series with expressions containing more than two terms?

• The general term of the series may have more than two terms, which can sometimes make spotting which terms will cancel more challenging
• For example,
• This can be written as  where
• Writing out the first five terms and the last three terms we get:
• (and so on until…)
• In this case, look at the diagonals starting at the top right
• We have  which sum to o
• This pattern repeats for the other diagonals
• We will eventually be left with only
• Evaluating this with  results in an answer of

What other uses are there for the method of differences?

• Method of differences can also be used to prove the formulae for the sum of
• For example, this can be used to prove that the result for the sum of squares is indeed
• By expanding brackets it can be shown that ,  and then the sum of both sides of that equation from  can be considered
• The left-hand side can be found in terms of  using method of differences, and the right-hand side can be rearranged to give
• That equation can then be rearranged to give an expression for
• When these proofs have appeared previously in exams, they have tended to be structured to help you work through the steps
• You may have to use your algebraic method of differences result to find a numerical answer, usually in the last part of a question
• The question will often ask you to evaluate the sum starting from  (or some other arbitrary value) rather than from
• To help with this, remember that:
• You may also find it helpful to recall that for constants  and :

Exam Tip

• Mark schemes often specify how many terms from the start and end of the series should be written down – it is usually two or three, so always write down the first three and last three terms
• Don’t be afraid to write out more terms than this to make sure you spot the pattern, and can easily decide which terms will cancel and which will not
• Check your algebraic answer by substituting in numbers to make sure it works; you can use your calculator to find summations in sigma notation

Worked Example

(a) Express  in partial fractions.

(b) Hence show that  using the method of differences.


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32.1.12 File/Write/Data...

The File/Write/Data... menu item is used to save a FLUENT data file. See Section  4.3.2 for details.

 When FLUENT writes a data file, the .dat extension is added to the file name specified, unless the name already ends with .dat. You can also write a compressed file by appending .gz or .Z to the file name. (See Section  4.1.5 for details about file compression.)

Previous: 32.1.11 File/Write/Case...

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# G Code Command List

The command performs an action. Color List for Admin Command Dino Coloring I couldn't find a simple list of the color codes anywhere to use for the dino color command, so I made one. If the last argument on the line is a single (, it is interpreted as the beginning of a command group. Code Time is an open source plugin that provides programming metrics right in your code editor. Downloading the source code and building it yourself puts you in great control and also makes it easier for you to update to newer versions or, even better, create patches for bugs you may find and contributing them back to the community so everyone benefits. Create an ASPX page with code behind. His previous assignment was as the Deputy Chief of Staff, G-3 for the 5th Signal Command (Theater) in Wiesbaden, Germany. T o control CNC machines we use commands called CNC G Codes. Here is a nice little cheat sheet pdf of the G Codes and M Codes used to control RepRap 3D Printers. It prepares or presets the control system to use a certain mode or operation. Learn about your speaker, control your home with your voice, get answers from Google and have some fun. Executive Summary: This document is a brief description of how to compile basic C++ programs using g++. , run) the command. In February 2018 he reported as the Command Master Chief to VFA-192, the World Famous Golden Dragons, in the middle of a Western Pacific Deployment. G code out of range - A G code greater than G99 was used, the scope of G codes in LinuxCNC is 0 - 99. The new PSC manual is available in multiple formats. Examples marked with • are valid/safe to paste without modification into a terminal, so you may want to keep a terminal window open while reading this so you can cut & paste. Aug 10, 2004 by Dave Cross Perl has a large number of command-line options that can help to make your programs more concise and open up many new possibilities for one-off command-line scripts using Perl. forces, execute emergency war orders and coordinate actions by civil authorities. Any of the three planes (XY, YZ, ZX) may be selected. The following is a list of useful DOS commands, with explanations. Not all standard G-code are supported by the MP Select Mini. 3 The list of command-line and menu entry commands. Are you considering the U. —Mad Warrior and Heroic Spirit of Berserker Rage. The results will be displayed in a sorted list, with the Code citation and document description indicated. However, Grbl also has two separate system command types that are outside of the normal g-code streaming. This is important for the profiler to be able to map instructions back to source line locations. You don't have to learn G-code to create CNC programs. codepad is an online compiler/interpreter, and a simple collaboration tool. Parameters Description Example G0 Axis [X/Y/Z] Position Rapid Movement G0 X50 G1 Axis [X/Y/Z/E] Position Feed [F] Controlled Movement G1 F150 X10 G4 Time in ms [P] Dwell / Wait G4 P500 G20 none Set units to inch G20 G21 none Set units to mm G21 G28 Home G28 X Y G90 none Absolute Positioning G90. – For standardizing. , directories) to return the file listing from. The du command can be used to track the files and directories which are consuming excessive amount of space on hard disk drive. Basic program structure. Wanna write your own game in less than 10 minutes? Try our. To view the commands divided into sections, go to the Command Overview. The feedrate. Open-source Linux is a popular alternative to Microsoft Windows, and if you choose to use this low-cost or free operating system, you need to know some basic Linux commands to configure, operate, and interact with your system smoothly. GOLD Gulf War code name for an XVIII Airborne Corps objective (Tallil Air Base) GOLDEN PHEASANT United States Army Forces Command deployment of forces to Honduras, 1987. Every command followed by a return is responded to when Grbl is ready to receive another command. code, which includes the G and M code groups. In-editor dashboard Get daily and weekly reports of your programming activity right in your code editor. Looking closer, however, these high-level weaknesses are often the parent of more detailed weaknesses that appeared in previous Top 25 lists. These are the common g-codes for CNC Lathes and turning. If the named. Talos 1 is a huge environment that holds many hidden secrets, locked safes and private rooms. The timeline for additions and updates to the codes and software ports is included, and. Using this command is not recommended. Custom Types. Looking to learn CNC G-Code? Need a quick and easy G-Code Tutorial or G-Code Course? Want some easy G-Code Training? Maybe you just want to learn more about a specific G-Code related topic or see particular G-Code examples. (17 JANUARY 2018) 2018. Hide menus, status bar, toolbars, command prompt, and windows title bar and maximize the Rhino window. Organization. This information is also included in our mill Operator's Manual, which you can download from our support site. Click the g-code link (if any) to visit a tutorial from our popuplar Online Free G-Code Training that shows examples and teaches how to program the g-code. This is the piece of code that you add to a program to indicate that the program should run the code inside a function at a certain time. List of Supported GCodes (and will manually handle some G-Codes so as to facilitate tool changes) Subscribe Share. If there are no errors in your source file, the Java compiler will produce one or more. Proposal for sending multiple lines of G-code. Created June 15, 2004. Get to Know Your CNC: How to Read G-Code. Most keyboard shortcuts require the user to press a single key or a sequence of keys one after the other. What is G-Code? G-code is a programming language for CNC that instructs machines where and how to move. Set G_DEBUG=fatal_warnings to make GStreamer programs abort when a critical warning such as an assertion failure occurs. Below is the list of G-codes that are used in most modern CN. P&G is made of many individual brands, each serving customers in different ways - but all with a focus on making peoples’ lives a little easier. If you have never dealt. Traci at Beneath My Heart calls her command center "giant" with pride. Programming the Spindle This chapter describes spindle programming. Set G_DEBUG=fatal_warnings to make GStreamer programs abort when a critical warning such as an assertion failure occurs. G-code is a language that humans use to tell a machine how to do something. Shows the text in the info screen. You can customize the keyboard shortcuts in Photoshop. Organization. Your three choices are the USA, the Chinese, and the Global Liberation Army (a group of freedom fighters/terrorists). Write a program PhoneWords. Use the chat box with a hashtag followed by the below server commands. Some G words alter the state of the machine so that it changes from cutting straight lines to cutting arcs. creativemenu cm Enables or disables the Creative Menu. sort is a standard command line program that prints the lines of its input or concatenation of all files listed in its argument list in sorted order. Use the lsof command to list all open files in use on the system, and pass the list to more to display it one screen at a time (rather than just spewing the whole thing directly to the terminal). Note that many of these characters are specific to font. G-codes tell the controller what sort of motion is desired. We are planning to add tooltips with comments for each G code or M code in the. 0 " it is best to "100. gz archives. All communication is in printable ASCII characters. View the current setting with M503. css using the command line. I have a file "myFile. CNC machines work by following the commands or instructions (G-codes / M-codes) which are given in Part Program. It does not provide exhaustive information about each resource. gcode for Skeinforge as of October 3rd 2012. Fanuc 6-M, 11M machines. In computing, a keyboard shortcut is a sequence or combination of keystrokes on a computer keyboard which invokes commands in software. Traci at Beneath My Heart calls her command center "giant" with pride. DTR Search Tips XClicking on any DTR document title that appears in the search results will open that PDF document in a new tab or window. Here is a list of some basic Git commands to get you going with Git. This command is used to start the SSH client program that enables secure connection to the SSH server on a remote machine. In case of national emergency or destruction of ground command and control centers, the E-4B provides a highly survivable command, control and communications center to direct U. Below is the list of G-codes that are used in most modern CN. LinuxCNC "G-Code" Quick Reference ; Code Parameters Description ; Motion (X Y Z A B C U V W apply to all motions) G0: Rapid Move; G1: Linear Move; G2, G3: I J K or R, P. One system command type is streamed to Grbl like g-code. Awk is, roughly speaking, a language oriented to manage tables. The operator can simply program takeover of the workpiece with ShopTurn in one cycle. See the website for a comprehensive list. Colonel Tim Norton assumed his current position as the Chief of Staff on March 1, 2017. In Command & Conquer: Generals gamers choose from three radically different fighting forces, build an army from the ground up, and seek out and destroy opposing players' armies and bases. In case of national emergency or destruction of ground command and control centers, the E-4B provides a highly survivable command, control and communications center to direct U. Murdock Ph. c, using the standard C compiler scc2. Is there a command to list files, exclude sub-directories and display size and date? 3. All the letters but G and M come right before specification values - a G or M followed by a number will trigger a specific type of behavior while any other letter followed by a number specifies a rate, offset, position, or other such thing. Apparently it was first posted in January, 1993, and the last update was in October, 1995. He was selected for the Command Master Chief Program which led to his early departure in January 2018. – Identify the office of origin for correspondence. Most of the command (e. The extrusion value keeps untouched. This value is normally correct and should only need to specified in extraordinary situations. CNC G Code: G02 and G03. All G codes not in group 0 behave this way. Below is a complete list of Command Prompt commands, often called CMD commands (and sometimes incorrectly as Command Prompt codes), available from the Command Prompt in Windows 8, Windows 7, Windows Vista, and Windows XP. Not every number between 0 and 99 is a valid G code. List directory /home/user/Documents/Books with absolute path. You can display or list hard drives in CMD/Command Prompt or PowerShell, using wmic, diskpart, fsutil, psdrive command line, in Windows 10/8/7. Quickly learn all G-code commands using our tutorial. , run) the command. The first step is to create a file that will contain our code for our Node. To obtain the list of options for each command, simply type the command name followed by -h:. With the exception of M126, M127 and M200, they are not presently supported by the standard ReplicatorG releases. All lines of machine code must start with either a G Code or an M Code, and software ports can be used to define the operation. GetDocumentUserText. FOR Parameters. For example, CWE-119 is the parent of CWE-120. OneCommand is the successful dealer’s secret weapon for increasing revenue, driving traffic, and enhancing owner loyalty, all while lowering marketing costs. Updated Friday, June 1, 2018 by Linode Written by Christopher S. Fields of interest may vary slightly, depending on the echelon of command, mission, and environment. Note that in C# the word 'operator' is a. See Sending G-code for more information on how to send the commands below. If you want to find specific text in files, in a command line output or elsewhere, you may use the findstr command on Windows to do so. java that takes a 7 digit string of digits as a command line input, reads in a list of words from standard input (e. [email protected] What were G-codes? G-codes were quality data codes that rehab therapy providers—including eligible physical therapists, occupational therapists, and speech-language pathologists—included on their Medicare claim forms to fulfill requirements for Functional Limitation Reporting (FLR). The name is an acronym for the ‘Bourne-Again SHell’, a pun on Stephen Bourne, the author of the direct ancestor of the current Unix shell sh, which appeared in the Seventh Edition Bell Labs Research version of Unix. Nearly all command names and most of their command line switches will be in lowercase. Here are G-codes for Fanuc cnc control which are necessary for a cnc machinists to learn to understand cnc programming. Examples marked with • are valid/safe to paste without modification into a terminal, so you may want to keep a terminal window open while reading this so you can cut & paste. G Codes List. Note about file extensions: Newer machines will allow for the reading of most any file extension, some machines require that the file extension be set to a certain name. Pause message will be displayed if the message is included in the G-code. We can run the below command from windows command prompt to get the list of local drives. , dates and names) are customized for each recipient. The code inside the loop includes a simple If Statement that terminates the macro with the command Exit Sub if a sheet with the specified name is found. The Lines of Code That Changed Everything Apollo 11, the JPEG, the first pop-up ad, and 33 other bits of software that have transformed our world. The Java Runtime (JRE) that you download from java. Recommended. Nmap users are encouraged to subscribe to the Nmap-hackers mailing list. It's a program that takes in commands, which it passes on to the computer's operating system to run. Your three choices are the USA, the Chinese, and the Global Liberation Army (a group of freedom fighters/terrorists). What's This all About? This is what G codes are active when you turn on the. Show List of Open Ports in Command Line. the System32 directory which is in the path. According to its proponent Henri Fayol (1841-1925), the more clear cut the chain of. same command G0 X12 (move to 12mm on the X axis) G Codes and M Codes for 3D printing G Codes and M Codes for 3D printing These are codes for the Marlin RepRap. Certain commands may require administrative access on Windows 7 or Vista. organizational structures and levels of command. The Foundation does not engage in political campaign activities or communications. CodeCombat is a game-based computer science program where students type real code and see their characters react in real time. Lots of input/output formats. See your slicer documentation for this feature. c, using the standard C compiler scc2. The Start/End-gcode contains a few lines of code to make sure. Machine control software that combines a graphical part program development, animation and verification into a powerful PC based machine tool controller. -e, --eval: Compile and print a little snippet of CoffeeScript directly from the command line. Install with npm. Generic G-code commands are usually the same for any machine, for example: G0 is a rapid move to another location; G1 is a straight-line cut. We are not including other gcode commands that are used to set up specific. G-Code is the most popular programming language used for programming CNC machinery. The exit status of the while and until commands is the exit status of the last do list command executed, or zero if none was executed. One of the gotchas that seems to bite people in the rear is that the standard says that if there is an unsupported feature on a line of G-Code, the controller can discard the entire line. Code categories are the groupings for the g-code Wizard (type Ctrl+G for the Wizard). Here is a list of common G codes. The Windows command-line tools are used to perform various tasks related to Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows 7, and Windows Vista. Retrieve source code from SVN. It supports the following G-code and M-code commands. Created June 15, 2004. C LIs (command-line interface) have existed since ages. LOCK EXAMPLE - NØ8Ø GØ1 Z-Ø. MORE TECHNICAL INFORMATION Using the Command-line to find Java Versions - Mac. Programming the Spindle This chapter describes spindle programming. This calculator will generate a G-Code tool path for a circle. Code - Use Code 1301) 13: 22: Expired Code - Do Not As : United States Travel Service (Exp. For the complete list of these flags, use the MBeans tab of the JConsole utility. We can find their. A command line typed on an early setups was thus not produced by a computer mirroring what you typed, but local echo. For the full list of all keyboard shortcuts, see Keyboard Shortcuts. In general, Grbl assumes all characters and streaming data sent to it is g-code and will parse and try to execute it as soon as it can. Also, there are several letters that are used in more than one function, but that depends on the input units. Browse and install apps that integrate with and enhance G Suite, including Administrative Tools, CRM, Task Management, and much more. This information is also included in our mill Operator's Manual, which you can download from our support site. 1 Abstract Syntax Notation 1 (ISO 8824 8825) AT Apple Talk AT ATtention (Hayes Modems Command Prefix) AT&T American Telegraph & Telephone ATE. The adb command facilitates a variety of device actions, such as installing and debugging apps, and it provides access to a Unix shell that you can use to run a variety of commands on a device. 999, either is acceptable to DeskCNC g-code interpreter. The dir command displays a list of files and subdirectories in a directory. Shows the text in the info screen. The command line is a text interface for your computer. Software for CNC Programming. Confirm this choice by clicking Yes when prompted. Some parts of the code are under the BSD 3-clause License. G-Code and M-Code Grand Master List Here's a combined and sorted list of all the G-Code and M-Code commands for (as many of) the Free Software G-Code interpreters (that I could find) relevant to DIY 3D printing. Javascript Char Codes (Key Codes) - Cambia Research. Instead, check out our List of Windows CMD Commands for all of the command-line options you have available to you in Windows. So far, this is a proposal, open for discussion. 0 our CNC Syntax Editor software supports syntax highlighting for all G and M codes from the table below. The purpose of the application is to generate G-Code for various milling, engraving, turning and drilling routines. The current plan is to continue to maintain the 1. Note that in C# the word 'operator' is a. 95 06/01/14 DES for the bond description. [email protected] Supercharge your team. The --heads option lists only branch names since the command can list tags too. The canned cycles G81 through G89 have been implemented as described in this section. Standard Marlin compatible G-codes can be found at the RepRap wiki: G-code. Commenting Out Code. Here are the g-code basics you need to know to efficiently understand and write programs that produce high quality products. Here are G-codes for Fanuc cnc control which are necessary for a cnc machinists to learn to understand cnc programming. Finally press ENTER once more followed by pressing the CONTROL and d keys simultaneously to execute (i. Don't wait hours for slicing that detailed model. gcode;This is a long one. Level B training and procedures. ALL CNC “G & M” CODES FANUC G code of mille G code Explanation G00 Positioning(rapid moveing) G01 Linear interpolation G02 Circular interpolation/Helical interpolation CW. I've used Easel enough to realize that I hate it, it feels like I'm working with MS Paint. Commons CLI 1. Admin commands on private servers are done using a [whitelist of Steam64IDs] that are allowed to use the commands. Directory Name Description; bsp/board/common. G CODES (PREPRATORY FUNCTIONS) Here is a list of the G codes for the HAAS VF-2 Machining Center. The body of the function is the list of commands within braces, each of which must be terminated with a semicolon or a newline. Some G words alter the state of the machine so that it changes from cutting straight lines to cutting arcs. The Windows command-line tools are used to perform various tasks related to Windows Server 2008 R2, Windows Server 2008, Windows Server 2003, Windows 7, and Windows Vista. G-Code Controller. MILITARY ABBREVIATION AND ACRONYM LIST. (A) Subject to the limitations prescribed in Section 56-5-930, the provisions of this chapter shall not be deemed to prevent local authorities with respect to streets and highways under their jurisdiction and within the reasonable exercise of the police power from:. css using the command line. Standard Marlin compatible G-codes can be found at the RepRap wiki: G-code. Discussion in 'Troubleshooting' started by JohnStack, Mar 27, 2014. API methods available to bots. In addition to G-codes, Smoothie understands a set of commands. G160 APL AXIS COMMAND MODE ON. I'm only familiar with Amada's codes, and that's what is. Code - Use Code 1301) 13: 22: Expired Code - Do Not As : United States Travel Service (Exp. 3 G-code grouping Group Command 0 One-shot command 1 Feed command 2 Constant surface speed command 3. Continue with reading or go to download page. The CURA website hasn't been too helpful in this regard. The above is the start. Internet-Draft Stateless OpenPGP Command Line Interface October 2019 at the end of a "PASSWORD", it will trim the trailing whitespace before using the password. If you forget a command, you can run the command help (see help). Yes, I have them in the same directory as the application i. 3 JConsole Utility), you can dynamically set, unset, or change the value of certain Java VM flags for a specified Java process. The mission of the Department of Defense is to provide a lethal Joint Force to defend the security of our country and sustain American influence abroad. The following command returns only the. Set G_DEBUG=fatal_warnings to make GStreamer programs abort when a critical warning such as an assertion failure occurs. ROGRAM EXAMPLE-B. Click here to connect with the 20th. gzip also refers to the associated compressed data format used by the utility. gcode is always prepended to the g-code of the sliced file in question. Shows the text in the info screen. MS-DOS was first introduced by Microsoft in August 1981 and was last updated in 1994 with MS-DOS 6. The Ultimaker Github page has a list of these commands and their. The find command is one of the most versatile commands in UNIX and Linux and I used it a lot in my day to day work. Such subordinate activities will indicate the Unit Identification Code of the major command in parentheses, e. To access the command-line interface: Windows 7 or Vista: Click Start, type cmd, and then press Enter. Just like the G and M codes, not every machine uses the same Letter codes. 5407 ILLEGAL COMMAND IN G41. Don't wait hours for slicing that detailed model. Like other APIs and integrations, bot users are free. G Suite is a set of applications, including Gmail, Docs, Sheets, Slides, Sites and more, as well as a set of messaging, collaboration, security, and compliance tools for organizations to use. The only requirement is that you add -gline-tables-only or -g to the command line. 0-beta planner G0, G1 - Linear Move. List the files in a directory in Unix. Open-source Linux is a popular alternative to Microsoft Windows, and if you choose to use this low-cost or free operating system, you need to know some basic Linux commands to configure, operate, and interact with your system smoothly. Don't wait hours for slicing that detailed model. This document is a G code tutorial for LinuxCNC the free CNC software. The commands in Windows are available from the Command Prompt and are called Command Prompt commands or CMD commands, but they are not DOS commands. 0 was formed from the merger of ideas and code from three different libraries - Werken, Avalon and Optz. See actions taken by the people who manage and post content. Exterior door prices vary based on material, glass and many other configurations, which is why we cannot list exact pricing online. G-Code and M-Code Grand Master List Here's a combined and sorted list of all the G-Code and M-Code commands for (as many of) the Free Software G-Code interpreters (that I could find) relevant to DIY 3D printing. CNC G Code: G02 and G03. Updated Friday, June 1, 2018 by Linode Written by Christopher S. Most commands in Stata allow (1) a list of variables, (2) an if-statement, and (3) options. J-1-Civilian Personnel J-1-Manpower J-1-Mission Support J-1-Programs J-1-Training. TinyG implements the NIST RS274v3/ngc dialect of Gcode. G-Code is the most popular. With any luck, I now know: What a given command does; What other interpreters do with that command. Army Tank-automotive and Armaments Command (TACOM), headquartered at Detroit Arsenal in Warren, Michigan. This list is ordered by size range then alphabetically within the size range. To access more information about the command, click on the command to go to the dedicated page for that command. The Ultimaker Github page has a list of these commands and their. For each command, we will provide a description of what the command does, specify what arguments may be needed, and even provide a few sample commands so that you can see how it is commonly used. With any luck, I now know: What a given command does; What other interpreters do with that command. How to Program Arcs and Linear Movement in G-Code Manually: Introduction G-code is used in a lot of automated manufacturing processes. The system of G-code and M-code commands differs, especially for turning, between the machines of INTEGREX e-Series and the other turning machines. Admin commands on private servers are done using a [whitelist of Steam64IDs] that are allowed to use the commands. Indo-Pacific Command USINDOPACOM. npm install less -g The -g option installs the lessc command available globally. Slic3r reads STL, AMF and OBJ files while it can output G-code and SVG files. Commands such as Program Stop or End Of Program refer to stopping or ending the. Otherwise, the G codes apply to either dialect. Topic: Improved start and end G-code I've not been happy with the default start and end g-code, so have been developing a better version based on the versions Ian posted on his blog. T>w28 initiates write for system file 28) These commands can also be used to read/write a specific volume/copy of a system file. Color List for Admin Command Dino Coloring I couldn't find a simple list of the color codes anywhere to use for the dino color command, so I made one. Debian provides more than a pure OS: it comes with over 59000 packages, precompiled software bundled up in a nice format for easy installation on your machine. In general, Grbl assumes all characters and streaming data sent to it is g-code and will parse and try to execute it as soon as it can. Found that Boxzy does not support all G-Codes and some nuances such as spacing between coordinates. Note that many of these characters are specific to font. Although print dialogs have evolved, it’s many times necessary to send a document to the printer with some extra options. See your slicer documentation for this feature. The Army, as one of United States Army Cyber Command is an operational level Army force, with ARCYBER designated by the Secretary of the Army as an Army Service Component Command. User customizable G codes will change based on application and user definition. G-Code Programming & Operation COURSE # TRCNC40-396 - 4 days Description: The FANUC G-Code Programming & Operation course explores the fundamentals of G-Code programming for milling and turning applications. Go is an open source programming language that makes it easy to build simple, reliable, and efficient software. \emph Toggles italics on/off for the text in curly braces following the command e. A field can be interpreted as a command, parameter, or for any other special purpose. It also uses multithreading for parallel computation. Roblox is a global platform that brings people together through play. Command Line Tools. No liability is assumed by U. By pressing the tilde key (~), you can unlock the console, a gateway that lets. I have only tried these G codes in MDI but what I am thinking is if inserted in a program when the control gets to one of G codes it might execute the command completely and then the G99 will return to that point in the program and then proceed with the next line of code. The language that programmers create and use to tell a computer what to do. Start G-code. One can also combine flags like ORC_CODE=backup,debug. There is no point in continuing the loop to look at any remaining sheets if the one being sought has already been found. These commands are usable in the command-line and in menu entries. List directory /home/user/Documents/Books with absolute path. A Day at the MEPS Recruit Travel Joining the Military MEPCOM Anniversary Headquarters. Executive Summary: This document is a brief description of how to compile basic C++ programs using g++. Before that, I'd like to walk you through the configuration process that explains how you can add one or multiple command line switches to the Chrome browser. Jump to bottom. 1 Abstract Syntax Notation 1 (ISO 8824 8825) AT Apple Talk AT ATtention (Hayes Modems Command Prefix) AT&T American Telegraph & Telephone ATE. Using the probe command in GRBL 0. This command will work regardless of the state of the current call (e. is the oldest and largest dedicated PostgreSQL support provider in North America. Get the gamer on your list a digital Xbox Gift Card to use at Microsoft Store online, on Windows, and on Xbox. DTR Search Tips XClicking on any DTR document title that appears in the search results will open that PDF document in a new tab or window. A full featured gcode platform used for interfacing with advanced CNC controllers like GRBL and TinyG. G-code (also RS-274), which has many variants, is the common name for the most widely used numerical control (NC) programming language. Here is the list for Grbl v0. Starting G-Code: This is the G-Code that will be ran after heating up but before your print.


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# Performance forecasts for the primordial gravitational wave detection pipelines for AliCPT-1

Authors
Publication Date
Jun 16, 2022
Source
HAL-IN2P3
Keywords
Language
English
AliCPT is the first Chinese cosmic microwave background (CMB) experiment which will make the most precise measurements of the CMB polarization in the northern hemisphere. The key science goal for AliCPT is the detection of primordial gravitational waves (PGWs). It is well known that an epoch of cosmic inflation, in the very early universe, can produce PGWs, which leave an imprint on the CMB in form of odd parity $B$-mode polarization. In this work, we study the performance of the component separation and parameter estimation pipelines in context of constraining the value of the tensor-to-scalar ratio. Based on the simulated data for one observation season, we compare five different pipelines with different working principles. Three pipelines perform component separation at map or spectra level before estimating $r$ from the cleaned spectra, while the other two pipelines performs a global fit for both foreground parameters and $r$. We also test different methods to account for the effects of time stream filtering systematics. This work shows that our pipelines provide consistent and robust constraints on the tensor-to-scalar ratio and a consistent sensitivity $\sigma(r) \sim 0.02$. This showcases the potential of precise $B$-mode polarization measurement with AliCPT-1. AliCPT will provide a powerful opportunity to detect PGWs, which is complementary with various ground-based CMB experiments in the southern hemisphere.


text:
# Hunt the Wumpus game in C++

I have created a simple version of the classic game Hunt the Wumpus in C++. The rules for the game can be found on Code Golf SE.

The rules of the game are (from PPCG):

The player starts in a random room on an icosahedral map (thus there are 20 rooms in total, connected to each other like the faces of an icosahedron, and every room has exactly three exits).

The wumpus starts in a randomly selected different room. The wumpus stinks, and its odor can be detected in any of the three rooms adjacent to its location, though the direction of the odor is impossible for the player to determine. The game reports only "you smell a wumpus."

The player carries a bow and an infinite number of arrows, which he may shoot at any time into the room in front of him. If the wumpus is in that room, it dies and the player wins. If the wumpus was not in that room, it is startled and moves randomly into any of the three rooms connected to its current location.

One, randomly selected room (guaranteed not to be the room in which the player starts) contains a bottomless pit. If the player is in any room adjacent to the pit, he feels a breeze, but gets no clue as to which door the breeze came from. If he walks into the room with the pit, he dies and wumpus wins. The wumpus is unaffected by the pit.

If the player walks into the wumpus's room, or if the wumpus walks into the player's room, the wumpus wins.

This is the first non-trivial program I have created and would like to know what I could have done better.

Does my code follow the best practices? Is there anything I can do to clean it up? Can there be any improvements?

#include<iostream>
#include<vector>
#include<algorithm>
#include<limits>

constexpr int ROOMS = 20;
constexpr int BATS = 3;
constexpr int PITS = 3;

constexpr int END_GAME = -1;

struct Room
{
bool player{false};
bool bat{false};
bool wump{false};
bool pit{false};
};

class Player
{
int currRoom;
public:
void setCurrRoom(int r){currRoom = r; setAdjRooms();}

int room() const {return currRoom;}
};

{
int t = 2+2*(currRoom&1);
}

class Map
{
std::vector<Room> cave{std::vector<Room>(20)};
std::vector<int> vacant; //vector to keep track of empty rooms

Player p;

void reportState();
int input();

int movePlayer(int);
int shoot(int target);
void batEncounter();
int moveWump();
public:
void init();
void play();
void printState(); //Only for debugging. Not part of the game.
};

//spawn player
{
int r = rand()%vacant.size();
cave[vacant[r]].player = true;
p.setCurrRoom(vacant[r]);

//std::cout<<"Player in room "<<vacant[r]<<std::endl;
vacant.erase(vacant.begin()+r);

//no enemies should spawn adjacent to player
for(int i = 0; i < 3; ++i)
}

//spawns the wumpus in a random room
{
int r = rand()%vacant.size();
cave[vacant[r]].wump = true;
//std::cout<<"Wumpus in room "<<vacant[r]<<std::endl;
vacant.erase(vacant.begin()+r); //remove vacancy
}

//spawns bats
{
for(int i = 0; i < BATS; ++i){
int r = rand()%vacant.size();
cave[vacant[r]].bat = true;
//std::cout<<"Bat in room "<<vacant[r]<<std::endl;
vacant.erase(vacant.begin()+r);
}
}

//place pits
{
for(int i = 0; i < PITS; ++i){
int r = rand()%vacant.size();
cave[vacant[r]].pit = true;
//std::cout<<"Pit in room "<<vacant[r]<<std::endl;
vacant.erase(vacant.begin()+r);
}
}

void Map::printState()
//for debugging
{
for(int i = 0; i < ROOMS; ++i){
std::cout << "Room #" << i << ":" << std::endl;
std::cout << "\tWumpus -> " << ((cave[i].wump)?"yes":"no") << std::endl;
std::cout << "\tBat -> " << ((cave[i].bat)?"yes":"no") << std::endl;
std::cout << "\tPit -> " << ((cave[i].pit)?"yes":"no") << std::endl;
std::cout << "\tPlayer -> " << ((cave[i].player)?"yes":"no") << std::endl;
std::cout << std::endl;
}
}

void Map::reportState()
{
std::cout << "You are in room " << p.room() << std::endl;

std::cout << "I hear a bat." << std::endl;

std::cout << "I feel a draft." << std::endl;

std::cout << "I smell the wumpus." << std::endl;
}

int Map::movePlayer(int pos)
{
std::cout << "Invalid choice. Please move to an ADJACENT room." << std::endl;
return 0;
}
cave[p.room()].player = false;
cave[pos].player = true;
vacant.push_back(p.room());
p.setCurrRoom(pos);

if(cave[p.room()].wump){
std::cout << "The Wumpus got you! YOU LOSE." << std::endl;
return END_GAME;
}
if(cave[p.room()].pit){
std::cout << "You fell into a bottomless pit! YOU LOSE." << std::endl;
return END_GAME;
}
if(cave[p.room()].bat){
std::cout << "A giant bat takes you to another room!" << std::endl;
batEncounter();
return 0;
}
}

int Map::moveWump()
//move wumpus to a random adjacent room
{
int r = rand()%3;
int pos = 0;
for(; !(cave[pos].wump); ++pos); //get the room that contains the wumpus
cave[pos].wump = false;
if((cave[pos].wump && !(cave[pos].bat)) || (cave[pos].wump && !(cave[pos].pit)))
vacant.push_back(pos);
std::cout << "The Wumpus got you! YOU LOSE." << std::endl;
return END_GAME;
}
return 0;
}

int Map::shoot(int target)
{
return 0;
}
if(cave[target].wump){
std::cout << "You killed the Wumpus! YOU WIN!" << std::endl;
return END_GAME;
}
return moveWump();
}

void Map::batEncounter()
{
int r = rand()%vacant.size();
cave[p.room()].player = false;
vacant.push_back(p.room());
cave[vacant[r]].player = true;
p.setCurrRoom(vacant[r]);
vacant.erase(vacant.begin()+r);
}

void Map::init()
//set up map
//place player, bats, pits and the wumpus
{
//generate the dodecahedral cave
for(int i = 0; i < ROOMS; ++i){
int t = 2+2*(i&1);
vacant.push_back(i);
}

//restore vacant rooms adjacent to player
for(int i = 0; i < 3; ++i)
}

void Map::play()
{
reportState();
while(input() != END_GAME){
reportState();
}
}

int Map::input()
{
char c = 0;
int r = -1;
std::cout << "Type mXX(sXX) to move(shoot) to(at) room XX." << std::endl;
while(1){
std::cout << "Enter command: ";
if(std::cin >> c >> r) { break; }
else if(std::cin.fail() || (c != 'm' && c != 's')){
std::cin.clear();
std::cin.ignore(std::numeric_limits<int>::max(),'\n');
std::cout << "Invalid input. Type mXX(sXX) to move(shoot) to(at) room XX." << std::endl;
}
}
return (c == 'm') ? movePlayer(r) : shoot(r);
}

int main()
{
srand(unsigned(time(0)));
Map game;
game.init();
game.play();
//game.printState();
}

• Your Map::shoot function doesn't fit the rules: the Wumpus only moves if he was adjacent to the player. Per the spec, the Wumpus should move unless he was shot. – TemporalWolf Jan 30 '19 at 19:41
• Oh shoot! I overlooked that detail. I'll have to get on that when I have time. – DS2830 Jan 31 '19 at 11:45

• #include <ctime> (for time()).

• The C++ versions of standard functions are declared in the std namespace, not the global namespace, so we should use std::srand and std::time.

• We can use the C++11 random number generation facilities in <random>, rather than srand and rand to generate random numbers. e.g.

std::mt19937 rng(std::random_device()()); // seed the random number generator (do this once)

...
std::uniform_int_distribution<int> dist(0, vacant.size() - 1);
int r = dist(rng); // generate an int with the given distribution

• int is not an appropriate type to store room indices. We should use the index type of the container (i.e. std::vector<Room>::size_type, which is std::size_t), since that covers the correct range of values.

• Constant variables (ROOMS, BATS, etc.) are better than #defines, but there's no reason these can't be normal member variables (e.g. in the Map class). This would, for example, give us the flexibility to start a new game with different number of rooms or pits.

• The Player stores the index of the current room. Each Room stores the adjacent room indices. There is therefore no reason for the Player class to store adjacent room indices as well. We can get these from the Map instead.

• warning C4715: 'Map::movePlayer': not all control paths return a value, warning C4715: 'Map::shoot': not all control paths return a value - we should fix that!

Map:

• Map is a slightly misleading name, since this class largely handles game logic. Perhaps the game logic could be split into a Game class, or the class itself renamed Game.

• Use the Map constructor to do initialization, removing the need to call a separate init function.

• One would expect the vector of Rooms in Map to be called rooms, not cave.

• Since the bats, wumpus, and pit can all coexist, the Map::add* functions may be slightly wrong - we only need to place a bat in a room with no other bats.

• We should probably check that we don't run out of vacant rooms in which to place things.

• Map::input returns an integer value. However, we're not using it as a number, but to represent game state. C++ has enums for this purpose, e.g. enum class MoveResult { END_GAME, CONTINUE }, and we should return one of these instead.

bit-flags:

• There is some duplication of code when referring to the .bat, .pit, .wump members of Room. It would be nice to remove this, and abstract some more functionality (e.g. checking for an adjacent feature) into a single function. This would be easier if we used bit-flags for the room contents. e.g.:

enum RoomFeatures
{
Player = 1 << 0,
Bat = 1 << 1,
Pit = 1 << 2,
Wumpus = 1 << 3,
};

struct Room
{
...
RoomFeatures features;
};

...

room.features |= RoomFeatures::Bat; // add bat to room
if (room.features & RoomFeatures::Pit) ... // test for pit
room.features &= ~RoomFeatures::Wumpus // remove wumpus from room

While the bitwise operators are admittedly rather awkward, we could wrap this in a neat interface, which lets us do something like this:

bool Map::isAdjacentTo(int roomIndex, RoomFeatures feature) const
{
if (cave[i].contains(feature)) // bool Room::contains() const tests the bit-flag
return true;

return false;
}

...

// e.g. in reportState
std::cout ... ;

• It would be nice to separate the input and output from the game logic:

• At the moment we output messages about the player losing or winning in Map::shoot, Map::moveWump, and Map::movePlayer .

• movePlayer() and shoot() are called from the input function, rather than as part of the main loop as one might expect.

I think your solution is a good start for a first bigger programming task. I'd probably structure the program a little bit differently but I'm not sure if this required or even good. For the size of the problem the layout really is appropriate (meaning exactly right).

I've found some stuff nevertheless. Here you go (simply search for the code parts):

Bugs

• in if((cave[pos].wump && !(cave[pos].bat)) || (cave[pos].wump && !(cave[pos].pit)))  the expression cave[pos].wump is always false, hence the line vacant.push_back(pos); is never run
• restoring the vacant rooms in Map::Init() does not consider non-player entities. If the player spawns by accident next to wumpus, the room will be considered vacant by the game.
• wrong input in Map::input() will lead to shoot being called. The input method should only return if the input is indeed acceptable. Ideally input returns some abstract command structure or is renamed to something like handleInput().

Possible Bugs

• in for(; !(cave[pos].wump); ++pos); add a check for the end of cave
• Map::MovePlayer() and Map::shoot() contain code paths that may not always return a value

Style Improvements

• use same name for a member in all locations, e.g. setCurrRoom() and room(). Note that room() offers enough information and is much shorter than currRoom
• use ROOMS only for initialization of the cave, stick to cave.size() in all other places
• it makes sense to somehow mark the member variables to make them distinguishable from local variables and globals, prepending m_ to the variable name is common: vacant -> m_vacant.
• add more whitespace: newlines and spaces can be used to show parts of a function that belong logically together
• You can reduce !(cave[pos].wump) to !cave[pos].wump.

General Hints

• you can hide debugging code behind a compiler switch:
#ifdef DEBUG
game.printState();
#endif

If you compile with -DDEBUG you will generate debug output

• Thanks a lot for the valuable comments and pointing out bugs which could be game-breaking if not fixed. However, I don't see why the second point you mention is a bug. The Player never spawns next to the wumpus. Instead, the wumpus never spawns next to the player, so to me, the rooms being restored are indeed vacant. Please correct me if I am wrong. Thanks again. – DS2830 Jan 30 '19 at 15:25
• Sorry, didn't see that you're removing adjacent rooms from the vacant list in addPlayer(). You should definitely put the removal of the rooms closer to the reinsertion of them. In the current state it is very easy to introduce a bug if you change addPlayer() and don't remember that you need to change something else in init() as well. Generally speaking: put things that belong together in the same entity (here: function). – Cornholio Jan 30 '19 at 15:36


text:
help.mashup

Jump to: navigation, search

Purpose: describe the mash-up tool.

Audience: scientists and interested developers

1. Using the Data Mashup Tool

In 2016 the Data Mashup Tool was introduced to Autoplot. The idea is to provide a graphical way to combine multiple datasets into new datasets without the need for a script.

Take for example the goal of calculating the electron gyrofrequency from the B-Field magnitude. In the past, a script was needed to load the B-Field magnitude and then multiply by 28. This trivial script worked fine, but often scripts would be lost or deleted, and a new failure mode was added to the .vap file. With the Mashup tool, you would graphically construct the dataset (figure right):

Mashup is implemented as a vap+inline script, which is a tiny and limited script that fits into a URI. The script loads data from multiple URIs into given variable names, synchronizes data to one set of timetags, and then combines the data into a result.

1. plot http://emfisis.physics.uiowa.edu/Flight/RBSP-A/L3/$Y/$m/$d/rbsp-a_magnetometer_4sec-gei_emfisis-L3_$Y$m$d_v$(v,sep).cdf?Magnitude&timerange=2012-320 2. Tools->"Mash Data..." 3. The existing URI should be available at the top of the GUI. Note that the droplist can select other datasets. 4. Select the mathematics tab, and drag "multiply(x,y)" onto the palette to the right. (On a Mac, select "multiply(x,y)" and then right-click (context click) on the palette.) 5. Dropping a function onto a function in the palette will replace the function, and put the function into the "my functions" tab. 6. double click on the "x" argument, and select ds1 (or whatever name has been given to it). 7. double click on the "y" argument, and enter the literal "28" 8. Hit the "plot" button. Here is a step-by-step tutorial with pictures: http://autoplot.org/data/tutorials/20180123_mashup/mashIntro.pdf and a video: https://www.youtube.com/watch?v=RkcYoZ8qpPw 2. Time Series Browse Time Series Browse is the ability of a data source to create new URIs for new time ranges, and allows the scientist to browse through a long data day by day. For example, Autoplot knows that /tmp/$Y$m$d.dat?timerange=2020-02-03 is followed by /tmp/$Y$m\$d.dat?timerange=2020-02-04 because Aggregation has Time Series Browse.

When one of the loaded data sets has the time series browse capability, then the mashup will also have the time series browse capability.


text:
# Artificial Intelligence Stack Exchange Community Digest

## Top new questions this week:

### Do we need automatic hyper-parameter tuning when we have a large enough dataset?

Hyperparameter tuning is the process of selecting the optimal hyperparameters for an ANN. Now, my guess is that, if we have sufficient data (say, 1.4 million for, say, 6 features), the model can be ...

neural-networks hyperparameter-optimization training-datasets

### What are the roles of the prior $\mathrm{p}(\mathbf{z})$ in a VAE?

I know the encoder is variational posterior $q_{\phi}(\mathbf{z} \mid \mathbf{x})$. I also know that the decoder represents the likelihood: $p_{\theta}(\mathbf{x} \mid \mathbf{z})$. My question is ...

generative-model variational-autoencoder

### What is the place of ontologies in artificial intelligence?

Very much a general question here, from a somewhat uneducated perspective. I'm currently part way through an MSc in AI, and at the minute I am taking a module on Knowledge Engineering and ...

ai-design ontology knowledge-based-systems

### How to train neural networks with multiprocessing?

I am trying to figure out how multiprocessing works in neural networks. In the example I've seen, the database is split into $x$ parts (depending on how many workers you have) and each worker is ...

### Demonstration of AI-powered Mario collecting lots of coins?

As part of a talk I'm giving, I'd like to show one of the many videos on YouTube where an AI is playing Mario, such as this one. What bothers me though is that the AI is trying to complete the level ...

reinforcement-learning game-ai atari-games

### In layman terms, what does "attention" do in a transformer?

I heard from many people about the paper titled Attention Is All You Need by Ashish Vaswani et al. What actually does the "attention" do in simple terms? Is it a function, property, or some ...

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### What are the major layers in a Vision Transformer?

Currently, I am studying deepfake detection using deep learning methods. Convolution neural networks, recurrent neural networks, long-short term memory networks, and vision transformers are famous ...

neural-networks deep-learning transformer layers vision-transformer
 asked by Pawara Siriwardhane 1 vote

## Greatest hits from previous weeks:

### What is the credit assignment problem?

In reinforcement learning (RL), the credit assignment problem (CAP) seems to be an important problem. What is the CAP? Why is it relevant to RL?

reinforcement-learning definitions credit-assignment-problem

### What is the difference between an agent function and an agent program?

In section 2.4 (p. 46) of the book Artificial Intelligence: A modern approach (3rd edition), Russell and Norvig write The job of AI is to design an agent program that implements the agent function — ...

terminology comparison norvig-russell

### How to choose an activation function for the hidden layers?

I choose the activation function for the output layer depending on the output that I need and the properties of the activation function that I know. For example, I choose the sigmoid function when I'm ...

neural-networks deep-learning activation-function hyperparameter-optimization hyper-parameters

### Why do we need common sense in AI?

Let's consider this example: It's John's birthday, let's buy him a kite. We humans most likely would say the kite is a birthday gift, if asked why it's being bought; and we refer to this reasoning ...

philosophy agi knowledge-representation commonsense-knowledge

### How do I show that uniform-cost search is a special case of A*?

How do I show that uniform-cost search is a special case of A*? How do I prove this?

comparison search proofs a-star uniform-cost-search

### What is the Bellman operator in reinforcement learning?

In mathematics, the word operator can refer to several distinct but related concepts. An operator can be defined as a function between two vector spaces, it can be defined as a function where the ...

reinforcement-learning terminology math bellman-equations bellman-operators

### Audio enhancing using AI? (removing background noise during lecture recording)

I wonder if it's possible to 'clean up' an audio recording of a lecture from a smartphone, using some type of AI system?

deep-learning

## Can you answer these questions?

### When is an object detection approach over a CNN approach appropriate?

I understand that CNNs are for image classification while object detection is for localization + classification of the objects detected. However, in particular, AI for chest radiographs, why is object ...

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 asked by Hi There 1 vote

### How to detect the sine wave signal with different frequency using neural networks?

I'm wondering if there is a way to use a neural network that can detect the noisy sine wave, where the frequency is not constant. In other words, I'm not looking for a solution that would detect the ...

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text:
# 9.1.1 - Confidence Intervals

9.1.1 - Confidence Intervals

Given that $$np \ge 10$$ and $$n(1-p) \ge 10$$ for both groups, in other words at least 10 "successes" and at least 10 "failures" in each group, the sampling distribution can be approximated using the normal distribution with a mean of $$\widehat p_1 - \widehat p_2$$ and a standard error of $$\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}$$.

Recall from the general form of a confidence interval:

General Form of a Confidence Interval
$$sample\ statistic\pm(multiplier)\ (standard\ error)$$

Here, the sample statistic is the difference between the two proportions ($$\widehat p_1 - \widehat p_2$$) and the standard error is computed using the formula $$\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}$$. Putting this information together, we can derive the formula for a confidence interval for the difference between two proportions.

Confidence Interval for the Difference Between Two Proportions
$$(\widehat{p}_1-\widehat{p}_2) \pm z^\ast {\sqrt{\frac{\widehat{p}_1 (1-\widehat{p}_1)}{n_1}+\frac{\widehat{p}_2 (1-\widehat{p}_2)}{n_2}}}$$

## Example: Confidence Interval for the Difference Between the Proportion of Women and Men in Favor of Legal Same Sex Marriage

A survey was given to a sample of college students. They were asked whether they think same sex marriage should be legal. Of the 251 women in the sample, 185 said "yes." Of the 199 men in the sample, 107 said "yes." Let’s construct a 95% confidence interval for the difference of the proportion of women and men who responded “yes.” We can apply the 95% Rule and use a multiplier of $$z^\ast$$ = 2

• For women: $$np=185$$ and $$n(1-p) = 251-185=66$$
• For men: $$np=107$$ and $$n(1-p)=199-107=92$$

These counts are all at least 10 so the sampling distribution can be approximated using a normal distribution.

$$\widehat{p}_{w}=\frac{185}{251}=0.737$$

$$\widehat{p}_{m}=\frac{107}{199}=0.538$$

$$(0.737-0.538) \pm 2 {\sqrt{\frac{0.737 (1-0.737)}{251}+\frac{0.538 (1-0.538)}{199}}}$$

$$0.199 \pm 2 ( 0.045)$$

$$.199 \pm .090=[.110, .288]$$

We are 95% confident that in the population the difference between the proportion of women and men who are in favor of same sex marriage legalization is between 0.110 and 0.288.

This confidence interval does not contain 0. Therefore it is not likely that the difference between women and men is 0. We can conclude that there is a difference between the proportion of women and men in the population who would respond “yes" to this question.

# 9.1.1.1 - Minitab Express: Confidence Interval for 2 Proportions

9.1.1.1 - Minitab Express: Confidence Interval for 2 Proportions

Minitab Express can be used to construct a confidence interval for the difference between two proportions using the normal approximation method. Note that the confidence intervals given in the Minitab Express output assume that $$np \ge 10$$ and $$n(1-p) \ge 10$$ for both groups. If this assumption is not true, you should use bootstrapping methods in StatKey.

## MinitabExpress – Constructing a Confidence Interval with Raw Data

Let's estimate the difference between the proportion of females who have tried weed and the proportion of males who have tried weed.

1. Open Minitab Express file:
2. On a PC: In the menu bar select STATISTICS > Two Samples > Proportions
3. On a Mac: In the menu bar select Statistics > 2-Sample Inference > Proportions
4. Double click the variable Try Weed in the box on the left to insert the variable into the Samples box
5. Double click the variable Biological Sex in the box on the left to insert the variable into the Sample IDs box
6. Keep the default Options
7. Click OK

This should result in the following output:

2-Sample Proportions: Try Weed by Biological Sex
 Event: Try Weed = Yes $$p_1$$: proportion where Try Weed = Yes and Biological Sex = Female $$p_2$$: proportion where Try Weed = Yes and Biological Sex = Male Difference: $$p_1-p_2$$
Descriptive Statistics: Try Weed
Biological Sex N Event Sample p
Female 127 56 0.440945
Male 99 62 0.626263
Estimation for Difference
Difference 95% CI for Difference
-0.185318 (-0.313920, -0.056716)
Null hypothesis $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
Method Z-Value P-Value
Fisher's exact   0.0072
Normal approximation -2.82 0.0047

Video Walkthrough

Select your operating system below to see a step-by-step guide for this example.

## MinitabExpress – Constructing a Confidence Interval with Summarized Data

Let's estimate the difference between the proportion of Penn State World Campus graduate students who have children to the proportion of Penn State University Park graduate students who have children. In our representative sample there were 120 World Campus graduate students; 92 had children. There were 160 University Park graduate students; 23 had children.

1. Open Minitab Express without data
2. On a PC: In the menu bar select STATISTICS > Two Samples > Proportions
3. On a Mac: In the menu bar select Statistics > 2-Sample Inference > Proportions
4. Change Both samples are in one column to Summarized data
5. For Sample 1 next to Number of events enter 92 and next to Number of trials enter 120
6. For Sample 2 next to Number of events enter 23 and next to Number of trials enter 160
7. Keep the default Options
8. Click OK

This should result in the following output:

2-Sample Proportions
 $$p_1$$: proportion where Sample 1 = Event $$p_2$$: proportion where Sample 2 = Event Difference: $$p_1-p_2$$
Descriptive Statistics
Sample N Event Sample p
Sample 1 120 92 0.766667
Sample 2 160 23 0.143750
Estimation for Difference
Difference 95% CI for Difference
0.622917 (0.529740, 0.716093)
Null hypothesis $$H_0$$: $$p_1-p_2=0$$ $$H_1$$: $$p_1-p_2\neq0$$
Method Z-Value P-Value
Fisher's exact   <0.0001
Normal approximation 13.10 <0.0001

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# How to multiply fractions

In this post we will learn methods for multiplying fractions.

First we will review the concept of fractions, then will understand the techniques to multiply fractions and finally move on to solve worksheets related to the concept

## Understanding Fraction Multiplication

Consider the below box as whole number 1

Multiplication with fraction (1/2)

The expression \Longrightarrow 1\times \frac{1}{2}\ means that the whole figure is divided into two equal halves.

This multiplication can be expressed as:
\Longrightarrow \ 1\ \times \frac{1}{2}\\\ \\ \Longrightarrow \frac{1}{2}

Hence only one half of the figure is selected as result

Further multiplication with fraction 1/3

Now we multiply \Longrightarrow \ \frac{1}{2} \times \frac{1}{3}\

It means that the half portion is divided into three equal parts

The multiplication can be expressed as:

\Longrightarrow \ \frac{1}{2} \times \frac{1}{3}\\\ \\ \Longrightarrow \ \frac{1}{6}\\\ \\

Hence \frac{1}{3} \ of \ \frac{1}{2} \ results \ in \ \frac{1}{6}

It means that final answer is \frac{1}{6} of the whole figure

The result is shown by following image:

Now we have understood the concept of fraction multiplication.
Let us now understand the method to multiply the fractions.

## How to multiply the fractions

The method is simple and straight forward.

Suppose two fractions are given:

You can do multiplication by following below steps

Step 01
Multiply the numerators (top numbers) of Fraction

Step 02
Multiply the denominators (bottom numbers) of fraction

Step 03
Simplify the result (if required)
Reduce the numerator and denominator to its lowest terms

Let us understand the method with the help of examples

Example 01
Multiply the below fractions
\Longrightarrow \frac{7}{3} \times \frac{4}{5}\

(a) Rearranging numbers
\Longrightarrow \ \frac{7\ \times 4}{3\times 5}\

(b) Multiplying numerator and denominator separately
\Longrightarrow \ \frac{28}{15}

(c) Simplify Number
Further simplification is not possible

Hence, \frac{28}{15} \ is the solution

Example 02
Multiply the below fraction
\Longrightarrow \frac{5}{6} \times \frac{8}{9}\

(a) Rearranging numbers
\Longrightarrow \ \frac{5\ \times 8}{6\times 9}\

(b) Multiplying numerator and denominator separately
\Longrightarrow \ \frac{40}{54}

(c) Simplify Number
Divide numerator and denominator by 2

Hence, \frac{20}{27} \ is the solution

## Multiplying Fractions Worksheet

Below is the collection of Fraction Multiplication for Grade 5.

All the questions have been provided with detailed solution.

Please take out pen and paper and try to solve each ofthe question

### Multiply the given fractions step by step

(a) \frac{6}{12} \ \times \frac{2}{10}

\Longrightarrow \ \frac{6}{12} \ \times \frac{2}{10}\\\ \\ \Longrightarrow \ \frac{6\ \times \ 2}{12\times 10}\\\ \\ \Longrightarrow \ \frac{12}{120}\\\ \\

Divide numerator and denominator by 12

Hence \frac{1}{10} is the solution

(b) \frac{11}{20} \ \times \frac{4}{14} \\\ \\ Read Solution

\Longrightarrow \ \frac{11}{20} \ \times \frac{4}{14}\\\ \\ \Longrightarrow \ \frac{11\ \times \ 4}{20\times 14}\\\ \\ \Longrightarrow \ \frac{44}{280}\\\ \\

Divide numerator and denominator by 4

Hence \frac{11}{70} is the solution

(c) \frac{7}{3} \ \times \frac{2}{5} \\\ \\ Read Solution

\Longrightarrow \ \frac{7}{3} \ \times \frac{2}{5}\\\ \\ \Longrightarrow \ \frac{7\ \times \ 2}{3\times 5}\\\ \\ \Longrightarrow \ \frac{14}{15}\\\ \\ \frac{14}{15} is the solution

(d) \frac{5}{7} \ \times \frac{15}{16} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{7} \ \times \frac{15}{16}\\\ \\ \Longrightarrow \ \frac{5\ \times \ 15}{7\times 16}\\\ \\ \Longrightarrow \ \frac{75}{112}\\\ \\ \frac{75}{112} is the solution

(e) \frac{11}{7} \ \times \frac{3}{4} \\\ \\ Read Solution

\Longrightarrow \ \frac{11}{7} \ \times \frac{3}{4}\\\ \\ \Longrightarrow \ \frac{11\ \times \ 3}{7 \times 4}\\\ \\ \Longrightarrow \ \frac{33}{28}\\\ \\ \frac{33}{28} is the solution

(f) \frac{13}{2} \ \times \frac{4}{3} \\\ \\ Read Solution

\Longrightarrow \ \frac{13}{2} \ \times \frac{4}{3}\\\ \\ \Longrightarrow \ \frac{13\ \times \ 4}{2\times 3}\\\ \\ \Longrightarrow \ \frac{52}{6}\\\ \\

Divide numerator and denominator by 2

\frac{27}{3} is the solution

(g) \frac{8}{9} \ \times \frac{1}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{8}{9} \ \times \frac{1}{2}\\\ \\ \Longrightarrow \ \frac{8\ \times \ 1}{9\times 2}\\\ \\ \Longrightarrow \ \frac{8}{18}\\\ \\

Divide numerator and denominator by 2

\frac{4}{9} is the solution

(h) \frac{20}{11} \ \times \frac{10}{7} \\\ \\ Read Solution

\Longrightarrow \ \frac{20}{11} \ \times \frac{10}{7}\\\ \\ \Longrightarrow \ \frac{20\ \times \ 10}{11\times 7}\\\ \\ \Longrightarrow \ \frac{200}{77}\\\ \\ \frac{200}{77} is the solution

(i) \frac{1}{3} \ \times \frac{2}{9}\\\ \\ Read Solution

\Longrightarrow \ \frac{1}{3} \ \times \frac{2}{9}\\\ \\ \Longrightarrow \ \frac{1\ \times \ 2}{3\times 9}\\\ \\ \Longrightarrow \ \frac{2}{27}\\\ \\ \frac{2}{27} is the solution

(j) \frac{0}{5} \ \times \frac{12}{6} \\\ \\ Read Solution

\Longrightarrow \ \frac{0}{5} \ \times \frac{12}{6}\\\ \\ \Longrightarrow \ \frac{0\ \times \ 12}{5\times 6}\\\ \\ \Longrightarrow \ \frac{0}{30}\\\ \\

0 is the solution

(k) \frac{2}{13} \ \times \frac{5}{4} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{13} \ \times \frac{5}{4}\\\ \\ \Longrightarrow \ \frac{2\ \times \ 5}{13\times 4}\\\ \\ \Longrightarrow \ \frac{10}{52}\\\ \\

Divide numerator and denominator by 2

\frac{5}{26} is the solution

(l) \frac{5}{14} \ \times \frac{17}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{14} \ \times \frac{17}{2}\\\ \\ \Longrightarrow \ \frac{5\ \times \ 17}{14\times 2}\\\ \\ \Longrightarrow \ \frac{85}{28}\\\ \\ \frac{85}{28} is the solution

(m) \frac{1}{2} \ \times \frac{2}{1} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{2} \ \times \frac{2}{1}\\\ \\ \Longrightarrow \ \frac{1\ \times \ 2}{2\times 1}\\\ \\ \Longrightarrow \ \frac{2}{2}\\\ \\

Divide numerator and denominator by 2

1 is the solution

(n) \frac{17}{4} \ \times \frac{5}{11} \\\ \\ Read Solution

\Longrightarrow \ \frac{17}{4} \ \times \frac{5}{11}\\\ \\ \Longrightarrow \ \frac{17\ \times \ 5}{4\times 11}\\\ \\ \Longrightarrow \ \frac{85}{44}\\\ \\ \frac{85}{44} is the solution

(o) \frac{5}{9} \ \times \frac{12}{6} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{9} \ \times \frac{12}{6}\\\ \\ \Longrightarrow \ \frac{5\ \times \ 12}{9\times 6}\\\ \\ \Longrightarrow \ \frac{60}{54}\\\ \\

Divide Numerator and Denominator by 6

\frac{10}{9} is the solution

### Multiply three or more fractions

This section is more difficult to solve. Here we involve three sets of number for multiplication.

The process for multiplication is same:
(a) Multiply numerators and denominators separately
(b) simplify the result by lowering the numerator and denominator to its lowest terms

(a) \frac{2}{3} \ \times \frac{3}{2} \ \times \frac{4}{6} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{3} \times \frac{3}{2} \times \frac{4}{6}\\\ \\ \Longrightarrow \ \frac{2\times 3\times 4}{3\times 2\times 6}\\\ \\ \Longrightarrow \ \frac{24}{36}

(b) \frac{1}{7} \ \times \frac{3}{5} \ \times \frac{6}{1} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{7} \times \frac{3}{5} \times \frac{6}{1}\\\ \\ \Longrightarrow \ \frac{1\times 3\times 6}{7\times 5\times 1}\\\ \\ \Longrightarrow \ \frac{18}{35}

(c) \frac{1}{3} \ \times \frac{2}{3} \ \times \frac{1}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{3} \times \frac{2}{3} \times \frac{1}{2}\\\ \\ \Longrightarrow \ \frac{1\times 2\times 1}{3\times 3\times 2}\\\ \\ \Longrightarrow \ \frac{2}{18}

(d) \frac{1}{5} \ \times \frac{0}{7} \ \times \frac{6}{1} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{5} \times \frac{0}{7} \times \frac{6}{1}\\\ \\ \Longrightarrow \ \frac{1\times 0\times 6}{5\times 7\times 1}\\\ \\ \Longrightarrow \ \frac{0}{35}

(e) \frac{2}{6} \ \times \frac{4}{3} \ \times \frac{3}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{6} \times \frac{4}{3} \times \frac{3}{2}\\\ \\ \Longrightarrow \ \frac{2\times 4\times 3}{6\times 3\times 2}\\\ \\ \Longrightarrow \ \frac{24}{36}

(f) \frac{7}{3} \ \times \frac{2}{1} \ \times \frac{9}{11} \\\ \\ Read Solution

\Longrightarrow \ \frac{7}{3} \times \frac{2}{1} \times \frac{9}{11}\\\ \\ \Longrightarrow \ \frac{7\times 2\times 9}{3\times 1\times 11}\\\ \\ \Longrightarrow \ \frac{126}{33}

(g) \frac{2}{4} \ \times \frac{8}{5} \ \times \frac{2}{3} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{4} \times \frac{8}{5} \times \frac{2}{3}\\\ \\ \Longrightarrow \ \frac{2\times 8\times 2}{4\times 5\times 3}\\\ \\ \Longrightarrow \ \frac{32}{60}

(h) \frac{1}{2} \ \times \frac{1}{2} \ \times \frac{1}{3} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{3}\\\ \\ \Longrightarrow \ \frac{1\times 1\times 1}{2\times 2\times 3}\\\ \\ \Longrightarrow \ \frac{1}{12}


text:
# Strange Mathematics

#### Dave

Joined Nov 17, 2003
6,970
you have divided both sides by x-y=0.division by zero is "illegal".why?
consider p/0 = q; p and q are non-zero.
we have p=0*q.say p=10
no value of q when multiplied with 0 will give you 10.
please comment,if you feel that there are faults with my posts or if i can improve my explanations...thank you
The solution of a/0 is undefined (it has real no meaning): http://en.wikipedia.org/wiki/Division_by_zero

Dave

Joined May 1, 2007
19
hello dave

the reason why xz=yz implies x=y for z<>0 is that such z has a multiplicative inverse: multiplying both sides of the equation by 1/z gives the required conclusion. zero has no multiplicative inverse: if w is supposed to be a multiplicative inverse of zero then by definition w(0)=1, contradicting the fact that x(0)=0 for all x.

hope that helps

peace
stm

#### kautilya

Joined Apr 26, 2007
39
Here's one:

Say: x = y

Then: x - y = 0

And: 2x - 2y = 0

So: x - y = 2x - 2y

Taking common factors: 1(x - y) = 2(x - y)

Therefore: 1 = 2 !!!

(I know this is not really the answer, but it certainly confuses many who see it!)

Dave
This question may be hilarious but it violates the very essence of mathematics. As rightly pointed out, division by zero is not permitted.

#### Dave

Joined Nov 17, 2003
6,970
This question may be hilarious but it violates the very essence of mathematics. As rightly pointed out, division by zero is not permitted.
But to the casual mathematician the sequence of steps to the result is wholly intuitive and correct. I suppose the message from this exercise is to verify any assumptions you make; for example when you state x - y = 2x - 2y ask yourself, what does that imply?

All subsequent steps from x - y = 2x - 2y are standard maths procedures, however the user is tricked into not realising that since x = y, x - y = 2x - 2y = 0.

Dave


text:
# Finding the RMS over all time of a difficult function

Well, I've to find the RMS (root mean square) over all time of the following function:

In the picture I plotted a case where I used values for components in the full bridge rectifier with capacitor filter but I want to solve the general case.

From $0\le t\le\frac{1}{4f}$ the function that describes the waveform is:

$$\left|u\sin\left(2\pi ft\right)\right|\tag1$$

When the sine wave is at its top, the function turn into a exponential function (because the capacitor discharges):

$$u\exp\left(-\frac{t}{\tau}\right)\tag2$$

The point where the sine wave returns is:

$$\left|u\sin\left(2\pi ft\right)\right|=u\exp\left(-\frac{t}{\tau}\right)\space\Longleftrightarrow\space t:=T=\dots\tag3$$

Where $\frac{1}{2f}<T<\frac{3}{4f}$

And then the proces starts over again: the exponential function comes back when the sine wave is at its top.

Now, I need to find the RMS over all time so I wrote:

$$\lim_{\text{n}\to\infty}\sqrt{\frac{1}{\text{n}}\int_0^\text{n}\left(\text{y}\left(t\right)\right)^2\space\text{d}t}\tag4$$

And in order to find $\int_0^\text{n}\left(\text{y}\left(t\right)\right)^2\space\text{d}t$ I wrote:

$$\int_0^\text{n}\left(\text{y}\left(t\right)\right)^2\space\text{d}t\stackrel{?}{=}\int_0^\frac{1}{4f}\left(\left|u\sin\left(2\pi ft\right)\right|\right)^2\space\text{d}t+\text{n}\cdot\int_0^T\left(u\exp\left(-\frac{t}{\tau}\right)\right)^2\space\text{d}t+\text{n}\cdot\int_T^\frac{3}{4f}\left(\left|u\sin\left(2\pi ft\right)\right|\right)^2\space\text{d}t\tag5$$

The question is, am I right and how do I proceed?

• what is the RMS? – uniquesolution Feb 15 '18 at 14:33
• @uniquesolution Root Mean Square, see my edit. – Jan Feb 15 '18 at 14:34
• It should suffice to calculate the RMS over a single period (the transient phenomenon at the beginning does not matter), which should be write-able as a sum of two integrals: one where the integrand is the square of the sine, one where the integrand is the square of the exponential. – Wouter Feb 15 '18 at 14:36
• what is the function $y$? – uniquesolution Feb 15 '18 at 14:36
• @jan Yes you can. If you truly take the $n\rightarrow\infty$ limit, the contribution of the transient phenomenon is zero. – Wouter Feb 15 '18 at 14:39

You are calculating an integral $$\lim_{n\rightarrow\infty}\sqrt{\frac{1}{n}\int_0^n y(t)^2 dt}$$ But your $y(t)$ is periodic aside from a transient phenomenon $$y(t)=\left\{\begin{matrix}y_{\text{transient}}(t) & t <T_0 \\ y_{\text{periodic}}(t-T_0) & T_0<t<T_0+P \\ y_{\text{periodic}}(t-(T_0+P)) & T_0+P<t<T_0+2P \\ \vdots\end{matrix}\right.$$ So the original integral becomes $$\lim_{n\rightarrow\infty}\sqrt{\frac{1}{n}\int_0^n y(t)^2 dt}=\lim_{n\rightarrow\infty}\sqrt{\underbrace{\frac{1}{n}\int_0^{T_0} y_{\text{transient}}(t)^2 dt}_{\rightarrow 0\text{ as }n\rightarrow\infty} + \frac{1}{n}\int_{T_0}^{n} y(t)^2 dt}$$ what remains is periodic.
• And $T_0$ is my equation $\left(3\right)$? – Jan Feb 15 '18 at 15:22
• You don't want $u\exp(-t/\tau)$ but $u\exp(-(t-t_{peak})/\tau)$ where $t_{peak}$ is the time where your sine peaks. otherwise your function is discontinuous. – Wouter Feb 15 '18 at 15:45
• I see, but how can the last existing integral be rewritten using this? Or must I ask is my equation $\left(5\right)$ right? – Jan Feb 15 '18 at 15:59


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# System identification of a resonant system

I want to write a matlab script that would identify a system from it's inputs and outputs. I have so far had good results with simple systems, but with this slightly more complex one I'm not able to arrive at the original equation. To do identification, I use a chirp signal and collect output data that covers a range of input frequencies. I then use arx() to estimate a transfer function from the input data.

My octave script is as follows:

pkg load signal

s = tf('s');

L = 0.1;
R = 80;
C = 1e-4;

% Alt2: LC in series, resistor in parallel with output (LRC circuit)
%G = (s * L + 1 / (s * C)) / (R + s * L + 1 / (s * C));

% Alt1: simple RC circuit
G = 1 / (1 + R * C * s);

% simplify G
G = minreal(G)

% number of samples
N = 10000;

% frequency range in hz
Fstart = 15; Fend = 200;

t = linspace(0, 1, N);
sample_time = (t(end) - t(1)) / N

% generate stimulus signal and generate the output data from "real" system
stimulus = chirp(t, Fstart, t(end), Fend)';
[response, T, X] = lsim(G, stimulus, t);

%plot(t, stimulus, t, response, 'r');

% now try to go back to the original transfer function based on the collected data
[Gest, x0] = arx(iddata(response, stimulus, sample_time), 2);
Gest = minreal(d2c(Gest)); [b, a] = ss2tf(Gest); Gest = tf(b, a)

% compare the transfer functions
bode(G, Gest)

input("..");

If I run the script using simple transfer function (Alt1), I'm able to identify the original system precisely using arx (original transfer function G and estimated transfer function Gest are identical):

Short of an error from arx about matrix A being unstable the approximation is 100% accurate (error is due to the fact that I'm using second order approximation on a system Alt1 which is really a first order system so this is irrelevant. If I pass 1 as last argument to arx this error disappears).

However, if I try to do the same experiment with Alt2, which has a resonance at around 25Hz, the method fails:

The estimated transfer function is way off the target.

What is going on? Why am I not able to identify the second system using this method? Is it because I need more data around the resonance? How can I get an accurate estimate of the second system?

• I tested this in matlab and I think your problem is that you did not increase the model order for Alt2. – Kwin van der Veen May 3 '18 at 17:23
• @KwinvanderVeen please test your suggestions before you post them. The original equation is second order so second order identification should suffice. I think the problem was that arx algorithm is simply not suitable for identifying a discontinuous model. I got the perfect result when I used moen4 instead. – Martin May 4 '18 at 6:57
• ARX tries to fit $A(q)\,y(t)=B(q)\,u(t)+e(t)$. I am not sure what octave does when you only specify n, but when you use arx(dat, 'na', na, 'nb', nb) instead, with na the order of the A(q) polynomial and nb the order of the B(q) polynomial plus one with the constraint that nb<=na. For Alt2 the order of B(q) is two, so nb=3, which would also imply na=3 (but at least in matlab I was also able to use na=2 as well). So I would expect that arx(iddata(response, stimulus, sample_time), 'na', 2, 'nb', 3) would give the correct results. – Kwin van der Veen May 4 '18 at 8:02
• Ah I see 'na', 2, 'nb', 3 worked. na = 3 did not work. The result is best so far with arx, but not a good fit as moen4 estimate. However, I'm confused. It says in docs for octave that following must be true: nb <= na yet I had to use nb = 3 and na = 2? It does make sense to me that the transfer function must be proper, however that would imply nb >= na instead. – Martin May 4 '18 at 9:06
• I also do not know why. Maybe it meant to say the order of B(q)<=order of A(q), because otherwise the model would not be causal. But since you have all the data it is still possible to fit a noncausal filter. – Kwin van der Veen May 4 '18 at 9:11


text:
Asymptotic expansion of inverse Laplace transform of $z^{-1} \tanh(z)$

Find the first term in the asymptotic expansion of $$f(t) = \frac1{2 \pi i}\int_{\alpha - i \infty}^{\alpha + i \infty} e^{tz} z^{-1} \tanh(z)dz$$ as $t \to \infty$

I am finding this problem difficult, as there are an infinite number of (simple) poles from $g(z) = z^{-1} \tanh(z)$, so that determining the way to deform the contour is unclear.

The poles of $g$ are at $z_n = \frac{\pi i}2 + n \pi i$ for $n\in \mathbb{Z}$, and the residues are $R_n = \text{Res}_{z = z_n} g(z) = \frac{-2i}{(2n+1)\pi}$

I figured I needed to determine which of these poles would have the largest asymptotic contribution to the integral, at which point I could expand $g$ around this pole as:

$$g(z) = \frac{R_n}{z - z_n} + O(1)$$

Which has a single simple pole at $z = z_n$. Hence, I could deform the contour into a circle around this pole, and from the Residue Theorem, I'd have that

$$f(t) \sim R_n e^{z_nt} \ \ \text{ as } \ \ t \to \infty$$

From this, it would appear that I should choose the $z_n$ such that $e^{z_nt}$ is asymptotically largest, however, such a $z_n$ doesn't exist, as $\lim_{n \to \infty} z_n = \infty$

So it would appear there is a flaw in my argument that I am not seeing. Any help is appreciated.

To check convergence of this integral, I found that $$|e^{tz}z^{-1} \tanh(z)| = \frac{e^{xt}(e^{4x} - 2e^{2x}\cos(2y) + 1)}{(x^2 + y^2)(e^{4x} + 2e^{2x}\cos(2y) + 1)}$$

And since $x$ is fixed on the contour from $\alpha - i \infty$ to $\alpha + i\infty$, the integral will converge for any $\alpha$.

We can deform the contour through the left half-plane, requiring $\alpha > 0$ for the method I used above.

All poles are located on the imaginary axis, thus the sum over the residues $$f(t) = -\frac {2i} \pi \sum_{k = -\infty}^\infty \frac {e^{(2k + 1)i \pi t/2}} {2k + 1}$$ is convergent by Dirichlet's test. This shows that $f(t + 4) = f(t)$; I'm not sure that the question about the asymptotic of $f$ is meaningful. A closed form for $f$ is $$f(t) = \operatorname{sgn} \sin \frac {\pi t} 2.$$


text:
6 Oct 13:10 2012

## Re: [BUG] Parsing consecutive stars

Hello,

William Léchelle <william.lechelle <at> ens-lyon.fr> writes:

> Hi list,
>
> It looks like the stars parser has a problem with 2 consecutive stars, hence
> with bold in 2nd level headers.
>
> The following sums up all the relevant tests I performed. Only 3rd and 4th
> lines seem to be related, in a strange fashion, even, but I couldn't find
> anything else that would indicate lines not being independant.

The fontification engine is not very powerful and get easily fooled. You
may use entities (i.e. \ast and \ast{}) for ambiguous stars.

Regards,

--

--
Nicolas Goaziou

Gmane


text:
# How does NMO reform Osmium tetroxide after reaction with an alkene?

After Osmium tetroxide adds to a double bond and is then hydrolysed the following species is formed:

Because Osmium tetroxide is toxic, NMO is used to transform the above back to Osmium tetroxide. NMO is:

What is the mechanism for this?

N-methyl-morpholine-N-oxide (NMO) is used to reoxidize and regenerate osmium tetroxide ($\ce{OsO4}$) in what is known as the "Upjohn Dihydroxylation" procedure.
Mechanistically, the redox occurs when a lone pair of electrons on the reduced $\ce{Os(VI)O3}$ are used to form a bond to the morpholine N-oxygen; the electrons from the former $\ce{N-O}$ bond are, in turn, transferred to the morpholine nitrogen. The $\ce{OsO3}$ gains an oxygen and is oxidized back to osmium (VIII) tetroxide and the NMO is reduced to N-methylmorpholine


text:
시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB0000.000%

## 문제

A prefix-free set is a set of words in which no element is a prefix of another element in the set. For example {"hello"} , {"hello", "goodbye", "giant", "hi"} and the empty set are examples of prefix-free sets. On the other hand, {"hello","hell"} and {"great","gig","g"} are not prefix-free. You will be given a set of words, and you must calculate the number of subsets of words that are prefix-free. Note that both the empty set and the entire set count as subsets.

## 입력

The first line of the input gives an integer T, which is the number of test cases. Each test case starts with a line containing N the number of words in the set. N is between 1 and 62 inclusive. Each of the next N line contains a word. The word contains only lowercase letter and length will not exceed 100.

## 출력

For each test case, the output contains a line in the format Case #x: M, where x is the case number (starting from 1) and M is the number of prefix free subsets.

## 예제 입력 1

3
3
hello
hell
hi
4
a
b
c
d
6
a
ab
abc
abcd
abcde
abcdef

## 예제 출력 1

Case #1: 6
Case #2: 16
Case #3: 7


text:
# Math Help - Quadratic Residues

Question:
If a and b are both quadratic residues of the odd prime p or both non-residues of p, show that the congruence ax^2 =b (modp) has a solution.

2. Because $a$ is a quadratic residue let $a\equiv s^2$ so $ax^{2}\equiv (sx)^{2}$ and since $b$ is a quadratic residue we know $b\equiv t^2$; let $t = sx$ and we are done.

EDIT:
I had failed to consider the case where they both are non-residues.

$ax^2 = b\ \pmod{p}$
$(ax)^2 = ab\ \pmod{p}$

This is solvable only when $ab$ is a quadratic residue; by euler's criterion, $ab$ is a quadratic residue iff and only iff both or neither of $a$ and $b$ are quadratic residues.

Let $ax\equiv s\pmod{p}$ be a solution to the congruence.

By the Euclidean algorithm, $a$ has a modular inverse since it is relatively prime to $p$ (if $p|a$, then there would be no such $s$ . If $a\equiv 0$,do we consider it a quadratic residue or what?).

In particular, then, $x\equiv a^{-1}s\pmod{p}$ is a solution to our original equation.