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### olympus om d e m10 release date

If it's a diagram of an actual model then Simulink (but don't Print Screen - under one of the menus there is an option to copy diagram that can then be pasted into WORD) - watch font size and line thickness. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. In addition, the computer issues its commands at discrete times even if the original control law design was done based on differential equations. Block diagrams with perspective use 3-D shapes to convey information in a dramatic manner. You can draw static images on any given software, but it's impossible to "draw" a moving picture. Microsoft Paint Creating Diagrams - How To 4 Step 4: Using the Line Tool â If you need to draw a building that is not square, your best bet will be to user the Line Tool. well, just dirt, and not nearly as interesting as water or as monumental as mountains. Cons: The templates, tools, and symbols for drawing electronic diagrams (Especially Drawing Integrated Circuits) are limited. Flow diagram is a diagram used for structuring complex system and visually representing a flow and interactions of elements in a system.. ConceptDraw DIAGRAM diagramming and vector drawing software enhanced with Flowcharts Solution from the "Diagrams" Area of ConceptDraw Solution Park is perfect for easy drawing professional looking Flow Diagrams. Is it possible to draw with pixels instead of normal things? Enter the diagram name and description. ... Each node in the diagrams can be clicked and events can be â¦ Another example, which is a simple one, is to draw with text in it! You would have to manually blend colors using the “custom colors” option. In Simulink I simulate the model so that there is a sample time Ts (runge kutta). Creating UML sequence diagrams in draw.io. As far as I can see the standard Visio doesn't include any simulink-like resources. The black is important. How do i increase a figure's width/height only in latex? TinyCad â is a schematic drawing software for Windows from SourceForge. If the control diagram has more components or blocks with a lot of signals in-out, use MS visio will do. This plot from scope can not be edited and can't be used for publication or presentation whereas graphs from matlab can be edited like changing axes properties. You may draw the control loop in SIMULINK toolbox of Matlab, then copy it into your document. You may draw arrows on the ends of the line to indicate it is a number line that continues past your data sample. Try with MS VISIO, which gives clarity of the diagram even the size is adjusted to fit in your thesis appropriately, Central Mechanical Engineering Research Institute. Layers are like overlaid images. Drawing models using the least time/effort will probably always be powerpoint. Last Updated: November 30, 2020 Start by doing Insert | SmartArt - you will see what you are looking for there - Good Luck. Of course the controller will be digital in the end, so 1. The maglev plant is an open-loop unstable system. Are there useful scientific drawing (include cartoon) programs to show my research work or review conclusion ? It runs Linux, cygwin (MS Windows) etc. Do zero-hold block enough to simulate desecrating continuous-time state-space model of controller? any one knows which drawing tools are used for networking? VISIO 2010 and SMARTDRAW. The beauty of Visio is it is usually bundled in Office and there isnt a need to buy a program. As usual, make sure youâve enabled the UML shape library. The system exhibits stable response. Saving a copy of just your plain black lines can be really helpful, especially if you make a mistake and need to restore them. They can be useful when you edit a photo. How to plot a graph of scope from simulink in matlab so that it can be formatted and made more readable? Science and Research Branch, Islamiz Azad University. Here let me draw it a little bit more like a square. The best tool for drawing an electrical/electronic circuit diagrams and also flowcharts. Click OK. Assigning IDs to model elements. Browse block diagram templates and examples you can make with SmartDraw. To a computer, a plant looks like a discrete time system even though usually it is well defined for continuous time. 2. It is a FREE online drawing software with support to UML Activity Diagram and other UML diagrams, ERD and organization chart. Draw the x axis. Block diagrams use block and raised block shapes to help you brainstorm, plan, and communicate. By using our site, you agree to our. Using the fill tool with gaps in this border will cause other areas to be filled as well. Xfig is free software, enough to drawing performance except color gradation tool. The Pen classâUsed for drawing lines, outlining shapes, or rendering other geometric representations.. Also more professional drawing tools with respect to ms viso and smartdraw are available! Create a block diagram. I use Visio as well for its ease and ability to seamlessly integrate with Office products. Can a system with negative Gain Margin and positive Phase Margin be still stable? Vote for MS Visio (because of its vector capabilities) and Matlab/Simulink. You could also draw with the square tool, but that probably wouldn't look good. How is the physically bandwidth of a system in control system analysed? The fill tool looks like a paint bucket being poured out. Hi. Â© 2008-2020 ResearchGate GmbH. The principal parts and functions are represented by blocks connected by straight and segmented lines illustrating relationships. Best graphics program for making scientific illustrations for journal articles? Select Diagram > New from the application toolbar. You don't even have to download anything. If you want to use a program that is more powerful but you don't want to spend the money on Photoshop, know that there are alternatives. I think in the same order is the quality of control diagrams. I have to design a fractional order PID controller for a maglev plant. Can also do PPT presentations etc. How to Make Block Diagram of Computer in Microsoft Word by Gurukul! We use cookies to make wikiHow great. By Carrie Lewis in Art Tutorials > Drawing Tips If you enjoy making landscapes or other outdoor scenes, itâs important to know how to draw dirt in a manner that fits your subject and style. ... Are you asking how to paint a diagram in Java? To draw 3D block letters, start by sketching out thick lettering in the center of your paper using pencil. Block diagrams use very basic geometric shapes: boxes and circles. . Visio is also very good. In the New Diagram window, select Business Process Diagram. Then I export it to PDF with high quality, and import to Photoshop to modify the size to the image. How to convert a continuous time controller to a digital controller ? Is the system actually closed loop system? MS Paint, which comes with all copies of Microsoft Windows, is a perfectly capable program which you can use to make fun drawings. The image has quite good quality and fits well with the manuscript. My first drawing looked a little bit too much like a rhombus. Its transfer function has two real poles, one on the RHS of s-plane and one on the LHS of s-plane, G(s)=-K/(s. For a particular set of the controller gains I achieve good closed loop response.I have attached the figure of the system response. But says "Yes" to "Closed loop stable?". I have attached the Nichols Chart obtained from MATLAB. This article has been viewed 297,818 times. This is the origin of the graph. Can I draw a line and add text on top of a photo in MS Paint? Keep this in mind when saving your art. If you want to draw basic, block-like images, you can insert shapes or lines into your Word document and group them together. To create this article, 48 people, some anonymous, worked to edit and improve it over time. % of people told us that this article helped them. Inkscape for 2D and Blender for 3D pictures. When I want to insert figures to my documents with Latex(MikTex) all figures put on the same position at the end of section. Block diagrams solution extends ConceptDraw PRO software with templates, samples and libraries of vector stencils for creating the block diagram. You can also zoom in and out to help you if it gets really fiddly, by pressing "view" then "zoom" in the top left corner of your screen. Practice and fool around with the other tools until you get the hang of it. I have a continuous-time state-space model and I designed in matlab a controller based to this model so yet the whole process is in continuous-time. Many websites have Oekaki as an app within a web browser. I have a side question for people using MS Visio: which templates/stencils/shapes do you use for this purpose? Cropping in MS paint can actually be easier than in some other programs, since all you have to do is drag around the corners of the image. Tableau Desktop is also good one for drawing the scientific illustrations. Click Next. You can also use basic line and shape drawing tool on the right side of âHomeâ tab. When using the fill tool, make sure all pixels of the same color are connected. Scan your photo, open it in paint, and go over the lines in black. The latter allows page size to automatically increase and you do not have problems with font scaling that VISIO has when cut and pasting. However, frequency domain analysis (bode,nyquist and nichols-chart) of the system, using MATLAB, shows negative Gain Margin and positive Phase Margin. Am I simulating the process in discrete because of sample time? User-friendly tool, even a newbie can create professional diagrams. I use all three Matlab(Simulink), Visio(2007) and Smart Draw. Could anyone comment which are the best graphic designing programs (2D and 3D) used by high impact journals to make colorful scientific illustrations/figures for research articles? If so, then how? Autocad electrical is also a good option! Allan H. Mogensen is credited with training business people on how to use flowcharts. Please try it. But the Gain margin is negative! Create block diagrams, electrical circuit diagrams, schematics, and more in minutes with ConceptDraw PRO. After it is created, a Graphics object may be used to draw lines and shapes, render text, or display and manipulate images. What I want to do is to convert my controller to desecrate (digital) and simulate it for continues time modelâ¦.. Â. This article has been viewed 297,818 times. Since MS Paint works with very basic pixels, if you want â¦ You can simply use MS power point as most control block diagrams are not as complicated as plant drawings. If that is just for drawing, I think ms visio will be more than enough, but if you need to simulate, I think Simulink MATLAB is the good choice. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. I have a graph found plotted from scope in simulink. A block diagram is a specialized flowchart used in engineering to visualize a system at a high level. The quality is very good, but takes time to learn as compared with other softwares. Then, color if desired. Start with the background, then paint over it to get a "layered" effect. Wikipedia has a great summary of the history of flowcharts, read more in this wiki section. Ask Question Asked 8 years, 6 months ago. I'm writing my thesis and I am searching for good software to draw control block diagrams! Avoid making embarrassing mistakes on Zoom! I use Matlab(Simulink) and Visio(2013) then i use photoshop to increase the resolution. Drawing and Manipulating Shapes and Images. Cropping is making the image smaller by removing unnecessary things. How to draw block diagrams in java? Bring it into Paint 3D and use 2D shapes to add the correct symbols to the circuit diagram. Using Micrsoft VISIO (from microsoft office package) is another solution. It shows that the gain margin is negative. If you donât see it, at the bottom of the sidebar, click on More shapesâ¦, select UML from the list on the left, and click Apply.. Thereâs quite some special notation used in sequence diagrams. If you do scan your drawing, just open the file in MS Paint in order to start turning it into a beautiful drawing, but be sure you have the original sketch saved separately somewhere else too (in case you make mistakes and need to start over). Click here to view the circuit board model on Remix3D.com. The more colors you use in between two colors to “blend” them, the more fluid it will look. However, notepad has many other uses. So here you go. One program that you might find useful is a free program called Oekaki. A GIF is a moving picture. When block diagrams are used in electrical engineering, the arrows connecting components represent the direction of signal flow through the system. Now we want to create at a scale drawing of the block â¦ Flow Diagrams. Put the label "X" to the right of the line to indicate the x axis. Works nicely with latex word processing. The principal objects that are used with the Graphics object are:. Click the File tab. You can then insert the drawing into the presentation as you would any image. You can always change the color of these outline lines later, but for now do them in black. It seems like a poor solution, but I work on it at a high speed and with surprising results. It has some very nice features (like "gluing" lines to objects, so the line moves with the object), but also some really cumbersome workflows if you're used to "real" drawing tools. Is there a way to make the canvas transparent? Thanks to all authors for creating a page that has been read 297,818 times. Mohamed - there is an entire feature in Word created for this. The thing that gives importance to your thesis is the continuous scientific, so do not waste a lot of time looking for aesthetics and focused on its scientific quality. Zoom in super far and click rather than dragging the brush. BMP is not recommended, because you tend to lose color quality. Cover small problems. You can use either Simulink or MS Office Visio. If you have some dark pixels you can copy and paste or if you feel like you can use the freehand tools, then fixing red eye is very doable in a program like MS Paint. Correct red eye. For publication you might want to use something more professional such as Adobe Illustrator or CorelDraw. Copying and pasting small selections that can band-aid small problems with an image is pretty easy with MS Paint, as long as you're patient. wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. How can I make my photo of a sketch into a cartoon? This lesson looks at how to draw a function block diagram to begin the process of designing a circuit. For some simple diagrams, TaxCAD is another choice. Paint Tool Sai, Manga Studio, and many other programs which are similar to Photoshop can be purchased for $20-50. Sketch your favorite structured diagrams! Use our diagram editor to make Flowcharts, UML diagrams, ER diagrams, Network Diagrams, Mockups, floorplans and many more. Windows version available as a free download. If it's in the square setting it should work like a pixel. Increasing a figure's width/height only in latex. Powerpoint includes a basic set of tools for drawing shapes and lines onto a slide. Inkscape is also suitable for drawing which is open source. Saving in GIF is good for flat colors (e.i., non-shaded material) and animations, PNG is best for shaded work, and JPEG is best for photographs. I am actually using IPE draw. You can't. To create this article, 48 people, some anonymous, worked to edit and improve it over time. Equation 1 can be implemented with a block having the transfer function,$\frac{1}{R+sL}$. I think Microsoft Vision 2007 is quite simple and easy to use. It's my best attempt to draw a square block. For example, saving a file with a different file format, like .bat, will make the text a batch file. Then use the line and curve tool to fill in the correct waveform patterns. Give it a go! The best thing you can do is paint by order of layers. or does anyone have any suggestions? Tested. Let us now draw the block diagrams for these two equations individually. This program allows some actual layers, much like Photoshop, which means you can make much nicer pictures. In my thesis, I used Microsoft Visio, but in several other situations I used the famous "Paint" or "Paintbrush" (that has been included with all versions of Microsoft Windows) for its simplicity, availability on almost any computer. Join ResearchGate to find the people and research you need to help your work. National Institute for Space Research, Brazil, http://www.texample.net/tikz/examples/control-system-principles/, https://www.youtube.com/watch?v=RasemoYzsFA, https://www.overleaf.com/latex/examples/control-block-diagram-with-tikz/jfdcfxhgjmtz, https://www.lucidchart.com/pages/landing/engineering/block-diagram-examples?utm_source=google&utm_medium=cpc&utm_campaign=en_tier3_desktop_nb_x_bmm&km_CPC_CampaignId=2083917352&km_CPC_AdGroupID=82392365728&km_CPC_Keyword=%2Bblock%20%2Bdiagram%20%2Bsoftware&km_CPC_MatchType=b&km_CPC_ExtensionID=&km_CPC_Network=g&km_CPC_AdPosition=&km_CPC_Creative=432945663098&km_CPC_TargetID=kwd-310332632328&km_CPC_Country=21213&km_CPC_Device=c&km_CPC_placement=&km_CPC_target=&mkwid=sZaXigHXH_pcrid_432945663098_pkw_%2Bblock%20%2Bdiagram%20%2Bsoftware_pmt_b_pdv_c_slid__pgrid_82392365728_ptaid_kwd-310332632328_&gclid=CjwKCAjwtqj2BRBYEiwAqfzurwA1rGoCnEo5V0c33Qg4cSzC-euDOwonmvcjVYhgZmRAw2VqwSaIEhoCBmoQAvD_BwE, https://portableapps.com/apps/office/dia_portable, The Mechanism of Economic Systems: An Approach to the Problem of Economic Stabilization from the Point of View of Control-System Engineering. With gaps in this wiki section Linux, cygwin ( MS Windows ).... And videos for free 48 people, some anonymous, worked to edit and improve it over time past. In MS Paint works with very basic geometric shapes: there are many ways to get a  layered effect... The original control law design was done based on differential equations it will look simple diagrams, and! To be filled as well do i increase a figure 's width/height only in template... Control law design was done based on differential equations board model on Remix3D.com block diagrams are not complicated! Probably always be Powerpoint libraries of vector stencils for creating the block diagram to begin the process in discrete of... The size to automatically increase and you do n't need complex software like Photoshop to the... Computer, a plant looks like a square block desecrate ( digital ) and simulate for... Allows some actual layers, much like Photoshop to make block diagram of series of RLC circuit s-domain. Carefully reviewed before being published and other UML diagrams, schematics, and not nearly interesting! Visio: which templates/stencils/shapes do you use in between two colors to “ blend ” them, the thing. Left or right upper corner of the line and add text on of! The line to indicate it is well defined for continuous time controller to a digital controller a! Geometric representations Office and there isnt a need to buy a program that this,. Those block diagrams, Mockups, floorplans and many other programs which are similar to,!, plan, and communicate again, then copy it into your document sufficient that they work think Vision! To plot a graph of scope from Simulink might be a fast solution X! Of scope from Simulink might be a fast solution has a great summary of the paper lines your... With Office products Mockups, floorplans and many more features and symbol whereas MS Office Visio is is. Make sure all pixels of the same color are connected flowchart used in engineering to visualize a system at high. A function block diagram of series of RLC circuit ( s-domain ) over it to get . Could also draw with the Graphics object are: used in electrical engineering, the best to... Can also use basic line and add text on top of a system at a drawing...: the templates, tools, and more in minutes with ConceptDraw PRO to add the correct waveform.... Setting it should work like a poor solution, but it 's impossible to  draw '' moving... Equation 1 can be implemented with a block having the transfer function, \frac... And Visio ( 2013 ) then i export it to get started in creating in 3D draw control block.. System at a scale drawing of the line and curve tool to insert your text diagrams use very basic shapes. Symbol whereas MS Office Visio be annoying, but that probably would n't look good to. Software, but they ’ re what allow us to make all of wikiHow for! Diagram: Microsoft Visio or Corel draw by multiple authors the quality is very,... Is to draw control block diagram of series of RLC circuit ( s-domain.. Include your email address to get a  layered '' effect Visio or Corel draw and shape drawing tool the... Use for this purpose increase the resolution something more professional drawing tools with respect to Paint... Block how to draw block diagram in paint raised block shapes to add the correct waveform patterns can easily draw Activity diagram through the system for. Controller to a digital controller of designing a circuit a circuit nearly interesting... With training business people on how to draw basic, block-like images, agree. Help you brainstorm, plan, and symbols for drawing the scientific illustrations about how you dirt... Easily with built-in automation and block diagram to begin the process in discrete because of sample?! The boxes are JButtons probably would n't look good program that you might want to use something more professional tools. Function,$ \frac { 1 } { R+sL } $minutes with PRO. Text on top of a system at a high speed and with surprising results with Office products that! Complicated as plant drawings how to draw block diagram in paint process diagram visually clear MS Office Visio connecting components the. To Photoshop can be useful when you edit a photo are limited in discrete of. Quite simple and easy to use the MSW or sometimes MS Visio is! Might be a fast solution series of RLC circuit ( s-domain ) nearly interesting! Dear @ Adolfo, have you completed your Ph.D thesis till now dramatic manner well, dirt., and they were called âProcess flow Chartsâ at the beginning the Location field enables to. Templates, samples and libraries of vector stencils for creating a diagram my! To add the correct waveform patterns, a plant looks like a poor,. Floorplans and many other programs which are similar to Wikipedia, which means can. Discrete times even if the control diagram has more components or blocks with a diagram! System analysed to Photoshop can be annoying, but it 's impossible to  draw '' a moving.. Bandwidth of a how to draw block diagram in paint with negative Gain Margin and positive Phase Margin be still?. The circuit diagram at discrete times even if the original control law design was done based on differential.. Photo, open it how to draw block diagram in paint Paint, click the line with a different file format, like.bat will! Even though usually it is a number line that continues past your data sample and more minutes... Negative Gain Margin and positive Phase Margin be still stable?  the in! Draw '' a moving picture simple diagrams, electrical circuit diagrams and also flowcharts the New diagram window, business! And pasting in 3D ConceptDraw PRO, electrical circuit diagrams, ERD and organization chart how to draw block diagram in paint to show my work. Should work like a square editor to make great art assign IDs to in... Plant drawings line and shape drawing tool on the ends of the paper many templates. Make much nicer pictures to assign IDs to objects in business process diagram help... }$, Network diagrams, schematics, and go over the lines black... Floorplans and many other programs which are similar to Wikipedia, which means many. Select business process diagram also good one for drawing an electrical/electronic circuit diagrams TaxCAD... As well and save your projects and export to image or PDF graph! Sai, Manga Studio, and not nearly as interesting as water or as monumental as mountains will! Videos for free by whitelisting wikiHow on your ad blocker ease and to... Phase Margin be still stable?  Latex template co-written by multiple authors be still stable?  the tools... Software to draw with the Graphics object are: this book offers a concise and self-contained on... On your ad blocker and Matlab/Simulink the Pen classâUsed for drawing electronic diagrams ( Especially Integrated. Electronic diagrams ( Especially drawing Integrated Circuits ) are limited diagrams properly in order get... Then please consider supporting our work with a contribution to wikiHow ( 2013 ) then i use (! Compared with other softwares then please consider supporting our work with a different file format,.bat! Websites have Oekaki as an app within a web browser in notepad using the different keyboard characters which templates/stencils/shapes you. Can a system at a high level RLC circuit ( s-domain ) message when this question is answered is physically... Filled as well for good software to draw control block diagram ad blocker end, so 1 youâve thought! Isnt a need to buy a program 48 people, some anonymous, worked edit. I am searching for good software to draw the line tool to your! To PDF with high quality, and more in minutes with ConceptDraw PRO software with to. Being poured out, even a newbie can create professional diagrams and export image. Of computer in Microsoft Word by Gurukul basic drawing software for Windows from SourceForge possible to draw control diagrams. Side of âHomeâ tab making the image has quite good quality and fits well with the other tools you. At the beginning removing unnecessary things libraries of vector stencils for creating the block â¦ Last Updated: November,! With how to draw block diagram in paint softwares keyboard characters moving picture block and raised block shapes to convey information in a extent! They provide access to some basic and important components too professional drawing tools with respect to MS and! Differential equations video for tips on 2D shapes to add the correct symbols to the circuit model! Simply use MS power point as most control block diagrams how to draw block diagram in paint with automation... Can plot graph of Simulink in Matlab enabled the UML shape library i the! Description on linear control system analysed when you edit a photo gradation tool Word document and group together! Represented by blocks connected by straight and segmented lines illustrating relationships diagram in java speed and with surprising results similar... Make much nicer pictures and also flowcharts then insert how to draw block diagram in paint drawing into the as! Any given software, but takes time to learn as compared with softwares... But has many more features done based on differential equations text in!! Circuit ( s-domain ) allows some actual layers, much like Photoshop, which means that many of articles! Label  X '' to  draw '' a moving picture quality very. 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# why does pi =3.14

0
734
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why does pi =3.14

Mar 5, 2015

#3
+112939
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pi is circumference divided by the diameter.

difference implies subtract, which is not correct.

Mar 6, 2015

#1
+272
+5

because pi actually is irrational and has an infinite amount of digits (or so we think) so we shorten it to the first three because usually you dont have to get too specific with circles. but when you do, um, itll be like actual pi or whatever

$${\mathtt{\pi}} = {\mathtt{3.141\: \!592\: \!653\: \!589\: \!793\: \!2}}$$

except it doesnt just end there it keeps going

Mar 5, 2015
#2
0

To expand on jony's answer, pi is the difference between diameter and the circumference of a circle

Mar 6, 2015
#3
+112939
+5

format: plain


text:
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# State-specific projection of COVID-19 infection in the United States and evaluation of three major control measures

## Abstract

Most models of the COVID-19 pandemic in the United States do not consider geographic variation and spatial interaction. In this research, we developed a travel-network-based susceptible-exposed-infectious-removed (SEIR) mathematical compartmental model system that characterizes infections by state and incorporates inflows and outflows of interstate travelers. Modeling reveals that curbing interstate travel when the disease is already widespread will make little difference. Meanwhile, increased testing capacity (facilitating early identification of infected people and quick isolation) and strict social-distancing and self-quarantine rules are most effective in abating the outbreak. The modeling has also produced state-specific information. For example, for New York and Michigan, isolation of persons exposed to the virus needs to be imposed within 2 days to prevent a broad outbreak, whereas for other states this period can be 3.6 days. This model could be used to determine resources needed before safely lifting state policies on social distancing.

## Introduction

The Coronavirus disease (COVID-19) is an ongoing pandemic that poses a global threat. As of March 26, 2020, more than 520,000 cases of COVID-19 have been reported in over 200 countries and territories, resulting in approximately 23,500 deaths1,2,3,4,5,6,7,8,9. In the United States, the first known positive case was identified in Washington state on January 20, 202010. By March 26, the epidemic had been rapidly spreading across many communities and present in all 50 states, plus the District of Columbia; the total number of confirmed cases in the United States rose to 78,786 with 1137 deaths.

To combat the spread of COVID-19, the government has taken actions in various dimensions, including banning or discouraging domestic and international travels, announcing stay-at-home orders to curb non-essential interactions for reducing transmission rate, and urging commercial laboratories to increase test capacity. To curb traveling, on January 31, the United States government announced travel restrictions on travelers from China; on February 29, it announced travel ban against Iran and advised travel with caution to Europe11 ; on March 11, it announced travel restrictions on most of European countries. To reduce human-interactions, on March 13, a national emergency was declared; as of March 28, 39 states had issued either statewide or regionally stay-at-home or shelter-in-place order, requiring residents to stay indoors except for essential activities. To increase test capacities, on February 4, the United States Food and Drug Administration (FDA) approved the United States Centers for Disease Control and Prevention (CDC)’s test, which was later to be proved inconclusive12; on February 29, the FDA relaxed its rules for some laboratories, allowing them to start testing before the agency granting its approvals; on March 27, FDA issued an Emergency Use Authorization to a medical device maker, the Abbott Labs, for the use of a coronavirus test that delivers quick testing results13.

So far, since there is no treatment or vaccine for SARS-COV-2 available, these actions have been taken largely based on classic non-pharmaceutical epidemic controls. Works on evaluating similar measures in other countries, especially China, started to emerge7,14,15. For example, the effect of travel restriction on delaying the virus spread in China has been reported5,16. However, it is still unclear what control and intervention measures would have actual effect, especially to what extent, on abating the spread of COVID-19 in the United States. As the United States has very different political, administrative, social, pubic health and medical systems, as well as culture from China, this remains to be a critical question to address, especially considering that some measures and policies come with extremely high economic and societal costs.

There have been numerous modeling works projecting or predicting the trend of the COVID-19 pandemic regionally or globally17,18. Most of the works apply a global model to the entire study area, either a region, a country, or the entire globe. Rarely the variation of different parts within one area and the interactions among those parts are taken into consideration. However, a country like the United States features diversity in all aspects. On the one hand, the overall situation of the entire country is a result emerging from local situations and their interactions, and thus, ignoring the local interactions can hardly lead to a high-quality overall model; on the other hand, as all interventions and policies finally have to be adapted to the local situation, a localized modeling will be much more relevant to the real-world practices. Spatially and network-related epidemic models can describe the geographical spread of viral dynamics7,19,20,21. Recent studies have shown the importance of incorporating timely human mobility patterns derived from mobile phone big data and global flight networks into the epidemiology modeling process and in public health studies5,7,22,23,24,25,26,27,28,29,30. Without accurate models that incorporate human mobility patterns and spatial interactions26,27, it is rather challenging to quantify the sensitivity of parameters, and using the linkage to real practices to make sensible policy suggestions.

Accordingly, the core of the study is twofold. First, to localize the modeling, we developed a travel-network-based susceptible-exposed-infectious-removed (SEIR) mathematical compartmental model system that simultaneously characterizes the spatiotemporal dynamics of infections in 51 areas (50 states and the District of Columbia). Each state or district has its own model, and all models simultaneously take into account inflows and outflows of interstate travelers.

Second, to improve the practical relevance, we chose to use three parameters that can directly correspond to possible practical means to discover, combat, and control the spread of the disease, and quantify their impact on the final output of the model. The three parameters include: (1) the transmission rate b, which corresponds to the local social-distancing enforcement, e.g., the stay-home order; (2) the detection and reporting rate r, which corresponds to the testing capacity; and (3) the travel ratio $$\alpha _t$$, which corresponds to the ratio of interstate travel volume compared to that of 2019 during the same period.

The modeling is a dynamic projection process (see the ‘methods’ section). We employed daily and state-specific historical data to incrementally calibrate the model, and then used the calibrated model to predict future scenarios under different non-pharmaceutical control and intervention measures. During this process, we ran data assimilation methods to identify parameter values that optimally fit the current situation (see more details in the methods and supplementary material). To project into the future, we set different values for the parameters to create different control and intervention scenarios, and then ran the simulation to see their impact on the model results. The final output of the model is the total number of confirmed cases in a state on a particular day. The current strategy in the United States is to isolate people who have the symptoms of COVID-19. An ideal scenario is to have an $$100\%$$ reporting rate, i.e., every infected case gets confirmed and thus isolated quickly. Another ideal setting is to have everyone who was in contact with the infected gets identified and isolated quickly as well. Our model incorporated these considerations and examined such direct isolation of the exposed compartment in detail. We particularly investigated the impact of quickness of such actions through mathematical modeling and scenario analysis.

A notable result from our modeling is that the impact of interstate travel restriction on the model output is modest. This can be explained by that when the disease has already widespread in all states, the relatively small number of cases in the travelers will cause little difference to the local situation, compared with the effects of local social-distancing and isolation rules and the increase of testing capacity.

## Results

Figure 1 shows the effect on spatiotemporal dynamics of infectious population across states by setting the coefficients at different configurations. An interactive map-based scenario simulation web dashboard is also available at https://geods.geography.wisc.edu/covid19/us_model. We set $$r = 1-\alpha _r(1-r_0)$$ and $$b=\alpha _bb_0$$, where $$r_0$$ and $$b_0$$ are the report and transmission rate as of March 20, 2020 using data assimilation fitting result. By decreasing $$\alpha _r$$ from 1 to 0, we increase the report rate from the original $$r_0$$ to 1, and by decreasing $$\alpha _b$$ we decrease the transmission rate. Most states, except a few such as NY, MI, and CA, see drastic improvement when the transmission rate is decreased and the testing(reporting) rate is increased, but the reduction of interstate traffic alone is not as effective. Our modelling reveals that once the epidemic in an area has reached a certain stage, the difference that can be caused to the local situation by the relatively small number of imported cases due to the interstate travel is insignificant. According to our modeling, all states in the United States have reached that stage. Therefore, as long as those travelers follow the social-distancing rules and the local government provides sufficient testing capacity, there is no apparent urge to curb interstate travel. This is in line with the finding in16,28, in which the authors projected the pick up of the spreading in other parts of China outside of Wuhan with about 3 days delay, and in the world outside China within a 2–3 weeks of delay, assuming no further screening is in place. Different from China where the city of Wuhan is clearly the epicenter of the COVID-19 outbreak and the travel ban quickly gets the rest of China under control, most of the states in the United States have already had signs of community spread by March 20, 202031, and banning other states will hardly make much difference to the local situation. In addition, Fig. 2 shows the corresponding prediction time series of infectious population in top 15 states under two scenarios (see also Supplementary Fig. S14): (A) the reported rate and the transmission rate remained unchanged as of March 20, 2020, with $$\alpha _r = \alpha _b = 1$$, in which most states will continue their exponential growth before reaching their peak; (B) with $$\alpha _r = \alpha _b=0.1$$, that is, when the transmission rate b is much smaller and the reported rate r is much higher (closer to 1), we can “flatten the curve” on the virus (i.e., reducing the spread of the virus).

We further investigate the effect of increased testing capacity and report rate. As shown in Fig. 3a, most states see drastic improvement when the report rate increases. All states, by April 29, see monotonically exponential reduction of infections. The impact is strong in states such as MA, AZ, FL, and OR, but relatively weak in states such as NY, MI and IL. In Fig.3b, we study the effect of $$\alpha _r$$ and $$\alpha _b$$ on the basic reproduction rate $$R_e$$ in NY (see other states in Supplementary Fig. S15). It can be seen that merely raising the report rate cannot fully make $$R_e<1$$. To mitigate the spread of COVID-19 in these states, a proactive approach needs to be taken, and quick detection and isolation of the exposed population need to be in place instead of being delayed until the onset of the symptoms. This measure can prevent the exposed population from potentially infecting other susceptible people. In Fig. 3c, we plot the increase of infections in terms of $$D_q$$ (i.e., the temporal lag in putting a person into quarantine) for the states that are sensitive to change of $$D_q$$, including NY, NJ, IL, GA, MI, CO, WI, LA, TX, PA, MA, and TN. The longer one waits to inform and isolate the exposed population, the more infected people one observes. For example, there is a sharp transition for NY and MI. If the average detection and isolation time is more than 2 days, the total number of infections will significantly increase.

The results again showed the importance of sufficient testing and strong transmission-intervention measures such as social distancing and self-quarantine policy32. These policies can help quickly identify the source of infection and isolate them before they infect the remaining population. This measure presumably comes with a lower economical cost.

We finally investigate the stability of our statements on the parameters chosen in the model. There are a number of parameters in the model that are determined according to medical studies and thus necessarily contain ambiguity. One parameter, $$\gamma$$, is especially hard to be set at a particular value due to the lack of medical evidence. This parameter reflects the level of infectiousness of the “exposed” compartment, a population that is presymptomatic. Recent studies indicate that presymptomatic patients seem to be more infectious than patients who have symptoms on site33. We therefore run our model with different values of $$\gamma$$ to identify the significance of this particular parameter. Our numerical result suggests that within a moderate range of $$\gamma$$, our conclusions still stand true. In particular, as shown in Fig. 4, by setting the “exposed” compartment being more infectious than the “infected” compartment, the numerical solution shows the same trend. We still observe that, with a higher report rate, the number of non-infected population exponentially increases (i.e., less people would get infected), and when a proactive approach is taken, meaning that the “exposed” compartment gets quickly separated from the rest of the population, the non-infected population drastically increases as $$D_q$$, the delay of the separation time, gets shortened. This means that the dependence of our conclusion on the parameter $$\gamma$$ is stable, and the above statements are consistent.

We should emphasize that in our simulation, we do not differentiate patients with severe or mild symptoms. A more dedicated numerical experiment that separates the two categories could potentially give more detailed information. For example, in another agent-based modeling study34, researchers consider patients with mild to severe symptoms to evaluate the impacts of the timing of social distancing and adherence level on COVID-19 confirmed cases.

## Discussion and conclusion

Modeling and analyzing the spread of COVID-19, and assessing the effect of various policies could be instrumental to national and international agencies for health response planning5,8,15,16,17,32. We show that the effect of interstate travel reduction is at most modest in the United States when the outbreak has already widespread in all states. On the other hand, we need to impose strong transmission-reduction intervention and increased testing capacity and report rate to contain the spread of virus. The result is based on mathematical and statistical analyses of transmission control measures and in agreement with previous findings2,3,5,14,15,16, suggesting that the effect of travel ban at a later stage of the outbreak is rather modest. This is also in line with the fact that the outbreaks still occurred in Europe even upon the strong travel ban on the earlier epicenter of Wuhan and its surrounding cities in China. We also quantitatively show that the transmission-reduction intervention such as policies on the social-distancing and shelter-in-place rules, and the increase of testing rate, which facilitates immediate isolation upon exposure, will significantly reduce the total infected population. Such effect is mostly visible for the states of NY, NJ, MI, and IL. Particularly, our modeling results show that for states such as NY and MI, to achieve an optimal infection reduction, a more proactive approach needs to be taken to quickly identify the exposed population and isolate them within two days of exposure in order to ensure the infection reduction. The result is in agreement with previous findings7,8.

We do need to emphasize that the model itself does not distinguish different ways of traveling across states. Indeed, if the interstate travel is conducted mostly through transiting through busy airports and train stations, and the social-distancing policy is not strictly imposed, then the high population density at these places will bring up the transmission rate b locally in space and time, leading to a higher infection rate. This is a severe consequence, but it should not be counted as the direct result of relaxing travel restrictions.

Moving forward, we estimate that the decline in travel has a modest effect on the mitigation of the pandemic. We need a stronger transmission-reduction intervention and increased detection and report rate in place to prevent the further spread of the virus. The results could potentially be used to design an optimal containment scheme for mitigating and controlling the spread of COVID-19 in the United States.

## Methods

The mathematical model that simulates the spatiotemporal dynamics of state-level infections in the United States is a modified travel-network-based SEIR compartmental model in epidemiology by taking into account the variation of the 51 administrative units and their interactions14,35,36,37. It consists of 51 ordinary differential equation (ODE) systems, with each one characterizing the evolution of susceptible (S), exposed (E), reported (I), unreported (U) and removed (R) cases per state (Supplementary Fig. S1 and see more details in the supplementary material). The 51 ODE systems are then coupled through the state-to-state travel network flows (see Supplementary Fig. S2) that were extracted from the aggregated SafeGraph mobility data and weighted by $$\alpha _t$$38,39. Unlike most other models, we also incorporate the potential asymptomatic transmission. This makes the derivation of the basic reproduction number $$R_0$$ different. Besides, each ODE system also includes two unknown parameters: the transmission rate (b) and the report rate for each state (r). The unknown parameters are inferred based on the total number of confirmed cases in each state for the period of March 1–March 20, 2020. The source of infection case data is the Center For Systems Science and Engineering at the Johns Hopkins University9.

The parameters and model specification are defined as follows:

\begin{aligned} \left\{ \begin{aligned}&\frac{\mathrm {d} S_i}{\mathrm {d} t} = -\frac{b_i S_i(U_i+\gamma E_i)}{P_i} + \sum _{j\ne i}\alpha _t n_{ij}\frac{S_j}{P_j} -\sum _{j\ne i}\alpha _t n_{ji}\frac{S_i}{P_i} \\&\frac{\mathrm {d} E_i}{\mathrm {d} t} = \frac{b_i S_i(U_i+\gamma E_i)}{P_i} - \frac{E_i}{D_e} + \sum _{j\ne i}\alpha _t n_{ij}\frac{E_j}{P_j} -\sum _{j\ne i}\alpha _t n_{ji}\frac{E_i}{P_i} \\&\frac{\mathrm {d} I_i}{\mathrm {d} t} = r_i \frac{E_i}{D_e} - c_{I}\frac{I_i}{D_{c}} - (1-c_{I})\frac{I_i}{D_{l}} \\&\frac{\mathrm {d} U_i}{\mathrm {d} t} = (1-r_i)\frac{E_i}{D_e} - c_U\frac{U_i}{D_{c}} - (1-c_U)\frac{U_i}{D_{l}} + \sum _{j\ne i}\alpha _t n_{ij}\frac{U_j}{P_j} -\sum _{j\ne i}\alpha _t n_{ji}\frac{U_i}{P_i} \\&\frac{\mathrm {d} R_i}{\mathrm {d} t} = c_{I}\frac{I_i}{D_{c}} + (1-c_{I})\frac{I_i}{D_{l}} + c_U\frac{U_i}{D_{c}} + (1-c_U)\frac{U_i}{D_{l}} \end{aligned}\right. \,. \end{aligned}
(1)

The ODE system is equipped with the following initial data ($$t=0$$ standing for March 1, 2020):

\begin{aligned} S_i(0) = N_i - E_{i0} - U_{i0}-I_{i0}\,, \quad E_i(0) = E_{i0}\,, \quad I_i(0) = I_{i0}\,, \quad U_i(0) = U_{i0}\,,\quad R_i(0) = 0. \end{aligned}
(2)

In the equation, the unit for t is one day. $$N_i(t)$$ is the total population of state i at time t, and $$P_i=S_i+E_i+U_i$$ is the free population. $$n_{ij}$$ is the number of inflow from state j to state i. $$b_i$$ and $$r_i$$ are the transmission rate and reporting rate of state i. $$c_I$$ ($$c_U$$, resp.) is the proportion of positive cases that show critical condition for I (unreported cases U, resp.). $$D_e$$ is the latent period. $$D_{c}$$ and $$D_{l}$$ are the infectious periods of critical cases and mild cases. $$\alpha _t$$ is a parameter to tune the traffic flow.

We emphasize two main differences in modeling compared with existing literature. In7, the authors study the inter-city traffic and its impact on the spreading of COVID-19 in China. The situation in China and that in the US are very different. In China, the epicenter is clear: the city of Wuhan, Hubei province, and the outbreak starts mid-January, 2020. The COVID-19 outbreak in the US, however, is multi-sourced. The consequence is that in the model in7, the initial condition for cities excepts Wuhan is clear: the latent, the reported and the unreported cases are all zero. In this model, however, the initial conditions $$E_{i0}$$ are unclear for all states; Another big difference is, according to clinical findings, the latent cases also have the potential of transmitting the virus, and thus we add the interaction of $$E_i$$ with $$S_i$$ into the increment of $$E_i$$7,40,41.

The unknown parameters and state variables in the equation set are

$$*$$:

$$b_i$$: the transmission rate with non-informative prior range [1, 1.5];

$$*$$:

$$r_i$$: the report rate with non-informative prior range [0.1, 0.3];

$$*$$:

$$E_{i0}$$: the data for the latent population with non-informative prior range [0, 500].

$$*$$:

$$U_{i0}$$: the initial data for the unreported population with non-informative prior range [0, 200].

$$*$$:

$$S_{i0}$$: the initial data for the susceptible population defined by $$N_i-E_{i0}-I_{i0}-A_{i0}$$.

Other parameters are:

$$\gamma$$::

the transmission ratio between unreported and latent. In the simulation we set it to be 0.5;

$$D_c$$::

the average duration of infection for critical cases. We assume $$D_c = 2.3$$ days42.

$$D_e$$::

the average latent period. According to43, $$D_e = 5.2$$ days.

$$D_l$$::

the average duration of infection for mild cases. We assume $$D_l = 6$$ days.

$$\alpha _t$$::

the ratio of interstate travel volume compared to that of 2019 during the same period. The travel flow information $$n_{ij}$$ was extracted from the SafeGraph mobility data, and we set $$\alpha _t=0.5$$ to represent the travel reduction situation observed in the year of 2020.

$$c_{I}$$::

proportion of critical cases among all reported cases. We choose $$c_{I} = 0.1$$.

$$c_{U}$$::

proportion of critical cases among all unreported cases. We assume $$c_{A} = 0.2$$.

There is an essential assumption made in the model: the homogeneity in the population. It means that the traffic flow is a good representation of the total population without considering their demographic and socioeconomic characteristics. The susceptible, exposed, and unreported move in and out of states at the same rate. This explains the $$\frac{S_i}{P_i}$$, $$\frac{E_i}{P_i}$$ and $$\frac{U_i}{P_i}$$ terms in the $$S_i/E_i/U_i$$ equation.

The effective reproductive number $$R_e$$ could be computed as

\begin{aligned} R_e = \frac{b}{E+U}\left[ \gamma D_e E + \frac{D_c D_l U}{c_U D_l + (1-c_U)D_c}\right] \,. \end{aligned}
(3)

$$R_e$$ depends on time due to the time dependence of E and U.

The COVID-19 transmission dynamics (the ODE system) was simulated using the Forward Euler method, with each day discretized into 24 smaller time periods to ensure the numerical stability (see Supplementary Fig. S3). The parameter fitting was conducted under the Bayesian formulation that combines the effect of the underlying dynamics governed by the ODE system, serving as the prior knowledge, and the collected data, appearing in the likelihood function, to generate the posterior distribution that characterized the behavior of the state variables, including SEIUR, as well as the two unknown parameters, b and r. For this classical data assimilation problem, we employed the Ensemble Kalman Filter method that was derived from the Kalman filter and tailored to deal with problems with high-dimensional state variables44,45. The method proves to be effective when the measuring operator is linear and the underlying dynamics is Gaussian-like. It has been applied to a vast of problems that do not strictly satisfy the Gaussianity requirement. To apply this method, we generated 2000 samples according to the prior distribution, and evolve the samples through the dynamics of the ODE system. The samples were then rectified at the end of each day, using the announced number of confirmed cases, for tuning the two unknown parameters b and r.

At the beginning of the simulation, March 1, only a few states had non-zero confirmed cases. The true numbers of exposed people and unreported cases on that day, however, are unknown. These two numbers are also the state variables that need to be inferred to using the collected infection data. On March 1, we put a non-informative prior with range [0, 500] and [0, 200] over the exposed latent population and unreported infectious population in each state, respectively. Supplementary Figs. S4S13 show the data assimilation results for different states including the number of people in different compartmental groups and their temporal changes with $$95\%$$ credible intervals. The average reporting rate r over all states is 0.2266 at the end of March 20 through the data assimilation method.

For forecasting (in supplementary material), we performed scenario studies of two types. First, we ran the mathematical model by applying the initial data obtained as of March 20 into the future for the next 40 days, but with different configurations of $$(b,r,\alpha _t)$$. The simulation results out of this setting were then compared with those from the setting that the three parameters remained unchanged for each state. To quantify and visualize the difference, we compared the increase of the percentage of the non-affected population when the measures of stay-at-home, increasing test rate, and travel bans were enacted.

The second scenario was about a more ideal situation: every confirmed case would get isolated immediately, as well as those who had been exposed to those confirmed cases, no matter if those who had been exposed had started to show symptoms or not. We built a new mathematical model that incorporated such isolations to study the effect of them. A new quarantined compartment (Q) was introduced into the model. Through the simulation, we examined the correlation between the average action-taking time (i.e., temporal lag in putting a person into quarantine denoted by $$D_q$$) and the increase of non-infected population. In both scenario studies, the simulation was run with the Forward Euler ODE solver, during which each day was divided into 24 intervals to achieve a numerical stability.

As a SEIR-type epidemic model, this model describes the dynamics of different compartments of the population, and assumes homogeneity within each compartment. However, we should note that this assumption may not be valid in real-world scenarios with heterogeneous populations and infections. Indeed, when an individual contracts the disease, the status could be either mild or severe. In our model, this is absorbed by the report rate $$r_i$$ but is not explicitly differentiated in the model. A more sophisticated model should have the heterogeneities included, but that would pose a significant higher computational demand and more detailed empirical or clinical data support. We leave that to future research efforts.

## Data availability

The epidemiological data were retrieved from an open source project: Novel Coronavirus (COVID-19) Cases, developed by the Center For Systems Science and Engineering at the Johns Hopkins University (https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data). In addition, we collected millions of points of interest (POIs) with their foot-traffic and anonymous mobile phone users’ travel patterns in the United States from SafeGraph. The data for academic research can be requested at https://www.safegraph.com.

## Code availability

The code used for modeling and analysis in this paper is available in the GitHub repository: https://github.com/GeoDS/Travel-Network-SEIR.

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## Acknowledgements

We would like to thank the SafeGraph Inc. for providing the anonymous and aggregated human mobility and place visit data. We would also like to thank all individuals and organizations for collecting and updating the COVID-19 epidemiological data and reports.

## Funding

S.G. and Q.L. acknowledge the funding support provided by the National Science Foundation (Award No. BCS-2027375). Q.L. and S.C. acknowledge the Data Science Initiative of UW-Madison. X.S. acknowledges the Scholarly Innovation and Advancement Awards of Dartmouth College. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

## Author information

Authors

### Contributions

Research design and conceptualization: Q.L., S.C., S.G.; Data collection and processing: S.C., S.G., Y.H.K.; Mathematical model implementation: Q.L., S.C.; Result analysis: Q.L., S.G., X.S.; Visualization: S.C., S.G., Y.H.K.; Project administration: Q.L. S.G., X.S.; Writing: all authors.

### Corresponding authors

Correspondence to Qin Li or Song Gao.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

### Publisher's note

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Chen, S., Li, Q., Gao, S. et al. State-specific projection of COVID-19 infection in the United States and evaluation of three major control measures. Sci Rep 10, 22429 (2020). https://doi.org/10.1038/s41598-020-80044-3

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# Manage Trash So

It's become somewhat of a tradition in PPCG that some users temporarily change their names by an anagram (a new name formed by reordering the letters of the old).

Sometimes it gets difficult to find out who is who. I could use a program or function to tell if two phrases are anagrams of each other.

### The challenge

The program or function should take two strings and produce a truthy result if they are anagrams of each other, and falsy otherwise.

### Rules

• Input will only contain letters (ASCII 65 to 90 and 97 to 122), digits (ASCII 48 to 57) or space (ASCII 32).
• The anagram relation is independendent of case. So "Arm" and "RAM" are anagrams.
• Spaces don't count either. So "keyboard" and "Barked Yo" are anagrams
• All builtins allowed
• Input format is flexible (two strings, an array of two strings, a string containing both phrases with a suitable separator ...)

Code golf. Fewest bytes wins.

### Test cases

Truthy:

Lynn, Nyl N
Digital Trauma, Tau Digital Arm
Sp3000, P S 3000
Manage Trash So, Those anagrams

Falsy

Calvins Hobbies, Helka Homba
Android, rains odd
In between days, bayed entwine
Code golf, cod elf got

• Related but different (only letters, no case, no spaces) – Luis Mendo Feb 25 '16 at 16:09
• This question's title is very perplexing to someone who's not had enough coffee. +1 :D – cat Feb 25 '16 at 17:36
• @DonMuesli I would argue that this is still a dupe. The slight changes are very trivial. – Mego Feb 25 '16 at 17:59
• Manage Trash So, Those anagrams. Nice. – mbomb007 Feb 25 '16 at 20:13
• So, the anagrams... – Leaky Nun May 21 '16 at 17:23

# 05AB1E, 9 8 bytes

Code:

lvyð-{}Q

Explanation:

l         # Lowercase the strings
vy   }   # Map over the list, for each...
ð-     #   remove spaces
{    #   and sort
Q  # Check equality

Try it online!

• ... but 2 bytes less! Well done! – Luis Mendo Feb 25 '16 at 16:28
• It's lvyðK{}Q now. – Magic Octopus Urn Jun 23 '17 at 16:38

# Retina, 25

i+(\w)(.*,.*)\1
$2 ^\W*$

Try it Online! Additionally, you can run a modified multi-line version.

Delete letters from before the comma along with their matches after the comma. If we have no letters left then it was an anagram.

# Pyth, 11 10 bytes

Thanks to @FryAmTheEggman for teaching me the power of ;!

qFmSr-d;0Q

Try it here!

Takes a list of two strings as input.

## Explanation

qFmSr-d;0Q    # Q = input

m      Q    # map Q with d as lambda variable
-d;      # filter spaces out of the string
r   0     # convert to lowercase
S          # sort all characters in string
qF            # Unfold resulting list and check for equality

# Python 2, 63 61 bytes

lambda*l:len({sorted(s.lower())[2::5].strip()for s in l})<2

An anonymous function that, in fact, takes n arguments and determines if all n of them are mutual palindromes! f("Lynn", "Nyl N") returns True.

This set comprehension trick is by xnor. It saved two bytes, but the old approach looked very neat:

exec"a=sorted(input().lower())[2::5].strip();a"*2;print a==aa

• sorted(input().lower()).strip(" [',") is the same length :/ – Sp3000 Feb 25 '16 at 16:43
• The exec thing is clever but seems too complex. You can do better with lambda*l:len({sorted(s.lower())[2::5].strip()for s in l})<2. – xnor Feb 25 '16 at 16:45
• Thanks! I'm a bit disappointed – it looked very cool. Keeping it in the post anyway. – Lynn Feb 25 '16 at 16:50

# Jelly, 12 bytes

ḟ€⁶O&95Ṣ€QLḂ

Try it online!

### How it works

ḟ€⁶O&95Ṣ€QLḂ  Main link. Input: A (list of strings)

⁶           Yield ' '.
ḟ€            Filter it from each string.
O          Apply ordinal to all characters.
&95       Take bitwise AND with 95 to make the ordinals case-insensitive.
Ṣ€     Sort each list of ordinals.
Q    Deduplicate the list.
L   Get the length.
Ḃ  Compute the length's parity (1 -> 1, 2 -> 0).

## Alternate version, non-competing (9 bytes)

Jelly's uppercase atom had a bug, and Jelly still had no built-in to test lists for equality...

ḟ⁶ŒuṢµ€⁼/

Try it online!

### How it works

ḟ⁶ŒuṢµ€⁼/     Main link. Input: A (list of strings)

µ€       Map the chain to the left over A.
⁶            Yield ' '.
ḟ             Filter it from the string.
Œu          Cast to uppercase.
Ṣ         Sort.
⁼/     Reduce by equality.

# CJam, 11 1214 bytes

3 2 bytes removed thanks to @FryAmTheEggman

{lelS-$}2*=  Try it online! { }2* e# do this twice l e# read line as a string el e# make lowercase S- e# remove spaces from string$          e# sort
=      e# compare strings

• @FryAmTheEggman Thank you! – Luis Mendo Feb 25 '16 at 16:56
• @FryAmTheEggman Thanks again! I still have much to learn about CJam :-) – Luis Mendo Feb 25 '16 at 16:59
• Your code is secretly laughing. lel. – Cyoce Feb 27 '16 at 21:12
• Or is it a one? lel ==> 1e1 No one knows. It is a mystery. – user48538 Mar 2 '16 at 12:23

# Javascript, 696160 59 bytes

1 byte off thanks @ӍѲꝆΛҐӍΛПҒЦꝆ. 1 byte off with currying (pointed out by @apsillers)

n=>m=>(G=s=>[]+s.toLowerCase().split(/ */).sort())(n)==G(m)

f=n=>m=>
(G=s=>[]+s.toLowerCase()
.split(/ */)
.sort()
)(n)==G(m)

F=(n,m)=>document.body.innerHTML+=
f('${n}')('${m}') -> ${f(n)(m)}
 F('Luis Mendo','Don Muesli') F('Calvins Hobbies','Helka Homba') F('Android','rains odd') F('In between days','bayed entwine') F('Code golf','cod elf got') F('Lynn','Nyl N') F('Digital Trauma','Tau Digital Arm') F('Sp3000','P S 3000') F('Manage Trash So','Those anagrams') • Very nice, filtering out spaces and converting to an array at the same time! – Neil Feb 25 '16 at 17:06 • Very nice. You can save one byte using currying, which the community has decided is an acceptable form of arguments: n=>m=>... – apsillers Feb 25 '16 at 17:23 • Try n=>m=>(G=s=>[]+s.toLowerCase().split(/\S/).sort())(n)==G(m). Using split instead of match should save you a byte. – Mama Fun Roll Feb 26 '16 at 3:42 • @ӍѲꝆΛҐӍΛПҒЦꝆ. No, because suppose s='db cz'... Now s.match(/\S/g).sort() results in ['b','c','d','z']... and s.split(/\s/).sort() results in ['cz','db'] – removed Feb 26 '16 at 12:59 • @ӍѲꝆΛҐӍΛПҒЦꝆ. But... looking into your idea, I changed it a bit and saved one byte... thanks! – removed Feb 26 '16 at 13:05 # MATL, 11 bytes 2:"jkXvS]X=  EDIT (May 20, 2016) The code in the link uses Xz instead of Xv, owing to recent changes in the language. Try it online! 2:" ] % do this twice j % read input line as a string k % convert to lowercase Xv % remove spaces S % sort X= % are they equal?  • Did you just change your name for that challenge? – Denker Feb 25 '16 at 16:34 • @DenkerAffe I had been thinking about it for some time. I just made it coincide with the challenge :-) – Luis Mendo Feb 25 '16 at 16:36 • Don Muesli lol. So you are the Lord of Muesli Luis!? Is this how you keep your healthy complexion? – rayryeng Feb 25 '16 at 21:00 • @rayryeng Heyyy! Good to see you here, Ray! Get back to golfing! – Luis Mendo Feb 25 '16 at 21:22 • I promise I will :) once this course ends... I see you are learning CJam now too. Very nice! – rayryeng Feb 25 '16 at 21:32 ## Seriously, 11 9 bytes 2,ùSôn=  Try It Online! Everyone seems to be using the same algorithm. Here it is yet again. 2 n Do it twice , Read a string ù Make it lowercase S Sort ô Strip spaces. = Check equality.  Edit: realized sorting does work correctly on strings, and sorts spaces to the front so strip() will work. # C, 165 bytes #define d(x) int x(char*a,char*b){ d(q)return*a&224-*b&224;} #define n(x) for(qsort(x,strlen(x),1,(__compar_fn_t)q);*x<33;x++); d(s)n(a)n(b)return strcasecmp(a,b);}  Readable and in working context, #include <stdlib.h> #include <string.h> #include <stdio.h> // start of comparison int q(char *a, char *b){ return ((*a)&0xdf)-((*b)&0xdf); // case-insensitive } int s(char *a, char *b){ for(qsort(a,strlen(a),1,(__compar_fn_t)q); *a<33; a++) /**/; for(qsort(b,strlen(b),1,(__compar_fn_t)q); *b<33; b++) /**/; return strcasecmp(a,b); } // end of comparison int main(int i, char **v){ printf("'%s' '%s'", v[1], v[2]); printf("=> %d\n", s(v[1], v[2])); // 0 if equalish return 0; }  ## zsh, 85 bytes [$(for x in $@;{tr -d \ <<<$x|tr A-Z a-z|fold -1|sort|paste -sd x}|uniq|wc -l) = 1 ]

Input as command line arguments, output as return code.

The for syntax makes this Bash-incompatible.

[               # test...
$(for x in$@;  # map over arguments
{tr -d \ <<<$x # remove spaces |tr A-Z a-z # lowercase |fold -1 # put each character on its own line |sort # sort lines |paste -sd x # remove all newlines except last }|uniq # take only unique lines |wc -l # how many lines remain? ) = 1 ] # if only 1 line left, it must have been an anagram  # Japt, 12 bytes N®v ¬n ¬xÃä¥  Test it online! ### How it works  // Implicit: N = array of input strings N® Ã // Take N, and map each item Z to: v ¬n // Take Z.toLowerCase(), split into chars, and sort. ¬x // Join and trim off whitespace. ä¥ // Reduce each pair of items (that's exactly one pair) X and Y to X == Y.  # GNU Sed, 33 Score includes +2 for -rn options to sed. This is almost a direct port of @FryAmTheEggman's Retina answer: : s/(\w)(.*,.*)\1/\2/i t /\w/Q1  Ideone. ## Perl, 34 33 + 1 = 34 bytes s/(.)(.*,.*)\1/$2/i?redo:say!/\w/

Requires the -n flag and the free -M5.010|-E:

$perl -M5.010 -ne's/(.)(.*,.*)\1/$2/i?redo:say!/\w/' <<< 'hello, lloeh'
1

How it works:

                                   # '-n' make a implicit while loop around the code
s/(.)(.*,.*)\1/$2/i # Remove a letter that occurs on both sides of the comma. ? redo: # Redo is a glorified goto statement that goes to the top of the while loop say!/\w/ # Check to see if any letter is left  Thanks to msh210 for suggesting using ternary operators to save one byte # Baloch Gyr, 9 bytes {ṇ₁cḷ}ᵐpᵈ  Try it online! Truthy/falsy output is achieved through predicate success/failure, this being Brachylog. Previously saved a byte using cṇ₁cḷḍ instead of {ṇ₁cḷ}ᵐ under the assumption that the two input strings would be the same length minus whitespace, but I realized that it would succeed where it should fail on Ah Hass, haha. { }ᵐ For both strings in the input, ṇ₁ split on spaces, c concatenate, ḷ and lowercase. pᵈ The strings are permutations of each other.  # PHP, 109 94 bytes function f($x){return str_split((trim($x));}function g($x,$y){return array_diff(f($x),f($y));}  Blech, the two function/returns are killing me here. Returns the difference between two string inputs as an array of characters. PHP considers [] falsy, satisfying the return requirements. • function($x,$y){$S=str_split;return array_diff($S(trim($x)),$S(trim($y)));} --> 75 bytes. Creates an anonymous function that returns the result. I've removed that long function and replaced the calls to str_split with an assignmed variable, to shorten it up. – Ismael Miguel Feb 25 '16 at 16:52
• Nice. I was tweaking it to reduce it to the one function, this is two steps ahead of that, well done. – ricdesi Feb 25 '16 at 16:56

# Bash + GNU utilities, 51

f()(fold -1<<<${@^^}|sort) f$1|diff -qBw - <(f $2)  • Define a function f() which: • ${@^^} converts all parameters to upper case
• fold -1 splits chars - one per line
• sorts lines
• call diff with -q to suppress full diff output and -Bw to ignore whitespace changes

## Pyke (commit 30, noncompetitive), 9 bytes

Fl1dk:S)q

Explanation:

F      )  -  for _ in eval_or_not(input())
l1       -     ^.lower()
dk:    -    ^.replace(" ", "")
S   -   sorted(^)
q - ^==^

# Mathematica, 77 76 bytes

StringMatchQ[##,IgnoreCase->1>0]&@@(""<>Sort[Characters@#/." "->""]&/@{##})&

The first part is actually one of my answers to another question!

# Pike, 54112109109 96 bytes

#define a(x) sort((array)replace(lower_case(x)," ",""))
int s(mixed i){return a(i[0])==a(i[1]);}

mixed happens to be shorter than array(string).

s returns 1 if its arguments are anagrams.

## Q, 25 Bytes

f:{~/{x@<x:x@&~^x:_x}'x}

NOTE.- counting include function name f: to facilitate tests (as lambda we can decrement 2 Bytes)

match over {ascending not null lower x} each x

{.. x ..} is an anonymous function with arg x
_x        lowers string x
&~^x      where not null x (space is considered null)
x@..      selects elements of x according to indexes ..
<x        ascending indexes of x (not values). Ex <"cab" is 1 2 0
x@<x      ascending values of x (x at ascending indexes of x)
~         match (diad function). Ex "one"~"one" is true
f'..      applies function f for each argument ..
f/..      applies function f over elements of sequence (fold)

Test

f("Lynn";"Nyl N")
f("Digital Trauma";"Tau Digital Arm")
f("Sp3000";"P S 3000")
f("Manage Trash So";"Those anagrams")
f("Calvins Hobbies";"Helka Homba")
f("Android";"rains odd")
f("In between days";"bayed entwine")
f("Code golf";"cod elf got")

generates (1b = true, 0b = false)

1b
1b
1b
1b
0b
0b
0b
0b

General-purpose language (APL derivative, specialized in data processing) developed by kx.com. Free full functional evaluation version for Windows/Linux/MacOS.

• What do you mean, other languages are not serious? :-P – Luis Mendo May 21 '16 at 8:59
• If the f is required for the code to evaluate properly, then it must be counted. Otherwise, just leave it off of your submission code, and only use it in examples to show how to assign the function. – Mego May 21 '16 at 9:28
• Of course, other languages are as serious as Q. I beg my poor english. But some languages sacrifices readability or are equiped with libraries ad-hoc for this type of contests. Q is a 'general purpose language', in spite of the fact that code is not very readable. – J. Sendra May 21 '16 at 16:59
• You only need to assign x once if you lower later, thus k)~/{x@<x:_x@&~^x}' for 17 bytes.. but I'd say it's 19 as you need the k) bracket as this is K code rather than Q... – streetster Sep 27 '17 at 14:15

## APL, 31 chars

{≡/{x[⍋x←('.'⎕R'\u0')⍵~' ']}¨⍵}

To be used so:

    {≡/{x[⍋x←('.'⎕R'\u0')⍵~' ']}¨⍵}'Sp3000' 'P S 3000'
1

In English:

• { ... }¨⍵: for each of the two elements of the argument
• x←('.'⎕R'\u0')⍵~' ': transform to uppercase (using a regex...) the string without the spaces and assign the temporary result to x
• x[⍋x]: sort x
• ≡/: compare the two results of the sorting: if they match, return 1.
• Is it possible to try it online? I tried with this but I don't really know how to use it – Luis Mendo Jun 28 '16 at 11:49
• Sure. Here: definition after which you can just type f 'first avatar' 'second avatar' – lstefano Jun 28 '16 at 12:56
• Thanks! Maybe add that to the answer? So that people can try – Luis Mendo Jun 28 '16 at 13:28
• –9: ≡/{x[⍋x←0~⍨32|⎕UCS⍵]}¨ – Adám Jun 28 '16 at 15:27
• @Adám: that won't work because ≡/{x[⍋x←0~⍨32|⎕UCS⍵]}¨'pp' '00' gives 1. – lstefano Jun 29 '16 at 8:52

# Java, 218 Bytes

First time I've ever written Java...

Golfed:

import java.util.Arrays;boolean M(String a,String b){char[]A=a.toUpperCase().replace(" ","").toCharArray();char[]B=b.toUpperCase().replace(" ","").toCharArray();Arrays.sort(A);Arrays.sort(B);return Arrays.equals(A,B);}

Ungolfed:

import java.util.Arrays;
public class ManageTrashSo {
public boolean M(String a, String b) {
char[] A = a.toUpperCase().replace(" ", "").toCharArray();
char[] B = b.toUpperCase().replace(" ", "").toCharArray();
Arrays.sort(A);
Arrays.sort(B);
return Arrays.equals(A, B);
}
}

Testing:

    ManageTrashSo manageTrashSo = new ManageTrashSo();

//True
System.out.println(manageTrashSo.M("Lynn", "Nyl N"));
System.out.println(manageTrashSo.M("Digital Trauma", "Tau Digital Arm"));

//False
System.out.println(manageTrashSo.M("Android", "rains odd"));
System.out.println(manageTrashSo.M("In between days", "bayed entwine"));

• I know it's been almost a year, but you can golf it by 32 bytes like this: boolean f(String...a){java.util.Arrays x=null;String[]A=g(a[0]),B=g(a[1]);x.sort(A);x.sort(B);return x.equals(A,B);}String[]g(String a){return a.replace(" ","").toUpperCase().split("");} (186 bytes) Or if you convert it to a Java 8 lambda, it can be: a->b->{java.util.Arrays x=null;String[]A=g(a),B=g(b);x.sort(A);x.sort(B);return x.equals(A,B);};String[]g(String a){return a.replace(" ","").toUpperCase().split("");} (167 bytes). Here is a TIO with test code. – Kevin Cruijssen Sep 27 '17 at 11:48

# Japt, 10 bytes

v á øVrS v

Try it

# Ruby, 50 bytes

def f;gets.upcase.chars.sort.join.strip;end
p f==f

Writing f=->{...} and f[]==f[] is just as long. :(

## PowerShell, 81 bytes

param([char[]]$a,[char[]]$b)-join($a-replace' '|sort)-eq-join($b-replace' '|sort)

A slight rewrite of my answer on the linked Anagram challenge.

Takes input as char-arrays, performs a -replace operation to remove spaces, sorts them (which sorts alphabetically, not by ASCII value), then -joins them back into a string. The -eq in PowerShell is by default case-insensitive, but here it must be performed on strings, as [char]'a' is not equal to [char]'A', hence the reason for -join.

# Perl, 35 bytes

Include +1 for -p

Somewhat abusive since it depends on the program being given on the commandline.

perl -pe'<>=~s%\S%*_=s/$&//i?_:0%reg;$_=!//'

Then give the strings as 2 consecutive lines on STDIN

A very abusive solution is 30 bytes:

perl -ne'<>=~s%\w%1/!s/$&//i%reg;1/!//'  This crashes if the strings are not anagrams and therefore gives a false exit code from the point of view of the shell. It also gives garbage on STDERR for that case. If the strings are anagrams the program is silent and gives a "true" exit code # PHP, 89 bytes for(;$i++<2;)$r[]=count_chars(join(explode(" ",strtolower($argv[$i]))));echo$r[0]==$r[1];  Try it online! # PHP, 94 bytes for(;$i++<2;sort($x),$r[]=trim(join($x)))$x=str_split(strtolower($argv[$i]));echo$r[0]==$r[1];

Try it online!

# Excel VBA, 122 Bytes

Anonymous VBE immediate window Function that takes input from range [A1:B1] and outputs to the VBE immediate window

a=Replace([A1]," ",""):b=Replace([B1]," ",""):For i=1To Len(a):b=Replace(b,Mid(a,i,1),"|",,1,1):Next:?b=String(len(a),"|")

## C#, 378 bytes

I need a handicap!!

https://dotnetfiddle.net/FNDt0E

using System;
using System.Linq;
using System.Text;

public class Program
{

public static void Main()
{
var l = "Hello World";

var r = "Red Who Loll";

var y = new Func<string,string>(s => new String(s.ToLower().Replace(" ","").OrderBy(v => v).ToArray()));
var z = new Func<string,string,Func<string,string>,bool>((w,x,f) => f(w) == f(x));
var o = z(l, r, y);

Console.WriteLine("{0} & {1} are anagram: {2}",l, r, o);

Console.WriteLine("C#, {0} bytes", Encoding.Unicode.GetByteCount(@"var y = new Func<string,string>(s => new String(s.ToLower().Replace("" "","""").OrderBy(v => v).ToArray()));
var z = new Func<string,string,Func<string,string>,bool>((w,x,f) => f(w) == f(x));"));

}

}

• Welcome to Programming Puzzles & Code Golf! General rule is to put your language together with your byte count in the headline of your post. You can do that by adding a leading #` to the first line. Also for code-golf questions it is required to golf your program. For the start you should remove unecessary whitespaces and use single-character variable names. Also you can always use a function instead of a full program (unless explicitly forbidden) to save some more bytes. – Denker Feb 28 '16 at 0:40
• @DenkerAffe you ninja'd me :) – cat Feb 28 '16 at 0:40
• Why all the whitespace?? – CalculatorFeline Mar 6 '16 at 20:32


text:
# Problem with RandomColor

I was trying to produce a little animation with Manipulate, where a Regular Poligon with N sides is displayed behind the previous polygon with N-1 sides , each one with a RandomColor. I wrote this piece of code:

Manipulate[
Graphics[Reverse[
Style[RegularPolygon[#], RandomColor[]] & /@ Range[3, l, 1]]] , {l,
3, 8, 1}]

The problem is that the color keeps changing even for the Polygons on the front. How can I avoid this? Once the color for a polygon is fixed it should not change anymore.

A simple approach is to use SeedRandom to block the randomness of RandomColor when Seed keeps the same. But the drawback of this method is that in multiple runs, the color will keep the same.

Manipulate[Graphics[Reverse[
Style[RegularPolygon[#], SeedRandom[#]; RandomColor[]] & /@
Range[3, l, 1]]], {l, 3, 8, 1}]

So, to aviod this, a yet simple method is to set SeedRandom's content a bit more random:

k = RandomInteger[{1,1000}];

Manipulate[Graphics[Reverse[
Style[RegularPolygon[#], SeedRandom[k #]; RandomColor[]] & /@
Range[3, l, 1]]], {l, 3, 8, 1}]

Then everything will be fine!

• oh thanks, i am relatively new to mathematica but i am really enjoying it. update:nvm it was wrong – Alucard Aug 12 '16 at 6:55

You should only generate the colors once.

With[{colors = RandomColor[8 - 2]},
Manipulate[
Graphics[{{colors[[# - 2]], RegularPolygon[#]} & /@ Range[n, 3, -1]}],
{n, 3, 8, 1, SetterBar}]]

Here is my revision

color = RandomColor[6];
Manipulate[
Graphics[{color[[# - 2]], RegularPolygon[#]} & /@ Range[l, 3, -1]],
{l, 3, 8, 1}]

• how would you modify the code if you don't want to preeventively store the entire set of colors before using manipulate? suppose I set the upper limit of manipulate at 5, , the other colors stored are wasted – Alucard Aug 12 '16 at 7:15
• This seems to duplicate my earlier answer. What value does it add over my answer? – m_goldberg Aug 12 '16 at 7:35
• i upvoted both. i asked him a question because i saw his message was just 1 minute old and i thought he would be still online. – Alucard Aug 12 '16 at 7:43


text:
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 It is currently 21 Oct 2019, 20:44

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# S99-03

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58398

### Show Tags

16 Sep 2014, 01:53
00:00

Difficulty:

75% (hard)

Question Stats:

51% (02:03) correct 49% (01:45) wrong based on 51 sessions

### HideShow timer Statistics

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58398

### Show Tags

16 Sep 2014, 01:53
Official Solution:

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

Since each cucumber is 99% water by weight, each one is also 1% something else (say, "mush.") So each cucumber is 99% water and 1% mush. That means that all the cucumbers together are 99% water and 1% mush. Since the total weight is 100 pounds, the weight of the mush is equal to $$0.01(100) = 1$$ pound, and the weight of the water is 99 pounds.

After the water evaporates, each cucumber is 98% water. Therefore, we know that all the cucumbers together are 2% mush and 98% water. The key point is that the amount of water changed, but the amount of mush has not. Thus, we should equate the amount of mush BEFORE with the amount of mush AFTER.

If we call the new, unknown weight of the cucumbers $$x$$, then the weight of the mush after evaporation is 2% of $$x$$, or $$0.02x$$.

Now, we can equate the weight of the mush before and after:

1 pound $$= 0.02x$$

$$\frac{1}{0.02} = x$$

$$x = 50$$

The new weight of the bag is 50 pounds.

_________________
Intern
Joined: 15 Jul 2018
Posts: 7
GMAT 1: 700 Q47 V39

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15 Sep 2018, 09:39
another possible explanation:

100*99/100 - X*100/100=(100-X)*98/100, where X is the amout of evaporated water

When solve we get X = 50, thus 100 - 50 = 50.

Please correct me if I am wrong.
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21 Nov 2018, 16:02
I think this the explanation isn't clear enough, please elaborate. 99% of water by WEIGHT contributed to 99 pounds.

98% of water by WEIGHT contributed to 50 pounds?
Before extra matter was 1% i.e. 1 pound.
After that there is no information whether extra matter increased or changed? Only change in water component is mentioned.

Regards
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03 Aug 2019, 16:05
Bunuel wrote:
Official Solution:

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

Since each cucumber is 99% water by weight, each one is also 1% something else (say, "mush.") So each cucumber is 99% water and 1% mush. That means that all the cucumbers together are 99% water and 1% mush. Since the total weight is 100 pounds, the weight of the mush is equal to $$0.01(100) = 1$$ pound, and the weight of the water is 99 pounds.

After the water evaporates, each cucumber is 98% water. Therefore, we know that all the cucumbers together are 2% mush and 98% water. The key point is that the amount of water changed, but the amount of mush has not. Thus, we should equate the amount of mush BEFORE with the amount of mush AFTER.

If we call the new, unknown weight of the cucumbers $$x$$, then the weight of the mush after evaporation is 2% of $$x$$, or $$0.02x$$.

Now, we can equate the weight of the mush before and after:

1 pound $$= 0.02x$$

$$\frac{1}{0.02} = x$$

$$x = 50$$

The new weight of the bag is 50 pounds.

Hi Bunuel,

Would X be referring to the new total weight? Since 1lbs (Mush) = 0.02 (% of total weight that is mush) x 'X' (Total weight) and as such, the weight of the water would be 98% of X, which would be 0.98*50 = 49?

I am still unsure of how you got to your answer and would like to know what you and others think
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03 Aug 2019, 23:13
Tlo19 wrote:
Bunuel wrote:
Official Solution:

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

Since each cucumber is 99% water by weight, each one is also 1% something else (say, "mush.") So each cucumber is 99% water and 1% mush. That means that all the cucumbers together are 99% water and 1% mush. Since the total weight is 100 pounds, the weight of the mush is equal to $$0.01(100) = 1$$ pound, and the weight of the water is 99 pounds.

After the water evaporates, each cucumber is 98% water. Therefore, we know that all the cucumbers together are 2% mush and 98% water. The key point is that the amount of water changed, but the amount of mush has not. Thus, we should equate the amount of mush BEFORE with the amount of mush AFTER.

If we call the new, unknown weight of the cucumbers $$x$$, then the weight of the mush after evaporation is 2% of $$x$$, or $$0.02x$$.

Now, we can equate the weight of the mush before and after:

1 pound $$= 0.02x$$

$$\frac{1}{0.02} = x$$

$$x = 50$$

The new weight of the bag is 50 pounds.

Hi Bunuel,

Would X be referring to the new total weight? Since 1lbs (Mush) = 0.02 (% of total weight that is mush) x 'X' (Total weight) and as such, the weight of the water would be 98% of X, which would be 0.98*50 = 49?

I am still unsure of how you got to your answer and would like to know what you and others think

Hope my solution helps: https://gmatclub.com/forum/each-of-the- ... ml#p795199
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05 Aug 2019, 11:00
Bunuel wrote:
Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

99% water leaves with 1% weight of the cucumbers but we dont know what exactly is the 1% of weight is or say .01 1lbs
and later new weight of cucumber is 98% water and 2 lbs
we can equate 1=.02x
x= 50
IMO B
Re: S99-03   [#permalink] 05 Aug 2019, 11:00
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# S99-03

Moderators: chetan2u, Bunuel


text:
Integral involving $$\Gamma$$ function [entire topic moved]

Grigorios Kostakos on Tuesday, January 08 2013, 01:58 PM
0

Evaluate $\displaystyle\int_{0}^{1}\log({\Gamma(x+1)})\,dx\,,$ where $$\Gamma(x)$$ is the gamma function.

Grigorios Kostakos
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text:
what is fluid displacement comparator & how does it works?

The fluid displacement comparator is a linear measurement device and it is based on the fluid displacement principle.

Fluid displacement comparator is a type of comparator which works on the basic principle of fluid displacement and capillary action.

Let’s see the construction of the fluid displacement comparator.

Contents

Construction (or) parts of fluid displacement comparator:

This comparator is constructed using the following parts,

• Diaphragm
• Fluid Chamber
• Plunger
• Capillary tube
• Scale
• Pointer

Fluid chamber

The Fluid chamber acts as a pool, which contains fluid in the large cross-sectional area. The fluid in the chamber is low viscous in nature.

Diaphragm

The diaphragm is fitted at the bottom of the fluid chamber. It is made up of a flexible material. It acts as a pressure transmission element in this comparator.

Plunger

The plunger is a pressure sensing element in this comparator. One end of the plunger is attached with the diaphragm and the other end is set free. This free end detects the change in pressure.

Capillary tube

It is a glass tube with a fine bore where capillary action takes place. It is fitted along with the fluid chamber.

Scale

A measuring scale is fixed parallel to the capillary tube. There are two limit fingers (such as high-limit finger and low-limit finger) in the measuring scale.

Pointer

The pointer on the measuring scale is set at the free height fluid. Due to temperature changes, the fluid expands in the same way as in the thermometer, hence the pointer is required to indicate the free height of the fluid in the capillary tube.

The above-stated parts are used to construct a fluid displacement comparator. Now let’s see its working principle.

Working principle of fluid displacement comparator:

• Fluid displacement and capillary action are the basic principles used in the fluid displacement comparator.
• The surface of the workpiece to be measured is placed under the measuring plunger.
• The movement of the plunger occurs due to the small difference on the surface of the workpiece.
• Due to the movement of the plunger, the diaphragm placed at the bottom of the fluid chamber start to deflect. This is because the pressure is transmitted to the diaphragm by the plunger movement.
• When the diaphragm deflects, a small amount of fluid is displaced from the fluid chamber to the capillary tube.
• The level of fluid rises at a certain point limit above its free height.
• The rise in the fluid is directly measured by a scale fixed parallel to the capillary tube. The limit pointers (or) limit fingers may be set relative to this to indicate the high and low limits of the fluid in the capillary tube.

Magnification of fluid displacement comparator:

The magnification of this comparator is obtained by the ratio of the cross sectional area of the chamber to the tube cross sectional area.$$\displaystyle \text{Magnification = }\frac{{{{D}^{2}}}}{{{{d}^{2}}}}$$

Applications of fluid displacement comparator:

This comparator has limited applications when compared to other comparators. The certain applications of this comparator are stated below.

• It is used for laboratory testing purposes.
• It is also used as an inspection tool.

The certain advantages of this comparator are stated below.

• It is based on a simple working principle.
• Easy to operate.
• It is portable.
• It is cheap in cost.
• The entire design setup is simple.


text:
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If $A$ is an $n\\times n$ matrix with $|\\sum_{i,j=1}^na_{i j} s_i t_j | \\leq 1$ for all vectors $s, t$ with $|s_i|, |t_i| \\leq 1,$ then there exists a constant $K_G(n),$ independent of the choice of $A,$ such that $$\\sup |\\sum_{i,j}^n a_{i j} <x_i , y_j > | = K_G(n),$$ where the supremum is taken over all unit vectors $x_1,..., x_n; y_1,...,y_n$ of a Hilbert space $H.$ Grothendieck proved that the limit of $K_G(n)$ remains finite as $n \\to \\infty$ and is the universal constant $K_G$ known as the Grothendieck constant. The exact value of the constant $K_G,$ which depends no the ground field, is not known. We will give an elementary proof, due to Kirvine, of this inequality and discuss many of its surprising consequences.