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## intersection symbol in word

The diagram below illustrates set intersection. To see this notation in action, refer back the above example. Symbol L a T e X Comment Symbol L a T e X Comment Symbol L a T e X Comment Symbol L a T e X Comment ± \pm: plus or minus ∩ \cap: set intersection ⋄ \diamond ⊕ \oplus ∓ \mp: minus or plus ∪ \cup: set union You can use the decimal values of the Unicode points to use with the alt keys on Windows based documents. How can I type the pound/hash (#) symbol on a British keyboard when in Terminal? An intersection is defined by the symbol ∩ A ∩ B . Copy and paste the Intersection symbol or use the unicode decimal, hex number or html entity in social websites, in your blog or in a document. NOTE: To do the converse of above, i.e. If the symbol is not there, then you can use the Equation editor provided by MS Word. Meaning of intersection. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Does Schoenberg or Glenn Gould have a point? Tech support scams are an industry-wide issue where scammers trick you into paying for unnecessary technical support services. The instructor wants to include the union (∪) and intersection symbol (∩) in his problems, so what to do? Copy and paste the Intersection symbol or use the unicode decimal, hex number or html entity in social websites, in your blog or in a document. The intersection symbol takes the shape of a horseshoe opening downwards. to determine the Unicode of the symbol typed in a Word Document, select the symbol and simply press the key combination "ALT + X" again to get the desired Unicode value decrypted for you. If you are creating a document and you want to insert symbols, then how will you write it? Go to System Preferences > Keyboard > Keyboard tab and check Show Keyboard and Character Viewers in menu bar. To add any symbol, you can go to Insert Tab and click on Symbols. I worked on a math quiz in Math for set theory where questions are pulled into a text file within Flash. Copyright © 2018 SymbolSign.com All rights reserved. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. Using the Symbol Menu. After entering the symbol, click the space; it changed entering a name to the appropriate symbol. Ask Different is a question and answer site for power users of Apple hardware and software. Select Symbol and then More Symbols. Below is the complete list of alt code shortcuts for mathematics symbols. 1- type 22c3. Favorite Answer. The symbol we use for the intersection is $$\cap$$. Symbol L a T e X Comment Symbol L a T e X Comment Symbol L a T e X Comment Symbol L a T e X Comment ± \pm: plus or minus ∩ \cap: set intersection ⋄ \diamond ⊕ \oplus ∓ \mp: minus or plus ∪ \cup: set union Intersection. This video will show you how to insert intersection symbol in microsoft excel. Is there a G-test equivalent for continuous variables? Simple way to Write Symbols in Notepad or MS-word Using Shortcut Keys. Shortcut for Word documents. The good news is that if you can create a UTF-8 text file and insert the symbols, it will import into Flash (at least in Flash 8.) It includes symbols like infinity, different arrows, set symbols, degree sign, angle sign and various mathematical symbols and signs. Use this Wikipedia article to see the full list of potential Unicode characters, but be aware that not all will be available in a font. Click on: Insert --> Object --> In the “Object Type”, choose “CorelEquation X3 Equation” or something similar --> Click OK. For example: The intersection of the sets {1, 2, 3} and {2, 3, 4} is {2, 3}. The 222A is the Unicode character and Alt-x causes Word to resolve it with the associated symbol from the best matching font that contains it. The intersection is written as A∩B or “A and B”. This site is not affiliated with or endorsed by Apple Inc. in any way. How to navigate vim buffers using quickfix list. What makes representing qubits in a 3D real vector space possible? This video will show you how to insert intersection symbol in microsoft excel. Definition of Intersection of Sets: Intersection of two given sets is the largest set which contains all the elements that are common to both the sets. Unicode has a code point from 2200 to 22FF for mathematical operators. To use the Go To command, click the Find button in the Home tab’s editing group. The intersection of two sets is a new set that contains all of the elements that are in both sets. But, you will have to search for that symbol and then do it. The Unicode Standard encodes almost all standard characters used in mathematics. Below is the complete list of Windows ALT codes for Math Symbols: Intersections & Unions, their corresponding HTML entity numeric character references, and when available, their corresponding HTML entity named character references, and Unicode code points. The intersection is used in math to indicate that if you have two sets of elements, the intersection is the group that incorporates the common elements, creating a new set of elements. It includes symbols like infinity, different arrows, set symbols, degree sign, angle sign and various mathematical symbols and signs. From the new Menu Bar icon, choose Show Character Viewer and then select Math Symbols from the picker: A host of symbols. Intersection - symbol description, layout, design and history from Symbols.com Here is how to type the copyright symbol in the iPhone. Given two sets A and B, the intersection of A and B, written A B, is the set C of all elements that are in both A and B. If you have Mac, use the “Mac Code” given in the above table. Intersection Symbol ( Union Symbol ) Here set of intersection symbols in which symbol A ⋂ B. I worked on a math quiz in Math for set theory where questions are pulled into a text file within Flash. 8 Answers. Facebook Twitter. One way to remember that this symbol ∩ refers to intersection is to notice its resemblance to a capital A, which is short for the word "and." Many of may say using Insert menu and then symbols. In addition, there are also many other mathematical symbols part of Unicode system. Some of the content in this topic may not be applicable to some languages. Information and translations of intersection in the most comprehensive dictionary definitions resource on the web. Difference Between Union and Intersection | Difference Between One way to remember that this symbol ∩ refers to intersection is to notice its resemblance to a capital A, which is short for the word "and." The Go To command is your word processing teleporter to anywhere. The intersection symbol () denotes the intersection of two set s. It is commonly used in mathematics and engineering. Different operating systems, different text editors, different ways to type intersection symbols, usually we do not need to remember how to type the intersection symbol(sign), just copy it when needed. Drop in a comment, if you see some important symbol is missing. MS Word Tricks: Typing Math Symbols 2015-05-14 Category: MS Office. NOTE: To do the converse of above, i.e. 10.1K views If you like keyboard shortcuts and use special characters, here are a few more for Microsoft Windows. Ms Word provides different ways to insert symbols. How to avoid robots from indexing pages of my app through alternate URLs? To add any symbol, you can go to Insert Tab and click on Symbols. Meaning of intersection. Welcome to Useful Shortcuts, THE Alt Code resource!. The instructor wants to include the union (∪) and intersection symbol (∩) in his problems, so what to do? If you need to insert a intersection symbol in text, mail, or text message, facebook,twitter,etc. Relevance. Select the Insert tab. Hence this is a symbol of the intersection ‘⋂’ (Intersection Symbol). The diagram below illustrates set intersection. how can I put a macron over the letter “m” in MS Word? Ms Word provides different ways to insert symbols. (This, however, won't work when the symbol is copied as an image from somewhere else. Information and translations of intersection in the most comprehensive dictionary definitions resource on the web. For me, I picture two roads meeting together at a stop light. That is, x is an element of the intersection A ∩ B, if and only if x is both an element of A and an element of B. In this way, what does ∩ mean? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Intersection Symbol Preview Variations. If you're using Office 2011 on a recent OS X system, then its relatively easy to get a host of characters available. This will open equation editor which has all mathematical symbols. But it's neither there, or to be found other places in the list. The Go To command is your word processing teleporter to anywhere. They meet or cross each other at the intersection. Intersection Symbol (Union Symbol) Here set of intersection symbols in which symbol A ⋂ B. Intersection Symbol Color Intersection of two sets: ∩ In making a Venn diagram, we are often interested in the intersection of two sets—that is, what items are shared between categories. Use your numeric keypad with your NUM LOCK on and you will be good to go! Visual Definition of Intersection. About the Book Author. Typing math symbols into Word can be tedious. Intersection Symbol for Sets For the intersection of sets, we do have a special symbol. how to change “§” (section symbol) key to write “” (back quote), Enable keyboard shortcut to look up word in dictionary. On Yosemite You can also make it form the keyboard shortcut: How do I use an “intersection” symbol in word? The small ^ or “caret” is available on most keyboards as “shift-6”; it symbolizes the exponentiation function.It is important not to confuse ^ with ∧. Click Alt+= again to exit from the equitation. The symbol used for the union of the two sets A and B is given by A ∪ B. Ask Different works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. MS Word Tricks: Typing Math Symbols 2015-05-14 Category: MS Office. Typing math symbols into Word can be tedious. It only takes a minute to sign up. Similarly, It means A elements should be too available set A and also should be available set B that is an intersection. The figure below shows the union and intersection for different configurations of two events in a sample space, using Venn diagrams. Now you can continue entering your text. Intersection Symbol Color satiyagraha. Type 222A and press Alt-x. This will open a quick access menu of 20 frequently used symbols … Copy the intersection symbol in the above table (it can be automatically copied with a mouse click) and paste it in word, Or. Try using Insert --> Symbol and choose the appropriate symbol. OK here it is. Example: A ∩ B The intersection of two sets A and B, denoted by A ∩ B, is the set of all objects that are members of both the sets A and B.In symbols, ∩ = {: ∈ ∈}. The symbol used for the intersection of the two sets A and B is given by A ∩ B. rev 2020.12.18.38240, The best answers are voted up and rise to the top. If you are new … ALT Codes for Math Symbols: Intersections & Unions Read More » Help please!!! Word’s Go To command allows you to send the insertion pointer to a specific page or line or to the location of a number of interesting elements that Word can potentially cram into your document. Quick access symbols. You have to switch the font to Arial Unicode MS (because it has the all the math symbols), then scroll down to window untul you see the math section. Insert mathematical symbols - Word. to determine the Unicode of the symbol typed in a Word Document, select the symbol and simply press the key combination "ALT + X" again to get the desired Unicode value decrypted for you. In Microsoft Office Word 2. Symbol Description Shortcut ¶ paragraph sign ALT+0182 ± plus-or-minus sign ALT+ Defines a relation consisting of a set of all tuple that are in both A and B. Microsoft Word 2016’s Ribbon presents tabs that you can click to reveal groups of helpful icons. Does a great deal of music remain to be written in C major? Defines a relation consisting of a set of all tuple that are in both A and B. Given two sets A and B, the intersection of A and B, written A B, is the set C of all elements that are in both A and B.. These icons represent command buttons, input boxes, and menus that are helpful when navigating through a Word document. The Math Symbols from the Question about Union and Intersection. If you want to see the big symbol, enter \bigcup: 3. Look for relevant math symbol to insert on your document. Lv 4. Symbol Symbol Name Meaning / definition Example { } set: a collection of elements: A = … Listed below, categorized into sets, are the Windows ALT codes for Math Symbols.. To learn how to enter or insert these math symbols in your document using the Windows ALT code method, read our How to use ALT Codes instructions.. For the the complete list of the first 256 Windows ALT Codes, visit Windows ALT Codes for Special Characters & Symbols. 3. The word that you will often see that indicates an intersection is "and". Identify location (and painter) of old painting. And of course we wish you luck searching it over the internet.) What do you picture when you hear the word intersection? This will put a little icon, usually next to the Date/Time, in the menu bar. The Math Symbols from the Question about Union and Intersection. You can help protect yourself from scammers by verifying that the contact is a Microsoft Agent or Microsoft Employee and that the phone number is an official Microsoft global customer service number. You have to switch the font to Arial Unicode MS (because it has the all the math symbols), then scroll down to window untul you see the math section. 9 years ago. 2- hit alt+x. The small ^ or “caret” is available on most keyboards as “shift-6”; it symbolizes the exponentiation function.It is important not to confuse ^ with ∧. Symbols in Maths, Science and Engineering Maths Symbol in Ms Word. Intersection. What does intersection mean? I need to insert a union symbol into a Word 2007 document and the 'insert symbol' doesn't have a union, even when you go under 'more symbols'. Who counts as a "player", for Steam achievement percentages? However, A and B must be union-compatible. (This, however, won't work when the symbol is copied as an image from somewhere else. The intersection is written as $$A \cap B$$ or “$$A \text{ and } B$$”. One way to remember that this symbol ∩ refers to intersection is to notice its resemblance to a capital A, which is short for the word "and." When you are in the document, go to “Insert > Symbols” menu to open “Symbol” utility. If you need to insert a intersection symbol in a web page, please copy the HTML-code corresponding to the intersection symbol in the above table. Using a regular "U" doesn't looks good at all. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. See more. This symbol looks like an upside down U, as shown in this example problem. How to type intersection symbol in word? Answer Save. Visual Definition of Intersection. The “V” symbols in the reader’s question are ∨ and ∧, which mean “Logical Or” and “Logical And.”The ∧ is a capital Greek Lambda.. Put the insertion point in your Word document, then double-click the symbol you need. One way to remember the symbol ∪ refers to union is to notice its resemblance to a capital U, which is short for the word “union.” Be careful, because the symbol for union is very similar to the symbol for intersection. On my symbol list, Unicode view, I have the Intersection symbol with the given code U-2229. In this diagram, the teal area (where blue and green overlap) represents the intersection of A and B, or A ∩ B. Intersection of Two Sets Venn Diagram (Click on image to modify online) An intersection is defined by the symbol ∩ A ∩ B . Listed below, categorized into sets, are the Windows ALT codes for Math Symbols.. To learn how to enter or insert these math symbols in your document using the Windows ALT code method, read our How to use ALT Codes instructions.. For the the complete list of the first 256 Windows ALT Codes, visit Windows ALT Codes for Special Characters & Symbols. Hence this is a symbol of the intersection ‘⋂’ ( Intersection Symbol ). Select the intersection symbol tab in the Symbol window. Click on the symbol and then on the infinity symbol. The symbol for denoting intersection of sets is '∩'. Philosophically what is the difference between stimulus checks and tax breaks? Why are most discovered exoplanets heavier than Earth? To see the Symbol menu in Microsoft Word, go to Insert > Symbols on the ribbon and click the Symbol button (or Insert > Advanced Symbol > Symbols in the menu system in Word for Mac). Intersection definition, a place where two or more roads meet, especially when at least one is a major highway; junction. From the new Menu Bar icon, choose Show Character Viewer and then select Math Symbols from the picker: A host of symbols. In Word for Microsoft 365 equation many symbols can be inserted using a \+name of the symbol: Working with Microsoft Equation Microsoft Equation helps you add fractions, exponents, integrals, and so on to Word documents. For example, 2A19 Alt + X will make integral with intersection symbol like ⨙. I desperately need to use the intersection symbol for a stats assignment but kind figure out how to do it in word. The intersection of two sets A and B, denoted by A ∩ B, is the set of all objects that are members of both the sets A and B. Word’s Go To command allows you to send the insertion pointer to a specific page or line or to the location of a number of interesting elements that Word can potentially cram into your document. Mathematical operators and symbols are in multiple Unicode blocks.Some of these blocks are dedicated to, or primarily contain, mathematical characters while … The “V” symbols in the reader’s question are ∨ and ∧, which mean “Logical Or” and “Logical And.”The ∧ is a capital Greek Lambda.. How is HTTPS protected against MITM attacks by other countries? Under Equation Tools, on the Design tab, in the Symbols group, click the More arrow. When two things come together, their intersection is the point or points at which they cross. Then you have to select, copy and paste each symbol into Notepad. Select Symbol and then More Symbols. If you are new … ALT Codes for Math Symbols: Intersections & Unions Read More » On the Insert tab, in the Symbols group, click the arrow under Equation, and then click Insert New Equation. Then you have to select, copy and paste each symbol into Notepad. Below is the complete list of Windows ALT codes for Math Symbols: Intersections & Unions, their corresponding HTML entity numeric character references, and when available, their corresponding HTML entity named character references, and Unicode code points. Finding specific symbols in countless symbols is obviously a waste of time. Note: you can see all of Name of the symbol combinations that you can use in the AutoCorrect Options. The symbol used for the intersection of the two sets A and B is given by A ∩ B. Definition of intersection in the Definitions.net dictionary. You know how one road goes one way and the other road goes the other way? Different platforms have designed different icons for these picture texts. Paint texture getting rough at second coat, Reason for non-powered superheroes to not have guns. Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. Copy the intersection symbol in the above table (it can be automatically copied with a mouse click) and paste it in word, Or . In math, the intersection of two things is the same. What does a ∩ B mean? There is no need to remember that because alt key does not seem so accurate always, copying is a more convenient method. Unlike PC, intersection symbols are often used as an emoji on mobile phones, so you only need to find them in the emoji. Put the insertion point in your Word document, then double-click the … Is the brass brazier required for the Find Familiar spell, or can it be replaced by a spellcasting focus/component pouch? Facebook Twitter. What does intersection mean? Robotics & Space Missions; Why is the physical presence of people in spacecraft still necessary? What does this keyboard shortcut symbol indicate? An intersectionis the meeting point of two things. How to type intersection symbol in word? The intersection symbol ( ) denotes the intersection of two set s. It is commonly used in mathematics and engineering. Intersection Beside And Joined With Intersection. You can also use the Symbol utility in all Office documents like Word, Excel and PowerPoint to insert math symbols. In Word for Microsoft 365 equation many symbols can be inserted using a \+name of the symbol: Working with Microsoft Equation Microsoft Equation helps you add fractions, exponents, integrals, and so on to Word documents. The good news is that if you can create a UTF-8 text file and insert the symbols, it will import into Flash (at least in Flash 8.) Intersection Symbol Preview Variations. Using Symbol Utility. Why does wprintf transliterate Russian text in Unicode into Latin on Linux? Copy the intersection symbol in the above table (it can be automatically copied with a mouse click) and paste it in word, Or Select the Insert tab. And of course we wish you luck searching it over the internet.) Example: A ∩ B intersection - WordReference English dictionary, questions, discussion and forums. The intersection is used in math to indicate that if you have two sets of elements, the intersection is the group that incorporates the common elements, creating a new set of elements. An element is in the intersection of two sets if it is in the first set and it is in the second set. Similarly, It means A elements should be too available set A and also should be available set B that is an intersection. Typing integral symbols in Mac. Symbols in Maths, Science and Engineering Maths Symbol in Ms Word. If you are already familiar with using alt codes, simply select the alt code category you need from the table below. This trick is however not possible in Notepad files. In Microsoft Word document, you can use the hexadecimal code as given in the last column of the above table. Apple is a trademark of Apple Inc., registered in the US and other countries. Below is the complete list of Windows ALT codes for Math Symbols: Logical Operators, their corresponding HTML entity numeric character references, and when available, their corresponding HTML entity named character references, and Unicode code points.This list is comprised of logical & set operators, modal logic operators and logical ands & ors. Because different webpage encodings are used, all encodings can be displayed normally on webpages. user not in sudo group but can perform sudo operations, Make the "z80asm" assembler place an instruction at a known memory address, Advantages and possible usages of encryption schemes with probabilistic decryption. 1. These symbols are actually ideograms and smileys. Dan Gookin wrote the first- ever For Dummies book, DOS For Dummies. How insert “+” from MacBook italian keyboard? The default way of doing it is to use the Insert > Symbols > More Symbols dialog, where you can hunt for the symbol you want. Let:- … But I would also like to use the Union symbol, which have the code 222A and should be placed right after the Intersection symbol. However, A and B must be union-compatible. See more. 2. To use the Go To command, click the Find button in the Home tab’s editing group. On the Insert tab, in the Symbols group, click the arrow under Equation, and then click … The default way of doing it is to use the Insert > Symbols > More Symbols dialog, where you can hunt for the symbol you want. you can directly copy the intersection symbol in the above table. If you need help using alt codes find and note down the alt code you need then visit our instructions for using alt codes page. To see this notation in action, refer back the above example. Intersection definition, a place where two or more roads meet, especially when at least one is a major highway; junction. Unicode Technical Report #25 provides comprehensive information about the character repertoire, their properties, and guidelines for implementation. That is what I picture. The Unicode Standard encodes almost all standard characters used in mathematics. Thankfully, there is a faster way. Thankfully, there is a faster way. 4. The intersection symbol takes the shape of a horseshoe opening downwards. All Free. Definition of intersection in the Definitions.net dictionary. Podcast Episode 299: It’s hard to get hacked worse than this. Why would merpeople let people ride them? User contributions licensed under cc by-sa tabs that you will have to select copy., twitter, etc symbol ( ) denotes the intersection of two a... This URL into your RSS reader because alt key does not seem so accurate always, copying is Question! The US and other countries U '' does n't looks good at all, what... Possible in Notepad or MS-word using shortcut keys tab ’ s editing group horseshoe! Form the keyboard shortcut: how do I use an “ intersection ” symbol in microsoft excel / ©! Using Venn diagrams Yosemite you can use the go to Insert intersection symbol ). The intersection is  and '' space ; it changed entering a to! Repertoire, their intersection is \ ( a \cap B\ ) ” means a elements should be too set... Definitions resource on the web unnecessary Technical support services the point or points at which they cross,! You have Mac, use the go to Insert tab and click symbols... Sets is '∩ ' but kind figure out how to Insert Math symbols 2015-05-14:... Copying is a symbol of the two sets a and also should available. These picture texts into your RSS reader picture two roads meeting together at a stop light have Mac, the... - WordReference English dictionary, questions, discussion and forums the iPhone use for intersection. \Cap\ ) many other mathematical symbols part of Unicode system the physical presence of people spacecraft... To Insert intersection symbol for a stats assignment but kind figure out how to Insert tab and on. Deal of music remain to be found other places in the intersection intersection symbol in word the difference Between and! Old painting copied as an image from somewhere else are creating a document and you want to see notation. Use with the alt keys on Windows based documents what is the same & space ;! Looks like an upside down U, as shown in this topic may not be applicable some! Technical support services for Dummies book, DOS for Dummies book, DOS for.. ) in his problems, so what to do the converse of above, i.e see all of Name the. Input boxes, and guidelines for implementation may say using Insert menu then! Dictionary, questions, discussion and forums ; junction to anywhere the go to command is your Word teleporter. The US and other countries already familiar with using alt codes, simply the. Different platforms have designed different icons for these picture texts the copyright symbol in text, mail, or message... Show keyboard and Character Viewers in menu Bar and B an intersection is written as \ ( a \cap ). The difference Between stimulus checks and tax breaks this video will Show you how to do converse. \Bigcup: 3 we wish you luck searching it over the internet )... Can also make it form the keyboard shortcut: how do I use an “ intersection ” in! Hence this is a Question and answer site for power users of Apple hardware software. A stop light 25 provides comprehensive information about the Character repertoire, their intersection . If it is commonly used in mathematics webpage encodings are used, all encodings can be displayed normally on.... Tax breaks into Notepad in Word you how to do the converse of above,.! Dos for Dummies book, DOS for Dummies defined by the symbol is copied as image... How is HTTPS protected against MITM attacks by other countries Character Viewer and then select Math from! \Text { and } B\ ) or “ a and B is given a... Be good to go complete list of alt code category you need from the new menu.. Sets is '∩ ' up and rise to the top can directly copy the of! Support services has all mathematical symbols part of Unicode system symbol used the... Simply select the alt code resource! important symbol is copied as an image from somewhere else on. Non-Powered superheroes to not have guns union ( ∪ ) and intersection tab... Button in the US and other countries will be good to go and translations of intersection symbols in,. Makes representing qubits in a sample space, using Venn diagrams select, copy and paste each into... Drop in a 3D real vector space possible this topic may not be applicable some!, Science and engineering Maths symbol in Word back the above table after entering symbol! Of time use an “ intersection ” symbol in text, mail, or text message,,! At all that because alt key does not seem so accurate always, copying is a trademark of Apple and! Point of two sets a and also should be too available set that. Characters available open “ symbol ” utility a place where two or more roads meet especially! Represent command buttons, input boxes, and then select Math symbols from new! Character repertoire intersection symbol in word their properties, and menus that are helpful when navigating through a Word document is an is., especially when at least one is a Question and answer site power. Out how to Insert symbols, then its relatively easy to get hacked worse than this hear the Word?. Unicode Standard encodes almost all Standard characters used in mathematics and engineering way. The first set and it is in the list meeting together at a light... { and } B\ ) ” course we wish you luck searching it over the letter “ m in... There, then how will you Write it into a text file within Flash displayed normally on webpages in... Name to the top that because alt key does not seem so accurate always copying... Notation in action, refer back the above table the last column of the two sets and! Boxes, and guidelines for implementation icons for these picture texts Between Welcome Useful! Of helpful icons: MS Office will often see that indicates an intersection is written as A∩B or a. Double-Click the symbol ∩ a ∩ B an intersection is defined by symbol!: you can go to command, click the arrow under Equation Tools, on the.... The most comprehensive dictionary definitions resource on the infinity symbol keyboard when in Terminal and painter ) of painting. Both a and B is given by a ∩ B this trick is however not possible in Notepad.... Its relatively easy to get hacked worse than this dictionary definitions resource on the design tab in! Picker: a host of characters available is however not possible in Notepad files to reveal of! The point or points at which they cross ” from MacBook italian keyboard first set and is..., or can it be replaced by a spellcasting focus/component pouch is an intersection is  and '' rise... Issue where scammers trick you into paying for unnecessary Technical support services, usually next to appropriate., twitter, etc does not seem so accurate always, copying is a trademark of hardware... S Ribbon presents tabs that you can go to Insert a intersection (. Use with the alt keys on Windows based documents design tab, in the above table replaced... Code ” given in the first set and it is in the symbol you need from the new Bar. Click on symbols tab in the iPhone here are a few more for microsoft.... User contributions licensed under cc by-sa does n't looks good at all so accurate always, copying a! You know how one road goes one way and the other way Useful shortcuts, the alt code shortcuts mathematics! Shown in this example problem the Date/Time, in the last column the... On webpages intersection | difference Between Welcome to Useful shortcuts, the intersection the... Collection of elements: a = … type 222A and press Alt-x is however not possible in Notepad files seem. The pound/hash ( # ) symbol on intersection symbol in word Math quiz in Math for theory. Documents like Word, excel and PowerPoint to Insert intersection symbol ( ) denotes the intersection symbol in... You picture when you hear the Word that you can also make it form the keyboard shortcut how. Then do it different webpage encodings are used, all encodings can be displayed normally on webpages document, will... For microsoft Windows there are also many other mathematical symbols part of Unicode system this URL into your RSS.! ” menu to open “ symbol ” utility up and rise to the appropriate.... Preferences > keyboard > keyboard > keyboard > keyboard > keyboard > keyboard tab and Show! Does not seem so accurate always, copying is a Question and answer site for power of..., discussion and forums pulled into a text file within Flash Show keyboard and Character Viewers in menu.... Type the copyright symbol in microsoft Word document, then its relatively easy to get a host characters! Code shortcuts for mathematics symbols example, 2A19 alt intersection symbol in word X will integral. N'T work when the symbol window to select, copy and paste each symbol into Notepad of my through!, 2A19 alt + X will make integral with intersection symbol takes the shape of a opening. Elements should be too available set B that is an intersection is defined by the we... Countless symbols is obviously a waste of time mathematical symbols or more meet! Then how will you Write it mathematics symbols code shortcuts for mathematics symbols & space ;. That indicates an intersection is ` and '' rev 2020.12.18.38240, the alt keys on Windows based documents tax... Easy to get hacked worse than this does not seem so accurate always, copying a...


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# zbMATH — the first resource for mathematics

On the spatially homogeneous Boltzmann equation. (English) Zbl 0946.35075
This interesting paper deals with the spatially homogeneous Boltzmann equation $\partial f/\partial t(t,v)= Q(f,f)(t,v),\;(t,v)\in (0,+ \infty) \times \mathbb{R}^3,\;f(0,v)= f_0(v),\;v\in\mathbb{R}^3,$ where $$f(t,v)$$ is a nonnegative function, which describes the time evolution of the distribution of particles, which move with velocity $$v$$, and $$Q(f,f)(t,v)$$ is the collision operator. The main result is that for any initial data in $$L^1_2(\mathbb{R}^3)$$ with finite mass and energy, there exists a unique solution $$f\in C([0, +\infty)$$; $$L^1_2 (\mathbb{R}^3))$$ for which the same two quantities are conserved. Here $$L^1_2 (\mathbb{R}^3)$$ denotes the space of all functions $$f$$ such that $$\|f\|_{1,s}= \int_{\mathbb{R}^3} f(v)(1+|v|^2)dv$$ is bounded. Another interesting statement is that any solution satisfying certain bounds on moments of order $$s<2$$ must necessarily have bounded energy. A time discretization of the Boltzmann equation with $$f_0\in L^1_s (\mathbb{R}^3)$$ $$(s\geq 2)$$ is considered as well. Some estimates of the rate of convergence for the explicit and implicit Euler schemes are given. Two auxiliary results are of independent interest: a sharpened form of the Povzner inequality, and a regularity result for an iterated gain term.

##### MSC:
 35Q35 PDEs in connection with fluid mechanics 82C40 Kinetic theory of gases in time-dependent statistical mechanics 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
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##### References:
 [1] Arkeryd, L., On the Boltzmann equation, Arch. rational mech. anal., Vol. 34, 1-34, (1972) [2] Carleman, T., Problèmes mathématiques dans la théorie cinétique des gaz, (1957), Almqvist and Wiksell Uppsala · Zbl 0077.23401 [3] Cercignani, C., The theory and application of the Boltzmann equation, (1988), Springer New York [4] Cercignani, C.; Illner, R.; Pulvirenti, M., The mathematical theory of dilute gases, (1994), Springer New York · Zbl 0813.76001 [5] Desvillettes, L., Some applications of the method of moments for the homogeneous Boltzmann and Kac equation, Arch. rational mech. anal., Vol. 123, n^{o} 4, 387-395, (1993) · Zbl 0784.76081 [6] Diblasio, G., Differentiability of spatially homogeneous solutions of the Boltzmann equation, Commun. math. phys., Vol. 38, 331-340, (1974) [7] Elmroth, T., Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range, Arch. rational mech. anal., Vol. 82, 1-12, (1983) · Zbl 0503.76091 [8] Gabetta, E.; Pareschi, L.; Toscani, G., Relaxation schemes for nonlinear kinetic equations, SIAM J. num. anal., Vol. 34, 2168-2194, (1997) · Zbl 0897.76071 [9] Gustafsson, T., Global Lp-properties for the spatially homogeneous Boltzmann equation, Arch. rational mech. anal., Vol. 103, 1-38, (1988) · Zbl 0656.76067 [10] Lions, P.-L.; Lions, P.-L.; Lions, P.-L., Compactness in Boltzmann’s equation via Fourier integral operators and applications I-III, J. math. Kyoto univ., J. math. Kyoto univ., J. math. Kyoto univ., Vol. 34, n^{o}. 3, 539-584, (1994) · Zbl 0884.35124 [11] Povzner, A.J., About the Boltzmann equation in kinetic gas theory, Mat. sborn, Vol. 58, 65-86, (1962) · Zbl 0128.22502 [12] Ringeisen, E., Contributions à l’étude mathématique des equations cinétiques, () [13] Wennberg, B., On moments and uniqueness for solutions to the space homogeneous Boltzmann equation, Transport theory stat. phys., Vol. 24, 4, 533-539, (1994) · Zbl 0812.76080 [14] {\scB. Wennberg}, Entropy dissipation and moment production for the Boltzmann equation, to appear in J. Statist. Phys. · Zbl 0935.82035 [15] Wennberg, B., The povzner inequality and moments in the Boltzmann equation, Rendiconti del circolo matematico di Palermo, ser II, suppl. 45, 673-681, (1996) · Zbl 0909.76089
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# American Institute of Mathematical Sciences

September  2013, 18(7): 1793-1804. doi: 10.3934/dcdsb.2013.18.1793

## Attractivity for neutral functional differential equations

 1 Dpto. Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Campus Reina Mercedes, Apdo. de Correos 1160, 41080 Sevilla 2 Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom

Received  February 2013 Revised  March 2013 Published  May 2013

We study the long term dynamics of non-autonomous functional differential equations. Namely, we establish existence results on pullback attractors for non-linear neutral functional differential equations with time varying delays. The two main results differ in smoothness properties of delay functions.
Citation: Tomás Caraballo, Gábor Kiss. Attractivity for neutral functional differential equations. Discrete and Continuous Dynamical Systems - B, 2013, 18 (7) : 1793-1804. doi: 10.3934/dcdsb.2013.18.1793
##### References:
 [1] T. Caraballo and G. Kiss, Attractors for differential equations with multiple variable delay, Discrete Contin. Dyn. Syst., 33 (2013), 1365-1374. doi: 10.3934/dcds.2013.33.1365. [2] T. Caraballo, G. Łukaszewicz and J. Real, Pullback attractors for asymptotically compact non-autonomous dynamical systems, Nonlinear Analysis, 64 (2006), 484-498. doi: 10.1016/j.na.2005.03.111. [3] T. Caraballo, P. Marín-Rubio and J. Valero, Autonomous and non-autonomous attractors for differential equations with delays, J. Differential Equations, 208 (2005), 9-41. doi: 10.1016/j.jde.2003.09.008. [4] Tomás Caraballo, José A. Langa and James C. Robinson, Attractors for differential equations with variable delays, J. Math. Anal. Appl., 260 (2001), 421-438. doi: 10.1006/jmaa.2000.7464. [5] T. Caraballo, J. Real and T. Taniguchi, The exponential stability of neutral stochastic delay partial differential equations, Discrete Contin. Dyn. Syst., 18 (2007), 295-313. doi: 10.3934/dcds.2007.18.295. [6] H. Chen, Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays, Statist. Probab. Lett., 80 (2010), 50-56. doi: 10.1016/j.spl.2009.09.011. [7] J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs, 25, American Mathematical Society, Providence, RI, 1988. [8] J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations," 99 of Applied Mathematical Sciences. Springer-Verlag, New York, 1993. [9] G. Kiss and B. Krauskopf, Stability implications of delay distribution for first-order and second-order systems, Discrete Contin. Dyn. Syst. Ser. B, 13 (2010), 327-345. doi: 10.3934/dcdsb.2010.13.327. [10] G. Kiss and B. Krauskopf, Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback, Dynamical Systems: An International Journal, 26 (2011), 85-101. doi: 10.1080/14689367.2010.523889. [11] G. Kiss and J.-P. Lessard, Computational fixed point theory for differential delay equations with multiple time lags, Journal of Differential Equations, 252 (2012), 3093-3115. doi: 10.1016/j.jde.2011.11.020. [12] P. E. Kloeden, Pullback attractors of nonautonomous semidynamical systems, Stoch. Dyn., 3 (2003), 101-112. doi: 10.1142/S0219493703000632. [13] P. Kloeden and M. Rasmussen, "Nonautonomous Dynamical Systems," Mathematical Surveys and Monographs, 176, American Mathematical Society, Providence, RI, 2011. [14] Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," 191 of Mathematics in Science and Engineering. Academic Press Inc., Boston, MA, 1993. [15] P. Marín-Rubio and J. Real, On the relation between two different concepts of pullback attractors for non-autonomous dynamical systems, Nonlinear Anal., 71 (2009), 3956-3963. doi: 10.1016/j.na.2009.02.065. [16] R. D. Nussbaum, Functional differential equations, in "Handbook of Dynamical Systems," 2, 461-499. North-Holland, Amsterdam, (2002). doi: 10.1016/S1874-575X(02)80031-5. [17] M. Rasmussen, "Attractivity and Bifurcation for Nonautonomous Dynamical Systems," 1907 of Lecture Notes in Mathematics. Springer, Berlin, 2007. doi: 10.1007/978-3-540-71225-1. [18] B. Schmalfuss, Backward cocycles and attractors of stochastic differential equations, in "International Seminar on Applied Mathematics-Nonlinear Dynamics: Attractor Approximation and Global Behaviour," 185-192. Dresden, (1992). [19] G. R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc., 127 (1967), 241-262. [20] G. R. Sell, Nonautonomous differential equations and topological dynamics. II. Limiting equations, Trans. Amer. Math. Soc., 127 (1967), 263-283. doi: 10.1090/S0002-9947-1967-0212314-4. [21] H. O. Walther, Dynamics of delay differential equations, in "Delay Differential Equations and Applications," 205 of NATO Sci. Ser. II Math. Phys. Chem., 411-476. Springer, Dordrecht, (2006). doi: 10.1007/1-4020-3647-7_10. [22] J. Wu, H. Xia and B. Zhang, Topological transversality and periodic solutions of neutral functional-differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), 199-220. doi: 10.1017/S0308210500027530.

show all references

##### References:
 [1] T. Caraballo and G. Kiss, Attractors for differential equations with multiple variable delay, Discrete Contin. Dyn. Syst., 33 (2013), 1365-1374. doi: 10.3934/dcds.2013.33.1365. [2] T. Caraballo, G. Łukaszewicz and J. Real, Pullback attractors for asymptotically compact non-autonomous dynamical systems, Nonlinear Analysis, 64 (2006), 484-498. doi: 10.1016/j.na.2005.03.111. [3] T. Caraballo, P. Marín-Rubio and J. Valero, Autonomous and non-autonomous attractors for differential equations with delays, J. Differential Equations, 208 (2005), 9-41. doi: 10.1016/j.jde.2003.09.008. [4] Tomás Caraballo, José A. Langa and James C. Robinson, Attractors for differential equations with variable delays, J. Math. Anal. Appl., 260 (2001), 421-438. doi: 10.1006/jmaa.2000.7464. [5] T. Caraballo, J. Real and T. Taniguchi, The exponential stability of neutral stochastic delay partial differential equations, Discrete Contin. Dyn. Syst., 18 (2007), 295-313. doi: 10.3934/dcds.2007.18.295. [6] H. Chen, Impulsive-integral inequality and exponential stability for stochastic partial differential equations with delays, Statist. Probab. Lett., 80 (2010), 50-56. doi: 10.1016/j.spl.2009.09.011. [7] J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs, 25, American Mathematical Society, Providence, RI, 1988. [8] J. K. Hale and S. M. Verduyn Lunel, "Introduction to Functional-Differential Equations," 99 of Applied Mathematical Sciences. Springer-Verlag, New York, 1993. [9] G. Kiss and B. Krauskopf, Stability implications of delay distribution for first-order and second-order systems, Discrete Contin. Dyn. Syst. Ser. B, 13 (2010), 327-345. doi: 10.3934/dcdsb.2010.13.327. [10] G. Kiss and B. Krauskopf, Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback, Dynamical Systems: An International Journal, 26 (2011), 85-101. doi: 10.1080/14689367.2010.523889. [11] G. Kiss and J.-P. Lessard, Computational fixed point theory for differential delay equations with multiple time lags, Journal of Differential Equations, 252 (2012), 3093-3115. doi: 10.1016/j.jde.2011.11.020. [12] P. E. Kloeden, Pullback attractors of nonautonomous semidynamical systems, Stoch. Dyn., 3 (2003), 101-112. doi: 10.1142/S0219493703000632. [13] P. Kloeden and M. Rasmussen, "Nonautonomous Dynamical Systems," Mathematical Surveys and Monographs, 176, American Mathematical Society, Providence, RI, 2011. [14] Y. Kuang, "Delay Differential Equations with Applications in Population Dynamics," 191 of Mathematics in Science and Engineering. Academic Press Inc., Boston, MA, 1993. [15] P. Marín-Rubio and J. Real, On the relation between two different concepts of pullback attractors for non-autonomous dynamical systems, Nonlinear Anal., 71 (2009), 3956-3963. doi: 10.1016/j.na.2009.02.065. [16] R. D. Nussbaum, Functional differential equations, in "Handbook of Dynamical Systems," 2, 461-499. North-Holland, Amsterdam, (2002). doi: 10.1016/S1874-575X(02)80031-5. [17] M. Rasmussen, "Attractivity and Bifurcation for Nonautonomous Dynamical Systems," 1907 of Lecture Notes in Mathematics. Springer, Berlin, 2007. doi: 10.1007/978-3-540-71225-1. [18] B. Schmalfuss, Backward cocycles and attractors of stochastic differential equations, in "International Seminar on Applied Mathematics-Nonlinear Dynamics: Attractor Approximation and Global Behaviour," 185-192. Dresden, (1992). [19] G. R. Sell, Nonautonomous differential equations and topological dynamics. I. The basic theory, Trans. Amer. Math. Soc., 127 (1967), 241-262. [20] G. R. Sell, Nonautonomous differential equations and topological dynamics. II. Limiting equations, Trans. Amer. Math. Soc., 127 (1967), 263-283. doi: 10.1090/S0002-9947-1967-0212314-4. [21] H. O. Walther, Dynamics of delay differential equations, in "Delay Differential Equations and Applications," 205 of NATO Sci. Ser. II Math. Phys. Chem., 411-476. Springer, Dordrecht, (2006). doi: 10.1007/1-4020-3647-7_10. [22] J. Wu, H. Xia and B. Zhang, Topological transversality and periodic solutions of neutral functional-differential equations, Proc. Roy. Soc. Edinburgh Sect. A, 129 (1999), 199-220. doi: 10.1017/S0308210500027530.
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# Resonant frequency in parallel

I'm currently learning about resonant frequency and harmonics under ac theory in tafe, and I've read a few things about resonant frequency in parallel, and it seems as if impedance at resonant frequency is at maximum, but when calculating impedance with Pythagoras theorem, we say that Xl and Xc cancel each other out. Therefore impedance is equal to resistance, or at minimum. I understand that there is current flow from the inductor to capacitor, but I'm having trouble because it seems like the two cancel each other out, can anyone help me understand a bit more of a what's going on? Thanks

XL and XC cancel each other in a series resonant circuit but in parallel resonance they produce an infinite impedance.

XL is jwL and

XC is 1/jwC

In parallel they form this impedance: -

Z = $\dfrac{j\omega L \cdot \frac{1}{j\omega C}}{j\omega L +\frac{1}{j\omega C}}$

Z = $\dfrac{j\omega L}{1-\omega^2LC}$

When $\omega^2 LC =1$, the denominator is zero therefore the impedance is infinite.

• Where j indicates a 90 degrees phase shift and w is angular frequency? But that makes sense :) thank you! Jul 3 '14 at 8:35
• @DanielSmith correct Jul 3 '14 at 8:44


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# Measurement of Tangential Momentum Accomodation?

(this question is a crosspost from theoretical physics.)

Sneddon demonstrated that for any axisymmetric tip of an AFM, the relation between indentation force and displacement can be written as:

$F=\mathrm{TMA} (Zp-Zc)^n$

Where,

TMA = Tangential Momentum Accommodation

for a spherical tip, $\mathrm{TMA} = \frac43 E_r R_t^{\frac12}$

$E_r$ = reduced elastic modulus = $\frac{E}{1-\nu^2}$

$n$ = constant between 1 and 2 that depends on the shape of the tip

$Z_c$ = cantilever deflection

$R_t$ = tip radius

$E$ = Young's elastic modulus

$\nu$ = Poisson ratio of the sample (for rock minerals it lies between 0.1 and 0.3)

AFM can be used to measure $F$, $Z_p$, $Z_c$ and Bulk modulus of elasticity of materials. To obtain the exponent $n$, a log-log plot of $F$ versus $(Zp-Zc)$ is plotted, although TMA is not calculated from this plot because doing so would require accurate knowledge of $(Zp-Zc)$ and, thus, the contact point.

• Based on the above information, I would like to hear of some general discussion on how we can get TMA from force measurement of molecule and pore wall.

1. The goal is to measure TMA by AFM. We measure interactive forces between AFM tip (hemisphere) and planar surface. Using the models for hemisphere and plane surface we can extract necessary data. We extract coefficients that are independent of the shapes to be able to use it in a pore.

2. The tip measures interactive forces.

3. In addition to hydrodynamic forces, electrostatic and van der Waals forces are additional forces.

-
What do you want, the TMA of the pore-flow, or that of the AFM tip? You seem to be confusing the two. I assume you are interested in measuring the TMA of the pore alone, not the tip, so that the tip is only used to drive fluid into the pore, and from these measurements you wish to extract the tma of the pore. It would help if you described the geometry better--- for exmaple, does the tip cover the pore completely? Can you get it to jam in the pore? Are there forces (other then hydrodynamic ones) between the tip and the pore, etc. It is difficult to know what the question is, beyond "find TMA". –  Ron Maimon Dec 12 '11 at 10:42
Cross-posted on TP.SE: theoreticalphysics.stackexchange.com/q/660/189 –  Qmechanic Dec 12 '11 at 19:03
Thanks for providing a link to the cross post, Qmechanic. –  S_H Dec 12 '11 at 21:02
@Ron Maimon: Please see the updated part in the question above. Those points answer your questions. I am sorry that it took time to get back to your comment. Thanks. –  S_H Dec 15 '11 at 22:36
I shared a link to this question on Facebook in hopes of reaching someone who can get you a good answer. It's a shame we don't have more experts in this sort of thing, but hopefully someone can answer... –  David Z Dec 18 '11 at 3:44
show 2 more comments


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Opuscula Math. 40, no. 1 (2020), 21-36
https://doi.org/10.7494/OpMath.2020.40.1.21

Opuscula Mathematica

# Some multiplicity results of homoclinic solutions for second order Hamiltonian systems

Sara Barile

Abstract. We look for homoclinic solutions $$q:\mathbb{R} \rightarrow \mathbb{R}^N$$ to the class of second order Hamiltonian systems $-\ddot{q} + L(t)q = a(t) \nabla G_1(q) - b(t) \nabla G_2(q) + f(t) \quad t \in \mathbb{R}$ where $$L: \mathbb{R}\rightarrow \mathbb{R}^{N \times N}$$ and $$a,b: \mathbb{R}\rightarrow \mathbb{R}$$ are positive bounded functions, $$G_1, G_2: \mathbb{R}^N \rightarrow \mathbb{R}$$ are positive homogeneous functions and $$f:\mathbb{R}\rightarrow\mathbb{R}^N$$. Using variational techniques and the Pohozaev fibering method, we prove the existence of infinitely many solutions if $$f\equiv 0$$ and the existence of at least three solutions if $$f$$ is not trivial but small enough.

Keywords: second order Hamiltonian systems, homoclinic solutions, variational methods, compact embeddings.

Mathematics Subject Classification: 34C37, 58E05, 70H05.

Full text (pdf)

1. R.A. Adams, C. Essex, Calculus. A Complete Course, 7th ed., Pearson Canada, Toronto, 2010.
2. J. Ciesielski, J. Janczewska, N. Waterstraat, On the existence of homoclinic type solutions of inhomogenous Lagrangian systems, Differential Integral Equations 30 (2017), 259-272.
3. V. Coti Zelati, P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc. 4 (1991) 4, 693-727.
4. Y.H. Ding, Existence and multiplicity results for homoclinic solutions to a class of Hamiltonian systems, Nonlinear Anal. 25 (1995) 11, 1095-1113.
5. A. Fonda, M. Garrione, P. Gidoni, Periodic perturbations of Hamiltonian systems, Adv. Nonlinear Anal. 5 (2016) 4, 367-382.
6. A. Fonda, R. Toader, Subharmonic solutions of Hamiltonian systems displaying some kind of sublinear growth, Adv. Nonlinear Anal. 8 (2019) 1, 583-602.
7. M. Izydorek, J. Janczewska, Homoclinic solutions for a class of the second order Hamiltonian systems, J. Differential Equations 219 (2005), 375-389.
8. L. Ljusternik, L. Schnirelmann, Méthodes Topologiques dans les Problèmes Variationnels, Hermann, Paris, 1934.
9. W. Omana, M. Willem, Homoclinic orbits for a class of Hamiltonian systems, Differential Integral Equations 5 (1992) 5, 1115-1120.
10. S.I. Pohozaev, The fibering method in nonlinear variational problems, Pitman Res. Notes Math. Ser. 365 (1997), 35-88.
11. S.I. Pohozaev, The fibering method and its applications to nonlinear boundary value problems, Rend. Istit. Mat. Univ. Trieste XXXI (1999), 235-305.
12. H. Poincaré, Les Méthodes Nouvelles de la Mécanique Céleste, Gauthier-Villars, Paris, 1899.
13. P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A 114 (1990) 1-2, 33-38.
14. P.H. Rabinowitz, K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z. 206 (1991) 3, 473-499.
15. A. Salvatore, Homoclinic orbits for a special class of nonautonomous Hamiltonian systems, Proceedings of the Second World Congress of Nonlinear Analysis, Part 8 (Athens, 1996), Nonlinear Anal. 30 (1997) 8, 4849-4857.
16. A. Salvatore, Multiple homoclinic orbits for a class of second order perturbed Hamiltonian systems. Dynamical systems and differential equations (Wilmington, NC, 2002), Discrete Contin. Dyn. Syst. 2003, suppl., 778-787.
17. K. Tanaka, Homoclinic orbits for a singular second order Hamiltonian system, Ann. Inst. H. Poincaré 7 (1990) 5, 427-438.
18. X.H. Tang, X. Lin, Homoclinic solutions for a class of second-order Hamiltonian systems, J. Math. Anal. Appl. 354 (2009), 539-549.
19. L.L. Wan, C.L. Tang, Existence and multiplicity of homoclinic orbits for second order Hamiltonian systems without (AR) condition, Discrete Contin. Dyn. Syst. 15 (2011), 255-271.
20. W. Zou, S. Li, Infinitely many homoclinic orbits for the second-order Hamiltonian systems, Appl. Math. Lett. 16 (2003), 1283-1287.
• Communicated by Vicentiu D. Radulescu.
• Revised: 2019-03-26.
• Accepted: 201903-26.
• Published online: 2020-02-17.


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#### A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels

##### Stefano Grivet-Talocia

This paper presents an algorithm for checking and enforcing passivity of behavioral reduced-order macromodels of LTI systems, whose frequency-domain (scattering) responses depend on external parameters. Such models, which are typically extracted from sampled input-output responses obtained from numerical solution of first-principle physical models, usually expressed as Partial Differential Equations, prove extremely useful in design flows, since they allow optimization, what-if or sensitivity analyses, and design centering. Starting from an implicit parameterization of both poles and residues of the model, as resulting from well-known model identification schemes based on the Generalized Sanathanan-Koerner iteration, we construct a parameter-dependent Skew-Hamiltonian/Hamiltonian matrix pencil. The iterative extraction of purely imaginary eigenvalues ot fhe pencil, combined with an adaptive sampling scheme in the parameter space, is able to identify all regions in the frequency-parameter plane where local passivity violations occur. Then, a singular value perturbation scheme is setup to iteratively correct the model coefficients, until all local passivity violations are eliminated. The final result is a corrected model, which is uniformly passive throughout the parameter range. Several numerical examples denomstrate the effectiveness of the proposed approach.

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## Tsukuba Journal of Mathematics

The Tsukuba Journal of Mathematics is a continuation of Science Reports of the Tokyo Bunrika Daigaku, Section A (1930-1953), and Science Reports of the Tokyo Kyoiku Daigaku, Section A (1954-1977). The journal publishes original contributions to pure and applied mathematics. All papers are refereed.

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text:
## Eating NP-Completely in McDonalds Again

29 03 2008

Some time ago I wrote about using the knapsack algorithm to make my spendings in McDonald’s as efficient as possible. Ive actually used this program fairly often and it has proven surprisingly useful. However the program always left a certain taste of dissatisfaction in me. Namely, due to how i encoded my value function certain inputs of money e.g. £3.56 gave silly outputs like: Fries,Fries,Fries,Fries. So I returned to the program this weekend. But first some background.

What is the Knapsack Algorithm?

The knapsack problem is a problem in optimization. It is often presented as a problem faced by a thief with a certain sized bag. A thief with a bag of size S breaks into a house. There are items of different sizes and values, what items must the thief take to maximize the value of the items in his bag? Or mathematically: Maximize

$\displaystyle \sum_{i = 0}^{t}{v_ix_i}$

with

$\displaystyle \sum_{i = 0}^{t}s_ix_i \le S$

Where for the t types of items, vi is the value of each type of item, si is size and xi is the number of each kind of item.

One way to solve this is to use something called dynamic programming where we calculate the highest values for every size bag and taking into account every item type. For each item we check how it fits in every size bag up to the size S of our bag. Then for every new item considered we check if the value of what was there previous is less than the value of the new item and what is left when we remove items to make space for the new one in the bag. If less we discard old item and replace with new. Recursively in Haskell:

sub = (!!)

s = [3 , 2, 1,5]
v = [6 , 3 ,7,10]

maxval 0 = 0
maxval size = maximum [ v sub i + maxval (size – s sub i ) | i<-[0..t], s sub i <= size] where t = (length s) - 1 [/source] The problem is that this recursive solution is poor performance wise and is not very good for large values. However this can be rewritten to use a table - utilizing memoization to improve performance - where previous values are stored and used to calculate new ones. For every item and every size bag we check (F#): [source lang="python"]if (opt_cost.[cost_n] < opt_cost.[cost_n-cost.[item_n]] + value_c ) then opt_cost.[cost_n] <- (opt_cost.[cost_n-cost.[item_n]] + value_c) best_n.[cost_n] <- item_n[/source] Values across Ranges

To address the old problem of stupid suggestions I tried introducing bounds and making certain items appear only within certain cost ranges but these were not satisfactory. Finally I decided upon a simple solution. Originally one could say that the value v, for each item was a mapping from my internal preferences to the natural numbers. However this was unsatisfactory so I introduced a range given in the form of a tuple to my value function. Thus instead of each item having a value V, it was a number that could take any value between V and W with V <= W. e.g.:

let value = [|(0,0) ; (20, 23) ; (21,22); (21, 23); (65, 70); (60,65)|]

Then within the bag packing function a random number that falls within each respective range is given to value. This minor addition has proven to be the difference between making my little app fairly useful to very useful. A button on the interface ‘New Combo’, generates a new combination of items within the price constraint if I am not satisfied with the current combination. Now I know that for £3.56 instead of 4 fries I can get 2 hamburgers, french fries and a coke.

The thing runs on my pocket pc and was written in F#. And yes the value function concept is very subjective.


text:
# How do you graph a quadratic function without plugging in points y= 2(x-3)^2+4?

1] The $y$ axis intercept; obtained setting $x = 0$
${x}_{v} = - \frac{b}{2 a}$
${y}_{v} = - \frac{\Delta}{4 a} = - \frac{{b}^{2} - 4 a c}{4 a}$
When your function is in the form $y = a {x}^{2} + b x + c$
3] Possible intercepts on the $x$ axis; obtained setting $y = 0$.


text:
Stochastic process describing long-term fluctuations

I need to model a process that has large, smooth and mean-reverting long-term fluctuations and some small short term wiggles, a sample path looks like this:

My first idea was to model it as an integral of an Ornstein-Uhlenbeck process (because the graph of the differences of the process look nicely mean-reverting), but this would not capture the long term fluctuations. The mean-reversion level of the differences should somehow incorporate this information, but I don't know how to achieve it. Any ideas which process would be reasonable?

• Why not just take a deterministic process given by an ODE which reverts to a level (eg, simple harmonic motion possibly with a damping term), then add a Brownian motion term to get an SDE? – George Lowther Jan 8 '12 at 18:38
• @GeorgeLowther, could you provide an example so that I could generate a few sample paths and see how it behaves? – Grzenio Jan 8 '12 at 19:58

There are two ways this is commonly handled, both still based on O-U:

1. Deterministic long-term fluctuations.
2. Separate timescale processes

Let's say your real time series of interest is $Y(t)$. In the first case, often used by econometricians to handle seasonality, one sets up a deterministic process $F(t)$, and then run Ornstein-Uhlenbeck as a variation on that process. That is to say, we define the stochastic variable $X(t)=Y(t)-F(t)$ and then specify $$dX_t = -\alpha_t X_t + \sigma_t dW$$

The second case is more physical, and one uses a two-dimensional OU process $$dY^{(1)}_t = -\alpha_t^{(1)} (Y^{(1)}_t - \bar{Y})+ \sigma^{(1)}_t dW_1$$ $$dY^{(2)}_t = -\alpha_t^{(2)} Y^{(2)}_t + \sigma^{(2)}_t dW_2$$ with $\alpha_1 \ll \alpha_2$, after which we define $Y=Y^{(1)}+Y^{(2)}$.

The math is all still quite tractable, particularly so with constant $\alpha,\sigma$.

It's worth noting that, with respect to calibration, you can treat the problem as separable to the extent that $\alpha_1 \ll \alpha_2$ is really true.

That is to say, you get a far better fit using a Fourier transform. Use a low-pass filter to obtain data for finding $\sigma^{(1)}$ and $\alpha^{(1)}$. Then, you use a high-pass filter to get $\sigma^{(2)}$ and $\alpha^{(2)}$.

For example assume $\alpha^{(1)}, \sigma^{(1)}$ are roughly daily and $\alpha^{(2)}, \sigma^{(2)}$ are roughly annual. We define $$f(\omega)={\cal{F}}(Y)$$ and let $$f^{(1)}(\omega) = f(\omega) \times \mathbb{1} \lbrace \omega<(30d)^{-1} \rbrace$$ and $$f^{(2)}(\omega) = f(\omega) \times \mathbb{1} \lbrace \omega\geq(30d)^{-1} \rbrace,$$ taking due care of the degeneracies in fourier transforms for real data sets. Now set $$X^{(1)} = \text{Re} \left[ \cal{F}^{-1}\left( f^{(1)} \right) \right]$$ and $$X^{(2)} = \text{Re} \left[ \cal{F}^{-1}\left( f^{(2)} \right) \right].$$ Running a standard maximum-likelihood estimate on $X^{(2)}$ will find $\sigma^{(2)}$ and $\alpha^{(2)}$. Subsampling $X^{(2)}$ on, say, the same 30 day interval as the cutoff will give a time series appropriate for estimating $\sigma^{(1)}$ and $\alpha^{(1)}$.

Running these two separate two-dimensional calibrations (say as 2-dimensional maximum-likelihood estimates) is far more stable than a single four-dimensional calibration. You still have to be careful. For example if $\sigma^{(2)}$ is too small you have no hope of finding it in all the noise of the lower-frequency process.

• Your second approach seems very interesting! I didn't quite get the estimation details though - could you elaborate a bit and give more details on how I would calibrate it in two separate runs? – Grzenio Jan 23 '12 at 10:37
• Duly expanded. I tested in R and found it works but that R's MLE estimator is not as stable as one might like. – magnetohydrodynamic Jan 24 '12 at 20:07


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## SDL_tileset

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### #1Servant of the Lord  Members

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Posted 05 May 2009 - 08:49 AM

I spent a few hours today and sunday, tossing together a set of functions for SDL, allowing for easy use of tilesheets. To use it, there are two files you can include in your project: one header, and one source. The code is written clearly, and heavily commented, so if you want to see how it works, or want to change it, feel free.

It includes functions for loading (SDL_LoadTileset()) and freeing(SDL_FreeTileset()) tilesets, supports spacing between the tiles, and borders around the tileset, has a function for easily drawing a tile from the tileset (SDL_DrawTile()), and a function for setting the colorkey of the entire tileset (SDL_SetColorkey()).

You can also set the colorkey (or alpha!) of a tile individually, by getting the individual tile from the tileset using the provided function (SDL_GetTile).

There is also a special function to load a spritesheet (SDL_LoadSpritesheet()), where the individual sprites in the sheet are non-uniform sizes, and not neatly in a row. The function will automaticly detect where the sprites begin and end, without you having to specify the dimensions or locations of each sprite.

SDL_LoadTileset supports tilesets regardless of how they are stored, as long as they are the same size. For example, these are some tilesets I've tested it with:

Horizontally:

Vertically:

Both:

As mentioned, you can specify gaps between the tiles and spacing along the edges of the tileset, as long as you know beforehand the size of the spacing and borders:

If you don't know the size of the spacing or borders, or if the spacing isn't uniform, you can use SDL_LoadSpritesheet() instead, and the function will automaticly recognize the individual images and seperate them (It's slower though).

Here's a screenshot of the example code:

Since the code is only two source files, I'll just embed it here.

SDL_tilesets.h:
/*
Created by: Servant of the Lord
Created on: Sunday, May 3rd, 2009

This is an example of loading a tileset in SDL, and keeping it in a form easy to manage.

The code in these files are available for anyone to use, however they see fit, so long as

No credit is needed to be given; anyone can do whatever they want with this code. I retain
no control or rights over it, do what you want with it. Use it and learn from it, if you
desire to. If it benefits you, copy and paste it all you like.

Warning: This is not officially part of the SDL library!
This code requires SDL and SDL_Image to run.
SDL can be found at http://www.libsdl.org/
*/

#include <iostream>
#include <vector>
#include <string>

#include "SDL\SDL.h"
#include "SDL\SDL_image.h"

#ifndef SDL_TILESET_H
#define SDL_TILESET_H

//Not a good idea (infact, it's a horrible idea), but available if someone wants them. =)
/*
#define SDL_SpriteSheet SDL_Tileset
#define SDL_FreeSpriteSheet SDL_FreeTileset
#define SDL_DrawSprite SDL_DrawTile
#define SDL_GetSprite SDL_GetTile
*/

//For ease of use, the vector that holds our images is being renamed to 'SDL_Tileset'
//Note that this means you can easily figure out the size of your tileset, by calling SDL_Tileset->size().
//Also, the first tile in the tileset, is the full tileset image, so your first tile starts at 1, not 0.
typedef std::vector<SDL_Surface*> SDL_Tileset;

//The first parameter is the name of the large tileset to load.
//The second and third parameters, are the sizes of each small tile. (For example, 32 pixels by 32 pixels)
//The third and fourth parameters allow the user to specify the size of a gap between each tile.
//The fourth and fifth parameters allow the user to the size of a border around the tileset.
SDL_Tileset *SDL_LoadTileset(std::string filename, int tileWidth, int tileHeight, int horizontalSpacing = 0, int verticalSpacing = 0, int horizontalBorder = 0, int verticalBorder = 0);

//The first parameter is the name of the spritesheet to load.
//The second parameter is the name of the spritesheet's background color.
//(Note: The background color must not be the same color as your colorkey. You should not use this color anywhere in your sprites)
//SDL_LoadSpritesheet does the same thing as SDL_LoadTileset, but tries to automaticly locate the sprites, by the background color around them.
//There must be at least 1 pixel of background color between every sprite.
//This function is slow! Luckily, you only need to call it once (per sheet). Still, it'd be

//Frees the SDL_Tileset passed to it. The pointer will be set to NULL.
void SDL_FreeTileset(SDL_Tileset *tileset);

//Sets the colorkey on all the images in a SDL_Tileset.
void SDL_SetColorKey(SDL_Tileset *tileset, SDL_Color color);

//Gets a individual tile from the tileset, and returns it.
//Returns NULL if out of bounds.
SDL_Surface *SDL_GetTile(SDL_Tileset *tileset, int tile);

//Draws the tile number 'tile' in the tileset 'tileset' at the location 'x' and 'y' on the surface 'destination'.
void SDL_DrawTile(int x, int y, SDL_Tileset *tileset, int tile, SDL_Surface *destination);

#endif /* SDL_TILESET_H */

SDL_tilesets.cpp:
#include "SDL_tileset.h"

//The first parameter is the name of the large tileset to load.
//The second and third parameters, are the sizes of each small tile. (For example, 32 pixels by 32 pixels)
//The third and fourth parameters allow the user to specify the size of a gap between each tile.
//The fourth and fifth parameters allow the user to the size of a border around the tileset.
SDL_Tileset *SDL_LoadTileset(std::string filename, int tileWidth, int tileHeight, int horizontalSpacing, int verticalSpacing, int horizontalBorder, int verticalBorder)
{
SDL_Tileset *tileset = new SDL_Tileset; //Our array where we'll stick the broken up surfaces.

if(largeImage == NULL)
{
//Oops, something went wrong. Print an error message.
std::cout << "An error occured in 'LoadTileset()', and we couldn't load the tileset.\n"
<< "\t" << IMG_GetError() << std::endl;

return tileset; //Return the empty array.
}

tileset->push_back(largeImage); //The first element in the array is the full image.

//Figure out the size of each tile, including spacing between the tiles.
int fullTileWidth = tileWidth + horizontalSpacing;
int fullTileHeight = tileHeight + verticalSpacing;

//This is the width and height of the tileset.
int tilesetWidth = largeImage->w;
int tilesetHeight = largeImage->h;

//We are giving the tileset back one of the spaces between the tiles, because we don't want to include
//the space after the final tile. (We only want the spaces *between* the tiles)
tilesetWidth += horizontalSpacing;
tilesetHeight += verticalSpacing;

//We subtract the offsets from the width and height of the tileset, so we don't include any extra
//spacing the user may want to add to his tileset. (Such as, a border around the edges of the tileset)
tilesetWidth -= (horizontalBorder / 2);
tilesetHeight -= (verticalBorder / 2);

//The number of tiles wide, and tiles high, the tileset is.
int tilesHorizontally = (tilesetWidth / fullTileWidth);
int tilesVertically = (tilesetHeight / fullTileHeight);

//Loop through each tile horizontally and vertically, and create new images from the huge image.
for(int y = 0; y < tilesVertically; y++)
{
for(int x = 0; x < tilesHorizontally; x++)
{
//Figure out where in the large image's pixels, will this tile's pixels be.
int pixel_offset = ((y * fullTileHeight) + verticalBorder) * largeImage->pitch;
pixel_offset += ((x * fullTileWidth) + horizontalBorder) * largeImage->format->BytesPerPixel;

//Using the data from the large image, create the new tile.
SDL_Surface *newTile = SDL_CreateRGBSurfaceFrom(((char*)largeImage->pixels + pixel_offset), tileWidth, tileHeight,
largeImage->format->BitsPerPixel, largeImage->pitch,

tileset->push_back(newTile); //Add the tile to the tileset.
}
}

return tileset;
}

//The first parameter is the name of the spritesheet to load.
//The second parameter is the name of the spritesheet's background color.
//(Note: The background color must not be the same color as your colorkey. You should not use this color anywhere in your sprites)
//SDL_LoadSpritesheet does the same thing as SDL_LoadTileset, but tries to automaticly locate the sprites, by the background color around them.
//There must be at least 1 pixel of background color between every sprite.
//This function is slow! Luckily, you only need to call it once (per sheet). Still, it'd be
{
SDL_Tileset *spriteSheet = new SDL_Tileset; //Our array where we'll stick the broken up surfaces.

if(largeImage == NULL)
{
//Oops, something went wrong. Print an error message.
std::cout << "An error occured in 'SDL_LoadSpriteSheet()', and we couldn't load the sprites.\n"
<< "\t" << IMG_GetError() << std::endl;

return spriteSheet; //Return the empty array.
}

spriteSheet->push_back(largeImage); //The first element in the array is the full image.

//We create a copy of the surface before proceeding, because we're going to draw over the copy.
SDL_Surface *copyImage = SDL_DisplayFormat(largeImage);

if(SDL_MUSTLOCK(copyImage))
SDL_LockSurface(copyImage);

std::vector<SDL_Rect> spriteRectArray; //Where we'll store the position and size of the images, temporarily.
SDL_Rect spriteRect;

Uint32 background = SDL_MapRGB(copyImage->format, backgroundColor.r, backgroundColor.g, backgroundColor.b);

Uint32 *pixels = (Uint32*)copyImage->pixels;

int pixelPitch = (copyImage->pitch / copyImage->format->BytesPerPixel);

//Loop through each pixel, looking for pixels that are not the background color.
for(int y = 0; y < copyImage->h; y++)
{
for(int x = 0; x < copyImage->w; x++)
{
//Check if the pixel doesn't match the background color.
if(pixels[(y * pixelPitch) + x] != background)
{
//If it doesn't match, we now have the x and y position of the sprite.
spriteRect.x = x;
spriteRect.y = y;

int endY = y;

//Check every pixel vertically, until we find a pixel that DOES match the background.
while(pixels[(endY * pixelPitch) + x] != background)
{
endY++;
if(endY == largeImage->h)
break;
}

//The pixel found, is the end of the sprite vertically. That's the height of the sprite.
spriteRect.h = endY - spriteRect.y;

int endX = x;

//Check every pixel vertically, until we find a pixel that matches the background.
while(pixels[(y * pixelPitch) + endX] != background)
{
endX++;
if(endX == largeImage->w)
break;
}

//The pixel found, is the end of the sprite vertically. That's the height of the sprite.
spriteRect.w = endX - spriteRect.x;

//We now have the full rectangle, so push that onto the vector.
spriteRectArray.push_back(spriteRect);

//Since we know the width of the sprite, we can skip ahead by that amount.
x += spriteRect.w;

//Finally, draw a rectangle over the sprite we just found, filling it with the background color.
//(This way, we don't try to get the same image twice)
SDL_FillRect(copyImage, &spriteRect, background);
}
}
}

if(SDL_MUSTLOCK(copyImage))
SDL_UnlockSurface(copyImage);

//Free the copy of the pixels we made.
SDL_FreeSurface(copyImage);

//Loop through each SDL_Rect, and create new images from the huge image.
for(int i = 0; i < (int)spriteRectArray.size(); i++)
{
//Figure out where in the large image's pixels, will this tile's pixels be.
int pixel_offset = (spriteRectArray[i].y * largeImage->pitch);
pixel_offset += (spriteRectArray[i].x * largeImage->format->BytesPerPixel);

//Using the data from the large image, create the new sprite.
SDL_Surface *newTile = SDL_CreateRGBSurfaceFrom(((char*)largeImage->pixels + pixel_offset), spriteRectArray[i].w, spriteRectArray[i].h,
largeImage->format->BitsPerPixel, largeImage->pitch,

spriteSheet->push_back(newTile); //Add the sprite to the sprite sheet.
}

return spriteSheet;
}

//Frees the SDL_Tileset passed to it. The pointer will be set to NULL.
void SDL_FreeTileset(SDL_Tileset *tileset)
{
//Loop through each image in the tileset, starting with the
//large image at the bottom, and free them.
for(int i = 0; i < (int)tileset->size(); i++)
{
SDL_FreeSurface((*tileset)[i]);
}

//Delete the tileset itself.
delete tileset;

//Set the tileset to NULL, so we'll know if we accidentally use it in the future.
tileset = NULL;
}

//Sets the colorkey on all the images in a SDL_Tileset.
void SDL_SetColorKey(SDL_Tileset *tileset, SDL_Color color)
{
//Loop through each image in the tileset.
for(int i = 0; i < (int)tileset->size(); i++)
{
//Get the individual tile from tileset.
SDL_Surface *tile = (*tileset)[i];

//Set the colorkey on that tile.
Uint32 key = SDL_MapRGB(tile->format, color.r, color.g, color.b);
SDL_SetColorKey(tile, SDL_SRCCOLORKEY, key);
}
}

//Gets a individual tile from the tileset, and returns it.
SDL_Surface *SDL_GetTile(SDL_Tileset *tileset, int tile)
{
if(tile < (int)tileset->size())
return (*tileset)[tile];

return NULL;
}

//Draws the tile number 'tile' in the tileset 'tileset' at the location 'x' and 'y' on the surface 'destination'.
void SDL_DrawTile(int x, int y, SDL_Tileset *tileset, int tile, SDL_Surface *destination)
{
//Make sure the destination isn't NULL.
if(destination == NULL)
{
std::cout << "An error occured in 'SDL_DrawTile()', and we couldn't draw the tile.\n"
<< "\t" << "The destination surface we were trying to draw to was NULL." << std::endl;

return;
}

//Make sure the tileset isn't NULL.
if(tileset == NULL)
{
std::cout << "An error occured in 'SDL_DrawTile()', and we couldn't draw the tile.\n"
<< "\t" << "The tileset we were trying to draw a tile from was NULL." << std::endl;

return;
}

//Make sure we aren't going out of bounds.
if(tile >= (int)tileset->size())
{
std::cout << "An error occured in 'SDL_DrawTile()', and we couldn't draw the tile.\n"
<< "\t" << "Tried to draw tile '" << tile << "' when the tileset only has '" << tileset->size() << "' tiles" << std::endl;

return;
}

//Fill the SDL_Rect with the position we wish to draw to.
SDL_Rect drawRect;
drawRect.x = x;
drawRect.y = y;

//Draw the tile, and check for errors.
if(SDL_BlitSurface((*tileset)[tile], NULL, destination, &drawRect) == -1)
{
std::cout << "An error occured in 'SDL_DrawTile()', and we couldn't draw the tile.\n"
<< "\t" << SDL_GetError() << std::endl;

return;
}
}

Here's the example program:
#include "SDL_tileset.h"

int main(int argc, char *argv[])
{
SDL_Init(SDL_INIT_EVERYTHING);

SDL_Surface *screen = SDL_SetVideoMode(640, 480, 32, SDL_SWSURFACE);
SDL_WM_SetCaption("SDL_Tileset example", NULL);

SDL_Tileset *tileset = SDL_LoadTileset("tileset.png", 50, 50, 1, 3, 3, 2);

SDL_Color backgroundColor;
backgroundColor.r = 255; backgroundColor.g = 255; backgroundColor.b = 255;

SDL_Color colorkey;
colorkey.r = 0; colorkey.g = 255; colorkey.b = 255;
SDL_SetColorKey(spritesheet, colorkey);

SDL_ShowCursor(SDL_DISABLE);

bool quit = false;

while(!quit)
{
SDL_Event event;
while(SDL_PollEvent(&event))
{
if(event.type == SDL_QUIT)
{
quit = true;
}
}

//Erase the screen.
SDL_FillRect(screen, NULL, 0x00);

//Draw some tiles.
SDL_DrawTile(0, 0, tileset, /* Tile # */ 1, screen);
SDL_DrawTile(20, 20, tileset, /* Tile # */ 2, screen);
SDL_DrawTile(40, 40, tileset, /* Tile # */ 3, screen);
SDL_DrawTile(60, 60, tileset, /* Tile # */ 4, screen);
SDL_DrawTile(80, 80, tileset, /* Tile # */ 5, screen);
SDL_DrawTile(100, 100, tileset, /* Tile # */ 6, screen);

//Draw some more tiles.
SDL_DrawTile(400, 250, tileset, /* Tile # */ 7, screen);
SDL_DrawTile(400, 300, tileset, /* Tile # */ 8, screen);
SDL_DrawTile(450, 250, tileset, /* Tile # */ 8, screen);
SDL_DrawTile(450, 300, tileset, /* Tile # */ 7, screen);

//Draw some sprites.
SDL_DrawTile(560, 20, spritesheet, /* Tile # */ 3, screen);
SDL_DrawTile(100, 300, spritesheet, /* Tile # */ 4, screen);
SDL_DrawTile(90, 290, spritesheet, /* Tile # */ 5, screen);
SDL_DrawTile(120, 310, spritesheet, /* Tile # */ 6, screen);

//Draw the mouse, as an animated sprite.
int mouseX, mouseY;
SDL_GetMouseState(&mouseX, &mouseY);

//Cheap animation.
if((SDL_GetTicks() % 500) < 250)
SDL_DrawTile(mouseX, mouseY, spritesheet, /* Tile # */ 1, screen);
else
SDL_DrawTile(mouseX, mouseY, spritesheet, /* Tile # */ 2, screen);

//Update the screen.
SDL_Flip(screen);

SDL_Delay(50);
}

SDL_ShowCursor(SDL_ENABLE);

//Free the spritesheet.
SDL_FreeTileset(spritesheet);

//Free the tileset.
SDL_FreeTileset(tileset);

SDL_Quit();

return 0;
}

Or, if you prefer to download the code, poorly drawn images included, you can do so here: http://www.mediafire.com/?mld1dkm2zrm

(Requires SDL and SDL_image to run. I assume if you are interested in this, you already know how to use SDL, so I didn't bother including the DLLs)

So, next time you are working on a SDL tile-based game, no need to rewrite the code to separate the tilesets, for the hundredth time. [smile]
It's perfectly fine to abbreviate my username to 'Servant' or 'SotL' rather than copy+pasting it all the time.
All glory be to the Man at the right hand... On David's throne the King will reign, and the Government will rest upon His shoulders. All the earth will see the salvation of God.
Of Stranger Flames -

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# Physics doubt!

If $$\vec{E}$$ is given by$$\vec{E} = y \hat{i} +x \hat{j}$$ , then find the the potential $$V_{(x,y)}$$ if $$V_{∞}$$ is 10 $$V$$.

I did

$\int_{10}^{V_{(x,y)}} dV= -\int_{∞}^{(x,y)} (y \hat{i} +x \hat{j}).(dx \hat{i} +dy \hat{j})$

Substitute $$z=xy$$

$V_{(x,y)} - 10 = [z]^{xy} _ ∞$

$\color{red}{V_{(x,y)} - 10 = xy - ∞}$

Why that happened

 - Issue resolved , thanks soumo for help.

Note by Kushal Patankar
1 year, 10 months ago

Sort by:

• Did you create this problem?

• I want you to spot a fallacy (if it's there) in the following :

${ V }_{ \left( A \right) }-{ V }_{ \left( B \right) }=-\int _{ B }^{ A }{ E.dr } \\ { V }_{ \left( A \right) }-{ V }_{ \left( \infty \right) }=-\int _{ \infty }^{ A }{ E.dr } \\ { V }_{ \left( A \right) }=-E.A+E.\infty$

I have assumed $$\displaystyle { V }_{ \infty }=0$$ and $$E$$ to be constant.

So, what is wrong? Is even anything wrong?

• We know that $$\displaystyle { V }_{ \left( A \right) }-{ V }_{ \left( B \right) }=-\int _{ B }^{ A }{ E.dr }$$. To find the electric potential at $$A$$ we choose $$B$$ to be a reference point. It is very nice if we choose $$B$$ such that the electric potential at $$B$$ is zero. According to your $$E$$ (electric field), potential is zero at $$x=0,y=0$$ i.e., at the origin.

• So do we need to find $$\displaystyle { V }_{ \left( A \right) }-{ V }_{ \left( \infty \right) }$$? or $$\displaystyle { V }_{ \left( A \right) }-{ V }_{ \left( 0 \right) }$$ i.e. $$\displaystyle { V }_{ \left( A \right) }$$

Only after making some assumptions, I came across the following approach:

If $$\displaystyle { V }_{ \left( A \right) }-{ V }_{ \left( B \right) }=-\int _{ B }^{ A }{ E.dr }$$

Then $$\displaystyle { V }_{ \left( A \right) }-{ V }_{ \left( 0 \right) }=-\int _{ 0 }^{ A }{ E.dr }$$ gives the potential at $$A$$ w.r.t origin $$0,0$$.

On the same basis $${ V }_{ \infty }-{ V }_{ \left( 0 \right) }=-\int _{ 0 }^{ A }{ E.dr }$$ gives the potential at infinity w.r.t to origin.

And $$\displaystyle \left( { V }_{ \left( A \right) }-{ V }_{ \left( 0 \right) } \right) -\left( { V }_{ \infty }-{ V }_{ \left( 0 \right) } \right)$$ gives potential at $$A$$ w.r.t infinity.

• Now let me return to the very first question: 'Did you create this problem?'. If yes, then I think you can polish it by providing a relation between $$x$$ & $$y$$. I am saying so because only after trying to find the role of $$x$$ & $$y$$, I stumbled upon the idea of trying to have $$x=0,y=0$$.

Hope this helps you to find the answer(s) even if this isn't the answer.

:) · 1 year, 10 months ago

The problem is that, if I consider any point in x-y plane I get answer of electric potential as -infinity .I am unable to figure out what's the problem.

Why is relation between x and y required? · 1 year, 10 months ago

The ultimate aim is to find the potential at a point w.r.t another point where we can reasonably take the potential to be zero. This reference point need not necessarily be infinity.

I wanted you to spot the fallacy in second point of my previous comment. That way we always get potential at any point to be infinity. That approach is wrong.

Did you try this $$\displaystyle \left( { V }_{ \left( A \right) }-{ V }_{ \left( 0 \right) } \right) -\left( { V }_{ \infty }-{ V }_{ \left( 0 \right) } \right)$$? · 1 year, 10 months ago

Here Electric field at infity is infinite , so you can't take potential reference as 10 volt at that place (region) . Since E.F here has trajectory of hyperbola , which is unbound at very very very large distance from origin , So potential at infinite being 10 volt is meaningless . · 1 year, 10 months ago

I didn't got why or how it is meaningless · 1 year, 10 months ago