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https://www.gradesaver.com/textbooks/math/algebra/elementary-algebra/chapter-1-some-basic-concepts-of-arithmetic-and-algebra-chapter-1-test-page-39/1
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## Elementary Algebra
$7$
We start with the given expression: $6+(-7)-4+12$ Since there is only addition and subtraction here, we simply add and subtract from left to right: $-1-4+12=-5+12=7$
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2018-06-25 18:12:50
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http://www.r-bloggers.com/2011/10/page/3/
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# Monthly Archives: October 2011
## Batman Equation Happy Halloween! Plot the Batman logo in…
October 31, 2011
By
Batman Equation Happy Halloween! Plot the Batman logo in CloudStat with the legendary Batman Equation.
## Power Tools for Aspiring Data Journalists: R
October 31, 2011
By
Picking up on Paul Bradshaw’s post A quick exercise for aspiring data journalists which hints at how you can use Google Spreadsheets to grab – and explore – a mortality dataset highlighted by Ben Goldacre in DIY statistical analysis: experience the thrill of touching real data, I thought I’d describe a quick way of analysing
October 31, 2011
By
## Risk parity
October 31, 2011
By
Some thoughts and resources regarding a popular fund management buzzword. The idea Given asset categories (like stocks, bonds and commodities) create a portfolio where each category contributes equally to the portfolio variance. Two operations There are two cases in creating a risk parity portfolio: the universe is the asset categories the universe is the assets … Continue reading...
## Sampling for Monte Carlo simulations with R
October 31, 2011
By
$Sampling for Monte Carlo simulations with R$
I've knocked together a quick function for generating efficient Monte Carlo samples. It takes a bit of the legwork out of running Monte Carlo simulations.
## Using IUCN-Data, ArcMap 9.3 and R to Map Species Diversity
October 31, 2011
By
..I'm overwhelmed by the ever-growing loads of data that's made available via the web. I.e., IUCN collects and hosts spatial species data which is free for download. I'm itching to play with all this data... And, in the end there may arise ...
## Reading Excel data is easy with JGR and XLConnect
October 30, 2011
By
Despite the fact that Excel is the most widespread application for data manipulation and (perhaps) analysis, R's support for the xls and xlsx file formats has left a lot to be desired. Fortunately, the XLConnect package has been created to fill this void, and now JGR 1.7-8 includes integration with XLConnect package to load .xls
## Learning R: Project 1, Part 2
October 30, 2011
By
So it's been a week since I started down this path. I worked most of this out over last weekend, went to a conference, had hectic week at work, and then realized I lost my work. Gah.I'll be posting my general thoughts on R later. Most...
## Bayesian ideas and data analysis
October 30, 2011
By
Here is another Bayesian textbook that appeared recently. I read it in the past few days and, despite my obvious biases and prejudices, I liked it very much! It has a lot in common (at least in spirit) with our Bayesian Core, which may explain why I feel so benevolent towards Bayesian ideas and
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2014-10-31 13:43:39
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https://hal.inria.fr/hal-01194686
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# A variant of the Recoil Growth algorithm to generate multi-polymer systems
Abstract : The Recoil Growth algorithm, proposed in 1999 by Consta $\textit{et al.}$, is one of the most efficient algorithm available in the literature to sample from a multi-polymer system. Such problems are closely related to the generation of self-avoiding paths. In this paper, we study a variant of the original Recoil Growth algorithm, where we constrain the generation of a new polymer to take place on a specific class of graphs. This makes it possible to make a fine trade-off between computational cost and success rate. We moreover give a simple proof for a lower bound on the irreducibility of this new algorithm, which applies to the original algorithm as well.
Keywords :
Type de document :
Communication dans un congrès
Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.283-294, 2008, DMTCS Proceedings
Domaine :
Littérature citée [7 références]
https://hal.inria.fr/hal-01194686
Contributeur : Coordination Episciences Iam <>
Soumis le : lundi 7 septembre 2015 - 12:51:09
Dernière modification le : mercredi 10 mai 2017 - 17:41:11
Document(s) archivé(s) le : mardi 8 décembre 2015 - 13:02:36
### Fichier
dmAI0118.pdf
Fichiers éditeurs autorisés sur une archive ouverte
### Identifiants
• HAL Id : hal-01194686, version 1
### Citation
Florian Simatos. A variant of the Recoil Growth algorithm to generate multi-polymer systems. Roesler, Uwe. Fifth Colloquium on Mathematics and Computer Science, 2008, Kiel, Germany. Discrete Mathematics and Theoretical Computer Science, DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science, pp.283-294, 2008, DMTCS Proceedings. 〈hal-01194686〉
### Métriques
Consultations de la notice
## 177
Téléchargements de fichiers
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2018-01-19 01:59:37
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https://mathematica.stackexchange.com/questions/138090/expanding-summation-with-terms
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# Expanding Summation with terms
I'm trying to expand this series:
Sum[(Binomial[n - 1, k]*(-1)^k*(θ/T)^(n - 1 - k))/
(m - (k + 1)*α), {k, 0, n - 1}]
to look something like this:
1/(m - 5 α) - (4 (θ/T)^α)/(m - 4 α) + (6 (θ/T)^(2 α))/(m - 3 α) -
(4 (θ/T)^(3 α))/(m - 2 α) + (θ/T)^(4 α)/(m - α)
But I keep getting things like this..
(-2 m^3 α (5 T - 7 θ) (T - θ)^3 + m^4 (T - θ)^4 +
m^2 α^2 (T - θ)^2 (35 T^2 - 94 T θ + 71 θ^2) +
24 α^4 (T^4 - 5 T^3 θ + 10 T^2 θ^2 - 10 T θ^3 + 5 θ^4) -
2 m α^3 (25 T^4 - 122 T^3 θ + 234 T^2 θ^2 -
214 T θ^3 + 77 θ^4))/(T^4 (m - 5 α) (m - 4 α)
(m - 3 α) (m - 2 α) (m - α))
So, how expand summation to look more like
1/(m - 5 α) - (4 (θ/T)^α)/(m - 4 α) + (6 (θ/T)^(2 α))/(m - 3 α) -
(4 (θ/T)^(3 α))/(m - 2 α) + (θ/T)^(4 α)/(m - α)
Also, how can I format code in here better when I ask questions?
• Feb 18 '17 at 16:54
• Thanks, but how can I get the symbols like "Sigma" - I.e., have it look just like in my notebook...
– PiE
Feb 18 '17 at 17:07
• The object should be to make it easy for others to copy and paste your code so that they can provide help--not to make it look like your notebook. Feb 18 '17 at 17:12
I am not sure what you're trying as you didn't include that, but on my system:
n = 5;
Sum[(Binomial[n - 1, k]*(-1)^k*(θ/T)^(n - 1 - k))/(m - (k + 1)*α), {k, 0, n - 1}]
• Wow. Really? I just ran the same command on my system and put it in a closed form expression - the Hypergeometric Function 2F1...Wierd...What do you think is going on?
– PiE
Feb 18 '17 at 18:01
• Never mind the previous comment...Sorry...I'm kind of new to Mathematica stuff...When I type i "n = 5", and input it, then this works...
– PiE
Feb 18 '17 at 18:04
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2021-09-27 09:24:16
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https://frapier.net/td17wk/8153ad-heating-element-resistance
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Unlike the Peltier effect, this process is independent of the direction of current. Basically, in order to test a heating element with a multimeter, you can use the continuity test or the resistance test mode. Indirect Resistance Heating: In this method of heating, the current is passed through a wire or other high resistance material forming a heating element. The manufacturer will choose a suitable resistance wire to achieve this. Include your email address to get a message when this question is answered. Is my (layman's) understanding correct, that the same resistance-type heating element can be driven by single-phase 120V or 240V current; that a different design is not required, one for each voltage, for example, a heavier gauge for the 240V? conduction, convection and radiation. If the resistance is higher than calculated or it's infinite (so the circuit is open) you can assume that the heating element has gone bad. Let's check the maths: A heating element would draw half as much current at 120 volts as at 240 volts, and consume one quarter of the power. To learn more, see our tips on writing great answers. Wouldn't 2400W element max out a 120V 20A circuit? Convert negadecimal to decimal (and back). The following calculations give a guide to selecting an electrical resistance wire heating element for your application . With the spa on, test both of the leads on the element at the same time. What would cause a microwave to not heat up food? @TRomano, Yes but my understanding is that (ordinary convenience) circuits in 240-V countries are typically limited to less than 10 A, so wouldn't there also be an issue getting 2400 W in Europe? This resistance converts the electrical energy into heat which is related to the electrical resistivity of the metal, and is defined as the resistance ⦠sufficient heat or they fail mechanically, and in either case they must be replaced. MathJax reference. The dryer must have 220-240 volts when checking across the two outside terminals of the terminal block or it will not heat. Take care when dealing with electricity. A heating element generates heat when an electric current runs through it. Wouldn't it max out a 120V 20A circuit? Use MathJax to format equations. User manuals, specification sheets, CAD drawings and more. Is the maximum current a resistance can draw limited by the maximum current available (current rating) in the power supply? 240V Spas. Of course several sockets are grouped on one 16A circuit breaker, so the limit is both per socket (due to socket design etc) and per circuit. Heating Element Design Calculations. With either a digital or analog multimeter, make sure the probes are connected to the multimeter on one end and with the free ends, make contact with each of the open terminals on the heating element. 15 A is the limit on the typical circuit available on the kitchen counter. But, in fact, as I explained above, there are dozens of interrelated factors to consider in the design of a heating element that works effectively in a particular appliance. (An example calculation is shown in the tips section). To create this article, 27 people, some anonymous, worked to edit and improve it over time. So if we run the 100 V model on 200 V we will get 400 W output. The motor operates off of 110-120 volts and the heating elements must have 220-240 volts in order to produce heat. Would two such 1200W elements running simultaneously in parallel on the same 20A circuit max it out? Can I use lower gauge wire for short runs of longer high amp circuits? Some homework: \$P = VI \$. Integral solution (or a simpler) to consumer surplus - What is wrong? Why does Taproot require a new address format? If your heating element is a dumb resistor then: Thus the same resistor will draw 2x the current on 240V versus 120V. Thanks to all authors for creating a page that has been read 296,737 times. @TRomano, power is how quickly energy is moved or transformed. We can calculate the resistance required for our heater by rearranging Ohms's Law to \$R = \frac {V}{I} \$. Then remove the heating element using a socket or a wrench and you can now check the element as shown in first method. A given power rating, e.g. Heating elements found in common appliances are made from metallic resistance alloys such as Fe-Cr-Al and Ni-Cr(Fe). Metal resistance heating elements for furnaces are normally in the form of wire, strip or tube. They have the ability to produce temperatures hot enough to get the element to glow red hot, in the neighborhood of 1112°F (600°C) and above. This is a general guide to test any type of heating element for failure using an multimeter to measure the resistance of the element. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. If your breaker is not tripping but your hot tub still isnât heating, testing voltage to the heater using a multi-meter will help determine the cause. 开一个生日会 explanation as to why 开 is used here? Ask some one who is, such as an electrician or an electrical engineer. simulate this circuit – Schematic created using CircuitLab. If you're not confident in your ability to work with electricity then don’t do it. The Kanthal ® program of electric heating elements is the widest on the market. While all electrical devices carrying current produce heat by the Joule effect, a heating element is one specifically designed to do so. We use cookies to make wikiHow great. Electrical Engineering Stack Exchange is a question and answer site for electronics and electrical engineering professionals, students, and enthusiasts. Most likely the wire is already there as NFC15100 norm makes it mandatory to have it in the kitchen in all new construction. Is it a synonym for "energy"? If you really can’t stand to see another ad again, then please consider supporting our work with a contribution to wikiHow. Find a replacement heater element. How is the Q and Q' determined the first time in JK flip flop? Overview â heating element design and calculation. An introduction to electrical resistance of tape ⦠Current, voltage and resistance are related by Ohm's Law: E = I x R (E = voltage or electromotive force, I = current, and R = resistance in Ohms.). to decide the ISS should be a zero-g station when the massive negative health and quality of life impacts of zero-g were known? It's the same resistor, so the value of R does not change. Leverage Watlow's growing toolkit of calculators, equations, reference data and more to help design your thermal system. If so, how do they cope with it? How can I tell if the switch or the element is bad? Does your organization need a developer evangelist? Resistive heating elements are either composed of metallic alloys, ceramic materials, or ceramic metals. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. You can verify this easily as almost every modern multi-meter reports Vrms, as that is the more useful and informative value as opposed to peak values. ELECTRICAL RESISTANCE HEATING ELEMENTS: AN OVERVIEW In the field of electrical resistance heating, a variety of materials are available for use as heating elements. Back at the circuit breaker, does it make a difference? This information can usually be found on the refrigerator specifications which are usually in the fridge door cell. As an electrical current passes through the element, heat is generated due to the resistive nature of the elementâs design. We were typing at the same time. All tip submissions are carefully reviewed before being published. If your microwave oven quits heating food, it's time for a new microwave oven. The dryer can run if one leg of voltage is dead but the heating element will not heat. So 120 V x 20 A = 2400 W. Asking for help, clarification, or responding to other answers. Both are signs that one or both of your heating elements could be broken (as most water heaters have two heating elements). We often refer to electrical heatingâwhat heating elements doâas "Joule heating" or "resistance heating," as though resistance is the only factor that matters. Turn off the power to the electric hot water heater. I'm new to chess-what should be done here to win the game? Since we know that the hot water electrical circuit feeds 220 VAC to the 16 ampere heating element the resistance of that element is equal to 13.75 ohms. For a given power, a 240 volt heating element would have a thinner resistance wire (for higher resistance) than a 120 volt element. For the 200 V model we get \$R = \frac {200}{0.5} = 400 \; \Omega \$. wikiHow is where trusted research and expert knowledge come together. 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. A heating element would draw half as much current at 120 volts as at 240 volts, and consume one quarter of the power. We can round that number up to 14 ohms. So, the resistance is chosen as low as possible to produce more heat, but with caution to the risk of damage to the element if the power drawn is too much that canât be withstood by the element. There are other smarter resistors (ie, PTC) whose resistance increases as they get hot, so they kinda regulate the power they draw, but they're not very common. Ohm's Law Calculator 3-Phase Delta / Wye Calculator. The typical heating elements are made of steel or stainless steel. Some units are wired to plug into a wall socket, ⦠For a given power, a 240 volt heating element would have a thinner resistance wire (for higher resistance) than a 120 volt element. If you don’t know the value of the voltage used by the element you could measure the voltage between the terminals of the heating element with the device powered and on. As I understand it (but please correct me if I'm wrong), the difference is that the same element on 240V will draw half the amps that would be drawn if it were powered by 120V. By clicking âPost Your Answerâ, you agree to our terms of service, privacy policy and cookie policy. You wouldn't want to put a 2400Watt load on a 120V line. Dual voltage heater arrangement. If your oven isnât turning on or thereâs something wrong with the temperature in the oven when you cook, the problem may be a faulty heating element. Can the automatic damage from the Witch Bolt spell be repeatedly activated using an Order of Scribes wizard's Manifest Mind feature? Power in a resistor is given by \$P = VI \$ where. Our heating elements outperform in all temperature ranges, from element temperature 50 to ⦠Conversely, if we run the 200 V model on 100 V we will get 1/4 power or only 25 W. [From comments:] I'm trying to understand, from a consumer's perspective, not an engineer's, how a European company with a 240V kitchen 240V, let's call it a "countertop air cooking appliance", with a 2400W heating element, will be able to adapt that appliance to the US market with 120V. Forms of construction of furnace heating elements are shown in Figure 9.5. Technologies. 4.0 Transient Resistance Increase With every heat up, the resistance of the heater will increase as much as 6 percent. Please help us continue to provide you with our trusted how-to guides and videos for free by whitelisting wikiHow on your ad blocker. Let's see if we can make sense of it. A heating element converts electrical energy into heat through the process of Joule heating. A heating element has neither "very high" nor "very low" resistance. Podcast 291: Why developers are demanding more ethics in tech, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2, 4, and 9 UTC…. To create this article, 27 people, some anonymous, worked to edit and improve it over time. If the power is the same and the voltage doubles then what happens the current? I don't have my head around "power" yet. If your refrigerator or freezer is not cooling you should check to see if it is going through the automatic defrost cycle. Heating Element Design. 9.4.1 Heating-element construction for ovens and furnaces. wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. In the USA for example, your everyday, normal household AC Voltage does in fact equal Vrms=120V, and of course 2-phase AV Vrms=240V. Connect the two elements in series for 240 V operation and in parallel for 110 V operation. It only takes a minute to sign up. For a big cooking stove you'd run a 20A or 32A dedicated line, no socket, the equipment will have wire terminals. How should I test a two-speed electric motor? This article has been viewed 296,737 times. We know ads can be annoying, but they’re what allow us to make all of wikiHow available for free. At the heart of every electric space heater is a heating element. You are using the formulas for D/C power, but the voltage you are calculating with is Peak to Peak A/C. Substitute V/R for I in the power formula gives us P=V/R*V or V*V/R, so resistance of the element should be the voltage squared divided by the power. The heaters manufactured by WATTCO⢠all electric heaters with heater elements made out of specially designed electric heating rods. The resistance for any heating element can be calculated if you know the power in Watts (W). Good heater elements between 4.0 and 5.5kw should have the following results: * 9-12 ohms of resistance * good continuity * draw 15-25 amps at 240v. DeepMind just announced a breakthrough in protein folding, what are the consequences? wikiHow is a “wiki,” similar to Wikipedia, which means that many of our articles are co-written by multiple authors. Don't I need to convert it to Vrms first? If you use a very small resistance, most of the voltage is dropped across the internal resistance of the battery, and you get little voltage across the element and you get little heating. I need to do a little reading on the difference between "in series" and "in parallel". Overview â Heating Element Design and Calculation. Also, 20-A circuits are not common in residences in North America. Right kind of resistance wire for near-skin heater? Oven elements, also known as heating elements, are the coils on the top and bottom of your electric oven that heat up and glow red when you turn your oven on. Why do Arabic names still have their meanings? Making statements based on opinion; back them up with references or personal experience. I fixed a typo in my comment (should read "240V kitchen appliance"). Power formula states that P=IV. So you can use a 240V heater on 120V, it will just heat 4x less. The numerical conversion is already built into the standard. But then I realized that when resistance of the heating element is too low, power drawn will be too high and can cause excessive heating on the element. For our 100 W, 100 V heater we get \$R = \frac {100}{1} = 100 \; \Omega \$. it will also burn 4x the power on 240V versus 120V. Here is an introduction to electrical resistance of tape and wire heating elemets, a calculation of element resistance and a temperature-resistance table. Similarly, if the test you conduct produces a reading of zero resistance (meter's needle moves to the other extreme of the scale), then that is also indicative of a faulty heating element, and you should replace yours. To perform as a heating element the tape or wire must resist the flow of electricity. Do PhD students sometimes abandon their original research idea? 2. Generalized Power Equation, Ohm's Law and Ohm's Power Loss? Is it more efficient to send a fleet of generation ships or one massive one? How can one plan structures and fortifications in advance to help regaining control over their city walls? {"smallUrl":"https:\/\/www.wikihow.com\/images\/thumb\/7\/74\/Test-a-Heating-Element-Step-4-Version-2.jpg\/v4-460px-Test-a-Heating-Element-Step-4-Version-2.jpg","bigUrl":"\/images\/thumb\/7\/74\/Test-a-Heating-Element-Step-4-Version-2.jpg\/aid241792-v4-728px-Test-a-Heating-Element-Step-4-Version-2.jpg","smallWidth":460,"smallHeight":345,"bigWidth":"728","bigHeight":"546","licensing":"
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2023-02-04 15:18:22
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http://vuntblog.blogspot.com/2013/07/is-in-details.html
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## Wednesday, July 03, 2013
### ... is in the details
Recently I took a closer look at the title pages of Tischendorf’s seventh and eighth major Greek New Testament edition. As often, the small differences are the most interesting. To name just one: in 1859, Tischendorf edited the text afresh “ad antiquos testes”, “according to old witnesses”; in 1869, the witnesses have become “antiquissimos”, ”the oldest” or ”very old”.
While it is not difficult to guess what prompted the change, it is nice to observe its traces even on the respective title pages.
Another example? Another example:
Griesbach’s first and second editions of 1777 and 1796, respectively (the dates are for the first volume only).
The change that caught my eye was between “emendavit” in 1777 and “recensuit” in 1796. Would it be too far-fetched to see the latter as an indication of things to come in the 19th century?
In any case, it is the term used by Tischendorf as well.
There is also a nice parallel in another change: it would seem that the less a scholar's name is established, the more important it is to include any marks of distinction that may apply ...
[For Tischendorf: HT Bart Kamphuis]
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2015-04-27 00:11:41
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http://www.physicsforums.com/showthread.php?p=3897538
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## 3z-1+2√z=32This equation gets solved when we assume the z as
3z-1+2√z=32
This equation gets solved when we assume the z as any variable's2 and turn that into a quadratic form.
Is there any other way of solving this equation?
Quote by Kartik. 3z-1+2√z=32 This equation gets solved when we assume the z as any variable's2 and turn that into a quadratic form. Is there any other way of solving this equation?
Well, when we square stuff, which ammounts to basically the same thing:
$3z-33=-2\sqrt{z}\Longrightarrow 9z^2-198z+1089=4z\Longrightarrow 9z^2-202z+1089=0\Longrightarrow z_1=13.444\,,\,\,z_2=9$ .
As many times with these exercises, only the second number above is a solution to the original equation.
DonAntonio
Quote by DonAntonio Well, when we square stuff, which ammounts to basically the same thing: $3z-33=-2\sqrt{z}\Longrightarrow 9z^2-198z+1089=4z\Longrightarrow 9z^2-202z+1089=0\Longrightarrow z_1=13.444\,,\,\,z_2=9$ . As many times with these exercises, only the second number above is a solution to the original equation. DonAntonio
Thanks :D
But, the assumption thing looks simple enough.
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2013-05-22 14:55:07
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https://homework.cpm.org/category/CON_FOUND/textbook/gc/chapter/7/lesson/7.2.4/problem/7-74
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Home > GC > Chapter 7 > Lesson 7.2.4 > Problem7-74
7-74.
For each figure below, determine if the two smaller triangles in each figure are congruent. If so, create a flowchart to explain why. Then, solve for $x$. If the triangles are not congruent, explain why not. Redraw and label the diagrams as needed.
Each set of triangles is congruent. Now show why or how.
1. Congruent because of $\text{SAS}≅$, $x=2$.
2. Congruent because of $\text{HL}≅$, $x=32$.
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2020-11-25 14:43:32
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https://community.spiceworks.com/topic/2292750-windows-is-changing-shortcut-s-target-and-start-in
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### 3 Replies
• There are some possible options discussed here:
How do I stop a Windows shortcut from updating its path? - Super User: https://superuser.com/questions/1231074/how-do-i-stop-a-windows-shortcut-from-updating-its-path
To quote:
Text
You can use PowerShell! This little script whacks the LNK file to produce the same effect as using the classic shortcut utility.
$linkfile = Resolve-Path$args[0]
$bytes = [IO.File]::ReadAllBytes($linkfile)
$bytes[0x16] =$bytes[0x16] -bor 0x36
[IO.File]::WriteAllBytes($linkfile,$bytes)
To use it, save that text as a .ps1 file, e.g. notrack.ps1. If you haven't already, follow the instructions in the Enabling Scripts section of the PowerShell tag wiki. Then you can run it from a PowerShell prompt:
.\notrack.ps1 C:\path\to\my\shortcut.lnk
Shortcuts that are tweaked in this way will not change when their target moves. If a shortcut like this gets broken, nothing at all will happen when you try to open it.
I gathered the binary math used in my script from this 48-page Microsoft PDF on the LNK format (https://winprotocoldoc.blob.core.windows.net/productionwindowsarchives/MS-SHLLINK/[MS-SHLLINK].pdf).
answered Jul 20 '17 at 2:45
Ben N
.....
You can enable the following GPO:
corresponding registry key: HKCU\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer\NoResolveSearch
corresponding registry key:
HKCU\Software\Microsoft\Windows\CurrentVersion\Policies\Explorer\NoResolveTrack
User Configuration\Administrative Templates\Windows Components\File Explorer\Do not track shell shortcuts during roaming
answered Jul 19 '17 at 22:03
Swisstone
1 found this helpful thumb_up thumb_down
• i’ve had this same issue and resolved it by enabling the policy:
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2022-07-03 09:33:03
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https://www.tutorialspoint.com/a-stone-is-dropped-from-the-top-of-a-tower-500-m-high-into-a-pond-of-water-at-the-base-of-the-tower-when-is-the-splash-heard-at-the-top-given-g-
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# A stone is dropped from the top of a tower $500\ m$ high into a pond of water at the base of the tower. When is the splash heard at the top? Given, $g=10\ ms^{-2}$ and speed of sound $=340\ ms^{-1}$.
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Given:
A stone is dropped from the top of a tower $500\ m$ high into a pond of water at the base of the tower.
To do:
To find out when is the splash heard at the top.
Solution:
Height of the tower, $s=500\ m$
Velocity of sound, $v=340\ m/s$
Acceleration due to gravity, $g=10\ m/s^2$
Initial velocity of the stone, $u=0$ $(since\ the\ stone\ is\ initially\ at\ rest)$
Time taken by the stone to fall to the base of the tower, $t_1$
According to the second equation of motion:
$S=ut_1+\frac{1}{2}gt_1^2$
$500=0\times t_1+\frac{1}{2}\times10\times t_1^2$
$t_1^2=100$
$t_1=10\ s$
Now, the time taken by the sound to reach the top from the base of the tower is, $t_2=\frac{500}{340}=1.47\ s$
Therefore, the splash is heard at the top after time, $t$
Where, $t=t_1+t_2=10+1.47=11.47\ s$
Updated on 10-Oct-2022 13:23:18
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2022-11-26 13:31:41
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https://plainmath.net/linear-algebra/99932-how-do-you-evaluate-a-matrix
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criminauiac
2022-12-14
How do you evaluate a matrix.
gamspoupshua
Expert
Step 1: Matrix
Then we need evaluate a matrix, it must be a square matrix of order $n×n$. it can be $2×2,3×3,4×4$
For eg:
$\left(a,b,c,d\right)2×2$ is a square matrix of order $2×2$
$\left(a,b,c,d,e,f,g,h,i\right)3×3$is a square matrix of order $3×3$
Step 2: Evaluating a matrix
$A=\left(a,b,c,d\right)2×2$we can evaluate the $2×2$ matrix by multiplying the and then subtracting it
$\left(A\right)=\left(ad-bc\right)$
For $3×3matrix$
Hide row and column along which we evaluating the matrix
Then the remaining element is $\left(e,f,h,i\right)then\left(A\right)=\left(e,i,-,f,h\right)$in this we evaluate the matrix along element $a$.
Similarly, if we evaluate the matrix along element $b$ then $\left(A\right)=\left(d,f,g,i\right)then\left(A\right)=\left(d,i,-,g,f\right)$
Hence, in this way we can evaluate a square matrix .
Do you have a similar question?
|
2023-02-05 07:49:45
|
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https://ask.wireshark.org/questions/21526/revisions/
|
Revision history [back]
Can't capture CANopen pakets
Hello Community, I'd like to capture some data on a CANopen Network with a Raspberry Pi 4B. If i run Wireshark, without allowing non root users to capture pakets, my "can0" interface appears but, as expected, I'm not able to capture anything from it.
So I reconfigured the installation with "sudo dpkg-reconfigure wireshark-common" and answered the question with "yes". I also run "sudo usermod -a -G wireshark {username}". Now I still see interfaces, but fewer then before. Especially my "can0" interface doesn't appear. I spent the past 3 days to find a solution but unfortunately I still stuck to add my right interface in the list.
Linux Kernel 5.10.11-v7l Using CAN Module: https://joy-it.net/en/products/SBC-CAN01
Can't capture CANopen pakets
Hello Community, I'd like to capture some data on a CANopen Network with a Raspberry Pi 4B. If i run Wireshark, without allowing non root users to capture pakets, my "can0" interface appears but, as expected, I'm not able to capture anything from it.
So I reconfigured the installation with "sudo dpkg-reconfigure wireshark-common" and answered the question with "yes". I also run "sudo usermod -a -G wireshark {username}". Now I still see interfaces, but fewer then before. Especially my "can0" interface doesn't appear. I spent the past 3 days to find a solution but unfortunately I still stuck to add my right interface in the list.
Linux Kernel 5.10.11-v7l Using CAN Module: https://joy-it.net/en/products/SBC-CAN01
//EDIT: Found the solution. I also need to add my user to "gpio" group with "gpasswd -a {username} gpio"
Can't capture CANopen pakets
Hello Community, I'd like to capture some data on a CANopen Network with a Raspberry Pi 4B. If i run Wireshark, without allowing non root users to capture pakets, my "can0" interface appears but, as expected, I'm not able to capture anything from it.
So I reconfigured the installation with "sudo dpkg-reconfigure wireshark-common" and answered the question with "yes". I also run "sudo usermod -a -G wireshark {username}". Now I still see interfaces, but fewer then before. Especially my "can0" interface doesn't appear. I spent the past 3 days to find a solution but unfortunately I still stuck to add my right interface in the list.
Linux Kernel 5.10.11-v7l Using CAN Module: https://joy-it.net/en/products/SBC-CAN01
//EDIT: Found the solution. solution to see amd choose my "can0". I also need to add my user to "gpio" group with "gpasswd -a {username} gpio"gpio". Now I can start the capture but can't see any traffic.
4 None grahamb 23665 ●4 ●877 ●227 https://www.wireshark.org
Can't capture CANopen pakets
Hello Community, I'd like to capture some data on a CANopen Network with a Raspberry Pi 4B. If i run Wireshark, without allowing non root users to capture pakets, my "can0" interface appears but, as expected, I'm not able to capture anything from it.
So I reconfigured the installation with "sudo dpkg-reconfigure wireshark-common" and answered the question with "yes". I also run "sudo usermod -a -G wireshark {username}". Now I still see interfaces, but fewer then before. Especially my "can0" interface doesn't appear. I spent the past 3 days to find a solution but unfortunately I still stuck to add my right interface in the list.
Linux Kernel 5.10.11-v7l
Using CAN Module: https://joy-it.net/en/products/SBC-CAN01https://joy-it.net/en/products/SBC-CAN01
//EDIT: Found the solution to see amd choose my "can0". I also need to add my user to "gpio" group with "gpasswd -a {username} gpio". Now I can start the capture but can't see any traffic.
5 None grahamb 23665 ●4 ●877 ●227 https://www.wireshark.org
Can't capture CANopen pakets
Hello Community, I'd like to capture some data on a CANopen Network with a Raspberry Pi 4B. If i run Wireshark, without allowing non root users to capture pakets, my "can0" interface appears but, as expected, I'm not able to capture anything from it.
So I reconfigured the installation with "sudo dpkg-reconfigure wireshark-common" and answered the question with "yes". I also run "sudo usermod -a -G wireshark {username}". Now I still see interfaces, but fewer then before. Especially my "can0" interface doesn't appear. I spent the past 3 days to find a solution but unfortunately I still stuck to add my right interface in the list.
Linux Kernel 5.10.11-v7l
Using CAN Module: https://joy-it.net/en/products/SBC-CAN01
//EDIT: Found the solution to see amd choose my "can0". I also need to add my user to "gpio" group with "gpasswd -a {username} gpio". Now I can start the capture but can't see any traffic.
|
2022-09-27 22:00:08
|
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http://www.haskell.org/pipermail/haskell-cafe/2009-September/066916.html
|
# [Haskell-cafe] i am missing something really trivial with parsec
Ryan Ingram ryani.spam at gmail.com
Tue Sep 29 04:29:49 EDT 2009
```I don't know, but:
number
-- definition
= do { num <- natural ; return \$ num }
-- desugar
= natural >>= \num -> return \$ num
-- apply (\$)
= natural >>= \num -> return num
-- eta elimination (f == \x -> f x)
= natural >>= return
-- monad law
= natural
(modulo monomorphism restriction, since number doesn't take any arguments
and doesn't have a type signature)
-- ryan
On Tue, Sep 29, 2009 at 12:54 AM, Anatoly Yakovenko
<aeyakovenko at gmail.com>wrote:
> number = do { num <- natural
> ; return \$ num
> }
> main = do
> txt <- hGetContents stdin
> print \$ parse number "stdin" txt
>
>
> why doesn't that work?
> _______________________________________________
> Haskell-Cafe mailing list
> Haskell-Cafe at haskell.org
> http://www.haskell.org/mailman/listinfo/haskell-cafe
>
-------------- next part --------------
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```
More information about the Haskell-Cafe mailing list
|
2014-10-25 18:13:01
|
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|
http://math.eretrandre.org/tetrationforum/showthread.php?tid=97&pid=1359
|
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Generalized recursive operators andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 02/11/2008, 09:47 PM Ivars Wrote:=...=0,007297583=1/137,0316766 I'm not sure, it seems like no one has mentioned that this value is also the ratio between the action potentials of (electron/photon), better known as the "fine structure constant", also known as alpha. However, your sum is only accurate to 4 decimal places, which is still better than the previous approximation of 1/137, which is only accurate to 3 decimal places. Good job. Andrew Robbins GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 02/11/2008, 10:53 PM (This post was last modified: 02/11/2008, 11:03 PM by GFR.) Concerning the two asymptotes of y = eta[5]x, with eta = e^(1/e): Ivars Wrote:GFR, ... The double values returned are also interesting, the positive asymptote value should correspond to some very slow operation- may be inverse pentation, what ever it means-is there a definition?. How did You show (it can be shown...) that what You have shown ? Analytically? ....As I said, it can be shown that, for b = eta = e^(1/e) = 1.444667861.., we have two fixpoints in y = b[4]x and that they probably (...) are: x = {-Pi/2, +Pi/2} = {-1.570796327..., +1.570796327..}, corresponding to two symmetrical horizontal asymptotes of y = eta[5]x, with those values (positive, for x -> +oo, and negative, for x -> -oo). Unfortunately, I was not able (to date) to show it analytically, but only graphically. This explains the word "... probably". See the attachment. GFR Attached Files Two tetra fixpoints.pdf (Size: 5.98 KB / Downloads: 343) Ivars Long Time Fellow Posts: 366 Threads: 26 Joined: Oct 2007 02/14/2008, 06:05 PM andydude Wrote:Ivars Wrote:=...=0,007297583=1/137,0316766 I'm not sure, it seems like no one has mentioned that this value is also the ratio between the action potentials of (electron/photon), better known as the "fine structure constant", also known as alpha. However, your sum is only accurate to 4 decimal places, which is still better than the previous approximation of 1/137, which is only accurate to 3 decimal places. Good job. Andrew Robbins Hi, Andy, Thanks. Of course I was aiming for fine structure constant, assumed everyone would notice- I live in assumptions, sometimes. I do not know how accurate are the assymptotic values You and JFox and GFR have derived. I they are accurate to enough decimal places, than this indeed is rather accurate SIMPLE symbolic approximation of fine structure constant (I mean You can always approximate any number using arbitrary values and constants,or infinite sums ) - I used only 5 terms, integer coefficients, integer powers , simple logic how they change, and the value of pentatition asymptote which must be a true mathematical constant. Perhaps this can be even written down as simple formula , just need a Symbol for the asymptote value. From my point of view, hyperoperations are exactly the place to look for alpha value. And having 5 terms in a 5-tation sum also seemed a nice fit. I would expect this formula is somehow extendable giving even better fit with either higher hyperoperations, or involving hyperoperations in formula itself, but for that there is a need to understand what does this pentation asymptote might mean, physically. Which is why I started to draw spirals, so far for me it remains unresolved issue. Ivars bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/07/2008, 06:58 PM andydude Wrote:I just found the asymptotes of pentation, hexation, heptation, octation, and beyond! And they're fascinating: \begin{align} \lim_{b \rightarrow -2}(a \begin{tabular}{|c|}\hline 4 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) & = -2 \\ \lim_{b \rightarrow -4}(a \begin{tabular}{|c|}\hline 6 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) & = -4 \\ \lim_{b \rightarrow -6}(a \begin{tabular}{|c|}\hline 8 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 9 \\\hline\end{tabular} b) & = -6 \end{blign} ... I suppose you could see this from the integer versions of these operators, but I think the continuous (or if not continuous, mostly real-valued) versions make it easier to see. First, Andrew, these are really fascinating findings. andydude Wrote:$\lim_{N\rightarrow\infty} (a \begin{tabular}{|c|}\hline N \\\hline\end{tabular} b) = b+1$ for all $a>1, b<0$ meaning, in the limit, all hyper-operators return to the successor operation, like the circle of life... I dare a proof by induction which only needs the integer operations. Proposition: If we have a sequence of operations [n] on the natural numbers (>0) that satisfy b[n+1]1=b, b[n+1](x+1)=b[n](b[n+1]x) for n$\ge$ 1, then we can extend the domain of the right operand of [n] to integer k with k$\ge$ 3-n and the only way to do so still satisfying the above conditions and injectivity of the functions f(x)=b[n]x is by b[n](-k)=-k+1 for 0$\le$ k$\le$ n-3. Proof: We prove by induction over k that b[n](-k)=-k+1 for all n$\ge$ k+3. Induction Start k=0: b[n]1=b=b[n+1]1=b[n](b[n+1]0), for n$\ge$2, by injectivity follows 1=b[n+1]0 for n+1$\ge$3=0+3 Induction Step k=k+1: by induction assumption for n$\ge$k+3 : b[n](-k)=-k+1=b[n+1](-k)=b[n](b[n+1]-(k+1)) by injectivity: -k = b[n+1]-(k+1) which is the induction assertion: -(k+1)+1=b[n+1]-(k+1) for n+1$\ge$k+1+3 GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 03/10/2008, 11:56 AM Now, Henryk will say: "But, Gianfranco, you are always late and .... approximated !" This will happen concerning: bo198214 Wrote:andydude Wrote:I just found the asymptotes of pentation, hexation, heptation, octation, and beyond! And they're fascinating: \begin{align} \lim_{b \rightarrow -2}(a \begin{tabular}{|c|}\hline 4 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) & = -2 \\ \lim_{b \rightarrow -4}(a \begin{tabular}{|c|}\hline 6 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 7 \\\hline\end{tabular} b) & = -4 \\ \lim_{b \rightarrow -6}(a \begin{tabular}{|c|}\hline 8 \\\hline\end{tabular} b) & = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 9 \\\hline\end{tabular} b) & = -6 \end{blign} ...... these are really fascinating findings.Indeed, they are! But, I think, they are not completely correct (Please, Andydude, correct me, if I'm wrong!! Please also remember my last msg to you "Sure thing"!). In fact, take the first two lines: $ \lim_{b \rightarrow -2}(a \begin{tabular}{|c|}\hline 4 \\\hline\end{tabular} b) = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -2 \ $ I agree that the first line is correct, for any $a > 1$. In case of $a < 1$, the limit is +oo. For $a =1$ and $a <0$, we are in trouble. Concerning the second line, I should like to recall the following relations, the first of which valid for tetration: a[3]b = a ==> h(a) = a[4]oo, depending on base a; which also should imply the following, for pentation: a[4]b = a ==> h(a) = a[5]oo, also depending on a. I mean that the fixpoints (of exponentiation) determine the limit heights of tetration (we know that). Similarly, the fixpoints (of tetration) should determine the limit heights of pentation. We had (I still have ...) a lot of problems in linking real and complex fixpoints with the tetration limit heights h and, I think, we are (I ... am) not yet completely prepared to study the fixpoints of tetration, for any base a. Nevertheless, there is an area of tetration where the "plots" are more or less symmetrical, for various bases "a", in the negative domains of the slog and of the sexp right (or second) operands, i.e.: [/a]sexp(x) and [/a]slog(x), for x < 0. In fact, let us consider: y = a[4]x and y = [/a]slog(x) The two plots, always increasing "functions" for x < 0, have their two "tails" that cross themselves in one fixpoint, the coordinate(s) of which we may call "Sigma", with definitely: -2 < Sigma < 0. (see: http://forum.wolframscience.com/attachme...ostid=4192 ). The values of Sigma are depending on base "a", i.e.: [b --> -oo] lim a[5]b = Sigma(a). We already found some approximated values of Sigma, in the following cases (always for operamd b < 0): Sigma(e) = - 1.841..., obtained by the KAR/GFR linear approximation (Andydude can do better) Sigma(Eta) = Sigma(e^(1/e)) = - Pi/2 = 1.570796327.. , graphically obtained by GFR, for b < 0 .... Sigma(oo) = -2 (is this true? I think it is ...). We should then write: $ \lim_{b \rightarrow -2}(a \begin{tabular}{|c|}\hline 4 \\\hline\end{tabular} b) = -\infty \\ \lim_{b \rightarrow -\infty}(a \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = Sigma(a)$ And ... the rest should follow, accordingly. For base a > 1, I also agree on the limit value of a[s]n, for s -> oo and n -> -oo, which (by calling w the first infinite ordinal, or something like it ...) are indeed given by: a[w]n = n + 1 We should therefore write, for a > 1, n < 0: [s --> +oo] lim a[s]n = a[w]n = n + 1 Quickfur would probably say: "Much ado about nothing!" . We proposed to call "Omegation" such funny titanical operation. By the way, Henryk, well done, for your induction proof. Please check what I said and see if I didn't confuse issues, variables or signs. My concern is what would probably happen in case of base a < 1. I wonder if the entire sequence, mentioned by Andydude collapses, without even reaching n + 1. In fact, I have even doubts on the possibility of correctly defining the slog operation, for base a < 1. But ... , Henryk, this is another story. If you allow me, I shall put an ad-hoc thread about that. GFR andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 03/10/2008, 09:38 PM (This post was last modified: 03/10/2008, 09:44 PM by andydude.) GFR Wrote:Indeed, they are! But, I think, they are not completely correct (Please, Andydude, correct me, if I'm wrong!! Please also remember my last msg to you "Sure thing"!). In fact, take the first two lines: You're right, I'm wrong. $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -1.85$ not -2 as I had first thought. Jay has found the more precise values in this thread which you should look to instead of this post, as I'm only accurate to 1 decimal place. Andrew Robbins GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 03/10/2008, 09:53 PM Agreed! Thank you Andydude! My "yellow zone" formula, as you know, is wrong too. I found another one, but I cannot "inverse" it. . I promised to discuss it with KAR. Then, I shall say something about it. I don't dare to do it now, because I might be wrong ... again. Please think also of the possible collapsation of the pentation "suite" in case of bases 0 < a < 1. What a strange mathematical landscape! GFR bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/11/2008, 07:11 AM andydude Wrote:You're right, I'm wrong. $\lim_{b\rightarrow-\infty}(e \begin{tabular}{|c|}\hline 5 \\\hline\end{tabular} b) = -1.85$ not -2 as I had first thought. Jay has found the more precise values in this thread which you should look to instead of this post, as I'm only accurate to 1 decimal place. May I ask if anyone has an idea how much this result depends on the actually chosen tetration extension to real numbers? I mean the b[n]-k=-k+1 for 0$\le$k$\le$n-3 does not depend on the extension. GFR Member Posts: 174 Threads: 4 Joined: Aug 2007 03/11/2008, 10:24 AM Mmmm! I think that we should have: [n -> + oo] lim (b[n](-k)) = -k + 1. In all other situations, b[n](-k) would depend on both n and k. Am I right ? But, perhaps I misunderstood the question. bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 03/11/2008, 10:53 AM (This post was last modified: 03/11/2008, 10:58 AM by bo198214.) GFR Wrote:I think that we should have: [n -> + oo] lim (b[n](-k)) = -k + 1. Ya thats guarantied already for the (unique) integer version. We have b[n](-k)=-k+1 for 0$\le$k$\le$n-3. If n goes to $\infty$ the k-range for b[n](-k)=-k+1 increases and in the limit reaches all positive integer k, i.e. $\lim_{n\to\infty}$b[n](-k) = -k + 1 for all k$\ge$0. But my question was about whether the limits $\lim_{x\rightarrow-\infty}$b [2n+1] x depend on the concrete extension of the hyper operation to the reals (for example by Andrew's method, by regular iteration at some fixed point, by matrix operator method, by Jay's method, by linear/polynomial/exponential base function, etc.). For example b[5](-k)=$\text{slog}_b^{\circ k}(1)$ depends surely on the choice of $\text{slog}$, which we per default regard to be Andrew's. However perhaps it can be that *in the limit* the specific choice of $\text{slog}$ does not matter. « Next Oldest | Next Newest »
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https://aakashdigitalsrv1.meritnation.com/ask-answer/question/the-denominator-of-a-rational-number-is-greater-than-its-num/rational-numbers/1325576
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# The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and denominator is decreased by 1, the number obtained is 3/2. Find the rational number.
Let the numerator of the rational number be x.Hence,the denominator=x+8.
According to the question,
(x+17)/(x+8-1)=3/2
x+17/x+7=3/2 =>2x+34=3x+21=>x=13.
Thus,the numerator is 13 and the denominator is 13+8=21.
• -3
I forgot to write the no.It's 13/21.
• 1
let numerator be x then denominator will be x+8
x+17/x+8-1=3/2
x+17/x+7=3/2
2{x+17}=3{x+7}
2x+34=3x+21
34-21=3x-2x
13=x
x/x+8=13/21
• 14
if the numerator=x
then the denominator=x+8
the fraction=x/x+8
if numerator is increased by 17&denominator is decreased by 1then the fraction is
x+17/ x+8-1=x+17/ x+7
x+17/ x+8=3/2
cross multiplication
=2(x+17)=3(x+8)
=2x+34=3x+24
3x-2x=34-24
x=10
numerator=x=10
denominator=x+8=18
• -5
sorry x+17/x+7=3/2
2(x+17)=3(x+7)
2x+34=3x+21
x=34-21
x=13
numerator=x=13
denominator=x+7=21
• 7
Let the numerator be x so the denominator is x +8
Now according to the question (x+17 )/(x + 8 -1) =3/2
=> (x+17)/(x+7) = 3/2
=> 2(x+17)=3(x+7)
=> 3x -2x = 34 -21
=> x = 13
So the rational number is 13/21
• -3
nahi batayenge
• -11
let the numerator be x
a/q
x+17/x+8-1=3/2
now cross multiply x+17/x+8-1 with 3/2
=>2(x+17)=3(x+8-1)
=>2x+34=3x+24-3
=>34-24+3=3x-2x
=>13=x
hence the rational number is 13 is
• -1
6252
• -6
A2+b2
• -3
Numerator=13; Denominator= 21
• -3
21 AND 13
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12:86 verify the following
• 0
20% defective n 25% not well in 480 what is original answer
• -1
Let the numerator be x
denominator= x+8
Acc. to question
Numerator is increased by 17= numerator= x+17
Denominator is decreased by 1= denominator = x+8-1=x+7
x+17/x+7=3/2
by cross multiplication : 2(x+17)= 3(x+7)
= 2x+34=3x+21
= 3x-2x=34-21
= x=13
numerator = x=13
denominator = x+8= 13+8=21
hence ,the rational number is 13/21
• 2
13/21
• -2
• 2
• 0
• 0
• 0
Let the numerator of the fraction on be x.
Therefore,denominator of fraction=x + 8.
Again,orginal fraction= x / x + 8
According to the given condition,
X + 17 / (x + 8) -1= 3/2
X + 17 / x + 7= 3/2
2 ( x + 17 ) = 3 ( x + 1)
2x + 34 = 3x + 21
2x - 3x = 21 - 34
-x = -13
x =13
Fraction = 13 / 13 + 8 = 13/21
• 1
Uuyg
• 1
• 0
Easy
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Let numerator=x Then denominator= x+8 If denominator is decreased by 1and numerator is incresed by 17 Then, numerator=x+17 denominator=x+8-1=x+7 So, According to the question, (x+17)/(x+7)=3/2 =2(x+17)=3(x+7) =2x+34=3x+21 =2x-3x=21-34 =-x=-13 =x=13 Therefore, Numerator=x=13 Denominator=x+8=13+8=21 So, The rational number=Numerator/Denominator The rational number=13/21 (Ans.) I HOPE THAT MY ANSWER WILL HELP YOU...
• 0
Let the numerator be x and the denominator be x+8.
Given that:
x+17/ x+8-1 = 3/2
x+17/ x+7 = 3/2
3(x+7) = 2(x+17) ( by cross multiplication)
3x+21 = 2x+34
3x-2x = 34-21
x = 13
Then, the rational no.= x/ x+8
= 13/21
Hope this helped:)
• 0
Let numerator be x+17
Let denominator be x+8-1
x+17/x+7=3/2
By cross multiplication,
3(x+17)=2(x+7)
3x+51=2x+14
3x-2x = 14-51
x=-37
Numerator = x+17=-37+17=-20
Denominator= x+7=-37+7= -30
• 0
X=13
• 0
Solution for the given question........
• 0
Let the numerator of the fraction on be x.?
Therefore,denominator of fraction=x + 8.?
Again,orginal fraction= x / x + 8?
According to the given condition,?
X + 17 / (x + 8) -1= 3/2?
X + 17 / x + 7= 3/2?
2 ( x + 17 ) = 3 ( x + 1)?
2x + 34 = 3x + 21?
2x - 3x = 21 - 34?
-x = -13?
x =13?
Fraction = 13 / 13 + 8 =
13/21
• 0
X = 13/21
• 0
Let the numerator be x
Then the fraction become
x/x+8
Then according to question
The fraction
x+17/(x+8)-1 = 3/2
Solve this equation
(x+17)?2 =(x+7)?3 {cross multiplication}
2x+34=3x+21
x=13
Fraction =13/21 Ans
• 0
• 0
Let numerator be x.
Then,
The denominator will be x+8
X+17/x+8-1=3/2
X+17/x+7=3/2
2(x+17)=3(x+7)
2x+34=3x+21
34-21=3x-2x
13=x
x/ x+8
=13/21
• 0
• 0
9 ka math class CBSE
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?let numerator be x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?then denominator will be x+8
x+17/x+8-1=3/2
x+17/x+7=3/2
2{x+17}=3{x+7}
2x+34=3x+21
34-21=3x-2x
13=x
x/x+8=13/21
?
• 0
• 0
• 0
identify the rational number and then write the numerator and denominator 5
• 0
• 0
?let numerator be x ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?then denominator will be x+8
x+17/x+8-1=3/2
x+17/x+7=3/2
2{x+17}=3{x+7}
2x+34=3x+21
34-21=3x-2x
13=x
x/x+8=13/21
?
• 1
Chapter-1
Democracy
Civics
1. Give two reasons why democracy is so popular?
Ans. The reasons of being the democracy so popular are:-
? the true essence of democracy is the rule of the people or there representatives .
? In a democracy, people have the power to elect their leaders.
? Thus, the participate in the process of governance directly through their elected representatives
2. Differentiate between a democratic and monarchial form of government.
Ans. Democratic form of government is a government where people have power to elect their representative and the electric candidate words for the Welfare of the people.
Monarchial form of government is a system where the rulers or Monarch has the power to do anything he/ she want to do and also the post of Monarch are hereditary, they do not follow any rule.
3. What were the three events that paved the way of modern democracy?
Ans. The three went that paved the way of modern democracy are:-
? introduction of Magna Carta in Britain for limiting the powers of king. It gave the power from the monarch to the common people.
? North America declared themselves Independent from Britain in 1776 and adopted democratic constitution in 1787.
? In 1789, taking inspiration from the British colonies there was a revolution in France which gave the power from Kings and novels to common people.
4. Why do we need a constitution?
Ans. Constitution is above everyone in a country. The constitution gives certain rights to the citizens which ensure that the government cannot misuse its power.
5. What do you understand by 'Rule of Law' ?
Ans. Rule of law is the base of the idea of equality. In a democracy, irrespective of whichever party comes in administration or whoever heads the country, rules have to be in accordance of constitution.l
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https://www.physicsforums.com/threads/trick-complicated-limit.562006/
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# Trick complicated limit
1. Dec 21, 2011
### namu
How do I find the following limit?
$lim_{x\rightarrow 0} (\frac{\tan x}{x})^{1/x^2}$
L'Hospital's rule gets really messy, and I cannot find a suitable
choice of functions to apply the squeeze theorem. Does anyone
have any suggestions? Thank you.
2. Dec 21, 2011
### dextercioby
Compute the natural logarithm of the limit with the help of l'Ho^pital's rule.
3. Dec 21, 2011
### namu
Thank you. That makes life so much easier. I forgot about that little trick.
4. Dec 21, 2011
### Staff: Mentor
It shouldn't, because L'Hopital's Rule doesn't apply here. It applies to quotients of functions -- f(x)/g(x) -- where both functions are approaching zero or both are approaching infinity.
And you can't simply use L'Hopital's Rule on the part being raised to the power, because the limit variable occurs in the exponent.
5. Dec 21, 2011
### namu
That's true, so we have
$\stackrel{lim}{x \to 0} \frac{\tan x}{x}^{1/x^2}= e^{\stackrel{lim}{x \to 0}\frac{ln \frac{\tan x}{x}}{\frac{1}{x^2} }}$
Now,
$\stackrel{lim}{x \to 0} \frac{\tan x}{x}=1$
hence,
$ln 1=0$
and
$\stackrel{lim}{x \to 0} \frac{1}{x^2}=0$
Therefore we can use l'Hospital's Rule here with $f=ln \frac{\tan x}{x}$ and $g=1/x^2$
6. Dec 21, 2011
### Staff: Mentor
What you wrote is pretty hard to read and comprehend, so I can't tell if you're on the right track, plus some of what you wrote is just wrong.
$$\lim_{x \to 0}\frac{1}{x^2} \neq 0!$$
When you work this problem, don't include the limit until you're ready to take the limit.
Write y = (tan(x)/x)^(1/x^2)
Now take ln of both sides, and you'll have a quotient.
Take the limit of ln y and of what you have on the right, and use L'Hopital's Rule on that. This is what dextercioby was saying.
Keep in mind that the limit you'll get is the limit of the ln of something, so you'll need to adjust for that.
LaTeX tips
1) For complicated fractions, use [ tex ] tags instead of [ itex ] tags.
2) For limits, don't use \stackrel -- use \lim, like this:
[ tex ]\lim_{x \to {\infty}\frac{f(x)}{g(x)}[ /tex ]
7. Dec 21, 2011
### namu
Thank you very much for the LaTeX tips. Sorry, I'm new to PF and was not aware that tex can be used. Oh I see, the i in itex stands for inline instead of the usual \$. That explains a lot. Also, I made a mistake when quickly typing this up, so yes, there is a mistake.
The correct response should be
$$\lim_{x \to {\infty}} \left ( \frac{\tan x}{x} \right ) ^{1/x^2}=e^{\lim_{x \to {\infty}} \frac{1}{x^2} ln \frac{\tan x}{x} }$$
So,
$$f(x)=ln \frac{\tan x}{x}$$
$$g(x)=x^2$$
Now $f(x) \to 0$ and $g(x) \to 0$
8. Dec 21, 2011
### Dick
Ok, so now you have a 0/0 limit. What do you get for the limit using l'Hopital? This whole thing is probably worked out easier using taylor series, if you know that approach.
Last edited: Dec 21, 2011
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2017-11-17 17:50:32
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https://dba.stackexchange.com/questions/44119/mysql-innodb-flush-log-at-trx-commit-clarification
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# mysql innodb_flush_log_at_trx_commit clarification
I have been reading up on innodb as a storage engine, mainly because I have recently moved to AWS and they do not recommend myISAM which my databases current run on (and have for about 10 years)
So moving to a new engine is a little bit of a scary operation.
I am apprehensive about the move, as it has been on myISAM for so long without issue, but if it gives me peace of mind long term, then it is better for the DB.
I have read the whitepapers on InnoDB and it seems fairly straight forward, The one thing that I want to clear in my mind is the innodb_flush_log_at_trx_commit option
By default this is set to 1, however from my reading this causes additional overheads, if the data was credit card transactions or something like that, I can understand its needs to be there, but it seems when dealing with non life changing data, that innodb_flush_log_at_trx_commit=2 is a better option.
What I want to know is, this does not affect the time that the query is actually committed does it? It only affects its recovery ?
I just want to make sure that when I do an insert or update that the query will run right at the time of processing and not 1 second later, no matter what the flush_log is set to.
My understanding is that in the case of a crash , setting to 1 will allow it to recover all queries run on the server, where as setting it to 2 may lose the last second or two of data when trying to recover from the crash, is this correct?
Also, if there is slow periods of updates/inserts (ie, not much happening on the server) does setting it to 2 add additional overheads on the server, or is it a case of the benefits of applying innodb_flush_log_at_trx_commit=2 to the database when the database is busy outweighs any additional overhead caused during slow times?
What I want to know is, this does not affect the time that the query is actually committed does it? It only affects its recovery ?
It only affects recovery.
I just want to make sure that when I do an insert or update that the query will run right at the time of processing and not 1 second later, no matter what the flush_log is set to.
Correct. There may be reasons to hide changes that other transactions see (as part of multi-version concurrency control). If you're trying to build tests to prove things - make sure you understand how transaction-isolation levels work :)
My understanding is that in the case of a crash , setting to 1 will allow it to recover all queries run on the server, where as setting it to 2 may lose the last second or two of data when trying to recover from the crash, is this correct?
Correct. To be able to recover all (setting: 1) ti also assumes that the underlying hardware is not adding additional buffering to improve IO performance. I have no reason to assume that Amazon doesn't do this, so I think setting it to 2 is a good cloud practice.
Also, if there is slow periods of updates/inserts (ie, not much happening on the server) does setting it to 2 add additional overheads on the server, or is it a case of the benefits of applying innodb_flush_log_at_trx_commit=2 to the database when the database is busy outweighs any additional overhead caused during slow times?
What happens when you set to 2 (and why you get better performance) is that you just buffer changes for longer, and therefor get more IO request merging, and better performance. It doesn't create more work.
• Hey, Morgan, that page seems to be gone. – Rick James Oct 18 '18 at 22:02
It really depends on your IO subsystem on how much of a performance impact there is. No matter what value is set for innodb_flush_log_at_trx_commit, the same amount of data is being written, the only difference is when a fsync is called after the write. How much overhead the fsync is will depends on your drives, raid controllers, and even filesystem. If you have a hardware raid controller with a BBU and write cache, fsyncs are likely to be extremely fast. If you're on a laptop, a fsync may be much slower. You'll only know be testing via sysbench or similar.
Honestly, I've never found anything more then a couple of percent difference in performance, no matter which value I've set it to. Never enough to switch it away from default, even for systems that aren't important.
• Thank you for your response, the server is an AWS RDS system, so I really can not tell you the specs of it, but basically it sounds like you are saying, try for the best performance and only if there is reason to change, should it be considered. Its just that I have been reading a lot of recommendations for setting it to 2 – Charlie Smith Jun 9 '13 at 2:55
• I would imagine RDS systems are going to have fairly fast fsyncs and wouldn't need to be tweaked, but it may also depend on how many transactions per second you are attempting to push though the database. My wager is that the network will be the limiting factor much faster then the disk will be for RDS instances. – R. S. Jun 9 '13 at 5:52
We need someone from Amazon to answer this question. I know that Aurora has a significantly different I/O layer than off-the-shelf InnoDB; I don't know if the differences hold true in AWS, too. If they do, then the details given by me (and probably by others) may not be complete.
With MyISAM, if you lose power in the middle of a multi-row UPDATE, some rows will be written to disk, some won't. MyISAM provides no way to clean up the mess.
With InnoDB, that UPDATE will be either completely finished, or not started (after automatically undoing the incomplete update).
With Aurora, the underlying I/O platform even assures that another instance of MySQL will have an equally accurate copy.
It's all magic.
Yes, you understand the tradeoffs wrt innodb_flush_log_at_trx_commit. 1 is secure; 2 is faster, with a slight risk. 1 limits the performance hit to approximately 1 fsync per COMMIT. This is fine on 90+% of systems.
Another workaround for the fsync is to have a hardware RAID controller with Battery Backed Write Cache. It makes most writes 'instantaneous'.
The COMMIT does not return to the client until the fsync is finished if flatc=1. (Sooner for 2 or 0, since not waiting for fsync.)
If you run with autocommit=ON, each DML effectively includes a COMMIT. With BEGIN...COMMIT, you are combining many DMLs into a single COMMIT -- thereby potentially running faster.
My understanding is that in the case of a crash , setting to 1 will allow it to recover all queries run on the server, where as setting it to 2 may lose the last second or two of data when trying to recover from the crash, is this correct?
Correct
There are several "delayed overhead" cases. Here's one: When a secondary, non-unique, index needs updating, its BTree is not immediately changed. Instead, information about the change is put into the "Change Buffer" (which lives in the buffer_pool). (Possibly similar to "delayed_key_write".) Later, multiple index changes will be batched together, thereby diminishing the number of reads and writes.
I'm pretty sure flatc=2 can be used on all nodes of a Galera cluster -- if a node crashes, it can be completely rebuilt automatically. Hence, no need for the fsync. (Group Replication may be similar.) (AWS -- I don't know.)
I/O request merging -- This probably refers to innodb_flush_neighbors, which can have a small benefit on HDD drives, but probably has no benefit on SDDs, nor with RAID caching.
Still -- Compared to MyISAM, InnoDB is inherently faster since it does not do table locking. Oracle will probably get rid of MyISAM because there will be (and mostly already is) no performance advantage to it.
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2019-10-16 06:16:51
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https://www.physicsforums.com/threads/find-symmetric-equations-for-the-line-of-intersection-of-the-planes.629383/
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# Homework Help: Find symmetric equations for the line of intersection of the planes
1. Aug 18, 2012
### smize
1. The problem statement, all variables and given/known data
Find symmetric equations for the line of intersection of the planes
The planes:
5x - 2y - 2z = 1
4x + y + z = 6
2. Relevant equations
r = r0 + tv
x = x0 + at
y = y0 + bt
z = z0 + ct
3. The attempt at a solution
I have attempted this in many different manners and would like to find a way to the solution. The answer is:
x = 1, y - 2 = - z
The book doesn't have a good example for this problem, and as classes haven't started for me, I have no notes from lectures (i need to learn this for another class...taking 2 classes in which 1 is a prereq for the other). Any help would be appreciated.
Last edited: Aug 18, 2012
2. Aug 18, 2012
### gabbagabbahey
I know you put what you were looking for in your thread title, but you really should also include the full problem statement in the first section of your post in future threads. Just writing two equations, does not qualify as a complete problem statement.
I'm not sure exactly what makes the equations in the given answer symmetric (as implied by your thread title), but realize that any point $(x,y,z)$ that lies on the line of intersection of two planes will simultaneously satisfy the equations of both planes. How do you normally solve a system of simultaneous equations?
3. Aug 18, 2012
### smize
I fixed it, thank-you.
We're apparently supposed to be using the cross product of the two normal vectors of the planes (which gives the same vector as the intersection line, just parallel). It doesn't give me a point, and I can't figure out how they got that specific answer.
Would that be the only answer? Or is there more than one answer (i spent 2 hours on this problem today after spending only 20-30 minutes on the other 20 problems in the lesson).
4. Aug 18, 2012
### gabbagabbahey
Why do you say that? Does the full problem statement tell you to use that method?
If I gave you the system of equations $x+2y = 1$ and $2x+6y = 4$, could you solve it for $x$ and $y$?
5. Aug 18, 2012
### smize
It's what the chapter & lesson is about.
x = -1
y = 1
6. Aug 18, 2012
### smize
5x - 2y - 2z = 1
4x + y + z = 6
So, for z = 0,
5x - 2y = 1
4x + y = 6
5x - 2y = 1
+ 8x + 2y = 12
13x = 13
x = 1
4 + y + z = 6
y + z = 2
y - 2 = -z
Thanks =D So just set up a simple system of equations? I thought I tried that -.- I must have set it up wrong. Thank-you though!
7. Aug 18, 2012
### gabbagabbahey
Careful, when you do this you are assuming that z=0 is on the line of intersection (it is in this case, but you have no reason to assume it beforehand). Instead, just add 2 times the second equation to the first equation if you want to get rid of $z$.
8. Aug 18, 2012
### smize
I assumed it because of how y and z cancel each other out. Plus i kinda knew that x held constant and y & z covers all integers =P (oops)
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2018-08-21 14:55:36
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http://www.onemathematicalcat.org/Math/MCAS_Objectives/10_N_2.htm
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# MCAS Objective 10.N.2
Jump right to the exercises!
## Number Sense and Operations:
Simplify numerical expressions, including those involving positive integer exponents or the absolute value,
e.g., $\,3(2^4 - 1) = 45\,$, $\,4|3-5| + 6 = 14\,$;
apply such simplifications in the solution of problems.
Order of Operations
Practice with Exponents
Simplifying Basic Absolute Value Expressions
This exercise gives you practice with MCAS-type questions.
On the actual MCAS test, many of these questions are multiple-choice.
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2019-04-22 22:15:55
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https://phys.libretexts.org/Bookshelves/Conceptual_Physics/Book%3A_Conceptual_Physics_(Crowell)/11%3A_Fields/11.01%3A_Fields_of_Force
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11.1: Fields of Force
Cutting-edge science readily infiltrates popular culture, though sometimes in garbled form. The Newtonian imagination populated the universe mostly with that nice solid stuff called matter, which was made of little hard balls called atoms. In the early twentieth century, consumers of pulp fiction and popularized science began to hear of a new image of the universe, full of x-rays, N-rays, and Hertzian waves. What they were beginning to soak up through their skins was a drastic revision of Newton's concept of a universe made of chunks of matter which happened to interact via forces. In the newly emerging picture, the universe was made of force, or, to be more technically accurate, of ripples in universal fields of force. Unlike the average reader of Cosmic Stories in 1941, you now possess enough technical background to understand what a “force field” really is.
10.1.1 Why fields?
Time delays in forces exerted at a distance
What convinced physicists that they needed this new concept of a field of force? Although we have been dealing mostly with electrical forces, let's start with a magnetic example. (In fact the main reason I've delayed a detailed discussion of magnetism for so long is that mathematical calculations of magnetic effects are handled much more easily with the concept of a field of force.) First a little background leading up to our example.
a / A bar magnet's atoms are (partially) aligned.
A bar magnet, a, has an axis about which many of the electrons' orbits are oriented. The earth itself is also a magnet, although not a bar-shaped one.
b / A bar magnet interacts with our magnetic planet.
The interaction between the earth-magnet and the bar magnet, b, makes them want to line up their axes in opposing directions (in other words such that their electrons rotate in parallel planes, but with one set rotating clockwise and the other counterclockwise as seen looking along the axes).
c / Magnets aligned north-south.
On a smaller scale, any two bar magnets placed near each other will try to align themselves head-to-tail, c.
Now we get to the relevant example. It is clear that two people separated by a paper-thin wall could use a pair of bar magnets to signal to each other. Each person would feel her own magnet trying to twist around in response to any rotation performed by the other person's magnet. The practical range of communication would be very short for this setup, but a sensitive electrical apparatus could pick up magnetic signals from much farther away. In fact, this is not so different from what a radio does: the electrons racing up and down the transmitting antenna create forces on the electrons in the distant receiving antenna. (Both magnetic and electric forces are involved in real radio signals, but we don't need to worry about that yet.)
A question now naturally arises as to whether there is any time delay in this kind of communication via magnetic (and electric) forces. Newton would have thought not, since he conceived of physics in terms of instantaneous action at a distance. We now know, however, that there is such a time delay. If you make a long-distance phone call that is routed through a communications satellite, you should easily be able to detect a delay of about half a second over the signal's round trip of 50,000 miles. Modern measurements have shown that electric, magnetic, and gravitational forces all travel at the speed of light, $$3\times10^8$$ m/s. (In fact, we will soon discuss how light itself is made of electricity and magnetism.)
If it takes some time for forces to be transmitted through space, then apparently there is some thing that travels through space. The fact that the phenomenon travels outward at the same speed in all directions strongly evokes wave metaphors such as ripples on a pond.
More evidence that fields of force are real: they carry energy.
The smoking-gun argument for this strange notion of traveling force ripples comes from the fact that they carry energy.
d / The second magnet is reversed.
First suppose that the person holding the bar magnet on the right decides to reverse hers, resulting in configuration d. She had to do mechanical work to twist it, and if she releases the magnet, energy will be released as it flips back to c. She has apparently stored energy by going from c to d. So far everything is easily explained without the concept of a field of force.
e / Both magnets are reversed.
But now imagine that the two people start in position c and then simultaneously flip their magnets extremely quickly to position e, keeping them lined up with each other the whole time. Imagine, for the sake of argument, that they can do this so quickly that each magnet is reversed while the force signal from the other is still in transit. (For a more realistic example, we'd have to have two radio antennas, not two magnets, but the magnets are easier to visualize.) During the flipping, each magnet is still feeling the forces arising from the way the other magnet used to be oriented. Even though the two magnets stay aligned during the flip, the time delay causes each person to feel resistance as she twists her magnet around. How can this be? Both of them are apparently doing mechanical work, so they must be storing magnetic energy somehow. But in the traditional Newtonian conception of matter interacting via instantaneous forces at a distance, interaction energy arises from the relative positions of objects that are interacting via forces. If the magnets never changed their orientations relative to each other, how can any magnetic energy have been stored?
The only possible answer is that the energy must have gone into the magnetic force ripples crisscrossing the space between the magnets. Fields of force apparently carry energy across space, which is strong evidence that they are real things.
This is perhaps not as radical an idea to us as it was to our ancestors. We are used to the idea that a radio transmitting antenna consumes a great deal of power, and somehow spews it out into the universe. A person working around such an antenna needs to be careful not to get too close to it, since all that energy can easily cook flesh (a painful phenomenon known as an “RF burn”).
10.1.2 The gravitational field
Given that fields of force are real, how do we define, measure, and calculate them? A fruitful metaphor will be the wind patterns experienced by a sailing ship. Wherever the ship goes, it will feel a certain amount of force from the wind, and that force will be in a certain direction. The weather is ever-changing, of course, but for now let's just imagine steady wind patterns. Definitions in physics are operational, i.e., they describe how to measure the thing being defined. The ship's captain can measure the wind's “field of force” by going to the location of interest and determining both the direction of the wind and the strength with which it is blowing. Charting all these measurements on a map leads to a depiction of the field of wind force like the one shown in the figure. This is known as the “sea of arrows” method of visualizing a field.
f / The wind patterns in a certain area of the ocean could be charted in a “sea of arrows” representation like this. Each arrow represents both the wind's strength and its direction at a certain location.
Now let's see how these concepts are applied to the fundamental force fields of the universe. We'll start with the gravitational field, which is the easiest to understand. As with the wind patterns, we'll start by imagining gravity as a static field, even though the existence of the tides proves that there are continual changes in the gravity field in our region of space. When the gravitational field was introduced in chapter 2, I avoided discussing its direction explicitly, but defining it is easy enough: we simply go to the location of interest and measure the direction of the gravitational force on an object, such as a weight tied to the end of a string.
In chapter 2, I defined the gravitational field in terms of the energy required to raise a unit mass through a unit distance. However, I'm going to give a different definition now, using an approach that will be more easily adapted to electric and magnetic fields. This approach is based on force rather than energy. We couldn't carry out the energy-based definition without dividing by the mass of the object involved, and the same is true for the force-based definition. For example, gravitational forces are weaker on the moon than on the earth, but we cannot specify the strength of gravity simply by giving a certain number of newtons. The number of newtons of gravitational force depends not just on the strength of the local gravitational field but also on the mass of the object on which we're testing gravity, our “test mass.” A boulder on the moon feels a stronger gravitational force than a pebble on the earth. We can get around this problem by defining the strength of the gravitational field as the force acting on an object, divided by the object's mass:
The gravitational field vector, $$\mathbf{g}$$, at any location in space is found by placing a test mass $$m_t$$ at that point. The field vector is then given by $$\mathbf{g}=\mathbf{F}/m_t$$, where $$\mathbf{F}$$ is the gravitational force on the test mass.
We now have three ways of representing a gravitational field. The magnitude of the gravitational field near the surface of the earth, for instance, could be written as 9.8 N/kg, 9.8 $$\text{J}/\text{kg}\cdot\text{m}$$, or 9.8 $$\text{m}/\text{s}^2$$. If we already had two names for it, why invent a third? The main reason is that it prepares us with the right approach for defining other fields.
The most subtle point about all this is that the gravitational field tells us about what forces would be exerted on a test mass by the earth, sun, moon, and the rest of the universe, if we inserted a test mass at the point in question. The field still exists at all the places where we didn't measure it.
Example 1: Gravitational field of the earth
$$\triangleright$$ What is the magnitude of the earth's gravitational field, in terms of its mass, $$M$$, and the distance $$r$$ from its center?
g / The gravitational field surrounding a clump of mass such as the earth.
$$\triangleright$$ Substituting $$|\mathbf{F}|= GMm_{t}/ r^2$$ into the definition of the gravitational field, we find $$|\mathbf{g}|= GM/ r^2$$. This expression could be used for the field of any spherically symmetric mass distribution, since the equation we assumed for the gravitational force would apply in any such case.
Sources and sinks
If we make a sea-of-arrows picture of the gravitational fields surrounding the earth, g, the result is evocative of water going down a drain. For this reason, anything that creates an inward-pointing field around itself is called a sink. The earth is a gravitational sink. The term “source” can refer specifically to things that make outward fields, or it can be used as a more general term for both “outies” and “innies.” However confusing the terminology, we know that gravitational fields are only attractive, so we will never find a region of space with an outward-pointing field pattern.
Knowledge of the field is interchangeable with knowledge of its sources (at least in the case of a static, unchanging field). If aliens saw the earth's gravitational field pattern they could immediately infer the existence of the planet, and conversely if they knew the mass of the earth they could predict its influence on the surrounding gravitational field.
Superposition of indexsuperposition of fieldsindexfieldssuperposition offields
h / The gravitational fields of the earth and moon superpose. Note how the fields cancel at one point, and how there is no boundary between the interpenetrating fields surrounding the two bodies.
A very important fact about all fields of force is that when there is more than one source (or sink), the fields add according to the rules of vector addition. The gravitational field certainly will have this property, since it is defined in terms of the force on a test mass, and forces add like vectors. Superposition is an important characteristics of waves, so the superposition property of fields is consistent with the idea that disturbances can propagate outward as waves in a field.
Example 2: Reduction in gravity on Io due to Jupiter's gravity
$$\triangleright$$ The average gravitational field on Jupiter's moon Io is 1.81 N/kg. By how much is this reduced when Jupiter is directly overhead? Io's orbit has a radius of $$4.22\times10^8$$ m, and Jupiter's mass is $$1.899\times10^{27}$$ kg.
$$\triangleright$$ By the shell theorem, we can treat the Jupiter as if its mass was all concentrated at its center, and likewise for Io. If we visit Io and land at the point where Jupiter is overhead, we are on the same line as these two centers, so the whole problem can be treated one-dimensionally, and vector addition is just like scalar addition. Let's use positive numbers for downward fields (toward the center of Io) and negative for upward ones. Plugging the appropriate data into the expression derived in example 1, we find that the Jupiter's contribution to the field is $$- 0.71$$ N/kg. Superposition says that we can find the actual gravitational field by adding up the fields created by Io and Jupiter: $$1.81-0.71$$ N/kg = 1.1 N/kg. You might think that this reduction would create some spectacular effects, and make Io an exciting tourist destination. Actually you would not detect any difference if you flew from one side of Io to the other. This is because your body and Io both experience Jupiter's gravity, so you follow the same orbital curve through the space around Jupiter.
i / The part of the LIGO gravity wave detector at Hanford Nuclear Reservation, near Richland, Washington. The other half of the detector is in Louisiana.
Gravitational waves
A source that sits still will create a static field pattern, like a steel ball sitting peacefully on a sheet of rubber. A moving source will create a spreading wave pattern in the field, like a bug thrashing on the surface of a pond. Although we have started with the gravitational field as the simplest example of a static field, stars and planets do more stately gliding than thrashing, so gravitational waves are not easy to detect. Newton's theory of gravity does not describe gravitational waves, but they are predicted by Einstein's general theory of relativity. J.H. Taylor and R.A. Hulse were awarded the Nobel Prize in 1993 for giving indirect evidence that Einstein's waves actually exist. They discovered a pair of exotic, ultra-dense stars called neutron stars orbiting one another very closely, and showed that they were losing orbital energy at the rate predicted by Einstein's theory.
A Caltech-MIT collaboration has built a pair of gravitational wave detectors called LIGO to search for more direct evidence of gravitational waves. Since they are essentially the most sensitive vibration detectors ever made, they are located in quiet rural areas, and signals will be compared between them to make sure that they were not due to passing trucks. The project began operating at full sensitivity in 2005, and is now able to detect a vibration that causes a change of $$10^{-18}$$ m in the distance between the mirrors at the ends of the 4-km vacuum tunnels. This is a thousand times less than the size of an atomic nucleus! There is only enough funding to keep the detectors operating for a few more years, so the physicists can only hope that during that time, somewhere in the universe, a sufficiently violent cataclysm will occur to make a detectable gravitational wave. (More accurately, they want the wave to arrive in our solar system during that time, although it will have been produced millions of years before.)
10.1.3 The electric field
Definition
The definition of the electric field is directly analogous to, and has the same motivation as, the definition of the gravitational field:
The electric field vector, $$\mathbf{E}$$, at any location in space is found by placing a test charge $$q_t$$ at that point. The electric field vector is then given by $$\mathbf{E}=\mathbf{F}/q_t$$, where $$\mathbf{F}$$ is the electric force on the test charge.
Charges are what create electric fields. Unlike gravity, which is always attractive, electricity displays both attraction and repulsion. A positive charge is a source of electric fields, and a negative one is a sink.
The most difficult point about the definition of the electric field is that the force on a negative charge is in the opposite direction compared to the field. This follows from the definition, since dividing a vector by a negative number reverses its direction. It's as though we had some objects that fell upward instead of down.
self-check:
Find an equation for the magnitude of the field of a single point charge $$Q$$.
Example 3: Superposition of electric fields
$$\triangleright$$ Charges $$q$$ and $$- q$$ are at a distance $$b$$ from each other, as shown in the figure. What is the electric field at the point P, which lies at a third corner of the square?
j / Example 3.
$$\triangleright$$ The field at P is the vector sum of the fields that would have been created by the two charges independently. Let positive $$x$$ be to the right and let positive $$y$$ be up.
Negative charges have fields that point at them, so the charge $$-q$$ makes a field that points to the right, i.e., has a positive $$x$$ component. Using the answer to the self-check, we have
\begin{align*} E_{-q,x} &= \frac{ kq}{ b^2} \\ E_{-q,y} &= 0 . \end{align*}
Note that if we had blindly ignored the absolute value signs and plugged in $$- q$$ to the equation, we would have incorrectly concluded that the field went to the left.
By the Pythagorean theorem, the positive charge is at a distance $$\sqrt{2} b$$ from P, so the magnitude of its contribution to the field is $$E= kq/2 b^2$$. Positive charges have fields that point away from them, so the field vector is at an angle of 135° counterclockwise from the $$x$$ axis.
\begin{align*} E_{q,x} &= \frac{ kq}{2 b^2} \text{cos}\ 135° \\ &= -\frac{ kq}{2^\text{3/2} b^2} \\ E_{q,y} &= \frac{ kq}{2 b^2} \text{sin}\ 135° \\ &= \frac{ kq}{2^\text{3/2} b^2} \end{align*}
The total field is
\begin{align*} E_\text{x} &= \left(1-2^{-\text{3/2}}\right)\frac{ kq}{ b^2} \\ E_{y} &= \frac{ kq}{2^\text{3/2} b^2} \end{align*}
Dipoles
k / A dipole field. Electric fields diverge from a positive charge and converge on a negative charge.
The simplest set of sources that can occur with electricity but not with gravity is the dipole, consisting of a positive charge and a negative charge with equal magnitudes. More generally, an electric dipole can be any object with an imbalance of positive charge on one side and negative on the other.
l / A water molecule is a dipole.
A water molecule, l, is a dipole because the electrons tend to shift away from the hydrogen atoms and onto the oxygen atom.
m / 1. A uniform electric field created by some charges “off-stage.” 2. A dipole is placed in the field. 3. The dipole aligns with the field.
Your microwave oven acts on water molecules with electric fields. Let us imagine what happens if we start with a uniform electric field, m/1, made by some external charges, and then insert a dipole, m/2, consisting of two charges connected by a rigid rod. The dipole disturbs the field pattern, but more important for our present purposes is that it experiences a torque. In this example, the positive charge feels an upward force, but the negative charge is pulled down. The result is that the dipole wants to align itself with the field, m/3. The microwave oven heats food with electrical (and magnetic) waves. The alternation of the torque causes the molecules to wiggle and increase the amount of random motion. The slightly vague definition of a dipole given above can be improved by saying that a dipole is any object that experiences a torque in an electric field.
What determines the torque on a dipole placed in an externally created field? Torque depends on the force, the distance from the axis at which the force is applied, and the angle between the force and the line from the axis to the point of application. Let a dipole consisting of charges $$+q$$ and $$-q$$ separated by a distance $$\ell$$ be placed in an external field of magnitude $$|\mathbf{E}|$$, at an angle $$\theta$$ with respect to the field. The total torque on the dipole is
\begin{align*} \tau &= \frac{\ell}{2}q|\mathbf{E}|\sin \theta+\frac{\ell}{2}q|\mathbf{E}|\sin \theta \\ &= \ell q|\mathbf{E}|\sin \theta . \end{align*}
(Note that even though the two forces are in opposite directions, the torques do not cancel, because they are both trying to twist the dipole in the same direction.) The quantity is called the dipole moment, notated $$D$$. (More complex dipoles can also be assigned a dipole moment --- they are defined as having the same dipole moment as the two-charge dipole that would experience the same torque.)
Employing a little more mathematical elegance, we can define a dipole moment vector,
$\begin{equation*} \mathbf{D} = \sum q_i \mathbf{r}_i , \end{equation*}$
where $$\mathbf{r}_i$$ is the position vector of the charge labeled by the index $$i$$. We can then write the torque in terms of a vector cross product (page 281),
$\begin{equation*} \boldsymbol{\tau} = \mathbf{D}\times\mathbf{E} . \end{equation*}$
No matter how we notate it, the definition of the dipole moment requires that we choose point from which we measure all the position vectors of the charges. However, in the commonly encountered special case where the total charge of the object is zero, the dipole moment is the same regardless of this choice.
Example 4: Dipole moment of a molecule of NaCl gas
$$\triangleright$$ In a molecule of NaCl gas, the center-to-center distance between the two atoms is about 0.6 nm. Assuming that the chlorine completely steals one of the sodium's electrons, compute the magnitude of this molecule's dipole moment.
$$\triangleright$$ The total charge is zero, so it doesn't matter where we choose the origin of our coordinate system. For convenience, let's choose it to be at one of the atoms, so that the charge on that atom doesn't contribute to the dipole moment. The magnitude of the dipole moment is then
\begin{align*} D &= (6\times10^{-10}\ \text{m})( e) \\ &= (6\times10^{-10}\ \text{m})( 1.6\times10^{-19}\ \text{C}) \\ &= 1\times10^{-28}\ \text{C}\cdot\text{m} \end{align*}
Example 5: Dipole moments as vectors
$$\triangleright$$ The horizontal and vertical spacing between the charges in the figure is $$b$$. Find the dipole moment.
n / Example 5.
$$\triangleright$$ Let the origin of the coordinate system be at the leftmost charge.
\begin{align*} \mathbf{D} &= \sum q_i \mathbf{r}_i \\ &= (q)(\text{0})+(-q)(b\hat{\mathbf{x}})+(q)(b\hat{\mathbf{x}}+b\hat{\mathbf{y}})+(-q)(2b\hat{\mathbf{x}}) \\ &= -2bq\hat{\mathbf{x}}+bq\hat{\mathbf{y}} \end{align*}
Alternative definition of the electric field
The behavior of a dipole in an externally created field leads us to an alternative definition of the electric field:
The electric field vector, $$E$$, at any location in space is defined by observing the torque exerted on a test dipole $$D_t$$ placed there. The direction of the field is the direction in which the field tends to align a dipole (from $$-$$ to +), and the field's magnitude is $$|\mathbf{E}|=\tau/D_t\sin\theta$$. In other words, the field vector is the vector that satisfies the equation $$\boldsymbol{\tau} = \mathbf{D}_t\times\mathbf{E}$$ for any test dipole $$\mathbf{D}_t$$ placed at that point in space.
The main reason for introducing a second definition for the same concept is that the magnetic field is most easily defined using a similar approach.
Discussion Questions
◊ In the definition of the electric field, does the test charge need to be 1 coulomb? Does it need to be positive?
◊ Does a charged particle such as an electron or proton feel a force from its own electric field?
◊ Is there an electric field surrounding a wall socket that has nothing plugged into it, or a battery that is just sitting on a table?
◊ In a flashlight powered by a battery, which way do the electric fields point? What would the fields be like inside the wires? Inside the filament of the bulb?
◊ Criticize the following statement: “An electric field can be represented by a sea of arrows showing how current is flowing.”
◊ The field of a point charge, $$|\mathbf{E}|=kQ/r^2$$, was derived in a self-check. How would the field pattern of a uniformly charged sphere compare with the field of a point charge?
◊ The interior of a perfect electrical conductor in equilibrium must have zero electric field, since otherwise the free charges within it would be drifting in response to the field, and it would not be in equilibrium. What about the field right at the surface of a perfect conductor? Consider the possibility of a field perpendicular to the surface or parallel to it.
◊ Compare the dipole moments of the molecules and molecular ions shown in the figure.
o / Discussion question H.
◊ Small pieces of paper that have not been electrically prepared in any way can be picked up with a charged object such as a charged piece of tape. In our new terminology, we could describe the tape's charge as inducing a dipole moment in the paper. Can a similar technique be used to induce not just a dipole moment but a charge?
Contributors
Benjamin Crowell (Fullerton College). Conceptual Physics is copyrighted with a CC-BY-SA license.
This page titled 11.1: Fields of Force is shared under a CC BY-SA license and was authored, remixed, and/or curated by Benjamin Crowell.
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2023-03-31 23:08:34
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http://nylogic.org/Poster?id=2389
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# Poster
Friday, March 14, 20142:00 pmCUNY Logic WorkshopGC6417
# Structurability and countable Borel equivalence relations
## Robin Tucker-Drob
### Rutgers University
The dynamical and descriptive set theoretic complexity of a countable Borel equivalence relation E can often be understood in terms of the kinds of countable first order structures which are compatible with E in a suitable sense. In this talk I will make this suitable sense precise by discussing the notion of Borel structurability. I will also discuss some recent joint work with Brandon Seward in which we show that the equivalence relation generated by the free part of the translation action of a countable group G on its powerset is structurably-universal among equivalence relations generated by free Borel actions of G.
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2020-11-29 01:10:58
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https://people.maths.bris.ac.uk/~matyd/GroupNames/321/Q16xC21.html
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## G = Q16×C21order 336 = 24·3·7
### Direct product of C21 and Q16
direct product, metacyclic, nilpotent (class 3), monomial, 2-elementary
Aliases: Q16×C21, C8.C42, C56.7C6, C24.2C14, C168.6C2, C42.56D4, Q8.2C42, C84.79C22, C4.3(C2×C42), C6.16(C7×D4), C2.5(D4×C21), (C7×Q8).8C6, C28.42(C2×C6), C14.32(C3×D4), (Q8×C21).4C2, (C3×Q8).2C14, C12.19(C2×C14), SmallGroup(336,113)
Series: Derived Chief Lower central Upper central
Derived series C1 — C4 — Q16×C21
Chief series C1 — C2 — C4 — C28 — C84 — Q8×C21 — Q16×C21
Lower central C1 — C2 — C4 — Q16×C21
Upper central C1 — C42 — C84 — Q16×C21
Generators and relations for Q16×C21
G = < a,b,c | a21=b8=1, c2=b4, ab=ba, ac=ca, cbc-1=b-1 >
Smallest permutation representation of Q16×C21
Regular action on 336 points
Generators in S336
(1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21)(22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42)(43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63)(64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84)(85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105)(106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126)(127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147)(148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168)(169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189)(190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210)(211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231)(232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252)(253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273)(274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294)(295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315)(316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336)
(1 267 39 82 309 63 231 172)(2 268 40 83 310 43 211 173)(3 269 41 84 311 44 212 174)(4 270 42 64 312 45 213 175)(5 271 22 65 313 46 214 176)(6 272 23 66 314 47 215 177)(7 273 24 67 315 48 216 178)(8 253 25 68 295 49 217 179)(9 254 26 69 296 50 218 180)(10 255 27 70 297 51 219 181)(11 256 28 71 298 52 220 182)(12 257 29 72 299 53 221 183)(13 258 30 73 300 54 222 184)(14 259 31 74 301 55 223 185)(15 260 32 75 302 56 224 186)(16 261 33 76 303 57 225 187)(17 262 34 77 304 58 226 188)(18 263 35 78 305 59 227 189)(19 264 36 79 306 60 228 169)(20 265 37 80 307 61 229 170)(21 266 38 81 308 62 230 171)(85 163 290 201 147 233 319 113)(86 164 291 202 127 234 320 114)(87 165 292 203 128 235 321 115)(88 166 293 204 129 236 322 116)(89 167 294 205 130 237 323 117)(90 168 274 206 131 238 324 118)(91 148 275 207 132 239 325 119)(92 149 276 208 133 240 326 120)(93 150 277 209 134 241 327 121)(94 151 278 210 135 242 328 122)(95 152 279 190 136 243 329 123)(96 153 280 191 137 244 330 124)(97 154 281 192 138 245 331 125)(98 155 282 193 139 246 332 126)(99 156 283 194 140 247 333 106)(100 157 284 195 141 248 334 107)(101 158 285 196 142 249 335 108)(102 159 286 197 143 250 336 109)(103 160 287 198 144 251 316 110)(104 161 288 199 145 252 317 111)(105 162 289 200 146 232 318 112)
(1 137 309 96)(2 138 310 97)(3 139 311 98)(4 140 312 99)(5 141 313 100)(6 142 314 101)(7 143 315 102)(8 144 295 103)(9 145 296 104)(10 146 297 105)(11 147 298 85)(12 127 299 86)(13 128 300 87)(14 129 301 88)(15 130 302 89)(16 131 303 90)(17 132 304 91)(18 133 305 92)(19 134 306 93)(20 135 307 94)(21 136 308 95)(22 284 214 334)(23 285 215 335)(24 286 216 336)(25 287 217 316)(26 288 218 317)(27 289 219 318)(28 290 220 319)(29 291 221 320)(30 292 222 321)(31 293 223 322)(32 294 224 323)(33 274 225 324)(34 275 226 325)(35 276 227 326)(36 277 228 327)(37 278 229 328)(38 279 230 329)(39 280 231 330)(40 281 211 331)(41 282 212 332)(42 283 213 333)(43 125 268 192)(44 126 269 193)(45 106 270 194)(46 107 271 195)(47 108 272 196)(48 109 273 197)(49 110 253 198)(50 111 254 199)(51 112 255 200)(52 113 256 201)(53 114 257 202)(54 115 258 203)(55 116 259 204)(56 117 260 205)(57 118 261 206)(58 119 262 207)(59 120 263 208)(60 121 264 209)(61 122 265 210)(62 123 266 190)(63 124 267 191)(64 156 175 247)(65 157 176 248)(66 158 177 249)(67 159 178 250)(68 160 179 251)(69 161 180 252)(70 162 181 232)(71 163 182 233)(72 164 183 234)(73 165 184 235)(74 166 185 236)(75 167 186 237)(76 168 187 238)(77 148 188 239)(78 149 189 240)(79 150 169 241)(80 151 170 242)(81 152 171 243)(82 153 172 244)(83 154 173 245)(84 155 174 246)
G:=sub<Sym(336)| (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)(64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105)(106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126)(127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147)(148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189)(190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231)(232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252)(253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273)(274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294)(295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315)(316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336), (1,267,39,82,309,63,231,172)(2,268,40,83,310,43,211,173)(3,269,41,84,311,44,212,174)(4,270,42,64,312,45,213,175)(5,271,22,65,313,46,214,176)(6,272,23,66,314,47,215,177)(7,273,24,67,315,48,216,178)(8,253,25,68,295,49,217,179)(9,254,26,69,296,50,218,180)(10,255,27,70,297,51,219,181)(11,256,28,71,298,52,220,182)(12,257,29,72,299,53,221,183)(13,258,30,73,300,54,222,184)(14,259,31,74,301,55,223,185)(15,260,32,75,302,56,224,186)(16,261,33,76,303,57,225,187)(17,262,34,77,304,58,226,188)(18,263,35,78,305,59,227,189)(19,264,36,79,306,60,228,169)(20,265,37,80,307,61,229,170)(21,266,38,81,308,62,230,171)(85,163,290,201,147,233,319,113)(86,164,291,202,127,234,320,114)(87,165,292,203,128,235,321,115)(88,166,293,204,129,236,322,116)(89,167,294,205,130,237,323,117)(90,168,274,206,131,238,324,118)(91,148,275,207,132,239,325,119)(92,149,276,208,133,240,326,120)(93,150,277,209,134,241,327,121)(94,151,278,210,135,242,328,122)(95,152,279,190,136,243,329,123)(96,153,280,191,137,244,330,124)(97,154,281,192,138,245,331,125)(98,155,282,193,139,246,332,126)(99,156,283,194,140,247,333,106)(100,157,284,195,141,248,334,107)(101,158,285,196,142,249,335,108)(102,159,286,197,143,250,336,109)(103,160,287,198,144,251,316,110)(104,161,288,199,145,252,317,111)(105,162,289,200,146,232,318,112), (1,137,309,96)(2,138,310,97)(3,139,311,98)(4,140,312,99)(5,141,313,100)(6,142,314,101)(7,143,315,102)(8,144,295,103)(9,145,296,104)(10,146,297,105)(11,147,298,85)(12,127,299,86)(13,128,300,87)(14,129,301,88)(15,130,302,89)(16,131,303,90)(17,132,304,91)(18,133,305,92)(19,134,306,93)(20,135,307,94)(21,136,308,95)(22,284,214,334)(23,285,215,335)(24,286,216,336)(25,287,217,316)(26,288,218,317)(27,289,219,318)(28,290,220,319)(29,291,221,320)(30,292,222,321)(31,293,223,322)(32,294,224,323)(33,274,225,324)(34,275,226,325)(35,276,227,326)(36,277,228,327)(37,278,229,328)(38,279,230,329)(39,280,231,330)(40,281,211,331)(41,282,212,332)(42,283,213,333)(43,125,268,192)(44,126,269,193)(45,106,270,194)(46,107,271,195)(47,108,272,196)(48,109,273,197)(49,110,253,198)(50,111,254,199)(51,112,255,200)(52,113,256,201)(53,114,257,202)(54,115,258,203)(55,116,259,204)(56,117,260,205)(57,118,261,206)(58,119,262,207)(59,120,263,208)(60,121,264,209)(61,122,265,210)(62,123,266,190)(63,124,267,191)(64,156,175,247)(65,157,176,248)(66,158,177,249)(67,159,178,250)(68,160,179,251)(69,161,180,252)(70,162,181,232)(71,163,182,233)(72,164,183,234)(73,165,184,235)(74,166,185,236)(75,167,186,237)(76,168,187,238)(77,148,188,239)(78,149,189,240)(79,150,169,241)(80,151,170,242)(81,152,171,243)(82,153,172,244)(83,154,173,245)(84,155,174,246)>;
G:=Group( (1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42)(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63)(64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84)(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105)(106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126)(127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147)(148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168)(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189)(190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210)(211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231)(232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252)(253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273)(274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294)(295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315)(316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336), (1,267,39,82,309,63,231,172)(2,268,40,83,310,43,211,173)(3,269,41,84,311,44,212,174)(4,270,42,64,312,45,213,175)(5,271,22,65,313,46,214,176)(6,272,23,66,314,47,215,177)(7,273,24,67,315,48,216,178)(8,253,25,68,295,49,217,179)(9,254,26,69,296,50,218,180)(10,255,27,70,297,51,219,181)(11,256,28,71,298,52,220,182)(12,257,29,72,299,53,221,183)(13,258,30,73,300,54,222,184)(14,259,31,74,301,55,223,185)(15,260,32,75,302,56,224,186)(16,261,33,76,303,57,225,187)(17,262,34,77,304,58,226,188)(18,263,35,78,305,59,227,189)(19,264,36,79,306,60,228,169)(20,265,37,80,307,61,229,170)(21,266,38,81,308,62,230,171)(85,163,290,201,147,233,319,113)(86,164,291,202,127,234,320,114)(87,165,292,203,128,235,321,115)(88,166,293,204,129,236,322,116)(89,167,294,205,130,237,323,117)(90,168,274,206,131,238,324,118)(91,148,275,207,132,239,325,119)(92,149,276,208,133,240,326,120)(93,150,277,209,134,241,327,121)(94,151,278,210,135,242,328,122)(95,152,279,190,136,243,329,123)(96,153,280,191,137,244,330,124)(97,154,281,192,138,245,331,125)(98,155,282,193,139,246,332,126)(99,156,283,194,140,247,333,106)(100,157,284,195,141,248,334,107)(101,158,285,196,142,249,335,108)(102,159,286,197,143,250,336,109)(103,160,287,198,144,251,316,110)(104,161,288,199,145,252,317,111)(105,162,289,200,146,232,318,112), (1,137,309,96)(2,138,310,97)(3,139,311,98)(4,140,312,99)(5,141,313,100)(6,142,314,101)(7,143,315,102)(8,144,295,103)(9,145,296,104)(10,146,297,105)(11,147,298,85)(12,127,299,86)(13,128,300,87)(14,129,301,88)(15,130,302,89)(16,131,303,90)(17,132,304,91)(18,133,305,92)(19,134,306,93)(20,135,307,94)(21,136,308,95)(22,284,214,334)(23,285,215,335)(24,286,216,336)(25,287,217,316)(26,288,218,317)(27,289,219,318)(28,290,220,319)(29,291,221,320)(30,292,222,321)(31,293,223,322)(32,294,224,323)(33,274,225,324)(34,275,226,325)(35,276,227,326)(36,277,228,327)(37,278,229,328)(38,279,230,329)(39,280,231,330)(40,281,211,331)(41,282,212,332)(42,283,213,333)(43,125,268,192)(44,126,269,193)(45,106,270,194)(46,107,271,195)(47,108,272,196)(48,109,273,197)(49,110,253,198)(50,111,254,199)(51,112,255,200)(52,113,256,201)(53,114,257,202)(54,115,258,203)(55,116,259,204)(56,117,260,205)(57,118,261,206)(58,119,262,207)(59,120,263,208)(60,121,264,209)(61,122,265,210)(62,123,266,190)(63,124,267,191)(64,156,175,247)(65,157,176,248)(66,158,177,249)(67,159,178,250)(68,160,179,251)(69,161,180,252)(70,162,181,232)(71,163,182,233)(72,164,183,234)(73,165,184,235)(74,166,185,236)(75,167,186,237)(76,168,187,238)(77,148,188,239)(78,149,189,240)(79,150,169,241)(80,151,170,242)(81,152,171,243)(82,153,172,244)(83,154,173,245)(84,155,174,246) );
G=PermutationGroup([[(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21),(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42),(43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63),(64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84),(85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105),(106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126),(127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147),(148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168),(169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189),(190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210),(211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231),(232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252),(253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273),(274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294),(295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315),(316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336)], [(1,267,39,82,309,63,231,172),(2,268,40,83,310,43,211,173),(3,269,41,84,311,44,212,174),(4,270,42,64,312,45,213,175),(5,271,22,65,313,46,214,176),(6,272,23,66,314,47,215,177),(7,273,24,67,315,48,216,178),(8,253,25,68,295,49,217,179),(9,254,26,69,296,50,218,180),(10,255,27,70,297,51,219,181),(11,256,28,71,298,52,220,182),(12,257,29,72,299,53,221,183),(13,258,30,73,300,54,222,184),(14,259,31,74,301,55,223,185),(15,260,32,75,302,56,224,186),(16,261,33,76,303,57,225,187),(17,262,34,77,304,58,226,188),(18,263,35,78,305,59,227,189),(19,264,36,79,306,60,228,169),(20,265,37,80,307,61,229,170),(21,266,38,81,308,62,230,171),(85,163,290,201,147,233,319,113),(86,164,291,202,127,234,320,114),(87,165,292,203,128,235,321,115),(88,166,293,204,129,236,322,116),(89,167,294,205,130,237,323,117),(90,168,274,206,131,238,324,118),(91,148,275,207,132,239,325,119),(92,149,276,208,133,240,326,120),(93,150,277,209,134,241,327,121),(94,151,278,210,135,242,328,122),(95,152,279,190,136,243,329,123),(96,153,280,191,137,244,330,124),(97,154,281,192,138,245,331,125),(98,155,282,193,139,246,332,126),(99,156,283,194,140,247,333,106),(100,157,284,195,141,248,334,107),(101,158,285,196,142,249,335,108),(102,159,286,197,143,250,336,109),(103,160,287,198,144,251,316,110),(104,161,288,199,145,252,317,111),(105,162,289,200,146,232,318,112)], [(1,137,309,96),(2,138,310,97),(3,139,311,98),(4,140,312,99),(5,141,313,100),(6,142,314,101),(7,143,315,102),(8,144,295,103),(9,145,296,104),(10,146,297,105),(11,147,298,85),(12,127,299,86),(13,128,300,87),(14,129,301,88),(15,130,302,89),(16,131,303,90),(17,132,304,91),(18,133,305,92),(19,134,306,93),(20,135,307,94),(21,136,308,95),(22,284,214,334),(23,285,215,335),(24,286,216,336),(25,287,217,316),(26,288,218,317),(27,289,219,318),(28,290,220,319),(29,291,221,320),(30,292,222,321),(31,293,223,322),(32,294,224,323),(33,274,225,324),(34,275,226,325),(35,276,227,326),(36,277,228,327),(37,278,229,328),(38,279,230,329),(39,280,231,330),(40,281,211,331),(41,282,212,332),(42,283,213,333),(43,125,268,192),(44,126,269,193),(45,106,270,194),(46,107,271,195),(47,108,272,196),(48,109,273,197),(49,110,253,198),(50,111,254,199),(51,112,255,200),(52,113,256,201),(53,114,257,202),(54,115,258,203),(55,116,259,204),(56,117,260,205),(57,118,261,206),(58,119,262,207),(59,120,263,208),(60,121,264,209),(61,122,265,210),(62,123,266,190),(63,124,267,191),(64,156,175,247),(65,157,176,248),(66,158,177,249),(67,159,178,250),(68,160,179,251),(69,161,180,252),(70,162,181,232),(71,163,182,233),(72,164,183,234),(73,165,184,235),(74,166,185,236),(75,167,186,237),(76,168,187,238),(77,148,188,239),(78,149,189,240),(79,150,169,241),(80,151,170,242),(81,152,171,243),(82,153,172,244),(83,154,173,245),(84,155,174,246)]])
147 conjugacy classes
class 1 2 3A 3B 4A 4B 4C 6A 6B 7A ··· 7F 8A 8B 12A 12B 12C 12D 12E 12F 14A ··· 14F 21A ··· 21L 24A 24B 24C 24D 28A ··· 28F 28G ··· 28R 42A ··· 42L 56A ··· 56L 84A ··· 84L 84M ··· 84AJ 168A ··· 168X order 1 2 3 3 4 4 4 6 6 7 ··· 7 8 8 12 12 12 12 12 12 14 ··· 14 21 ··· 21 24 24 24 24 28 ··· 28 28 ··· 28 42 ··· 42 56 ··· 56 84 ··· 84 84 ··· 84 168 ··· 168 size 1 1 1 1 2 4 4 1 1 1 ··· 1 2 2 2 2 4 4 4 4 1 ··· 1 1 ··· 1 2 2 2 2 2 ··· 2 4 ··· 4 1 ··· 1 2 ··· 2 2 ··· 2 4 ··· 4 2 ··· 2
147 irreducible representations
dim 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 type + + + + - image C1 C2 C2 C3 C6 C6 C7 C14 C14 C21 C42 C42 D4 Q16 C3×D4 C3×Q16 C7×D4 C7×Q16 D4×C21 Q16×C21 kernel Q16×C21 C168 Q8×C21 C7×Q16 C56 C7×Q8 C3×Q16 C24 C3×Q8 Q16 C8 Q8 C42 C21 C14 C7 C6 C3 C2 C1 # reps 1 1 2 2 2 4 6 6 12 12 12 24 1 2 2 4 6 12 12 24
Matrix representation of Q16×C21 in GL2(𝔽337) generated by
26 0 0 26
,
324 13 324 324
,
244 198 198 93
G:=sub<GL(2,GF(337))| [26,0,0,26],[324,324,13,324],[244,198,198,93] >;
Q16×C21 in GAP, Magma, Sage, TeX
Q_{16}\times C_{21}
% in TeX
G:=Group("Q16xC21");
// GroupNames label
G:=SmallGroup(336,113);
// by ID
G=gap.SmallGroup(336,113);
# by ID
G:=PCGroup([6,-2,-2,-3,-7,-2,-2,1008,1033,1015,7564,3790,88]);
// Polycyclic
G:=Group<a,b,c|a^21=b^8=1,c^2=b^4,a*b=b*a,a*c=c*a,c*b*c^-1=b^-1>;
// generators/relations
Export
×
𝔽
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2021-09-24 03:54:07
|
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9694071412086487, "perplexity": 845.6847021906575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057496.18/warc/CC-MAIN-20210924020020-20210924050020-00601.warc.gz"}
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https://mailman.ntg.nl/pipermail/ntg-context/2012/064796.html
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# [NTG-context] \startitemize[columns] broken with backgrounds?
Mon Jan 23 08:45:58 CET 2012
Am 23.01.2012 um 08:39 schrieb Otared Kavian:
> Hi all,
>
> It seems that when using background, \startitemize[columns] does not work as expected: there are no columns, and the numbers of the items are pushed to the left.
You can use the columns environment (which is used by itemize) in a framed, framed text or background environment.
What you can do is to replace the background environment with text background or you use the simple columns environment which does work in framed etc.
Wolfgang
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2016-07-24 04:53:59
|
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https://proofassistants.stackexchange.com/questions/1818/how-do-i-work-with-ints-when-using-coq-of-ocaml-for-ocaml-to-coq-conversion
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# How do I work with ints when using coq-of-ocaml for OCaml to Coq conversion?
I am trying to use coq-of-ocaml to convert a simple recursive factorial function written in OCaml into Coq. I have a testing_factorial.ml file which defines the factorial function as follows:
let rec factorial (n[@coq_cast] : int) = match n with
| 0 | 1 -> 1
| n -> n * (factorial (n - 1))
Running coq-of-ocaml testing_factorial.ml yields a Testing_factorial.v file with the below contents:
(** File generated by coq-of-ocaml *)
Require Import CoqOfOCaml.CoqOfOCaml.
Require Import CoqOfOCaml.Settings.
Fixpoint factorial (n_value : int) : int :=
match n_value with
| (0 | 1) => 1
| n_value => Z.mul n_value (factorial (Z.sub n_value 1))
end.
However, when I run this Coq program, I get the following error:
Recursive definition of factorial is ill-formed.
In environment
factorial : int -> int
n_value : int
p : positive
p0 : positive
Recursive call to factorial has principal argument equal to
"n_value - 1" instead of a subterm of "n_value". Recursive
definition is:
"fun n_value : int =>
match n_value with
| 0 => 1
| Z.pos p =>
match p with
| 1%positive => 1
| _ => (n_value * factorial (n_value - 1))%Z
end
| Z.neg _ => (n_value * factorial (n_value - 1))%Z
end".
Not in proof mode.
I am at a lost with how to fix this. A native Coq implementation of the factorial function would use Natural numbers (Coq's nat). There is no native nat data type in OCaml. I know that it is possible to create a nat type manually in OCaml, but this would require defining from scratch all nat functions (+, -, *, etc.). This is painful to do and would likely complicate Coq proofs on the functions. For a project that I am working on, I would like to prove a number of "math-y" OCaml functions, so learning how to do this would be very helpful! Does anybody have a fix to this error, or how to avoid it in the first place with the coq-of-ocaml translation?
The easiest thing to do seems to be to disable termination checking. There is a setting in coq-of-ocaml to insert Unset Guard Checking in the generated file.
Of course, that jeopardizes logical consistency (although a nonterminating factorial alone won't lead to a contradiction). Note that this factorial is simply not well-defined on negative numbers, so there will be no free lunch. Here are some alternative approaches that a tool could implement.
• You could rely on the technicality that int in OCaml is bounded so factorial terminates after underflowing. Implementing this logic in Coq would still be rather involved.
• You could modify factorial to actually terminate, either at the source, or during/after generation (like hs-to-coq does using edits). There are many possible strategies here. One idea I like is to restrict the domain of factorial, so you wouldn't ever reason about negative inputs, and require all callers to prove that they provide arguments in that domain. (hs-to-coq has a variant of this idea, by annotating data types with invariant.)
• You could translate factorial into a monad that explicitly features nontermination (e.g., using fuel or coinduction). This moves the burden of reasoning about termination out of the tool; this has its pros and cons.
• Thanks for the helpful response. I had seen the Unset Guard Checking option but was a little afraid of using it... I honestly didn't understand it entirely. I included it and am now able to accomplish what I wanted. Regarding your suggestion to restrict the domain in OCaml, could you elaborate a bit on how to do this? I looked at annotating data with invariant in hs-to-coq, but not sure how to do this for OCaml. Nov 3, 2022 at 18:54
• My other suggestions were more hypothetical, as features that don't exist yet. Restricting the domain would mean adding an extra argument to the Coq function that says that the first argument is non-negative in a way that enables writing recursive functions. factorial : forall (z : Z), is_nonnegative z -> Z where is_nonnegative z := Acc (fun x y => 0 <= x < y) z; we have is_nonnegative z <-> 0 <= z, but Acc is more suitable for writing fixpoints. Nov 3, 2022 at 19:23
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2023-01-30 14:54:58
|
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|
https://mathoverflow.net/questions/327503/jordan-decomposition-of-a-block-matrix/328255
|
# Jordan decomposition of a block matrix
Assume $$A$$ is a block matrix of the form:
$$A=\left[\begin{array}{cccc} A_{11}&A_{12}&\ldots&A_{1n}\\ A_{21}&A_{22}&\ldots&A_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ A_{n1}&A_{n2}&\ldots&A_{nn}\\ \end{array}\right]$$
and let $$A^e$$ denote an extended version of $$A$$ given by:
$$A^e=\left[\begin{array}{cccccccc} A_{11}&0&A_{12}&0&\ldots&A_{1n}&0\\ 0&(A_{11}^*)^\top&0&(A_{12}^*)^\top&\ldots&0&(A_{1n}^*)^\top\\ A_{21}&0&A_{22}&0&\ldots&A_{2n}&0\\ 0&(A_{21}^*)^\top&0&(A_{22}^*)^\top&\ldots&0&(A_{2n}^*)^\top\\ \vdots&\vdots&\vdots&\vdots&\ddots&\vdots&\vdots\\ A_{n1}&0&A_{n2}&0&\ldots&A_{nn}&0\\ 0&(A_{n1}^*)^\top&0&(A_{n2}^*)^\top&\ldots&0&(A_{nn}^*)^\top\\ \end{array}\right]$$
where $$A_{ij}^*$$ is the conjugate transpose of the block $$A_{ij}$$ and $$(\cdot)^\top$$ is the transpose operation.
If $$VJV^{-1}$$ is the Jordan canonical decomposition of $$A$$ and $$V_eJ_eV^{-1}_e$$ is the Jordan canonical decomposition of $$A^e$$, can we find a relation between the Jordan blocks $$J$$ and $$J_e$$ (and $$V$$ and $$V_e$$)?
• Looks complicated, Jordan form comes after eigenvalues, and the eigenvalues of $A^e$ don't seem to be clearly related to those of $A$. IMO you should look into this eigenvalue question first: if that does work, there's a hope for Jordan too. – Richard Apr 8 '19 at 19:40
• I’m not sure what you mean by the transpose of the conjugate transpose. Do you just mean the elementwise conjugate? – Anthony Quas Apr 9 '19 at 6:14
• You matrix is equivalent to a block diagonal matrix with A in the top left, some conjugated transpose version of A in the bottom right, and 0s elsewhere. So your question boils down to what the Jordan form of the conjugate transpose part looks like. – Anthony Quas Apr 9 '19 at 6:18
• Thank you @AnthonyQuas. It is true! – user293017 Apr 10 '19 at 7:15
I assume that the $$A_{ij}$$ are square blocks of the same size (say $$m \times m$$), but I suspect that this will work whenever the blocks diagonal $$A_{ii}$$ are all square.
Note that we can find a permutation matrix $$P$$ such that $$M = PAP^{-1} = \pmatrix{A & 0\\0 & \bar A}$$ where $$\bar A = (A^*)^T$$ is simply the conjugate of the matrix $$A$$. Thus, if $$A = VJV^{-1}$$, then we can take $$M = V_mJ_e V_m^{-1}$$ with $$V_m = \pmatrix{V & 0\\0 & \bar V}, \quad J_e = \pmatrix{J & 0\\0 & \bar J}$$ To find the $$V_e$$ corresponding to this same Jordan form, take $$V_e = V_m P$$.
• Am I missing something? Is it not true that $(A_{ij}^*)^T = \bar A_{ij}$? – Ben Grossmann Apr 17 '19 at 13:07
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2021-08-05 10:27:10
|
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|
https://elibm.org/article/10000280
|
## Integration of vector fields on smooth and holomorphic supermanifolds
### Summary
Summary: We give a new and self-contained proof of the existence and unicity of the flow for an arbitrary (not necessarily homogeneous) smooth vector field on a real supermanifold, and extend these results to the case of holomorphic vector fields on complex supermanifolds. Furthermore we discuss local actions associated to super vector fields, and give several examples and applications, as, e.g., the construction of an exponential morphism for an arbitrary finite-dimensional Lie supergroup.
### Mathematics Subject Classification
58A50, 37C10, 57S20, 32C11
### Keywords/Phrases
supermanifolds, vector fields, flows, group actions
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2023-02-06 00:21:57
|
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|
https://math.stackexchange.com/questions/2858209/would-this-suffice-in-a-visual-type-theory-to-define-an-abstract-list-type/2858274
|
# Would this suffice in a visual type theory to define an abstract List type?
See the image. I got that from: wikipedia article. In that, I don't understand the first function nil : () -> L. What is ()?
I want to make a visual type theory so that we aren't stuck comprehending pure text for eternity.
Also, is the abstract type List a product of some sort? The diagram doesn't indicate this since it's based on a product diagram of $E \times L$.
Assume that product has already been defined by a similar diagram and that there is a system that can interpret these smallish diagrams, so that ideally $E\times L$ and $p_L$ as well as the graphical arrows and blocks show up in a different color indicating that you cannot edit them.
Additionally in the wikipedia article, they say:
for any element e and any list l. It is implicit that
cons (e, l) ≠ l
cons (e, l) ≠ e
cons (e1, l1) = cons (e2, l2) if e1 = e2 and l1 = l2
Note that first (nil ()) and rest (nil ()) are not defined.
But isn't the last one already true!?? How should I indicate the first two in diagram form?
Q: I don't understand the first function nil: () → L. What is ()?
It is an atom, written as an abstract data type. The List is created and initialized as empty, using the atom. In Lisp: Set an atom to NIL and initialize the list with that atom.
nil: () → L
That creates an empty list. It's like: char *L = (char *)malloc(0);
Q: Also, is the abstract type List a product of some sort?
It's a list, see link above for "list".
Q: But isn't the last one already true!??
It says:
for any element e and any list l. It is implicit that
cons (e, l) ≠ l
cons (e, l) ≠ e
cons (e1, l1) = cons (e2, l2) if e1 = e2 and l1 = l2
It's implicit.
Q: How should I indicate the first two in diagram form?
CONS takes its first argument [which may be either an atom or a list] and inserts it just after the first left parenthesis in the second argument. This second argument should be a list. CONS will actually connect things onto atoms as: "(cons 'a 'b)", but this creates a special form of list called a dotted pair.
• how is the first one implied? – OlympicComputerChairSitter Jul 21 '18 at 16:53
• It is "any element e and any list l" that is implicit to the following conditions, which are explained. The "first one" isn't implicit, it's stated clearly that it's !=l . – Rob Jul 21 '18 at 17:39
• I don't see where it's stated.... – OlympicComputerChairSitter Jul 21 '18 at 18:00
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2021-06-15 17:15:20
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http://love2d.org/forums/viewtopic.php?p=73175&sid=fd4174a3ec2065dd729193e9085ad36e
|
Party member
Posts: 399
Joined: Mon Jan 10, 2011 8:25 am
Location: Oklahoma
Karai17 wrote:A thought. How feasible would it be to use ATL without grid locking? And further on that notion, How feasible would it be to detect collisions with objects without grid locking? For instance, if I have a rock sitting in the middle of a tile, How could I detect only the part of the tile that is not transparent? Would I maybe need semi-complex polygons over top the collision area, or would it be possible to determine if the sprite's opaque pixels are going to collide with the rock's opaque pixels?
I like ATL very much; working with Tiled maps is quite easy and I wouldn't want to lose such a great tool for this thing I am about to start working on.
You can definitely do those things. Just because the rendering is grid-based doesn't mean your game logic has to be. But collision detection is complicated and outside the scope of ATL so I can't help you with the specifics. That is something you have to decide on. For per-pixel stuff you will likely just have to load the tileset image separately and take what information you need from the pixel data.
Uhfgood
Prole
Posts: 35
Joined: Sat Jul 28, 2012 10:04 pm
Location: Oregon, US
Contact:
I've noticed it will draw flipped tiles, however is there a way I can tell if a tile in the tile layer has been flipped?
This kind of functionality is important to me in my current game. Thanks!
Party member
Posts: 399
Joined: Mon Jan 10, 2011 8:25 am
Location: Oklahoma
Sort of. There isn't a public interface for it. A single binary value represents the flipped status of a tile and it's stored in TileLater._flippedTiles, which is a grid. The 1's binary digit represents the diagonal flip, the 2's digit represents the vertical flip, and the 4's digit is horizontal.
I'll add a public interface for it soon but in the mean time here is how you can do it yourself:
Code: Select all
local function tileIsFlipped(layer, direction, x, y)
if direction == "diagonal" then
return layer._flippedTiles(x,y) % 2 == 1
elseif direction == "vertical" then
return layer._flippedTiles(x,y) % 4 >= 2
elseif direction == "horizontal" then
return layer._flippedTiles(x,y) >= 4
end
end
Karai17
Party member
Posts: 909
Joined: Sun Sep 02, 2012 10:46 pm
A thought. How would one go about multi-layering? For instance. Being able to walk under a bridge, but then walk up a flight of stairs so you are now on the same layer as the bridge and able to walk over it.
My first thought would be to make a custom layer between each tile layer and use some property to determine a change-in-layer but that seems like a horrible idea, haha.
STI - An awesome Tiled library
LÖVE3D - A 3D library for LÖVE 0.10+
Dev Blog | GitHub | excessive ❤ moé
Party member
Posts: 399
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Location: Oklahoma
The simplest way would be to use a visual trick instead of layering. Have the bridge be a simple image instead of a tileset and just have a collision box covering each entrance to the bridge (above and below) and depending on the last one hit draw the bridge before or after the player sprite. Or you could just have multiple layers before and after the bridge and switch the player object between them.
danbo
Prole
Posts: 18
Joined: Thu Jan 03, 2013 8:11 pm
I was having an issue with ATL where what's being rendered would fade out over the course of about 5 seconds, including stuff that ATL doesn't draw (eg. calls to graphics.rectangle).
I don't know what causes it, but I found it only seems to happen if there's just a tile layer in the TMX file. If you add even an empty Object Layer in Tiled, the issue no longer seems to happen.
Just in case anyone else gets the same issue.
Karai17
Party member
Posts: 909
Joined: Sun Sep 02, 2012 10:46 pm
This may be a rounding issue on some systems. if you place the following line after your map:draw(), it should fix the problem:
Code: Select all
love.graphics.setColor(255, 255, 255, 255)
STI - An awesome Tiled library
LÖVE3D - A 3D library for LÖVE 0.10+
Dev Blog | GitHub | excessive ❤ moé
Ubermann
Party member
Posts: 146
Joined: Mon Nov 05, 2012 4:00 pm
I got a "Unknown event q" when I press [ESCAPE]
It should be love.event.push("quit").
Party member
Posts: 399
Joined: Mon Jan 10, 2011 8:25 am
Location: Oklahoma
Ubermann wrote:I got a "Unknown event q" when I press [ESCAPE]
It should be love.event.push("quit").
Thanks. I swear I have fixed this same bug 5 times now.
Uhfgood
Prole
Posts: 35
Joined: Sat Jul 28, 2012 10:04 pm
Location: Oregon, US
Contact:
My slope stuff is using 16x16 sized tiles now, and even though the map itself isn't very big -- It's apparently got too many tiles because it takes seconds to load (like you can actually tell that it's taking the time to load up the whole map).
My game is probably going to have a map even bigger than this test map I made for my sloping code.
The way I would think it would work is if you have load method that takes a chunk size maybe how many tiles in the x and y to load up or where to start and stop... This way I could call this whenever my camera got to the edge of the chunk I previously loaded up. In this way it wouldn't take as much time loading up the whole map at the start.
Also, could you tell me how the tiles are loaded into memory -- that is... are they individual images, or is it like a sprite sheet/ tile sheet? (In other words is a tileset in the loader a table of individual images, or one image that each of the tiles are taken from) -- if this makes any sense?
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2021-04-18 17:38:55
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https://eprint.iacr.org/2022/1744
|
Worst and Average Case Hardness of Decoding via Smoothing Bounds
Abstract
In this work, we consider the worst and average case hardness of the decoding problems that are the basis for code-based cryptography. By a decoding problem, we consider inputs of the form $(\mathbf{G}, \mathbf{m} \mathbf{G} + \mathbf{t})$ for a matrix $\mathbf{G}$ that generates a code and a noise vector $\mathbf{t}$, and the algorithm's goal is to recover $\mathbf{m}$. We consider a natural strategy for creating a reduction to an average-case problem: from our input we simulate a Learning Parity with Noise (LPN) oracle, where we recall that LPN is essentially an average-case decoding problem where there is no a priori lower bound on the rate of the code. More formally, the oracle $\mathcal{O}_{\mathbf{x}}$ outputs independent samples of the form $\langle \mathbf{x}, \mathbf{a} \rangle + e$, where $\mathbf{a}$ is a uniformly random vector and $e$ is a noise bit. Such an approach is (implicit in) the previous worst-case to average-case reductions for coding problems (Brakerski et al Eurocrypt 2019, Yu and Zhang CRYPTO 2021). To analyze the effectiveness of this reduction, we use a smoothing bound derived recently by (Debris-Alazard et al IACR Eprint 2022), which quantifies the simulation error of this reduction. It is worth noting that this latter work crucially use a bound, known as the second linear programming bounds, on the weight distribution of the code generated here by $\mathbf{G}$. Our approach, which is Fourier analytic in nature, applies to any smoothing distribution (so long as it is radial); for our purposes, the best choice appears to be Bernoulli (although for the analysis it is most effective to study the uniform distribution over a sphere, and subsequently translate the bound back to the Bernoulli distribution by applying a truncation trick). Our approach works naturally when reducing from a worst-case instance, as well as from an average-case instance. While we are unable to improve the parameters of the worst-case to average-case reductions of Brakerski et al or Yu and Zhang, we think that our work highlights two important points. Firstly, in analyzing the average-case to average-case reduction we run into inherent limitations of this reduction template. Essentially, it appears hopeless to reduce to an LPN instance for which the noise rate is more than inverse-polynomially biased away from uniform. We furthermore uncover a surprising weakness in the second linear programming bound: we observe that it is essentially useless for the regime of parameters where the rate of the code is inverse polynomial in the block-length. By highlighting these shortcomings, we hope to stimulate the development of new techniques for reductions between cryptographic decoding problems.
Available format(s)
Category
Foundations
Publication info
Preprint.
Keywords
code-based cryptography hardness reductions smoothing bounds
Contact author(s)
thomas debris @ inria fr
n a resch @ uva nl
History
2022-12-25: approved
See all versions
Short URL
https://ia.cr/2022/1744
CC BY
BibTeX
@misc{cryptoeprint:2022/1744,
author = {Thomas Debris-Alazard and Nicolas Resch},
title = {Worst and Average Case Hardness of Decoding via Smoothing Bounds},
howpublished = {Cryptology ePrint Archive, Paper 2022/1744},
year = {2022},
note = {\url{https://eprint.iacr.org/2022/1744}},
url = {https://eprint.iacr.org/2022/1744}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.
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2023-03-21 04:27:11
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http://steamcommunity.com/sharedfiles/filedetails/?id=98323667
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Killing Floor
### Killing Floor
277 ratings
Map Pack - Killing Floor
Rate
Description
Maps released on the Steam Workshop for Killing Floor located in one single Map Pack. Credit goes to map maker. Don't forget to rate and comment!
Last updated: August 24, 2015
Use the 'Subscribe to all' button at your own risk
A. Press the giant green "Plus" symbol next to the map you want to subscribe to, the map will automatically start to download when Killing Floor is next launched.
A. That is a limitation of the Steam Workshop, If you are wanting to subscribe to more than 50 you will have to remove already subscribed Killing Floor subscriptions. Although they will be unsubscribed, the files necessary to play the maps are already downloaded and thus can be played at your leisure.
Here is a list of every 50 to keep track.
50 - KF-Fabulous
100 - KF-ElecFields
150 - KF-Wolf wolfenstein remake.
200 - KF-HallCrawl
250 - KF-A-Starship
300 - KF-DefenceLondonFinal
350 - KF-BuddhaTemple-Final-3
400 - KF-Fortin
450 - KF-3Bridges-Final-fix3
500 - KF-Seaports
550 - KF-Evasion
600 - KF-Stronkhold(stronghold better version)
650 - [Survival] KFO-Manor
700 - KF-ALTTP-ZELDA-NIGHT
750 - MGS Space Station NO MUSIC EDITION
2. How do I get these map in-game?
A. Maps can be found where you normally select maps in Killing Floor. If the map is missing try restarting Killing Floor.
FAQ: Часто задаваемые вопросы
1. Как я могу скачать карты?
A. Нажмите на гигантский зеленый символ «плюс» рядом с картой вы хотите подписаться, карта автоматически начнет загрузку, когда Killing Floor будет запущен следующий.
2. Как я могу получить эти карты в игре?
А. Карты можно найти, где вы обычно выбирают карты. Если карта отсутствует перезагрузки Killing Floor.
FAQ：よくある質問
1。どのように私はマップをダウンロードすることができますか？
A.あなたがを購読するマップの横に巨大な緑色の "+"記号を押すと、マップは自動的にKilling Floorの次回起動したときにダウンロードを開始します。
2。どうすれば、これらのマップでゲームを取得するのですか？
あなたが通常のマップを選択する場所A.マップを見つけることができます。マップは、再起動のキリングフロアが不足している場合。
Items (772)
Last Resort Beta 1.1vB
Created by TNT1992
I am ending support for this map and remaking it from scratch with a new idea and theme. I will return to this and fix the current bugs and complete what isnt finished but apart from that I will stop working on this map. Please let me know of any bugs that...
Doom 2 SP - Maps 01-10, 30-32
Created by Marco
A part of all of the Doom 2 single player campaign.
These maps requires Doom 2 pack to be installed.
Credits:
Maps are originally created by Lethal_Vortex, I only added Doom 2 stuff for them.
To play you must select game mode "Doom SinglePlayer" an...
Doom 2 pack
Created by Marco
Contains a complete pack of all Doom 2 monsters, weapons and powerups. Including a single player/cooperative game type.
Mod files:
System/DoomPawnsKF.int
Syst...
GG-CamoTime
Created by Mr.RoBoT
Map for GunGame mode
Grab your weapon get into the forest, its camo time!
Files:
...\Killingfloor\Maps\GG-CamoTime.rom...
GG-Purplish
Created by Mr.RoBoT
GunGame map based of my KF-Purplish
Files:
...\Killingfloor\Maps\GG-Purplish.rom...
GG-Streetv2
Created by Mr.RoBoT
One of the oldest custom maps since KF retail release made for GunGame gamemode !
Files:
...\Killingfloor\Maps\GG-Streetv2.rom...
Glasshouse
Both teams spawn with M79 grenade launchers and must blow up the opposing team's building floor by floor. Respawns are infinite, but each time a floor is destroyed you will spawn on the next available floor down. Once the last spawn area in your building i...
Created by FUBAR!
This map is based off of the Doom II map of the same name. It features small and simple level layout in part of an underground industrial complex. Comfortably plays with 6 people or less. Play with more people at your own risk.
Oh yeah, if you try it...
Raccoon International Airport - WB
Created by Hodor (KiCk3R)
Raccoon International Airport - Wave Based Gametype
Raccoon International Airport - MP
Created by Hodor (KiCk3R)
Raccoon International Airport - Multiplayer Version
Pride Hill Shopping Center
Created by Hodor (KiCk3R)
You and your friends go for a bite to eat. Except... you turn out to be the meals!
Its kill or be killed in this action packed shopping center. You may even find a few missions!
Mountain Pass Night
Created by [TW]Yoshiro
The Classic Killing Floor map KF-MountainPass reimanged as a night map. Enjoy!
Kf-SilentHillBeta2-0
Created by swift_brutal_death
Fist off, I have only briefly played a couple Silent Hill games. This is not an authentic representation. I started this map using reference from the movie. If you hated the movie you probably will feel the same way about this map. I enjoyed recreating...
KF-420-Ganja-Farm-Reweeded
Created by avp2501
Small classic defense map by KINGshinobi that I modified into my own variation adding weather effects, improved bot pathing, boss cut scene and various other tweaks....
KF-BioTech-Incident
Created by avp2501
Small map used as a Teaser for my story based mission "BioTech"
Sadly BioTech is miles off being released and so we're just left with this nice Teaser...
KF-Cabin
Created by Mr.RoBoT
dark,creepy and small house
Files:
...\Killingfloor\Maps\KF-Cabin[WB].rom
...\Killingfloor\Music\cabinofzombies1.ogg
...\Killingfloor\Music\cabinofzombies2.ogg...
KF-ContactCentreB1
Created by Chael Sonnen
Small map based in some kind of office, games are quick and to the point, no pointless running around for traders that don't need to be there...
KF-Crystal-Lake
Created by avp2501
This is the most stable exploit free version but still isn't final.
This version also adds a new area to the map.
...
KF-DreddStationFinal1-3
Created by swift_brutal_death
Set on a space station near a massive space port. From what I've experienced it is not easy. Working on a new version with reworked lighting....
KF-Harbor
Created by TheRealMoney
Reports are coming in from the Port Authority about a bizarre attack on the Harbour.
A number of cargo containers were offloaded from a cargo vessel belonging to a London Biotech researcher. According to one of the surviving dock workers, they had barely ...
KF-Killing-V
Created by Mr.RoBoT
A valentine map I guess...
Files:
...\Killingfloor\Maps\KF-Killing-V.rom
...
KF-LostCity
Created by Krull0r
Detailed city based Killing Floor map with In- and outdoor areas....
Created by Mr.RoBoT
- There are 3 areas in the map, each one spawns 2 players.
- Around each area barricades aren't welded, you can weld and not unweld them after but there is big metal door you could unweld it.
- When the wave is over it opens a teleporter in each area to ...
KF-Purplish
Created by Mr.RoBoT
An Abandoned world where is nothing left except your squad and the flesh eating specimens...
Files:
...\Killingfloor\Maps\KF-Purplish.rom
...\Killingfloor\Music\begin.ogg
...\Killingfloor\Music\KF_ChainsawChaos.ogg
...\Killingfloor\Music\Survival-Be...
KF-RainyDay
Created by Mr.RoBoT
Simple map with new idea "Topview" you play your character as your screen viewing from above such like NationRed or Alien Swarm gameplay, although its kinda hard to control so I suggest you to try it on beginner or normal at first.
note: crouch and shoot...
KF-Resistance
Created by SORROW
My First Map on Killing Floor. There is a outside and an inside area to explore. Plus it has a secret room. Follow me if you like. Thanks.
Some of the Textures are from cgtexture...
KF-SecurityFloorB1
Created by Chael Sonnen
a bigger map with a similar theme to my contactcentre one, still pretty small though, many places to camp, and routes for kiting fags...
KF-Streetv3
Created by Mr.RoBoT
It was my first custom map since Killing Floor release
Files:
...\Killingfloor\Maps\KF-Streetv3-FiX.rom
...\Killingfloor\Music\begin.ogg
...\Killingfloor\Music\KF_ChainsawChaos.ogg
...
KF-Survival-v2
Created by Mr.RoBoT
face against endless wave of specimens...
rise and shine for your own death
Files:
...\Killingfloor\Maps\KF-Survival-v2.rom
...\Killingfloor\Music\Survival.ogg
...\Killingfloor\Music\Survival2.ogg
...\Killingfloor\Music\Survival3.ogg
...\Killingfl...
KF-TheBombShelter
Created by [JC]FishMissile
The only safe place left on the block. A small indoor map modeled after an actual location. Its completely dark outside, good luck surviving anywhere but the basement! B.Y.O.B
Submitted for Whitelist approval in December of 2011 -No response...
KF-TheHallway
Created by Mr.RoBoT
Sci-fi map was made for dead space mod in kf, its simple long hallway where zeds comes from both sides
Files:
...\Killingfloor\Maps\KF-TheHallway.rom
...\Killingfloor\Music\Hallway01.ogg
...\Killingfloor\Music\Hallway02.ogg
...\Killingfloor\Music\Ha...
KF-TrailOfTheWoods-Reborn
Created by avp2501
Originally made by Boxxxed and modified by me to improve the pathing, trader pathing wisp, blocking volumes and various other tweaks.
Kf-BrewPubBeta1-1
Created by swift_brutal_death
Modeled after my place of employment. Referenced over 100 pictures to make as accurate as possible. This is unfinished, but, I ran into some problems with having to many BSP shapes so I made it playable/exploit free and put it out. Not sure I'll ever co...
Kf-HellGateFinal1-2
Created by swift_brutal_death
Monsters spawn almost entirely on one side of the map. Intended for 10+ players. One trader located in center of map. Designed almost like a tower defense with focus on chokepoints and assigning posts for various team members.
All my maps can be fo...
Kf-Multifarious
Created by swift_brutal_death
First map. I learned how to use this editor while creating this map, which probably explains why it is so unorganized and huge.
All my maps can be found here on the steam workshop: http://steamcommunity.com/id/swift_brutal_death/myworkshopfiles/...
Swamp
Created by Kyben
The moody swamps of a now abandoned property serve as the final base of operations for the Delta Battalion. The Specimens have wiped out most inner-city defences, all that remains is the uncharted wilderness and isolated, country homesteads. The terrain on...
Testmap6p FiringRangeV2
Created by Jさん
Press E key to spawn specimen
2012/12/13 Xmas update!
Testmap6p FiringRangeV2_Xmas
http://steamcommunity.com/sharedfiles/filedetails/?id=113031799
[file list]
KF-Testmap6p_FiringRangeV2.rom
KF-Testmap6p_FiringRangeV2.ucl
KF-Testmap6p_FiringRange...
KF-2Doors1Fort
Created by Chael Sonnen
Another small map, it's based on my gun game map "1Fort", you spawn inside the fort with 2 pre-welded doors, if you fall outside the doors then you're stuck unless you grenade the doors open, the map is pretty easy with a bunch of Demo's and 1 or 2 support...
KF-NecrotelB2
Created by Chael Sonnen
This map......kinda shitty, I made it about a year ago, pretty simple layout, but quite tough.
The colour red doesnt work on this map (except HUD) so the trader whisp is grey/blue, no idea why, too lazy to fix. It's supposed to be a hotel of some sort....
BioticsLab Lights Out!
Created by miks
KF-BioticsLabLightsOut-v6a
This was my first attempt at mapping, its just a dark version of BioticsLab by Tripwire Interractive. And by dark I mean REALLY dark, basically on lights at all.
Notes: Updated the map with a fix for the "black screen" bug,...
Carden Hill
Created by miks
KF-CardenHill-v3a
An asylum themed map...
Cube_563
Created by Crasher563
Cube_563 is a somewhat small, mostly cubemap that has paths down to the london underground. It has 4 traderooms, biohazardous waste that kill you and the specimens, lots of zombiezone spawners, somewhat prewelded doors, average detaling with static meshes ...
Dragged Into Hell KF doom MAppack
Created by FluffyCelix
Map pack for the doom mutator custom story based on dante's inferno
Warning this maps are really hard
you will need doom mutator by marco in order to play this
marco doom mutator
http://steamcommunity.com/sharedfiles/filedetails/?id=97737990&searchte...
Funmap
Created by Marco
This is just a map to chill out in, away from the zombie apocalypse.
Requires Doom 2 monsters pack to run.
Credits:
Part of the map was created by Lethal_Vortex.
Wildfish car model is from UnWheel mod for UnrealTournament 2004.
Medium Tank model is ...
KF-Atlas
Created by Sam
Sci-fi city environment.
(fixed servercrash)
Credits:
Hourences for his texture packs; cgtextures.com; layout from a Gears of War 2 map...
KF-Barzakh
Created by Sam
Small Middle-Eastern style map.
(fixed servercrash)
Credits:
cgtextures.com...
KF-Cave
Created by Sam
Cave/jungle themed map.
Credits:
cgtextures.com; Hourences for his nature texture pack and his DM-Sae tutorial...
KF-Chiron TL-34 (thats right - halo in Killing Floor!
Created by bacon932
A classic halo map re-created by me for Killing floor. ENJOY!
The .ogg files go in the music folder btw (i have no idea if the files automatically go into the correct folders)...
KF-Dammage
Created by Sam
Sci-fi dam.
Credits:
cgtextures.com...
KF-Fabulous
Created by Sam
A Killing Floor map emulating the atmosphere from "Fable".
(fixed servercrash)
Credits:
cgtextures.com for the basis of most of the textures, Hazel H. for the skybox textures...
KF-Forest
Created by Sam
Forest theme. Rivers, log-cabins, a cave..
Fixed server crash! (but had to remove emitters)
Credits: cgtextures.com; cgskies.com...
KF-MuskratCastle
Created by Sam
Tiny island. The building is based on the townhall of Hinterschmieding.
Fixed Servercrash (had to remove glitter effect on sunset to do it)
Credits:
cgtextures.com...
KF-PhantomCastle
Created by Sam
Castle themed map.
(Fixed Servercrash)
Credits:
cgtextures.com...
KF-WaterCanal
Created by Saics
...
Manor Lights Out!
Created by miks
KF-ManorLightsOut-v2
Dark version of Manor (original version by Tripwire of course)
If you want custom music for the map, go here http://steamcommunity.com/sharedfiles/filedetails/?id=98667423
Otherwise there will be no music I believe, it might be ...
Offices Lights Out!
Created by miks
Yeah another dark version of the stock maps. Sorry for the lack of screenshots but you cant really see anything except for the outside bits :)
The map is at its best when using a mutator that provides extra light sources such as glowstick or flares. Wit...
Still Alive
Created by miks
KF-StillAlive-v1
A portal themed map with some funny features such as
1. A button controlled moving platform for "quick" escapes
2. A tube you can use to travel accross the map in seconds, does heavy damage on exit so avoid using with less than 80 hea...
Trial Challenges Jump/Shooting
Created by FluffyCelix
Trials are puzzel maps where u gotta finish 1 trial before u can move to the next one. only one of your teamates have to make it to the finish of 1 trial to move on to the next one.
mostly involved jumping but some also contain shooting. bonus Tip Shoot ...
Trials Lego Jumping Map
Created by FluffyCelix
Trials are puzzel maps where u gotta finish 1 trial before u can move to the next one. only one of your teamates have to make it to the finish of 1 trial to move on to the next one.
mostly involved jumping but some also contain shooting. bonus Tip Shoot ...
Trials PowerGenerator Jumping Map
Created by FluffyCelix
Trials are puzzel maps where u gotta finish 1 trial before u can move to the next one. only one of your teamates have to make it to the finish of 1 trial to move on to the next one.
mostly involved jumping but some also contain shooting. bonus Tip Shoot ...
UAT - Nerf Warz Apocalypse
Created by Sheath
This map is almost an exact 1 to 1 scale of the University I went to: University of Advancing Technology.
At UAT, we had a lot of Nerf Warz battles, and especially HumansVsZombies... This gave me a great idea...
Basically, I wanted to recreate some...
Trials i wanna be the map Jumping/Shooting part1
Created by FluffyCelix
Trial map based on i wanna be the guy it has some custom monsters that i made in it
Trials are puzzel maps where u gotta finish 1 trial before u can move to the next one. only u need part 2 as well
Requires Marco doom Mutator to run
marco doom mutato...
Trials i wanna be the map Jumping/Shooting part2
Created by FluffyCelix
This is the missing files from part1 due to limit on upload space. if u download this u need part 1 to
marco doom mutator
http://steamcommunity.com/sharedfiles/filedetails/?id=97737990&searchtext=doom
choose gametype doom story to start the trial ma...
kf-the hallway
Created by Target Practice
pretty basic map that i made...
Kf-Defence-b4
Created by || RaVs ||
Defense thy self!...
Laser Challenge - V3
Created by Hodor (KiCk3R)
You have been hired by the UBCS (Umbrella Biohazard Countermeasure Service) and you are currently in training. Your training is simple. The Laser is your enemy. The Specimens are your enemy. Other Players are your enemy. Gear up. And Head Out.
NOTE: This ...
The Hive - V1 - Rev 3
Created by Hodor (KiCk3R)
5 hours ago, Red Queen went homicidle. She sealed down The Hive and killed everyone down there. Your job is to disable The Red Queen and to rescue any survivors. Take A Flashlight…Its dark down there…
Raccoon International Airport - SP
Created by Hodor (KiCk3R)
Raccoon International Airport - Single Player
NOTE: Click "Story" to play.
Guys, there is a fix. You must download and install a mutator to enable the old specimens. First, download the Mutator from HERE: http://team-gmk.com/dox/CustomSpawnFix.rar , On...
Defiance
Created by Jsh
Current state of map: Alpha version 2
Full file size: 29 MB, 7-Zip file size: 10,3 MB
This shopping center themed map features both kinds of playable areas: Outside - parking area and loading bay - and inside - shops, stock and corridors.
It comes w...
KF-AkihabaraVer1.05
Created by YOUJO
Hi! I am YOUJO! I made first map .
Akihabara Electric Town is a district in Tokyo, Japan.
Excuse me for big file size and many bugs.
This map is still in progress, but my fixing is slow.
Any bug report would be appreciated.
Known issue:
-Ammo spaw...
KF-ArenaWarsV3-LightsOut
Created by Shinkichi
This is a modification of the KF-ArenaWarsV3
"not Whitelisted"...
KF-HuskgunHuskgunHuskgun
Created by Shinkichi
This is a modification of the KF-LAWLAWLAW
"not Whitelisted"...
Metal Gear Solid - WB
Created by Hodor (KiCk3R)
Here is a sneak preview on my upcoming MOD - Metal Gear Solid. This is a waved based map, based on the beginning level of MGS.
Guys, there is a fix. You must download and install a mutator to enable the old specimens. First, download the Mutator from HE...
KF-Arena-meatV2
Created by Как Цапля
еще одна бредовая карта от меня,переработанная немного,просто хороша для мяса,и все...
Another crazy map from me, a little recycled, just good for meat, and all ......
KF-Shipment
Created by =[PMC]= breakfast
Heres my remake of the CoD4 map "Shipment"
Hope you enjoy / Have fun...
Portal Gun
Portal Gun that can be used as a tool or weapon. Will upload readme file asap as too many thank yous to mention here
Also includes test map made by Marco,...
KF-TheTestmap-2
Created by Mutant
This is a vastly improved version of Anaemix's original testmap. The map has been designed to be the perfect practise environment and for multiplayer usage.
You can neither level up your perks nor gain achievements on it, it's for practise purpose only...
Vehicle Mod
Vehicle mod for Killing Floor by Braindead. Includes new gametype and 1 map.
This is an updated version of the original, which can now be updated constantly, thanks to the workshop. For more info, please visit TWI forums
Update: 1/10/12
- Change...
Gun Game
Created by [TW]Ramm-Jaeger
Gun Game With Killing Floor Weapons. Every kill instantly gets you the next weapon in the list. Be the first player to get a kill with every weapon on the list to win!
Looking for some fast past player vs player action with a Killing Floor spin? Look no...
VM-BloodMountain - Vehicle Mod Map
VM-BloodMountain by Arramus
...
VM-CornerMarket for Vehicle Mod
VM-CornerMarket for the vehicle mod...
KF-KFpub-Deck17
Created by cyberpunk^2.0
Enter Deck 17 - Magma Refinery... Deck 16's HOT neighbor.
By Teddie Tapawan, ported by Kazachidla....
KF-LogovoFIX
Created by BAHO[21RUS]
Author - ApostJI
Fixed - BAHO[21RUS]...
Kf-WestLondonWinter
Created by bacon932
A Winterised variant of the stock map Kf-westlondon. Bring a gun... and maybe a coat......
MountainPass_Defense
Created by Crasher563
Ive re-made the map mountainpass into a "clusterf**k format*. Your squad has set up a barricade at the end of the road to await evacuation after having killed the patriarch in the original map. You have suited the broken brige for airial evactuation and pi...
KF_Farm_day(morning)
Created by ☆Pacifist☭☮
вся карта осталась без изменений ,я изменил лишь текстуру неба!!!
the entire map has been no change, I changed only the texture of the sky!!!...
Vehicle Map Pack 2 - Mountian Pass Special
VM-MountainPass
VM-MountainPassNight...
Vehicle Map Pack 3
VM-ManorMini
VM-MosEiseyScum
VM-MultiStory_CarPark
VM-TheddlePedal...
Vehicle Map Pack 4
VM-Suburbia
VM-Tricky...
Vehicle Map Pack 1
VM-DeathBasin
VM-DeathBasinSandsNight
VM-FarmFuzz
VM-ManorForkLiftFrenzy...
DEnCich
Created by Den069721(RUS60)
...
KF-Constriction
Created by Swanky
Welcome to the mansion. What mansion? What do I know? Simple indoor map with plenty of rooms and corridors, multiple levels. Enjoy. :)...
KF-Corruption
Created by Swanky
Techmap designed for Killing Floor, complete with custom content. Music-file made by Xenogenocide, used with permission....
KF-HiddenFacility
Created by avp2501
This is the first map I made for KF: It's not the latest version however this one is whitelisted
Map Size: HUGE
Players spawn at random points so you will start alone. Find each other for the best chance of survival
=====Map Description=====
15:22 - ...
KF-WestCross
Created by avp2501
kf-WestLondon + kf-filthscross = kf-WestCross...
Kf-DreddStationFinal1-4
Created by swift_brutal_death
Lighting revisions since previous version.
All my maps can be found here on the steam workshop: http://steamcommunity.com/id/swift_brutal_death/myworkshopfiles/...
The Lighthouse
Created by LATTEH
Hello! thank you for considering for downloading my map! But before you do could you download from this site to give this legendary Custom mod site some support?
http://gamebanana.com/kf/maps/155826
You Sir! you like hardworked on levels for fr...
KF-China
Created by K-2
A small chinese-style map based on Unreal Tournament DM-AChina by AngelHeart.
Version: beta 4...
KF-ElecFields
Created by K-2
KF version of wonderful rusty map from official UT2003 DE Bonuspack.
Original author - Juan Pancho 'XceptOne' Eekels.
Version: 1.2...
KF-Hyperblast2
Created by K-2
KF port & adaptation of UT2k4 DM map.
Author of the original map - Rogelio Olguin.
Version: 1.2...
KF-TheGreatPyramid-Arena
Created by K-2
Another remake of Serious Sam map for KF.
This is an arena-style map with special wave-based zombie spawn places.
Version: 1.2...
KF-Tomb-of-Ramses
Created by K-2
Remake of Serious Sam TFE map for Killing Floor
Version: 1.3 + fix...
Night of the Living Dead --Beta Revision 6
Created by Blackbeard
A recreation of the farmhouse from the 1968 Night of the Living Dead.
Tweaked some things here and there to improve zed pathfinding.
Coming Soon: Deactivation of indoor spawns once doors have been barricaded...
GG-VR_Corridor_Tiny
Created by avp2501
Small corridor = Pure chaos...
Created by avp2501
Large sized map which isn't very chaotic. Play the smaller versions if you prefer no-cover madness....
Created by avp2501
Tiny sized map which is just chaotic. Play the bigger versions if you prefer cover fire....
GG-VR_OpposingFronts
Created by avp2501
3 levels divided into Red VS Blue on opposing sides....
KF-VR_OpposingFronts
Created by avp2501
3 levels divided into Red VS Blue on opposing sides. Now includes Zombies...
KF-Deck16][-fix
Created by Fobos
A Killing Floor map based on Unreal Tournament DM-Deck16][. Conversion made by {CB}Owl{BG}. * Map is into the Official Whitelist, allowing players to level up their Perks. Credits: Conversion made by {CB}Owl{BG}. Exploit Fixing by Mamoo. Spanish T...
KF-DOOMedv1-3
Created by Fobos
A Killing Floor map based on DOOM map E1M1. Remake made by Pectabyte.com
* Map is into the Official Whitelist, allowing players to level up their Perks.
Credits:
Spanish Translation by Fobos.
----------------------...
GG-VR_MultiStory
Created by avp2501
MultiStory VR simulation: 4 levels of semi chaotic fun with limited cover....
KF-SewersPrisonV4
Created by AsNetu
It's time to battle through the sewer's prison!...
KF-MysteriousTreesV3
Created by AsNetu
Action take place in the old castle, which is surrounded by mysterious trees......
KF-StalkersOutpostV2
Created by AsNetu
More action in an abandoned stalkers outpost......
Mario Clouds
Created by SneakyKNG
Its a me Mario!Play a small but fun map of mario!!!Thank you so much for playing my game!...
kf-the hallways UPDATE
Created by Target Practice
just a tiny update for my very simple map that ive made
ps: i called it the hallwayS becaus theres more than onne hallway...
KF-Sniper_yard
Created by Как Цапля
Очередная бредовая карта,созданная мной.Из названия понятно что она хорошо подходит для снайперов,ну и для коммандо.
Покажите этим трупоедам,что вы умеете стрелять!
The next crazy map created by me. From the name it is clear that it well is suitable ...
KF-Duke Nukem
Created by E-Rock
Duke nukem now brought to you, in Killing Floor! Play through the first mission on L.A. Meltdown and remember the old Duke Nukem 3D days! No credit to me, its all Ro_Sauce!
OH? and even better! ITS WHITELISTED! So go grab that secret rocket and fume-agate...
KF-ALTTP-ZELDA
Created by Grug
[img]https://dl.dropboxusercontent.com/u/67342297/Number9.png[/img]
[img]https://dl.dropboxusercontent.com/u/67342297/Info.png[/img]
A small map resembling kakariko village from the 1991 Super Nintendo game
Zelda: A Link To The Past.
The map has t...
KF-Defence-Sunset-B4.rom
Created by BATMAN
карта создана не мной просто решил выложить...
Kf-PWNIES!
Created by E-Rock
Darkness - Map
Created by RUSTIK
This simple yet difficult map forces players to hole up inside an abandoned house out in the middle of the woods while the ZEDs attempt to break down the barriers. The one and only trader is located about 100 meters from the house in the woods, return quic...
KF-TowerDefender
Created by Wolfer
You must protect Dr. Gary Glover and Mr. Foster towers to complete this map, otherwise... you will die.
//Info//
Beta nº3
This map uses KFDoorMoverPlus from Falidell's Trigger Pack
...
Pollution Factory
Created by HIUFIGYO
Just a small map I made in a short time while trying out Killing Floor SDK. Takes place in a factory campground in the middle of the forest which purpose is to dump polution into the atmosphere which got out of hand in that area, it also caught the attenti...
The Grimpen Marshland
Created by Tundra Puppy
Quiet and morose, the marshland known as Grimpen sits, brooding and humid in the heavy air. The Specimens have come and gone, but their return is imminent - your presence draws them inexorably closer to feed. And inevitably, the swamps will run red for a...
KF-Cuber
Created by SkLiN
A good map for Killing floor, subscribe , evaluate ...
Хорошая карта для Killing floor, подписывайтесь, оценивайте...
Update...
7.12.12 Start Map
- Check output map "KF-Cuber" for Workshop
7.12.12 Fixed
- Fixed the door at the upper level...
Overrun
Created by HyPNOS
Defend a deserted base that's overrun with zombies who insist on making your life hell, for some reason.
Map info: Not much really, it's a simple map, but can be hard if not defended well. There are usable jump pads from the top of each Trader for quick...
The Mountain
The Mountain is our last hope. The last place where the infection didn't kill every human being... Our chopper dropped us there to buld a new base, a new hope for the human race. But the undead smelled our blood and came there to disrupt our still living b...
Doom 2: Hi-Res
Created by Berq
Update of the venerated Doom 2 KF map using textures from the Doom Hi-Res Texture Pack (DHTP) at dhtp.freelanzer.com
*** Additional thanks to Commie Joe for getting the file size down by half ***
Based on KF-Doom2-Final-V7
Play Doom 2: Hi-Res on my de...
KF-Afghanistan
Created by KINGshinobi
This is a Afghanistan theme map with a garden in the middle , damaged houses and desert-textures. hf...
Created by KINGshinobi
This is a map that i made for the original mod back some time. Actually the 2nd map i ever made for KF....
Created by KINGshinobi
This is a Disco theme map with alot of music and other cool stuff in it.
[Note] If the Map doesnt show up download and install this animation file for the dancing girl: http://www.mediafire.com/?4hlil0tb46m20s6...
Created by KINGshinobi
This is a Gasstation theme map with a basketball cord and mad driving cars around it.
...
Created by KINGshinobi
This is a small very intense map. If you wanna test how hard it can get , try to beat it :)
It also has some changed pickups....
Created by KINGshinobi
This is a giant mall with a outdoor part also....
Created by KINGshinobi
This is like the name says a shopping center with alot shops, hallways around it and skatebords....
Created by KINGshinobi
This is a Skatepark theme map with a skatepark in the middle , sport- an arcade and pool halls around it. There also moveable objects in the map like balls and skatebords. hf...
Created by KINGshinobi
This is a city part like map that i made inspired by a picture....
Created by KINGshinobi
This a orient/asian city map with alot car traffic in it. hf...
KF-Bamboo-Forest-beta-1
Created by KINGshinobi
This is a Bamboo forest with lots of trees , rivers, lakes , a house and alot other stuff....
KF-Ganja-Farm-V1
Created by KINGshinobi
This is Ganja-Farm :) hf...
KF-Leveling-PerkyV5_1059fix (and 100p version)
Created by Shinkichi
- include -
KF-Leveling-PerkyV5_1059fix.rom
KF-Leveling-PerkyV5_1059fix_100p.rom
100p Version very very solooooo
Mirror:
https://onedrive.live.com/?cid=57B33CF5BB83FE2A&id=57B33CF5BB83FE2A%21402&sc=documents...
KF-Riverside
Created by K-2
After the invasion of London all survivors rushed to leave the city and surrounding areas. Only bands of marauders and the brave ones, who didn't want to give up so easily, stayed in the city, but they were forced to retreat under constant onslaught of Hor...
KF-LostContact wave based map
Created by FluffyCelix
This was my very first map ever made for KillingFloor. its really not good its a big arena with zeds spawning in. thats all....
KF-NpcStadiumv4 spawn npcs & fight them
Created by FluffyCelix
This map u can spawn any zed in the arena all you got to do is press the switch of one of the zeds
there is a respawn every 30seconds but it requires 2 players to be in the game & 1 alive
...
KF-OldCity
Created by Swanky
A thematic blend of London, some Steampunk and Gears of War influences, this map is fully functional. Updated Dec.1/13 Zeds can now jump out of the river...
KF-Pruebe
Created by Bionik
...
KF-Strangev12 Strange story map
Created by FluffyCelix
This is my second map every made. For killingfloor it wanted to make a story map. So it kind turned out really strange.
Best played with friendlyfire on. Otherwise u can't damage the enemies well u can still melee them but that's hard...
KF-Wolf wolfenstein remake.
Created by FluffyCelix
killing floor remake wolfenstein in killingfloor style...
Testmap6p FiringRangeV2_Xmas
Created by Jさん
Press E key to spawn specimen
2012/12/13 Xmas update!
[file list]
KF-Testmap6p_FiringRangeV2_Xmas.rom
KF-Testmap6p_FiringRangeV2_Xmas.ucl
Testmap6p FiringRangeV2
http://steamcommunity.com/sharedfiles/filedetails/?id=98128132...
kf-minecraftv3 Minecraft wavebased map
Created by FluffyCelix
A minecraft based wave type map
Last edited by lethalvortex; 04-29-2011
You have my permission to edit the map in any way you like as long as u give me credit :)...
kf-towerdefenderv3 defend the towers
Created by FluffyCelix
The towers lost power. Your squad needs to defend the towers. from the endless horde....
Killingfloor doom3 Mut addon mappack part 1/3
Created by FluffyCelix
This is a mappack for the doom3 mutator. by marco there is 3 parts
-marco doom3 muator-
http://steamcommunity.com/sharedfiles/filedetails/?id=98458017
the map na...
Killingfloor doom3 Mut addon mappack part 2/3
Created by FluffyCelix
This is a mappack for the doom3 mutator. by marco there is 3 parts
-marco doom3 muator-
http://steamcommunity.com/sharedfiles/filedetails/?id=98458017
the map na...
Killingfloor doom3 Mut addon mappack part 3/3
Created by FluffyCelix
This is a mappack for the doom3 mutator. by marco there is 3 parts
-marco doom3 muator-
http://steamcommunity.com/sharedfiles/filedetails/?id=98458017
the map na...
Doom 2 MapPack Wave based maps 01-10 + 30 / 31 /32 Part 1/2
Created by FluffyCelix
Doom2 mappack Wave based contains 13maps total
These maps where never really released.
since i not really work on them anymore i though i release the maps
make sure u get part 1 & 2...
Doom 2 MapPack Wave based maps 01-10 + 30 / 31 /32 Part 2/2
Created by FluffyCelix
Doom2 mappack Wave based contains 13maps total
These maps where never really released.
since i not really work on them anymore i though i release the maps
make sure u get part 1 & 2...
KF-ArmyBase-1-0-0 By Eskarn Productions
Created by Eskarn™
This is my second released map in my storyline
Intro--------------------50% done
Hospital----------------20% Done
ArmyBase -------------Realesed
ToySoilders------------70% done
LaunchSite-------------Not Started
Nightmare--------------Not Started
S...
KF-Croosfire_HL1
Created by DpaKc
I completely forgot about this map. Map converted from all the popular game Half-Life. She also has a night :)...
KF-Pool_Day
Created by DpaKc
My first conversion map of Counter-Strike 1.6 in KF
It turned out okay but the only negative is that the water is just a texture, and it was all well done to the mobs did not sink....
KF-Testmap6p_XMas2012
Created by Shinkichi
Xmas 2012 Event fix Version...
KF-UndergroundTemple by Eskarn Productions
Created by Eskarn™
This is my 1st released map in my storyline, was released 2 year ago just fixed up some exploits and put it in my workshop
Intro--------------------50% done
Hospital----------------20% Done
ArmyBase -------------Realesed
ToySoilders------------70% don...
KF-Winter_Assault
Created by DpaKc
Map to convert from Counter-Strike 1.6 and decorated with Christmas ornaments as well sewn 3 songs.
Song titles:
Bullet For My Valentine - Hand of Blood
Celldweller - One Good Reason
Celldweller feat.Styles of Beyond - Shapeshifter...
Antarctic Outpost--Beta
Created by Blackbeard
An outpost set amidst a snowy landscape. Beta....
HighRise
Created by Jsh
Beta1:
My second project for Killing Floor game. This time it takes place at the roof top inside and outside of a penthouse.
It's a very narrow map, due to this fact it includes only one trader.
It features a few rooms: e.g.
- main area meant to be ...
KF-HellishTavern
Created by _Qu[AA]rK_
This is my first map. I've been making it for 4 days. Notify me if there are any issues/glitches.
This map utilizes custom soundtrack.
Short Description:
Narrow East-London Streets, soldiers strive to survive. They stayed near Local Tavern, thought it...
KF-SunnyLandSanitariumBeta1-5
Created by swift_brutal_death
This is an updgraded version. The start and end of the map are now joined by a hallway system so the whole map can be traveled in a large circle rather than dead ends.
KF-TestZSpawningZone
Created by Ventura
*Zed Spawning Zone is currently Killing Floor's TOP RATED Training/Leveling map of ALL TIME!*
Thank you all !!! :D
▒█░░▒█ █▀▀█ ░ █▀▀█
░▒█▒█░ ░░▀▄ ▄ █▄▀█
░░▀▄▀░ █▄▄█ █ █▄▄█
▒█▀▀█ ▒█▀▀▀ ▒█░░░ ▒█▀▀▀ ░█▀▀█ ▒█▀▀▀█ ▒█...
KF-bilateral assault by RunneR
Created by Как Цапля
Узкий коридор,Вы,Ваша пушка,и целая орда зомби которая рвется к Вам С ДВУХ СТОРОН!!!
Ну что,Вы готовы отразить двухстороннее нападение?
Чтобы скачать нажмите кнопку "+Подписаться"...
KF-music-1058-66
Created by Cszhu
Shoot player to play/Stop music
use The 9mm or knife or Single shoot weapon.
New Add a Restart map Point,If you make any mistake....
Archives
Created by McQuiggle
It's a library!
We made this level not too long after the game initially launched. Recently we started working on an updated version. Might have that coming soon....
Hidden Complex
Created by HandCann0n
Ok community. This is my first map. I hope you enjoy this map.
PD1: I fixed all bugs i found, but if you find anyone, tell me.
"We have ecaped from the city after everything gone to hell...Someone told us about a complex under constuction in the mounta...
KF-SnipersFunFair-Beta2
Created by -MGSa- Sniper
For the first time in KF a WORKING FUNFAIR!
Enjoy and feedback appreciated...
KF-WareHouse
Created by NAKED GI JOE
The H.E.C.U WareHouse was a safe zone. Your team has been sent to secure it again. Do not get trapped.
KF-ZedDiscoThe1stFloor
Created by [ScrN]The Janitor
My first map ever made for a game so its pretty simple made. The Husks start to dance when ammo spawns. The one behind the turn tables starts to dance when the Patriarch leaves one of the spawn rooms. The little Husk upstairs dances if u shoot or knife the...
Elementary School
Created by Flame
An elementary school, turned refuge for the local survivors, has been overrun by Kevin Clamely's specimens.
I first built version 1 for the Grindhouse Mapping Contest. Two versions and many bug fixes later this was the result. After the first version I ...
Helms Deep
Created by M6dEEp
Where is the horse and the rider? Where is the wind that was blowing? They have past like rain on the mountains, like wind in the meadow. The days have come down on the West, behind the hills into shadow......Now for wrath...now for Rohan...and the red daw...
KF- AspenManor
Created by Fel
This map i made awhile ago for the KF mapping contest. This is a good map, not one of my best, but its still enjoyable. Should give it a whirl....
KF- Cain
Created by Fel
This is my skyscraper map. 5 traders, but only 3 floors are accesable, so theres not alot of running around.
...
Created by Fel
This is S821 and I 1st mission map together. Alot of cenematic events and really fun gameplay. Watch out for the bombing atacks as you make your way to Perdition City helping others on the way.
Features the 1st apperiance of our brand new weapon the Mo...
KF-BlockParty
Created by Fel
Imagine your neighborhood. Now imagine it with zombies.
...
KF-Candlesmoke Revamp - Mission Map
Created by Fel
This is a revamp version of our 1st mission map Candlesmoke. This version is way better and more ballanced. Authors: Fel & Dextronaut
...
KF-Choclate Factory
Created by Fel
This is my Easter present to the community. Medium 4 trader map that will make you hungry while playing it.
...
KF-Keo32
Created by KeMiCol-KiD97
How did you even get here. This map is my first one and an experimental. Will possibly add props.
Music over here:
https://www.dropbox.com/s/cqrj8lm5aefqlz0/Keo32.zip
(Some brony music involved)
Drag the .ogg files in the killing floor directory
All m...
KF-Obsidian- Mission Map
Created by Fel
One of my favorite mission map. This map has player interactve objectives where players have to interact with the enviroment and defend each other while they try to accomplish each obj. NOTE: Because of the custom emiters the map sometimes crashes on resta...
KF-SantasRetreatFinal1-1
Created by swift_brutal_death
The update function of the workshop does not recognize my prior maps so I had to re-upload as a brand new file. There are significant changes from prior version including:
KF-Vostroya
Created by Fel
This map is my RO2 Tribute map, really fun map. Authors: Fel & S281...
KF-The Hood - Central Mayhem
Created by Fel
This is a map taken out of a inprogress mission map im working on (Central Mayhem) This map is really hard so make sure you have a good team.
MapName: KF-CentralMayhem-TheHood
If anyone wants to help test out projects message me...
KF-TrooperDefence
Created by Fel
This map is the new defence. Total custom spawns based off of player count, so the more players the longer the waves (just like a normal game) NOTE: The trader arrow is a bit off, the trader is on the heli pad....
The Hive - V3 - Rev 1
Created by Hodor (KiCk3R)
The year is 2017. The world has been devastated from the T-Virus escaping from The Hive; A hidden biological underground station in Raccoon City. Umbrella Corporation have assigned Delta Team to enter "The Hive". A top secret Silo facility hidden deep beni...
Dynamic maze
Created by Marco
This is a small boring little maze map where the maze slowly alters over time, blocking paths and opening new areas.
If you look up you can see a mirror which will basically act like a map for you.
I wrote all of the codework on this map, feel free to us...
KF-BugHunt
Created by miks
Aliens themed map, ment to be played with the Aliens mod but works with regular gamemodes aswell.
Special thanks to Hemi, Gartley and the rest of their team for the Alien related models and textures....
KF-Chamber7
Created by miks
Another portal themed map, this one is much smaller than my first one.
Includes the typical moving platform, surprise deployer, tube transports etc. I was planning on adding a laser too but so far couldnt make it work, if anyone knows how let me know....
KF-CountyJail
Created by [ScrN]The Janitor
Sort of a Roundhouse some Jails have so yeah why not?^^ Thanks to [ScrN]PooSH for suggestions and to the I need DOSH and Scrn Balance Fans ...
KF-HallCrawl
Created by PaperKut
Simple basic map design with long hallways and corner rooms with upper levels to shoot down on zombies. This is for beginners and Levelers wanting a good map to level but not cheat either. Designed by PaperKut (with assistance by Tripwire); testing by FAM ...
KF-LastStand
Created by PaperKut
You spent years of time, hundreds of thousands of dollars to build your little complex. And while everyone laughed at your dreams. You knew THEY were coming. But you best do with what you have, at least until the Trader opens.. You and yours prepared for t...
Hiufigyo Labs
Created by HIUFIGYO
My Second Map
This map is bigger, more closterfobic with lots of tunnels, and dark.
Don't Get Lost
KF-HolyDays
Created by HekuT
Helpers: Ksu, BatYsaU, UltraKill, mihopol, Rainishe, fozik.
Description (Russian Language):
Заброшенная Советская военная база 80-х годов. Там мало кто был, и шли слухи, что сюда отправилась группа людей, которая оттуда не вернулась... Вам и вашей кома...
KF-A-AliensTunnelBeta1-2
Created by swift_brutal_death
Mod: WPC
Map:Swift_Brutal_Death
All my maps can be found here on the steam workshop: http://steamcommunity.com/id/swift_brutal_death/myworkshopfiles/...
KF-FavelaTown
Created by Chael Sonnen
So I finally decided to finish this map after having it gather dust for several months, enjoy.
UPDATED:
KF-FavelaTownB2
Made the light a little more saturated.
Added another way up to the rooftops, should even out the z...
KF-HarbourV3-fix
Created by [ScrN]The Janitor
This map was made by Sergiusz Ustyniak. I just fixed the issue with the Server crash on map change. Tested on Windows and Linux Servers and worked fine so far.
Thanks to the I need DOSH, [url=http:/...
KF-PandorasBoxV2-fix
Created by [ScrN]The Janitor
Kinda a old map but one of my favorites. This map was made by Matt / =Z.E.D=Sudo. Not sure if it ever got fixed in any other version since i could not find any other working download link but i just fixed the issue with the server crash on mapchange. Teste...
KF-SwiftBoxyDeath1-1LG
Created by swift_brutal_death
Intended for play with lots of players. Video is just to show you what the map does.
Up for a challenge? Play with normal gravity and brutes.
Normal Gravity Direct Mediafire Link=====>> http://www.mediafire.com/?aq4qbck9p559hl9
Low Gravity Direc...
KF-Temple-of-The-God
Created by K-2
Version: 1.0
Pretty simple arcade map in egyptian-mystical style.
Map concept by Gaiver.
Textures & meshes are taken from UT2k4....
Casa De La Muerte
Created by Mutant
KF-LaCasaMuerta is a remake from scratch of JacksonL's map for Killing Floor Mod (UT2004) which was one of my favourite maps back then.
I tried to keep the original feeling as good as possible but had to add many things to make it suitable to retail gam...
Winter Frost
Created by HekuT
Helpers: Gwynbleidd, Likvidator, Ksu, K-2, and those who helped give the name of the map.
Описание (Russian Language):
В зимний морозный вечер, на заводе, который был рядом с нами, работали люди, но через пару минут у них случилась поломка и вся связь ...
Barn
Created by FORCE
Killingfloor level, which is a replica of a reallife location. Pretty small map with only a couple of places to hold, all with up and downsides for you to find out.Feedback always welcome.
Enjoy!
Catacombs
Created by Formless
This is my first killing floor map so please let me know what you think in the comments....
KF-Farm-Day-v1
Created by -hg- Forrest Mark X
This is something I did in my spare time to get myself familiar with the map editor with things such as zones, skyzones, and lights. Decided to release it since I've pretty much finished it...
KF-HillbillyHorror-Night
Created by -hg- Forrest Mark X
This is something I did in my spare time to get myself familiar with the map editor with things such as zones, skyzones, and lights. Decided to release it since I've pretty much finished it...
KF-Yellow Bunker
Created by V@nOVG@VnO
My first map for Killing Floor!!
Remake Sniper_Yard by RunneR(Rus)
**********
Моя первая карта для Killing Floor!!
Что-то наподобии Sniper_Yard от моего друга RunneR(Rus)...
Lil Big Clot - Kitchen UPDATED
Created by Rei
This is an edited version of Lil Big Clot that fixed a minor bug. Version 3-3 is still availible at http://steamcommunity.com/sharedfiles/filedetails/?id=132947195.
Map Destription: Now you know why your mother told you to never follow white rabbits...
Lil Big Clot -Kitchen Version 3-3
Created by Rei
This is the version of the map that was whitelisted. There is a newer version of the map that fixed a minor bug.
Newer version can be found at http://steamcommunity.com/sharedfiles/filedetails/?id=132947393
Level Description: Now you know why your ...
Temple Underground
Created by Formless
KF Bounce
Created by PaperKut
Bounce is a simple yet challenging map (aiming as you are jumping). It has no purpose really other than to have fun bouncing from platform to platform, avoiding jumping and floating zeds, plus open space areas that cause damage. It is meant to have fun wit...
KF-A_Japanese_Kid_Room_Betav8
Created by Zoogomy
This is my first steamworkshop upload and custom map. This custom map is a Japanese kid room.
I use textures from pixiv and free pictures to use, so now I say 'thank you very much to all painters of these textures and players who play this custom map. I ...
KF-ArenaWars
Created by [UGS]Mythril
First version of KF-ArenaWars. The map is supposed to be one of many entrances to the Horzine laboratorys which has to be cleared by you. I tryed to create a simple defensive map, you get flooded from all 4 sides.
For server owners, get it from here: h...
KF-ArenaWarsV2
Created by [UGS]Mythril
Second version of KF-ArenaWars. The map is supposed to be one of many entrances to the Horzine laboratorys which has to be cleared by you. I tryed to create a simple defensive map, you get flooded from all 4 sides.
Changes in this version:
- Overhaul...
KF-ArenaWarsV3
Created by [UGS]Mythril
Third version of KF-ArenaWars. The map is supposed to be one of many entrances to the Horzine laboratorys which has to be cleared by you. I tryed to create a simple defensive map, you get flooded from all 4 sides.
Changes:
- Removed static high tier...
KF-Distrikt
Created by [UGS]Mythril
Well my idea was to create something similar to west london, because I freaking love it, so this is the outcome, I hope you like it. The heavy weather condition's give it a nice horror-like feeling, the map is complely playable in multiplayer and singlepla...
KF-GIGAToilet
Created by Bo-si[nipon]
Map Name :KF-GIGAToilet
Playable: Yes
Players: 6-10...
KF-IndustryFIX
Created by BAHO[21RUS]
After escape from Foundry. The Foundry worker Aldridge told his new friend there is an industry where the metal was packed, checked and then sended. Now you are moving in this Industry for check if anyone is alive…
После спасения с литейного завода, ряд...
Created by [UGS]Mythril
ShadowAlleys is a very dark set map covered with alot of rain which make's it even scaryer! This is the first version of it, which got made some year's ago.
For server owners, you can get it from here: http://www.moddb.com/members/shocktrooper114/addons...
Created by [UGS]Mythril
ShadowAlleys is a very dark set map covered with alot of rain which make's it even scaryer! This is the second version of it, which got made some year's ago.
Changes in this version:
- Armory content changed.
- Armory door now harder to unweld.
- F...
Created by [UGS]Mythril
ShadowAlleys is a very dark set map covered with alot of rain which make's it even scaryer! This is the third version of it.
Changes in this version:
- Improved pathing.
- Armory content changed.
- Fixed some blocking volumes.
For server owners,...
SecretLab
Created by codehisui
KF-SecretLab
Enemy comes only from the front.
This is my first map.
I dont know how to make the Trader's Navigator.
Whoopsee...
The Room - First Level
Created by The1StudMuffin
My first attempt at making a killing floor map. There are probably some bugs and kinks in the map so let me know what they are or ways that I can make the map better :D . It is a fairly basic level with zombies spawning both above and below you, but you ca...
Firing Room v 0.2
Created by Shkire
[Map in progress] Join the battle against the specimens in the Firing Room and protect the doors to still alive!!...
First Vinegar v0.1
Created by Ser Maximus
This is my first project with the Unreal Level Editor and it is still in development!
If you have any suggestions, bugs or glitches to report, please let me know!
I hope you enjoy the map - GL HF
PLANNED:
* 1st floor - with cantina and an entry (coll...
Halo Lockout
Created by rEkTum
Based on Lockout from Halo. First full attempt at a map.
KF-BigSunriseBeta1-6
Created by swift_brutal_death
You will have to manually unzip this file into your killingfloor/maps folder for it to work
Destroy all the gnomes to activate the iKill floor cleaners. They do not always crush the zeds d...
KF-ElectricCentral
Created by PaperKut
You and your Squad have been sent into the Central Power station from beneath. You need to clear out the building from the inside out, so electricians can get in and restore the power. But be careful, things are hidden around every corner. - by PaperKut
...
KF-Energy-Core-beta2
Created by KINGshinobi
Well you made it into the basement of Horzinelabs to the Energycore the lab runs on. Strange things going on around the core, try to shut it down and prevend more horrorfying sientific experiments....
KF-ForestNight
Created by Sam
Night version of KF-Forest....
KF-PuppetPhilia
Created by Bo-si[nipon]
Map Name :KF-PuppetPhilia
Playable: Yes
Players: 1-10...
KF-WaternabelArtGallery
Created by Zoogomy
This is a art gallery map.
You can see lots of paintings including Renaissance, Northern Renaissance, Baroque, Rocaille, NeoClassicism.
You can buy weapons everywhere in this map in order that you can see them.
...
KF-ROMAN-ARENA [UltraMapping]
Created by UltraK!11[CL]
Roman Arena by UltraKill & "Wolv34ine"Walker
Updated.
Changeslist:
- Fixed textures.
- Changed textures reflections.
- Remaked zed spawn systems.
- Fixed Blox.
- Fixed Packages.
Let test ;)...
KingOfTheHill2013
Created by TAP-CHAN
This is the updated and fixed version of my map King the Hill that I made in 2009.
Special thanks to Mutant, MRU and Juna_gi_s_kombaina ! ;)...
LostBoys
Created by GoR
This map is a small fortress in the far-far away forest.
On this map should be possible to qualitatively cooperate with the team, or the waves of monsters will crush you....
KF-A-Starship
My second map made for Aliens: Killing Floor mod.
MAP MAY WORKING ONLY WITH AKF MOD!!!...
KF-A-Outpost
My first small map for Aliens:Killing floor mod...
KF-Backalley
Created by Chael Sonnen
A map with an alleyway that wraps around a large office building with 4 floors, many places to hold out with no cheap zed spawns, might be quite tough to kite but not impossible.
KF-TinySurgery
Created by Bo-si[nipon]
Map Name :T-Surgery
Playable: Yes
Players: 6-10...
AlienHatchery-fix
Created by Whinem
Created by U.N.C.L.E.
You have been taken to the place where Aliens are converting their young into zombies. Here they will learn to feast on human flesh. It's time to put an end to the outbreak of Alien invasion. Or in this case Zombies. Kill them all,...
KF-Dropping_and_Death
Created by Bo-si[nipon]
Map Name :KF-Dropping_and_Death
Playable: Yes
Players: 6-10...
KF-KFunServerFarm
Created by EvilWiffles
Don't be afriad to venture away from the house. Make sure you keep an eye out....
KF-Flatgrass
Created by EvilWiffles
Open and easy on FPS. This is a great map for servers that are running higher players and lots of zeds. Also great for sharpshooters....
KF-BlueShift
Created by Chael Sonnen
Yet another Wave-based map.
Description: A remake of a small section from the Half-Life: Blue Shift single player campaign that I thought would make a good PVP map for a game like CS or something, but I only know how to map for KF, so here you go.
Al...
Temple Of Inquisicion
Created by UltraK!11[CL]
An good map with elements of quake and hell.
Idea to make this map is from Qauke 3 map (q3dm7)
My Greatest project....
KF-Tower of Defense
Created by Zangan
Took a few days out of playing Killing Floor to actually make a map for it. It should be in Alpha but, the map itself is already playable. This map will have a total possible count of 5 - 10 floors. Currently, there's 3 floors. Added parameters for floors,...
AlienNationV5
Created by Whinem
An alien underground breeding site. Not an Alien mode map.
You can now get all my maps from the following link.
KF-BusStationV4
Created by AsNetu
Action takes place in a bus station......
Created by KINGshinobi
The theme playes in the deep jungle of afrika where your squad has been sent to check and clear the hidden genetic-research-laboratory. Local newsreports indicate that something went bad wrong in the area around the lab. Keep the eyes open....
KF-SewerEscape
Created by EvilWiffles
The zombies poppout of the hazardous sewer. Play defensively to pertect yourself.
Works very great with portal turrents mut....
KF-HaveMyAxe
Created by Kathy
Kill 30 Fleshpounds with the Dwarfs Axe with back Attacks...
KF-ManorLastStand
Created by Chael Sonnen
A version of KF-Manor that locks you inside the house, but don't worry as the house isn't as much of a death trap anymore, all zombie spawns inside the house have been removed so you'll only have to guard the 3 main entrances into the house, but some good ...
KF-Gubeni
Created by Darky
What's the point of making a large map if people will always camp at that one single awesome spot?...
KF-Y-junction_beta
Created by Bo-si[nipon]
Map Name :Y-junction_beta
Playable: Yes
Players: 6-10...
KF-420-Ganja-Farm-V1
Created by More Work?
I Did Not Make This Map
Original Map Author/Maker: KINGshinobi
Original Site I Got The Map From: http://sykosis.co.uk/...
KF-DoshorAlive2
Created by one_wonder
DoshorAlive1 has broken out last year, so I just created a new map.
Have Fun.
Size:Small(1-6Players)
5 Secrets
Last Update:18/7/13
Fixed Some Bugs.
[Doom2] KF-Grosse
Created by Cakedog
Wolfenstein themed Map32 Grosse from Doom 2 ported to KF. Including original textures from the game upscaled and ported for use with KF.
There is a 'secret' on the map, any Doom player will be able to easily recognise it, ...
KF-FelsHell
Created by Kathy
a long long time ago my boyfriend found it super funny to make KF-KathysHell
it is survivavle if you figure out to choose the perk you usually never choose against husks...
Testmap6p FiringRangeV2 Summer Sideshow
Created by Jさん
summer sideshow version 2013/07/07...
The Pits
Hold out in the pit for as long as you can. Each member of your team will be tested to their limits in this epic struggle for survival. With two sides to protect your team must work together to ensure victory and be prepared to support other players at a m...
KF-Corridors-FS
Created by Fess
Hello. This is my little map for Killing Floor. I think the map is very hard but if you are bold enough you can subscribe and try it by yourself :D...
Dark Corridors
Created by Dino Dan
My first Killing Floor map.I tried to make it dark, so the falshlight is your friend. Items and ammo spawn in the darkest areas. Since this is my first map, there might me some bugs. Any feedback is appreciated. Enjoy :)...
KF-FoundryLightsOut
Created by [ScrN]The Janitor
Because lights are overrated. Thanks to the members of the Scrake Naders and the ScrN Balance Fans groups for testing.
[url...
KF-music-1050-64_v2
Created by Cszhu
just a music map to play music 64 of all official music.
in the music box Area,press E to play to any songs, press E to stop music.
if you want to play others.
...
The Walking Dead : Prison map
Created by Johnny Cache
We are after the night, when The Governor attacks the prison. Your job is to clean, and save the prison yard from the walkers. Good luck.
Me and my friend started making the prison from The Walking Dead.
ITS HARDLY W.I.P. This is just an early "open"...
Acid Stash Map
Created by Lucky Skills
My first ever map, very small and not very interesting, just uploading so I can play with friends.
Note: This was only made for me and my friends so there are only 4 player spawn points....
Building of horrors
Enter the building of horrors if you dare! The most of the out most experienced players will find that this map is not any ordinary map, but full of surprises around each corner. Walk into the deep depts of the Building of horrors and find yourself lost an...
Compound Beta
Created by Lusacan
...
Contaminated Town
Created by Punisher
It's a dark town. Be aware of the test objects. They are contaminated with a danger virus.
This is my first map. The map is not completed but I am helpfull for some tips and bug reporting. The map will be finished in some weeks....
Fleshpound Arena
Created by Lusacan
...
Hellride MoverCoaster
Created by karashi
coaster ugokuyo
Filename:KF-Hellride_MoverCoaster.rom
Update:5 Aug 2013 @ 12:49am
glitch fixed...
KF - Site B Maintenance Tunnels
Created by FUBAR!
Hole up in the Site B maintenance tunnels and survive the Horizon Hordes, keep in the light and find a way out into the control center....
KF-Abandoned-Moonbase
Created by [ScrN]The Janitor
Original by Tripwire Interactive
Lights destroyed by some stinky Clots
Results shared by [ScrN]The Janitor
Now working with the Z.E.D. gun (But It's All Red!) achievement!
[url=http://www.getoffmylawn.de...
KF-BigClotToiletR
Created by Bo-si[nipon]
Map Name :KF-BigClotToiletRemake
Playable: Yes
Players: 6-20
...
KF-Bloody 1000$Created by Shepherd This is my first map, which I did it in high school KF-Bloody 1000$ is a remake of most popularity map for Counter Strike in Russia and Ukraine - 1000\$
share their feelings...
KF-Close Quarters
Created by MAV3N
A map that was started by *STRS*Medic. After he stopped working on it I finished it.
Another warehouse full of infected specimens to clean out....
KF-CryOnFloor-v2
Created by Mr.RoBoT
If you prefer the old version (without jumpscares) you can download it from here:
KF-CryOnFloor[www.gamefront.com]
Inspired by Cry of fear and Afraid of monsters.
credits to CoF for the...
KF-DefenceLondonFinal
Created by Ferenos
Description: Defend yourself and take cover in this fortress built between the streets of London
Current Version: Final
Size: Small
Globa Environment: Outdoor
Exte...
KF-DepartedNight
Created by [ScrN]The Janitor
Map is whitelisted.
Like the Title says its a Night version of KF-Departed and some other changes like access to the pier, making a common camping spot less camper friendly, Tesla Husk in a dumpster and a WUB WUB Easter egg(needs to be triggered). ...
KF-DepositRisk-FInal (Updated 24/09/2013)
Created by Ferenos
* Final Version
* Description:Busca refugio en esta abandonada estructura y evita ser devorado por las feroces criaturas que habitan y diambulan en los alrededores. Apartate de la oscuridad y no te separes de tu equipo porque de el y tu cooperacion dep...
KF-Doom2-Final-v7
Created by FiB. Ângelo [IDLE]
Author: lethal_vortex
KF-Doom2Map07v1
Created by FiB. Ângelo [IDLE]
Author: lethal_vortex...
KF-F_ChaosTemple
Created by Ferenos
* Final Version
* Based on the map HeresyBeta3
* Global Environment: Indoor
* Size: Medium
* Ideal Player count: 3-6
* Soundtracks from game Chaos Legion
Music Fi...
KF-F_ScorpionsLair
Created by Ferenos
*Description: Scorpion's lair, a distant and hidden place where fall the bodies of soldiers killed by Scorpion . Now, the bodies have appeared in the form of horrific creatures, and you have been sent with the sole purpose of preventing these creatures esc...
KF-F_VortalCoil-Final
Created by Ferenos
* Description: This is an underground shelter where you must defend and hold your position while the specimens approaching from the depths of the cave. Luckily, you have an alarm system to warn you when they approach, but pay close attention to how many li...
KF-HallwaysV20
Created by J!nxyy
My very first map... ever... reuploaded (aka it sucks). Used it as a learning experience to learn how kf sdk works. You know, learn by doing... anyways enjoy. Or at least pretend to.
If it doesn't show up in list then go into sdk and save it under a dif...
KF-HappyForest
Created by Bo-si[nipon]
beta...
KF-Haunted Lab
Created by MAV3N
After a recent escape of specimens at the Lab a team was sent in to clean up. Soon after they left and would not return. Your squad is being sent to investigate anomalies at the Analytical Lab. No one else will go there.
NOTE: This map has a surprise sp...
KF-HospitalhorrorsLightsOut
Created by [ScrN]The Janitor
Author: JustFilth and Gusone
Lights off and stuff: [ScrN]The Janitor
Because the Name wasn't already long enough. Playable on the Official ScrN Custom Servers.
Downloa...
KF-MedievalNerYFortress
Created by Ferenos
Description: En esta ocasion, tu mision te ha llevado a esta tenaz estructura medieval en la que sobrevivir es tu maxima prioridad.
*Final version
*Size:Medium
*Ambient:Outdoor
*Ideal players num: 6-12
Credits to my friend NerY for the desi...
KF-MidwinterBaseR[fog/night]
Created by Bo-si[nipon]
Map Name :MidwinterBaseRe[fog/night]
Playable: Yes
Players: 6-15...
KF-MillPier
Created by HIUFIGYO
As far as I know zombies cant't swim, but when you run out of supplies on your sanctuary you have no choice but to return to land. This facility may have some supplies, lets just hope its abandoned...
KF-Nightmare-In-The-Skatepark (Final)
Created by Ferenos
Some Features:
Description: Not sure if this is a secret mission of survival, or whether it is a horrible nightmare from which I have to wake up soon. Anyway, I will try to stay alive ...
State: Final Version
Ideal Players: 6 - 12
Global enviro...
KF-Parking Garage
Created by NAKED GI JOE
Now that you have left the Bio Lab, you enter the Parking Garage. Look for survivors or be a survivor. Where did you park the car?...
KF-PosthumusCathedral
Created by Ferenos
* Description: An ancient and forgotten temple inhabited by horrible creatures where you have to survive
* Final Version
* ideal players num: 4-8
* Size:Medium-Large
* Global Environment: indoor
* Imported Serveral Textures and Staticmes...
Created by Ferenos
* Description: On an isolated road outside of England, a strange event caused a massive collision between vehicles moving there, so you were sent with a rescue team to assist injured people and make them safe from harm. However, flying over the area, you r...
KF-School Beta
Created by ScorchedIce
First of all, i don't know how to introduce that this is my first map.
Second, It's a not-so-abandoned primary school heavily based on a local highschool.
Tried to give the map a "open-but-no-so-open" feel to it, and im pusblishing as a beta since it's ...
KF-Shichirin
Created by Bo-si[nipon]
Map Name :Shichirin
Playable: Yes
Players: 6-10...
KF-Simple-Shooter
Created by Shinkichi
b1...
KF-Soko
Created by yone1218[JP]
KF-So↑Ko↓
Ver 1.0
player 6-10...
KF-Subway
Created by Mattdude
Most of the level is made now but there are still some things I need to fix before it's done....
KF-TheForestHouse
Created by Ferenos
Description: Are you claustrophobic? You must put aside the fear of enclosed spaces because your only chance to survive is to maintain your position in this old house with narrow aisles located deep within a dark and scary forest.
*Final Version
*Siz...
KF-Train-fix
Created by [ScrN]The Janitor
Author: Corey(Kyben)
Tweaked by Gregs2k2
Fixed by [ScrN]The Janitor
Fixes/Changes
Tested and playable on the Official ScrN Custom Servers.
KF-TrippyStairs
Created by J!nxyy
The Trippiest map you have ever seen! You will be Trippin' balls... on stairs.
Have a nice day full of killing floors.
If it does not show up in the listing, then go into the sdk and save it under a new name....
KF-ZedDisco
Created by [ScrN]The Janitor
Combined version of KF-ZedDiscoThe1stFloor and KF-ZedDiscoThe2ndFloor.The Husks start to dance when ammo spawns. The one behind the turn tables starts to dance when the Patriarch leaves one of the spawn rooms. The little Husk upstairs (1st Floor VIP Lounge...
KF-ZedDiscoThe2ndFloor
Created by [ScrN]The Janitor
Same simple design as KF-ZedDiscoThe1stFloor and a lot darker just without spawn camping. The Husks start to dance when ammo spawns. The 3 behind the turn tables starts to dance when the Patriarch leaves one of the spawn rooms. Thanks to [ScrN]PooSH...
KF-ZombieAndTrap
Don't be scared...
KFO-Manufractured
Created by Chael Sonnen
UPDATED TO B2 SEE NOTES FOR CHANGES.
An objective map set in some sort of warehouse part of the city, probably impossible on the higher difficulties but that's why it's a beta right now
Feel free to post suggestions, bugs and stuff.
Alternate Dow...
KFO-Snuff
Looks like you woke up in another goshdarn snuff dungeon..
THIS IS A SINGLE PLAYER MAP ONLY....
KF_Resurrection
Created by Vicar of the Cosmos
After escaping westlondon through the sewers you soon realize.... The sewers are a graveyard of those who were dumped after being experimented on from Horizine's labs.......
OutPost Whiskey
Created by S281
A defensive outpost set in a remote forest....
Portal Skyward
[RU]
После проявления первых признаков заражения вы и ваши спутники нашли странное место в глубине земли для укрытия от зараженных. Но увы куда без них... Щели в сооружении и вентиляция послужили проходом для них. Не долго думая вы приготовили оружие и р...
STARS Repair Station
Created by MAV3N
There's an abandon Helicopter at a Train Repair Station. Were sending the Special Tactics And Rescue Squad in to clean out the area and retrieve the transport.
My 3rd map.
Oct. 8, 13 - Updated to V2, fixed windows, did some optimization to map....
Stars Warehouse
Created by MAV3N
The survivors are running low on supplies. Your team is searching warehouses for food. The locale STARS warehouse has everyone's favorite. BACON! But first you'll have to clear the bulding. Good luck and bring home some bacon..
Trapped
Created by Lusacan
...
VM-UpAndDown
Created by Fire
Inspired by a Bomberman 64 multiplayer map into a Killing Floor map converted for Vehicle Mod.
VM-UpAndDown.rom
VM version of the map is to be used with the latest version of the Vehicle Mod that can be found on the Steam Workshop.
Updated for kf v...
3Bridges-Forest-Beta9
Created by Whinem
Forest is a beautiful large map that played well. 3Bridges is a midsized map that is played often. This is a combination of the two ideas with many changes. Very tough challenging map. No place to stop and rest. No place to hide. Zombies will jump out bush...
Caged In
Created by Dino Dan
Caged In is my second official Killing Floor map. You and your team are caged in with hallways in each direction. These hallways seem to be spitting out zombies. With nowhere to run you must hold your ground and fend off these fiends. For those who don't k...
Endless Map Pack
Created by one_wonder
Original:Tripwire
for Super Players.
3 maps Included:
KFO-BioticsLab-challenge-endless.rom
KFO-Biohazard-challenge-endless.rom
KFO-EvilSantasLair-challenge-endless.rom
and
KF-BioticsLab-challenge-endless.rom(will be removed.)
- 12Stages & 2...
KF-AbandonedTrainStation By Ferenos
Created by Ferenos
* Description: This old station seems to be the perfect stage to face those bastards. Stay away from dark areas where death lurks. Maybe you still alive at dawn
* Version: Final
* Ideal Player Count: 6-10
* Global Environment: Outdoor
* Size: L...
KF-BioticsLabSpawnEasy v1.2 Created By Le_SniperPatrizio
Created by Le_SniperPatrizio
This modified version of BioticsLab makes the gameplay easier because there are spawn of weapons and ammunition almost everywhere. I hope you like it as an idea ... This map is still under construction aid and comments make the job simpler. Thanks to every...
KF-BrickroomV2
Created by Memester
I'll frequently update this....
KF-BuddhaTemple-Final-3
Created by Whinem
This is fictional Buddha Temple with gates to a river. In the trader are fuse boxes to be unwelded to open gates to outer areas and weapons lockers.
You can now get all my maps from the following link. Thanks go to killingerk.
https://www.mediafire.co...
KF-BuddhaTemple_EZ
Created by Whinem
This is an easier version from the original. There are no gates to open at trader time or anytime. There arre only two fuse boxes that unlock weapons storage areas. But the water isn't as safe as before. LOL
You can now get all my maps from the followin...
KF-Coast
Created by S281
The map takes place around a small coastal town that has been slaughtered. There are three traders. Enjoy!...
KF-Corridors
Created by mano eliseu
Version ALPHA! (1.1) Map made by KFDrakar!
Added just a lil' camera! :3
Just fixed spawn locations / some brushes / guns, ammo, kevlar spawns....
KF-D-Day
Created by S281
D-Day style map....
KF-Demo beta v3(Departed)
Created by Falloutboy™
This is a modified version of KF-Departed. It is meant to make camping in the small room much easier. I removed all traders except the one that is across from the small room. Also, I removed the ZED-spawn in that room and the rear door is already welded. ...
KF-fight_your_own_Battles-1cellV4
Created by Whinem
Although this not a FYOB format, by request I made it all in one room. The room is pie shaped so plan your stategy.
KF-FinalHope By Ferenos
Created by Ferenos
Description: When the extinction of the human race is imminent, the final hope is to defend the last weapon resourses
Current version: Final
Ideal player count: 3-6
Size: medium
Global Ambient: Indoor
*Custom Music
*Imported several Staticmeshes, t...
KF-FireAndForget
Created by Kathy
Achievement Map "Fire and Forget" and "Have my Axe" also to level up for other perks
And for all Killing Floor Starters: the higher difficulty it is, the more damage amount you earn to level up your perks the zeds are prisoned with invisible blockers they...
KF-FYOB_3cells-Revised2
Created by Whinem
Here is a challenge for you and yours friends. Three idenitcal rooms with entrance for zeds but not players. You are trapped in that room as long as you live. If you die you may spawn in another room. I can't control that. As one player dies, the zeds from...
KF-HeartAttack-AcidpitV3
Created by Whinem
A slightly large room than HeartAttack with a twist. The floor is a acid pool. Yes it hurts. But make it to the outer walls and there is relief and teleporters in the four corners.
KF-HeartAttack2-2
Created by Whinem
It's a small room only. The reason I named it HeartAttack is because I almost had one when I test ran it as Bezerker with Flamerthrower.
You can now get all my maps from the following link. Thanks go to killingerk.
https://www.mediafire.com/folder/rw2...
KF-Home(Hospitalhorrors)
Created by Falloutboy™
KF-Home:
This is a modified version of KF-Hospitalhorrors
Changes:
- Added an "always open"-Trader in the elevator near the "common" camp spot (room with the hospital beds)
- Removed ...
KF-KameHouse
Created by Wolfer
KF-KameHouse Version 1
Small size map based in Roshi's Island, from the popular Akira Toriyama's anime, Dragon Ball.
[url]http://drunkenwolfer.wordpress.com/2014/11/22/kf-kamehou...
KF-LevelUpThatPerk! 2
Created by mano eliseu
The v2 is so cool bro. i wanna marry it. omg...
Created by RC.Aleksandr.MSI
Welcome to my map.You need to survive as long as you can.Don't cheat.Play fair.
Players supported 1-12
It's now version 2.5 but still some bugs are to be fixed.
This map has been made by [RC]Made <3 for RenCorner and it took me like 4 hours.Enjoy!...
KF-RomanOasis-Final
Created by Whinem
U.N.C.L.E.'s version of UltraMapping's Roman-Arena. Completely rebuilt and redesigned using UltraMapping's textures and many of it's Staticmeshes.
To get to the roof top, ask the goddess for help. To get down without to much damage, well you'll have to fi...
KF-TestZSpawningZone (HALLOWEEN)
Created by Ventura
*WARNING* Since the Halloween event is over, this map no longer works! The zeds will be invisible and you won't be able to get any achievements. To spawn normal Zeds, use the original map.
This map is basically the same as the regula...
KF-TestZSpawningZone (x-mas 3rd party solo only)
Created by Nar Trig
As I was waiting for the original creators (Ventur/\, Pr0Sn1p3r_PT, D.A.R.) to make the xmas update I decided to do a quick and dirty fix as well as post it on the workshop for all to use. This is only the SOLO map and I have not received permission etc.,...
KF-TheRum
Created by mano eliseu
Funny Joke map made by brazilians.
A.K.A : KFDrakar / Hitoshi / Talyths
V. 1.8: Fixed textures, players able to stop spawn, static meshes bugs.. yep. all is fixed.
V. 1.8: Added a Room. More easter eggs. More spawns. More wow.
KFO-777
Created by Kathy
Each slot machine counts as first try
so you usually dont have to restart the map to get the achievement
Dont forget to press the button for "drop cash" usually its V at the slot machines and not the "E use button"...
KFO-Haunted-Hotel
Created by Mr.RoBoT
A Horrific Objective map Inspired by an Indie game called Damned[www.mediafire.com]
I recommend not to use any mutator that could modify the gameplay if you want the map to work as it should.
Feature
...
KFO-OnceUponATimeInMexico
Created by Fel
It's BACK!!! And in vengence. This is a remake of the KF version of this map. Fight your way across the bridge of death as zeds parade towards you destryoing everythgin in their path. Once you make it to the end, there is a boss fight and then victory :...
KFO-Peak
Created by Fel
Your team was sent to investigate the muders of Peak Mannor when something hits your heli and it suddenly spins out of controll and crashes into a canyon. Seeing a rocket came from somewhere nearby, the team now knows the location of the killer and must st...
The Arena
Created by Quirk76
Captured and enslaved, you are now forced to fight for your life against waves of mutated creatures....
The Ruins
Created by Quirk76
You are part of an elite task force sent to investigate a top secret archaeological dig, which has stoped responding to all comunications.
UPDATE 11/26/2013
-Reduced map size by ~50%
BioLab
Created by Slark
this map was built by the example bioticslab...
Colon
Created by Mark-James
A small map bouncing up and down , watch out for sirens and bloats....
Copy And Paste
Created by Mark-James
A small map I made to watch my friends die.
Gravity set to -250...
Defend the Elevator
Created by Ellis in Wonderland
Defend the elevator - or die trying. Complete with working elevator*, self defense mechanism**, giant controllable gate*** and null gravity zone****.
*without guarantee / ** only usable once / *** only limited usage / **** health insurance required
U...
de_dust2
Created by Zetanoid
It's NOT my work I found this on Gamebanana.com I thought that none would know anymore about this Map that it was Ported into the Killing Floor Enigne.
You are A little bit too big so dont mind it that all other thing like doors.
So I decided to Upload i...
Extermination Chamber (Patty's Revenge)
Created by Ellis in Wonderland
This map is no fun.
Instead its design makes the player lose as fast as possible. The question is: will you die in wave 2 or in wave 3 (assmuning long game)? Including a player triggered pitfall* for lulz.
*Bonus points for luring bloats in...
Horrors of The Past
Created by Mark-James
V2 - This map became broken at some point, I removed the fleshpound chaingunner, so it should be fixed now....
House
Created by Mark-James
KF-404Apartment
Created by ON
Welcome to 404 Apartment
*Update*
Edit bug door corner...
Created by Skater Andrey
Hardcore!...
KF-Antigone
Created by Vman
Welcome to the Legend of Antigone....
KF-Basement
Created by El Grindero
Fight your way through the basement of a mysterious building! Enjoy battling in this rather small, arena-style map. This map is highly recommended for anyone wanting a challenge. At least three players are recommended for a good challenge and lots of fun!...
KF-Comarcal_Brutal
Created by [T.V.I]XeNoMoRfO
Mapa simple. Te encuentras en una ciudad, cae lentamente la noche, una carretera y dos búnkers por debajo de ella. Ambos se comunican entre sí gracias a un túnel que las veces hará de escapatoria o de tumba... depende de lo bien que juegues o de la suerte ...
KF-Crash_Bandicoot
Created by DpaKc
Convert map CSS for Killing Floor...
KF-Esperanza
Created by [T.V.I]XeNoMoRfO
Esperanza es un mapa especial. Un pequeño tributo a aquellos clanes que entran o entraban al servidor MANTIS. Posee una ambientación semi-oscura y un cielo encapotado que ayuda a crear una atmósfera opresiva. Una larga carretera (divida por un no menos lar...
KF-Faroh
Created by ON
.......
KF-Far_West_2
Created by [T.V.I]XeNoMoRfO
Espectacular segunda parte de mi popular mapa Far West. En el caso que nos ocupa, Far West 2 supera al primero prácticamente en todo. Más edificios (gran iglesia, morgue, enorme hotel, cantina de dos pisos, oficina del sheriff, almacén, granero, tiendas, v...
KF-Far_West_Mantis
Created by [T.V.I]XeNoMoRfO
Primera adaptación de mi popular mapa Far West para el servidor y clan MANTIS. En mi workshop también está disponible la segunda adaptación del susodicho, llamado KF-[MANTIS]-Far_West. A pesar de que ambos son parecidos en su arquitectura tienen variopinta...
KF-Fortin
Created by [T.V.I]XeNoMoRfO
Un mapa perfecto para francotiradores. Se divide en dos líneas defensivas bien definidas. La primera, a través de las rampas que presiden todo el perímetro y que otorgan buena posición de tiro cercano y la segunda, en lo más alto de las torres, que brindar...
KF-Galeones
Created by [T.V.I]XeNoMoRfO
Adaptación que he creado para Killing Floor partiendo del mapa original del Unreal Tournament 99, creado por Juan Pancho (DM-KGalleon). En este caso he añadido dos galeones más (tres en total) y una mar picada. Podrás recorrer todo su interior con varios n...
KF-HellFreezesOver
Created by swift_brutal_death
Merry Christmas from Skell and Swift!!
KF-IcaruS
Created by [T.V.I]XeNoMoRfO
IcaruS, la estación orbital situada en un universo paralelo. Tal vez mi mapa más original. Realizado para que sea necesaria una buena colaboración entre los jugadores. Espacios cortos, escasas vías de salida que se resumen en ocho teleportadores que te env...
KF-i[P*D]Hangar
Created by Skater Andrey
Map for group i[P*D]PROJECT
Карта для группы i[P*D]PROJECT
http://steamcommunity.com/groups/ipodproject
...
KF-Kranus
Created by [T.V.I]XeNoMoRfO
Lo más destacado son las nuevas texturas incluídas en el oportuno archivo .utx Posee una arquitectura rectangular. Los especímenes salen de la zona central, presidida por unas extrañas máquinas. Los humanos hacen lo propio en ambas puntas del mapa.
Hay do...
KF-No_MercyIII
Created by [T.V.I]XeNoMoRfO
Otro de mis mapas que tienen más de dos años en la red. Uno de los más jugados en la categoría de "no oficiales" en servidores. Esta versión de No Mercy es la más "lamera" por decirlo así. Dos únicas puertas de entrada hacen que los especímenes se amontone...
KF-No_MercyIII_BS
Created by [T.V.I]XeNoMoRfO
Adaptación de otro de mis mapas más populares; No Mercy III. En este caso y a pesar de ser muy similar al original se presentan importantes diferencias ya no sólo en lo concerniente a la arquitectura sino también a las nuevas ubicaciones de los especímenes...
KF-OSVbase
Created by [T.V.I]XeNoMoRfO
Map tribute to OSV team. Visit --> http://team-osv.com
KF-PulasR_Ligths_out
Created by Zobi
well i played the orginal PulsaR map and it was a bit "easy" so i had the urge to make it harder hope you enjoy DL below incase SteamWorkshop dosent work/instal all so id like to thank captain for helping me with with this version of the map !!!!NOTE!!!! i...
KF-PulsaR
Created by [T.V.I]XeNoMoRfO
PulsaR es un complejo preparado para emitir y recibir todo tipo de señales, en su mayoría centradas en intereses gubernamentales. Es un mapa grande, ideal para más de veinte jugadores. Hay cuatro tiendas y dos niveles, el inferior (para los que gusten de m...
KF-Pyramid_AVA
Created by [T.V.I]XeNoMoRfO
Segundo mapa que he creado basado en el original de otro juego (anteriormente Galeones, del Unreal Tournament). En este caso que nos ocupa el susodicho pertenece a "Alliance of valiant arms" más conocido como AVA, un FPS gratuito que podéis descargar desde...
Created by [T.V.I]XeNoMoRfO
Aquí os presento otro de mis mapas que tienen más de dos años en el candelero. Es la versión final de la beta del mismo nombre que cojeaba de algunos pequeños fallos en lo tocante a especímenes que se quedaban "pillados" en las rampas. Pero volviendo a lo ...
KF-StairwayOfBlood
Created by Cendwar
A stairway that will soon be filled with blood... either yours or theirs....
KF-Survival_room
Created by Skater Andrey
Mini room with boxes and zombies...
KF-Tercio
Created by [T.V.I]XeNoMoRfO
Mapa fortaleza tributo a los grandes Tercios españoles y por descontado a nosotros; el Clan [T.V.I]. Se incluyen nuevas texturas sobre escenas e imágenes de los susodichos. Ideal para ocho jugadores, aunque pueden ser más.
Una única tienda. Los jugadores ...
KF-Tercio_Ligths_out
Created by Zobi
ook after a long figth i got map working thanks to help and here is Ligths out version of tercio, i fixed the maps only 2 exploids with out low grav <.< and here is link if subcribe button dosent work: http://www.mediafire .com/download/uprxir4o1xvpgp8/KF-...
KF-TheCemetery By Ferenos
Created by Ferenos
* Description: No site nowhere to run, nowhere to hide, the darkness dwells in every corner of this abandoned cemetery. Death is approaching quickly from all sides, you have a single objective: fight or die devoured. Send those monsters to the depths of he...
KF-TheWolfLair
Created by Vman
simple map...
KF-The_Far_West
Created by [T.V.I]XeNoMoRfO
Esta fue la primera versión que saqué de "The Far West", hace dos años, tal vez algo más. Pequeño y rectángular, adictivo por su simplicidad. Como contrapunto tiene un pequeño bug que no influye a la hora de jugar pero resulta cuanto menos pintoresco. Ese ...
KF-ZedCraft
Created by Krull0r
My version of a Minecraft themed map :)...
KF-[MANTIS]-AquA
Created by [T.V.I]XeNoMoRfO
Adaptación para el servidor MANTIS de mi mapa KF-AquA_Mantis y a su vez del KF-AquA (que por fin dejó se der una beta). Básicamente la única diferencia con respecto al original es la inclusión de cinco rampas que comunican la parte alta con la baja, dónde ...
KF-[MANTIS]-BiG_ShoW
Created by [T.V.I]XeNoMoRfO
BiG Show es sin duda el mapa más complicado. Y con esa idea lo he creado, pequeño; simple. Sin escapatorias ni donde esconderse. Hará falta un gran juego de equipo para sobrevivir a las distintas oleadas.
Los jugadores salen de un punto central "blinda...
KF-[MANTIS]-Far_West
Created by [T.V.I]XeNoMoRfO
Adaptación para el servidor dedicado MANTIS de mi popular mapa "The Far West". La temática está bien clara, el viejo oeste. Poco puedo añadir ya que es prácticamente igual al original pero eso sí, he añadido ciertas modificaciones tales como edificios nuev...
KFO-Foundry-SE (ScrN Edition)
Created by [ScrN]PooSH
A conversion of one of the best stock map to the Objective Mode
Map is WHITELISTED!
KFO-Foundry is fully compatible with vani...
kru[yk]
Created by kru
Its still kruykcrap. Updating from time to time, for my own pleasure. I dont know why I already upload this, so dont download unless you enjoy a crap. I put things in it I like, not you!
Theme: Train
Gameplay: Normal...
Lobby
Created by Mark-James
Small map...
MountainPassSnow
Created by DED
winter came unnoticed.
...
Resident Evil 1 Mansion Story
Created by AestheticGamer
The story is nonsensical, the difficulty sometimes a bit straining, but this map is a classic! A remake of the first Resident Evil's mansion. Follow the go signs, use your ammo sparingly (the ammo and weapon pick-ups are spaced out), and work together to e...
Small
Created by Mark-James
First map that I made , it's small and dark , extremely basic....
Space Station
Created by Mark-James
...
Space Tower
Created by Mark-James
A small map with zeds flying at you...
Square
Created by Mark-James
A small dark square map with a biotics lab theme to it
Using the mixed crawler with the siren skin...
Theboxofhall map by killingfloorcustom
Created by killingerk
this map is a Alpha V0.0.0.4 map
is map will not be finish...
Vatican City Underground Bunker map by killingfloorcustom
Created by killingerk
Full version
this is 1 of The Seventh Secret Bunker map Website {LINK REMOVED}
Are steamcommunity
http://steamcommunity.com/groups/killingfloorcustom
are https://www.facebook.com/killingfloorcustommap0430 pz help find bug...
City
Created by Demon Of Razgriz
A small city based map. I will update it more later once i figure out how to make doors and stuff....
Coburg city Underground Bunker by killingfloorcustom
Created by killingerk
Full version we fix all the bug we now
First National Socialist City of Germany 1939...
Cutback Drop - Final V01
Created by GunsForBucks
First map, scale is off a little from what I expected, but I liked the layout and dealt with it.
Thanks to those that played and commented, Map is pretty much Final unless some issues come up during play,
Special Thanks to Grayve Rose and Lethal...
Diamond Scape Arena
Created by howedho
You find yourself trapped in an underground chamber, no way out! Ahead of you lies a single staircase down... you survive the drop into darkness but... how long will you survive? Enjoy the arena!
This is the re-release of my DSA map... made better!
-...
Dream Gate
Created by GunsForBucks
Last stand at the Gate of Delirium? Defending the last shreds of your sanity? Whateve's, just kill stuff in Dreamscape.
Farm Fun Map
Created by =(H)=maikmk2
New Farm Map with new Fun
Am Boden des Turmes liegen gute Waffen. Man kann die Riesen Bälle mit Waffen abschießen, dass sie runterfallen.
Special light
The balls can fall down when you shooting at them
When you kill the pat then the game begin...
GG-Vortex
Created by PiX
Killing Floor's first randomly generated map. Two planes of 12 "rooms" each that are randomly set on start of map. Has been tested on Tonio's Gun Game server and works pretty good.
Needs Gun Game mod:
[url]http://steamcommunity.com/sharedfiles/filede...
Irrenhaus
Created by =(H)=maikmk2
A new Fun Map from Bio Lab "Irrenhaus"
Clot Pat, Mg Fp"s Bloat Stalker Chainsaw Gorefast
strange enemies and more
kill the clot pat then the game Start...
KF - 1.815906
Created by GunsForBucks
You find yourself transported 4.5 million years by an out of control time machine, fighting in the desert sands of a giant hourglass.
Map is a small battle pit with two traders. Most textures used are screenshots from Steins Gate anime
KF-3Bridges-Final-fix3
Created by Whinem
This is a cutdown version made from KF-TBAHybzBeta1-1a. You have a choice of 3 bridges to defend, if you choose. If not, good luck, it can get nasty out there.
Note:
It has been brought to my attention that there are a number of safe spots that shouldn't...
KF-Al_Qaeda_Stakeout
Created by Zulukiller
You are the last line of defense to prevent a total outbreak of ZEDs the Private millitary that was hired FAILED,Now its up to you and your mates to stakeout the ZED....
KF-ArmyBase
Created by ON
Map Name KF-Army Base
Map size Medium-Large
KF-Bezerker's_Island-beta5
Created by Whinem
Design idea came from a fishing spot. Spooky at night so I thought it might make a good KF map. You be the judge. Run because they fall from the trees....
KF-BoilerRoom
Created by Zulukiller
The Boiler Room of an Asylum that is a small,cramped place to die...
KF-Box187
Created by Zulukiller
You are hired to complete a "ZED Test Box" In a private military test facility Simply known as "Box One Eighty Seven"...
KF-Box188
Created by Zulukiller
You are hired to complete a "ZED Test Box" In a private military test facility Simply known as "Box One Eighty Eight"...
KF-Bridged_Arena
Created by Vman
Another arena this time with a bridge down the middle to the shop, and if you look hard enough you will find a secret room...
KF-Chamber-of-Horror-Final2
Created by Whinem
This was my first map. It is on the hard side of hard. Trader has free weapons to use or sell. Plenty of ammo available during play time.No vests.
You can now get all my maps from the following link.
KF-C_Block
Created by Zulukiller
An Insane Asylum that needs some "Spring Cleaning"...
KF-DarkOmenBETA3R
Created by Vman
Your squad was destroyed in "Pripyat" district, only 5 persons have survived. Now the only objective of the detachment is to find uninfected people and evacuate them to a safe place...
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2016-08-25 04:16:52
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https://www.physicsforums.com/threads/how-long-do-you-feel-an-ipad-lasts.988123/
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# How long do you feel an iPad lasts?
## Main Question or Discussion Point
I have seen people say that PCs should be replaced every four or so years. This is because they become vulnerable over time to malware more easily and also they naturally start to break down. ...At least, that's what I've been told here.
How about iPADs? Are they as vulnerable and/or break down naturally every four or five years?
Related Computing and Technology News on Phys.org
Wrichik Basu
Gold Member
I have seen people say that PCs should be replaced every four or so years.
Don't want to derail the thread, but you are talking about replacing software (specifically upgrading the OS) rather than hardware, right? Our desktop is >15 years old and it's working fine.
russ_watters
Staff Emeritus
2019 Award
This is because they become vulnerable over time to malware more easily a
That's nonsense.
At least, that's what I've been told here.
Where? I mean, you've made that claim, but I don't see where someone else has.
russ_watters, phinds and Wrichik Basu
anorlunda
Staff Emeritus
I see no difference between iPad and other computers. Many people keep them for many years. My iPad2 is 9 years old. It is no longer supported by Apple so I can't update any of the apps. But it still works very well. I see no reason to replace it.
IMO, the main thing that motivates people to replace old computers is that upgraded software needs more resources, digital cameras produce higher resolution pictures, and web pages require more data than they used to. In the case of laptops and tablets, newer models have less weight, better displays, and less power consumption. Smart phones also compete with old tablets.
DavidSnider
Gold Member
It's not that they become *more* vulnerable to malware, it's that companies no longer support it after a while and won't even bother patching it. 4 years is usually fine though.
Staff Emeritus
2019 Award
That's a function of software, not hardware. Windows 7 has just moved to end-of-life, Windows 8.1 has three years left, and Windows 10 runs on most ten-year old hardware. That says that ~13 years is the sort of window we are talking about, and that's why I asked @kyphysics to point us to what he thinks he heard.
DavidSnider
Gold Member
Hardware and software go together. All the hardware in your machine has drivers and probably a fair share of vendor created bloatware as well. The longer something is out there the longer attackers have had to find weaknesses in it and less likely that the vendor will bother patching it.
kyphysics
How long do they last?. Well, for my desktop, its a Dell I inherited from work. Built date 1994. Running windows XP and used daily for at least 8 hours..
We started with windows3.1in the 80s and then switched to windows 95 which I used for long time till i was finally "forced" to switch to windows XP.
My desk top has had memory upgrade and thats about all. Still runs reliably although there are some programs which can't be used due to no support. I certainly won't be changing soon until its on its last legs and nothing works any more.
Bought a laptop running windows 10 last year and I have to say it is the greatest abomination of an operating system I have ever come across. A lot of tasks and features are hard to locate and it is not easy to use. And I still have continual trouble with socalled "features" and "upgrades" not installing.
I just wish Microsoft would have left windows XP alone and just improved it as problems arose. I really like the user interface and generall operability of XP. It is far more intuative than WIN10.
russ_watters
Getting to thr question of iPads, don't have one , don't want one. I have a dislike of touch screens. My partner has a Surface tablet and it is, to me, so frustrating to use, a few times I was tempted to throw it out the window, preferably from a fast moving vehicle.
Mark44
Mentor
How long do they last?. Well, for my desktop, its a Dell I inherited from work. Built date 1994. Running windows XP and used daily for at least 8 hours.
That computer is very long in the tooth. If you access the internet using that machine, I sincerely hope you keep your antivirus software up-to-date.
We started with windows3.1in the 80s and then switched to windows 95 which I used for long time till i was finally "forced" to switch to windows XP.
Which could be very vulnerable to attackers. Both Win XP and the newer version, Win 7, are no longer supported by MSFT, as you might know.
My desk top has had memory upgrade and thats about all. Still runs reliably although there are some programs which can't be used due to no support. I certainly won't be changing soon until its on its last legs and nothing works any more.
Hard drive might be one of the first things to go.
Bought a laptop running windows 10 last year and I have to say it is the greatest abomination of an operating system I have ever come across. A lot of tasks and features are hard to locate and it is not easy to use. And I still have continual trouble with socalled "features" and "upgrades" not installing.
I disliked Win 8 when it came out, and didn't upgrade to it. The most irritating feature IMO was its attempt to mimic the screen on a cell phone. Win 8.1 was slightly better, but Win 10 still has that same appearance.
However, ninite.com has a large collection of free software, one item of which is Classic Shell. Someone told me about it, and I downloaded it, and am very happy with it. Once it's installed, you can easily configure the desktop to look like Win XP or Win 7, both with the Start button that doesn't appear in Win 8, 8.1, or 10.
I have a dislike of touch screens.
Me, too. I don't want to be looking at a screen through layers of fingerprints and oily residue from fingers.
pbuk
Gold Member
Well, for my desktop, its a Dell I inherited from work. Built date 1994. Running windows XP and used daily for at least 8 hours.
The other day I bought a second hand Dell with an i5 processor, 8GB of memory, Dual HD display capability and Windows 10 Pro for GBP130 on Amazon. Treat yourself - you might find that you get that 8 hours work done in 6!
Mark44
Mentor
Well, for my desktop, its a Dell I inherited from work. Built date 1994.
If it has an Intel processor, it's very likely an 80486 or maybe the first generation Pentium, which was the one that had the floating point FDIV error. Recalling the faulty processors set Intel back almost a half Billion dollars.
The other day I bought a second hand Dell with an i5 processor, 8GB of memory, Dual HD display capability and Windows 10 Pro for GBP130 on Amazon.
Seems like a pretty good deal -- about US$165 or so. I bought a new Dell laptop a few months ago, with tenth gen i7 processor, 8GB of RAM, 256GB SSD, Win 10 Pro -- about$750. Cars have gone up and up in price, but computers are pretty cheap, considering what you get.
Svein
Sigh. I recently had to exchange the printer attached to my server, and it started a long chain of events:
1. Getting a printer driver for the new printer seemed more or less impossible, and I had to do some fancy software juggling to finding an acceptable driver and forcing it to install.
2. Along the way I discovered that the server OS (Windows Foundation Server 2008r2) had gone the way of Windows 7 - not supported anymore.
3. So - do I install a new server OS or what? When starting to analyze that problem, I was reminded the hard way that the server hardware (a Dell T110) was from 2011. It was by far the oldest PC-type hardware in the house. Do I really want to put a new server OS on that?
4. So I started looking for some new server hardware (and a server OS on top of that). I found several examples of server hardware to reasonable prices, but nobody was willing to tell me what server OS would run on that hardware - or what the OS would cost!
5. So I gave up on that and built a server PC from readily available components. I also found a good deal on a server OS and installed it. Apart from from a couple of hours spent on making the server OS accept the LAN driver, it was more or less straight driving. Moving al data from the old server to the new was just a case of a large USB3 disk and walking from one server to another.
6. Then it was time to transfer all the server roles from the old to the new hardware. That turned out to be a real headache, since the old server refused to die. Even when every role was transferred and I had turned the old server off, it stubbornly turned itself on again. I had to physically pull the plug on it!
7. So - the new server is running as it should (with a lot less noise and a lot less power), I tried to install some other OS on the old server. A Linux server? Linux gave up before even trying to install. Windows 10 could not find an applicable driver (it did not specify what kind of driver). So - now there is an old server in my cellar waiting for its eventual doom and disposition.
anorlunda
Staff Emeritus
Can't you print with a generic driver? It may miss special features such as double-sided, but it could do the basics.
I would expect the same problem regardless of the OS. You might find a printer from the 50s or 60s, and the only drivers for that were written for computers and OSes that no longer exist.
Staff Emeritus
2019 Award
Amazingly, Windows 10 still supports Epson FX-80 printers from the min-1980's!
How about iPADs? Are they as vulnerable and/or break down naturally every four or five years?
I see no difference between iPad and other computers. Many people keep them for many years. My iPad2 is 9 years old. It is no longer supported by Apple so I can't update any of the apps. But it still works very well. I see no reason to replace it.
The lithium ion batteries in modern electronics do degrade over time, losing capacity. The iPad2 is documented to last 10 hours on a charge. @anorlunda, what kind of battery life does your iPad have now?
anorlunda
Staff Emeritus
The lithium ion batteries in modern electronics do degrade over time, losing capacity. The iPad2 is documented to last 10 hours on a charge. @anorlunda, what kind of battery life does your iPad have now?
I haven't done the test explicitly. All I can say is that I have not noticed any degradation.
I read once that the life of a Lithium battery is proportional to how long it spends below 80% charge. I follow that. I try to remember to end charging at 75%, and I never leave it plugged in overnight. Since I started doing the same with my phones and laptops, I've had very good luck with their batteries also.
I bought an iPad when they first came out, and it cost quite a bit (like \$800). After 4 years (if I recall correctly) they no longer would upgrade the operating system and pretty soon things stopped working (can't view youtube videos, etc.) I will never buy another Apple product.
How long do they last?. Well, for my desktop, its a Dell I inherited from work. Built date 1994. Running windows XP and used daily for at least 8 hours..
We started with windows3.1in the 80s and then switched to windows 95 which I used for long time till i was finally "forced" to switch to windows XP.
My desk top has had memory upgrade and thats about all. Still runs reliably although there are some programs which can't be used due to no support. I certainly won't be changing soon until its on its last legs and nothing works any more.
Bought a laptop running windows 10 last year and I have to say it is the greatest abomination of an operating system I have ever come across. A lot of tasks and features are hard to locate and it is not easy to use. And I still have continual trouble with socalled "features" and "upgrades" not installing.
I just wish Microsoft would have left windows XP alone and just improved it as problems arose. I really like the user interface and generall operability of XP. It is far more intuative than WIN10.
I sympathize regarding your preference for XP over its successors. You can to a worthy extent alleviate the problem of finding settings by using a special folder name that presents most system options in a single folder:
Right-click on the desktop and choose New > Folder.
Name the folder: whatever_name_you_want.{ED7BA470-8E54-465E-825C-99712043E01C}.
You can also go into the search box and type compmgmt.msc, and when the search finds it and puts it at the top of the results bar, right-click on it, and select 'Run as administrator'. When it comes up, go into Services, stop Windows Update, and change its startup status from Automatic to Disabled. That will stop Windows from looking for updates or trying to auto-install them. If you later decide you need an update you can re-enable it, but if you do that, it will try to install all the updates you missed while updating was disabled.
You might want to do a search on 'windows 10 annoyances' -- you'll find some good tips on making it run with fewer gadflies.
This is something that I use on all of my post-XP PCs:
The version there works very well and allows an XP=style taskbar and menu tree, with a menu option to go to the Windows 10 screen and back whenever you wish.
The originators have stopped developing it, but some volunteers have adopted it and you can get their latest as Open Shell on github:
I think you'll like Classic Shell. I have yet to try the more recent Open Shell. I have no reason to do so at present.
DrClaude
Mentor
I read once that the life of a Lithium battery is proportional to how long it spends below 80% charge.
Do you have a source for that? I'm curious.
anorlunda
Staff Emeritus
DrClaude
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2020-07-13 11:56:33
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https://socratic.org/questions/if-q-is-a-right-angle-in-pqr-and-pr-pq-9-pr-qr-18-then-find-the-perimeter-of-tri#576111
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If hatQ is a Right-angle in DeltaPQR and PR-PQ=9 , PR-QR=18 then what is the perimeter of the triangle?
Mar 18, 2018
Perimeter is $108$
Explanation:
As in right angled triangle $P Q R$, $m \angle Q = {90}^{\circ}$, $\overline{P R}$ is hyptenuse and te largest side. Further, according to Pythagoras theorem
$P {R}^{2} = Q {R}^{2} + P {Q}^{2}$ .......................(A)
Now let $P R = x$, then as $P R - P Q = 9$, $P Q = x - 9$
and as $P R - Q R = 18$ and therefore $Q R = x - 18$
Putting these values in (A), we have
${x}^{2} = {\left(x - 9\right)}^{2} + {\left(x - 18\right)}^{2}$
or ${x}^{2} = {x}^{2} - 18 x + 81 + {x}^{2} - 36 x + 324$
or ${x}^{2} - 54 x + 405 = 0$
or ${x}^{2} - 45 x - 9 x + 405 = 0$
or $x \left(x - 45\right) - 9 \left(x - 45\right) = 0$
or $\left(x - 9\right) \left(x - 45\right) = 0$
Observe that as all sides are positive, we must have $x > 18$
and hence only solution is $x = 45$
and sides are $45$, $36$ and $27$
and perimeter is $45 + 36 + 27 = 108$
Mar 18, 2018
Perimeter = $27 + 36 + 45 = 108$
Explanation:
If $\hat{Q}$ is 90°, then $P R$ is the hypotenuse.
$P Q \mathmr{and} R Q$ can be written in terms of the hypotenuse.
Let $P R = x$
Then $P Q = x - 9 \mathmr{and} R Q = x - 18$
Write an equation using Pythagoras' Theorem:
${\left(x - 9\right)}^{2} + {\left(x - 18\right)}^{2} = {x}^{2}$
${x}^{2} - 18 x + 81 + {x}^{2} - 36 x + 324 = {x}^{2}$
${x}^{2} - 54 x + 405 = 0$
$\left(x - 45\right) \left(x - 9\right) = 0$
$\therefore x = 45 \mathmr{and} x = 9 \rightarrow$ reject $9$ as being too short
If the hypotenuse is $45$, then the sides are
$45 - 9 = 36 \mathmr{and} 45 - 18 = 27$
Perimeter = $27 + 36 + 45 = 108$
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2022-08-11 21:14:10
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https://www.meritnation.com/ask-answer/question/please-solve-question-no-29/solutions/13583413
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# Please solve question no 29
We have,
Molar concentration= partial pressure x henry constant
Hence, C = p xKh
Or, n/V =p xKh
Or, n =p xKh xV
'Putting the values we get, no. of moles of oxygen gas as:
$n=0.5atmx0.1Lx1.4x10-3mol/atmL=0.00007$
Thus, 1 mole of oxygen gass= 32 g
Hence, 35.7 mole of oxygen gas = 0.00007x 32=2.24 x10-3 g = 2.24mg
Correct answer is d). 2.24 mg
• 9
What are you looking for?
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2020-01-17 21:36:05
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http://jesse.codes/blog/Fix-Sweave-Not-Found-in-Latex/
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January 3, 2016
I write most of my papers in LaTeX. This time, I’m writing an IB Biology IA and need to include R-generated graphs and figures. Usually I just generate the PDFs seperately and include them inside of the document using `\includegraphics`, but I wanted to give Sweave a try.
I created a Makefile and setup my documents just so then gave it a spin. Aaaand error!
``````! LaTeX Error: File `Sweave.sty' not found.
``````
Sigh… LaTeX errors.
After a bit of internet investigation, here’s how I fixed the problem. (This is for my own personal reference, but I hope it helps you as well.)
First we need to find the path where R was installed. If you didn’t install it via homebrew, then just find `R.framework` in your filesystem.
``````\$ brew info R
Software environment for statistical computing
http://www.r-project.org/
# a lot of output, but here is what we're looking for
/usr/local/Cellar/r/3.2.2 (2175 files, 59M) *
# ...
\$ sudo ln -s /usr/local/Cellar/r/3.2.2/R.framework/Resources/share/texmf/ /usr/local/texlive/2015/texmf-dist/tex/latex/Sweave
\$ sudo texhash
# Success!
``````
The symlink paths might be different depending on your version and installation of LaTeX, but the general idea is to make LaTeX aware of R’s `sty` files.
Hope this helps!
Next post: Make Awesome (Easy) Aeropress Coffee
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2017-06-29 01:56:59
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https://sciencing.com/calculate-water-pressure-tank-volume-6326635.html
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How to Calculate Water Pressure from Tank Volume
••• RoschetzkyIstockPhoto/iStock/GettyImages
Print
Water pressure is not a direct function of water tank volume, but of depth. For example, if you spread out 1,000,000 gallons of water so thin as to be only 1 inch deep at any point, it wouldn't have much pressure at all. If the same volume were poured into a column with sides measuring 1 foot wide, the pressure at the bottom would be ten times greater than at the bottom of the ocean. If you know some lateral measurement of the tank in addition to the volume, you can calculate the water pressure at the tank’s bottom point.
Determine the water pressure at the bottom of a full, upright cylinder by dividing the volume by the product of pi (π) multiplied by radius squared (R2):
\frac{V}{\pi R^2}
This gives the height. If the height is in feet, then multiply by 0.4333 to get pounds per square inch (PSI). If the height is in meters, multiply by 1.422 to get PSI. Pi, or π, is the constant ratio of the circumference to the diameter in all circles. An approximation of pi is 3.14159.
Determine the water pressure at the bottom of a full cylinder on its side. When the radius is in feet, multiply the radius by 2 and then multiply the product by 0.4333 to get the water pressure in PSI. When the radius is in meters, multiply the radius by 2 and then multiply by 1.422 to get PSI.
Determine the water pressure at the bottom of a full spherical water tank by multiplying the volume (V) by 3, dividing it by the product of 4 and pi (π), taking the cube root of the result and doubling it:
2(\frac{3V}{4\pi})^{1/3}
Then multiply by 0.4333 or 1.422 to get PSI, depending on whether the volume is in feet-cubed or meters-cubed. For example, a spherical tank of volume 113,100 cubic feet that’s full of water has a water pressure at its bottom of :
2(\frac{3\times 113100}{4\pi})^{1/3}\times 0.4333=26\text{ PSI}
Tips
• The calculations in Step 3 are based on the height being twice the radius (R) and the formula for the volume of a sphere being four-thirds of pi (π) times the cube of the radius (R): V = ( π/3) x R3.
Dont Go!
We Have More Great Sciencing Articles!
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2022-05-28 09:48:41
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https://blog.selfshadow.com/publications/practical-visibility/
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# Practical, Dynamic Visibility for Games
## 1. Introduction
With the complexity and interactivity of game worlds on the rise, the need for efficient dynamic visibility is becoming increasingly important.
As luck would have it, this article covers two complementary approaches to visibility determination that have shipped in recent AAA titles across Xbox 360, PS3 and PC: Splinter Cell: Conviction and Battlefield: Bad Company 1 & 2.
These solutions should be of broad interest, since they are capable of handling entirely dynamic environments consisting of a large number of objects, with low overhead, straightforward implementation, and only a modest impact on asset authoring.
But before we describe our approaches in detail, it is important to understand what motivated their development through the lens of existing techniques that are more commonly employed in games.
## 2. Surveying the Field
Static Potentially Visible Sets (PVSs) is an approach popularised by the Quake engine [Abrash 96] and still in common use today, in part because of its low run-time cost. Put simply, the world is discretised in some way (BSP, grid, etc.) and the binary visibility from each sector (leaf node, cell or cluster respectively) to all other sectors is pre-computed and stored. At run-time, given the current sector containing the camera, determining the set of potentially visible objects becomes a simple matter of retrieving the potentially-visible sectors (and by extension, their associated objects) and performing frustum culling.
One major drawback of using this technique by itself is that any destructible or moving objects (e.g. doors) typically have to be treated as non-occluding from the perspective of visibility determination. This naturally produces over-inclusion – in addition to that coming from sector-to-sector visibility – and can therefore constrain level-design choices in order to avoid pathological situations.
Another disadvantage stems from the fact that a PVS database can be extremely time consuming to pre-compute1, which may in turn disrupt or slow production.
Portals are another approach that can complement or replace static PVS. Here, sectors are connected via convex openings or portals and the view frustum is progressively clipped against them [Möller et al. 08], whilst objects are simultaneously gathered and tested against the active sub-frustum.
Since this clipping happens at runtime, the state of portals can be modified to handle a subset of dynamic changes to the world, such as a door closing or opening. But, even though portals can ameliorate some of the limitations of a static PVS solution, they are still best suited to indoor environments, with corridors, windows and doorways providing natural opportunities to constrain and clip the view frustum.
Anti-portals are a related technique for handling localised or dynamic occlusion where, instead of constraining visibility, convex shapes are used to occlude (cull away) objects behind them with respect to the player. Though they can be effective in open areas, one can only employ a limited number in any given frame for performance reasons. Similarly, occluder fusion – culling from the combined effect of several anti-portals – is typically not viable, due to the much higher cost of inclusion testing against concave volumes.
In recent years, hardware Occlusion Queries (OQs) have become another popular tool for visibility determination [Soininen 08]. The canonical approach involves rendering the depth of a subset (or a simplified representation) of the scene – the occluders – and then rasterising (without depth writes) the bounds of objects, or groups of objects. The associated draw calls are bracketed by a query, which instructs the GPU to count pixels passing the depth test. If a query returns that no pixels passed, then those objects can be skipped in subsequent rendering passes for that camera.
This technique has several advantages over those previously discussed: it is applicable to a wider range of environments, trivially adapts to changes in the world (occluders can even deform) and handles occluder fusion effortlessly, by nature of z-buffer-based testing. In contrast, whilst static PVS and portals can also handle dynamic objects via sector relocation, those same objects cannot act as occluders in general.
## 3. Query Quandaries
On paper OQs are an attractive proposition, but personal experience has uncovered a number of severe drawbacks, which render them unsuitable for the aforementioned titles. We will now outline these problems one by one.
### 3.1 Batching
Firstly, though OQs can be batched in the sense being able to issue more than one at a time [Soininen 08] – thereby avoiding lock-step CPU-GPU synchronisation – one cannot batch several bounds into a single draw call with individual query counters. This is a pity, since CPU overhead alone can limit the number of tests to several hundred per frame on current-generation consoles, which may be fine if OQs are used to supplement another visibility approach [Hastings 07], but is less than ideal otherwise.
### 3.2 Latency
To overcome this limitation, and as a general means of scaling OQs up to large environments, a hierarchy can be employed [Bittner et al. 09]. By grouping, via a Bounding Volume Hierarchy (BVH) or octree for instance, tests can be performed progressively based on parent results, with sets of objects typically rejected earlier.
However, this dependency chain generally implies more CPU-GPU synchronisation within a frame since, at the time of writing, only the CPU can issue queries2. Hiding latency perfectly in this instance can be tricky and may require overlapping query and real rendering work, which implies redundant state changes in addition to a more complicated renderer design.
### 3.3 Popping
By compromising on correctness, one can opt instead to defer checking the results of OQs until the next frame – so called latent queries [Soininen 08] – which practically eliminates synchronisation penalties, while avoiding the potential added burden of interleaved rendering.
Figure 1: Camera or object movement can lead to popping with latent queries
Unfortunately, the major downside of this strategy is that it typically leads to objects “popping” due to incorrect visibility classification [Soininen 08]. Figure 1 shows two cases where this can occur. Firstly, the camera tracks back to reveal object A in frame 1, but A was classified as outside of the frustum in frame 0. Secondly, object B moves out from behind an occluder in frame 1 but was previously occluded in frame 0.
Such artifacts can be reduced by extruding object bounding volumes3, similarly padding the view frustum, or even eroding occluders. However, these fixes come with their own processing overhead, which can make eliminating all sources of artifacts practically impossible.
Sudden changes such as camera cuts are also problematic with latent queries, potentially leading to either a visibility or processing spike [Hastings 07] to avoid rampant popping. As such, it may be preferable to simply skip rendering for a frame and only process visibility updates behind the scenes.
The GPU is a precious resource and a common bottleneck in games, as we seek to maximise visual fidelity for a given target frame-rate. Therefore, a visibility solution that relies heavily on GPU processing is less than ideal, particularly on modern consoles where multiple CPU cores or SPUs are available. While it is true to say that OQs should only be issued when there is an overall GPU saving [Soininen 08], this cannot be guaranteed in general and we would ideally like to dedicate as much GPU muscle as possible to direct rendering.
### 3.5 Variable Costs
A final disadvantage with OQs is that the worst case cost of testing an object is roughly proportional to its size on screen, which typically does not reflect its true rendering cost. While one can, for instance, choose to always render objects with high screen-space coverage to avoid this penalty, it is a less viable strategy when working with a hierarchy.
Even if one develops a more sophisticated oracle [Bittner et al. 09] to normalise performance, this can come at the cost of reduced culling effectiveness. Furthermore, a hierarchy requires additional CPU overhead when objects move, or parts become visible or occluded. As with queries, the per-frame update cost can be bounded by distributing work over multiple frames, but this can similarly compromise culling.
Ideally we would like to avoid these kinds of unfortunate trade-offs, especially when major changes to the environment occur; whilst leveraging coherency can be a great way to reduce the average per-frame processing time, it should not exacerbate worst-case performance!
## 4. Wish List
Ideally we would like to take the strengths of OQs but reduce or eliminate the negatives.
Here is our wish list:
In common with OQs Improvements No pre-computation Low latency Generality Reduced CPU-GPU dependency Occluder fusion No reliance on coherency Bounded, high performance Simple, unified solution
In summary, we would like to be able to handle a wide range of dynamic scenes with the minimum of fuss and no less than great performance. Essentially, we want it all and in the case of Conviction – as you will now learn – we wanted it yesterday!
## 5. Conviction Solution
One of the initial technical goals of Splinter Cell: Conviction was to support dense environments with plenty of clutter and where, in some situations, only localised occlusion could be exploited.
We initially switched from PVS visibility to OQs because of these requirements, but having battled for a long time with the drawbacks outlined earlier and becoming increasingly frustrated by mounting implementation complexity, hacks and failed workarounds, we started to look for alternatives. Unfortunately, by this point we had a scarce amount of time and resources to dedicate to switching solutions yet again.
Luckily for us, [Shopf et al. 08] provided a guiding light, by demonstrating that the Hierarchical Z Buffer (HZB) [Greene et al. 93] could be implemented efficiently on modern GPUs – albeit via DX10 – as part of an AMD demo. This largely validated that the HZB was a viable option for games, whereas we had previously been skeptical, even with a previous proof of concept by [Décoret 05].
Most importantly, it immediately addressed all of our requirements, particularly with respect to implementation simplicity and bounded performance. In fact, the elegance of this approach cannot be understated, comparing favourably with the illusory simplicity of OQs, but without any of the associated limitations or management complexity in practice.
### 5.1 The Process
Render Occluder Depth. As with OQs, we first render the depth of a subset of the scene, this time to a render target texture, which will later be used for visibility testing, but in a different way than before.
For Conviction, these occluders were typically artist-authored4 for performance reasons, although any object could be optionally flagged as an occluder by an artist.
Create a Depth Hierarchy. The resulting depth buffer is then used to create a depth hierarchy or z-pyramid, as in [Greene et al. 93]. This step is analogous to generating a MIP-map chain for a texture, but instead of successive, weighted down-sampling from each level to the next, we take the maximum depth of sets of 4 texels to form each new texel, as in Figure 2.
Figure 2: Generating successive levels of the HZB
Figure 3: The resulting depth hierarchy. Note how the sky
in the distance increasingly dominates at coarser levels.
This step also takes place on the GPU, as a series of quad passes, reading from one level and writing to the next. To simplify the process, we restrict the visibility resolution to a power of two, in order to avoid additional logic of [Shopf et al. 08].
We render at 512x2565 as this seems to strike a good balance between accuracy and speed. This could theoretically result in false occlusion for objects of 2x2 pixels or less at native resolution, but since we contribution-cull small objects anyway, we have not found this to be a problem in practice.
Test Object Bounds. We pack object bounds (world-space AABBs) into a dynamic point-list vertex buffer and issue the tests as a single draw call. For each point, we determine in the vertex shader the screen-space extents of the object by transforming and projecting the bounds. From this, we calculate the finest MIP level of the hierarchy that covers these extents with a fixed number of texels or less and also the minimum, projected depth of the object.
Figure 4: The object’s world-space AABB (blue),
screen extents (green) and overlapping HZB texels (orange).
Listing 1: HZB query vertex shader
This depth, plus the UVs (sbox: the screen-space AABB) and MIP level for HZB lookup are then passed to the pixel shader. Here we test for visibility by comparing the depth against the overlapping HZB texels and write out 1 or 0 as appropriate.
Listing 2: HZB query pixel shader
In practice, we chose to use 4x4 HZB depth comparisons in contrast to the simpler example code above, as this balanced ALU instructions and texture lookups on Xbox 360.
Another thing to note is that we perform world-space frustum testing and screen-bound generation separately. While the two can be combined as in [Blinn 96], we found that we got better code generation this way and could add extra planes to the frustum test when processing reflections.
It is also possible to improve upon the MIP level selection for situations when an object covers less texels (see Listing 3).
Listing 3: HZB level refinement
Process the results. Finally, the results are read back to the CPU via memexport on Xbox 360. On PC, under DX9, we instead emulate DX10 stream-out by rendering with a point size of 1 to an off-screen render-target, followed by a copy to system memory via GetRenderTargetData.
By using a fixed number of lookups in place of rasterisation, the performance of the visibility tests is highly predictable for a given number of objects. That said, this bounded performance comes at the cost of reduced accuracy for objects that are large on screen.
However, an alternative way to view this approach is that it is probabilistic: large objects are on average more likely to be visible anyway, so performing more work (in the form of rasterisation with OQs) is counter-productive. Instead, with HZB testing, accuracy is distributed proportionally. This proved to be a particularly good fit for us, given that we wanted a lot of relatively small clutter objects, where instancing was not appropriate for various reasons.
We also benefited from the high granularity afforded by a query per object, whereas wholly OQ-based methods require some degree of aggregation in order be efficient (as we already argued), leading to reduced accuracy and more variable performance. This showed up in our own analysis when switching to HZB visibility from OQs. We started off with a 2x2 depth-test configuration and even that out-performed hand-placed occlusion query volumes, both in terms of performance and the amount of culling. Essentially, what we lost in terms of occlusion accuracy, we gained back from being able to test objects individually.
Point rendering with a vertex buffer was primarily chosen for ease of development as vertex buffers offered the convenience of heterogeneous data structures. However, a more efficient option could be to render a single quad and fetch object information from one or more textures instead. Not only would this ensure better pixel-quad utilisation on some hardware, but it would also play to the strength of GPUs with a non-unified shader architecture such as the PS3’s RSX, where the bulk of the shader hardware is dedicated to pixel processing.
### 5.3 Performance
Table 1 represents typical numbers seen in PIX on Xbox 360, for a single camera with around 22000 objects, all of which are processed each frame.
Pass Time (ms) Occlusion 0.06 Resolve 0.04 HZB Generation 0.10 HZB Queries 0.32 Total 0.52
Table 1: Performance timings
### 5.4 Extensions
Once you have a system like this in place, it becomes easy to piggy-back related work that could otherwise take up significant CPU time compared to the GPU, which barely breaks a sweat. Contribution fading/culling, texture streaming and LOD selection, for instance, can all be determined based on screen extents or similar6, with results returned in additional bits.
On Xbox 360, we can also bin objects into multiple tiles ourselves, thereby avoiding the added complexity and restrictions that come with using the Predicated Tiling API, not to mention the extra latency and memory overhead when double-buffering the command buffer.
Finally, there is no reason for limiting visibility processing to meshes. We also test and cull lights, particle systems, Ambient Occlusion volumes [Hill 10] and dynamic decals.
Later in development, we extended our system to accelerate shadow map rendering, with a two-pass technique initially inspired by [Lloyd et al. 04], but a lot more straightforward. For instance, we do not slice up the view frustum and test sub-regions as they do. This is mostly because we are not using shadow volumes for rendering and therefore not aiming to minimise fill-rate7, only the number of casters – for CPU and vertex transform savings. Development time and ease of GPU implementation were also factors.
In the first pass, we test caster visibility from the light’s point of view, in exactly the same way that we do for a regular camera: via another HZB. If a given caster is not visible, it is culled as before. If it is visible, we write out the active shaft bounds, which are formed from the 2D light-space extents, the caster’s minimum depth, and the maximum depth from the HZB:
Figure 5 shows this in action for a parallel light source. Here, caster C is fully behind an occluder8, so it can be culled away as it will not contribute to the shadow map.
In the second pass, we transform these shafts into camera space and test their visibility from the player’s point of view via the existing player camera HZB – again just like regular objects. Here, as the shafts of A and B have been clamped to the occluder underneath, they are not visible either.
Conceptually, we are exploiting the redundancy of shadow volume overlap across two viewpoints in order to reduce our set of potential casters.
### 5.6 Summary
To reiterate, this entire process takes place as a series of GPU passes; the CPU is only involved in dispatching the draw calls and processing the results at the end.
In retrospect, a CPU solution could have also worked well as an alternative, but we found the small amount of extra GPU processing to be well within our budget. Additionally, we were able to leverage fixed-function rasterisation hardware, stream processing and a mature HLSL compiler, all with literally man-years of optimisation effort behind them. In contrast to the simple shaders listed earlier, a hand-optimised VMX software rasteriser would have taken significantly longer to develop and would have been harder to extend.
If you already have a PVS or portal visibility system, then there can still be significant benefits to performing HZB processing as an additional step. For one thing, either system can act as an initial high-level cull, thus reducing the number of HZB queries. In the case of portals, the “narrow-phase” sub-frusta testing could also be shifted to the GPU. Indeed, from our own experience, moving basic frustum testing to the GPU alone was a significant performance win over VMX tests on the CPU. Finally, in the case of BSP-based PVS, the faces could be pre-converted to a number of large-scale occluders for direct rendering.
## 6. Battlefield Solution
When developing the first game (Battlefield: Bad Company) with our new in-house Frostbite engine, we knew that we needed a solution for removing objects occluded by others. We discussed many methods, but it all came down to a list of things that we wanted the system to have:
• Must be fully dynamic, since the environment – both objects and terrain – can deform
• Results accessible from the CPU, so we can skip updating certain aspects of occluded objects, such as animation
After reading about Warhawk’s solution [Woodard 07] based around software rasterisation on SPUs, we decided to try a similar approach as we had spare processing power available on the CPU side. The resulting implementation was subsequently rolled out across all of our target platforms (Playstation 3, Xbox 360 and PC), but we will focus in particular on the details of the PS3 version.
At a high-level, the steps involved are very similar to those of Conviction: a software occlusion rasteriser renders low polygon meshes to a z-buffer, which occludees are then tested against to determine if they are visible or not.
In reality, the work is broken down into a number of stages, which are job-scheduled in turn across several SPUs. We will now describe these in detail.
### 6.1 The Process
Occluder Triangle Setup. This stage goes through all occluders in the world (a flat array) in preparation for rasterisation:
1. Each job grabs a mesh from the array using InterlockedIncrement.
2. The job checks if the mesh is inside the frustum. If it is not, it continues to the next one (step 1).
3. If the mesh is fully inside the frustum, its triangles are immediately appended to an output array (also interlocked and shared between the jobs).
4. If the mesh was not fully inside, its triangles are clipped before being added.
Terrain Triangle Setup. This is effectively the same as the previous stage, except that it generates and adds conservative triangles for the terrain9 to the array.
Occluder Render. This is the stage that actually rasterises the triangles. Each SPU job has its own z-buffer (256 x 114) and grabs 16 triangles at a time from the triangle array generated previously.
When the jobs are finished getting triangles from the triangle array, they will each try to lock a shared mutex. The first one will simply DMA its z-buffer to main memory, unlock the mutex and exit so that the next job can start running.
As the mutex gets unlocked, the next job will now merge its own buffer with the one in main memory and send back the result, and so on. (Note: There are several ways to improve on this and make it faster. We could, for example, DMA directly from each SPU.)
Frustum Cull. This stage performs frustum versus sphere/bounding box (BB) checks on all meshes in the world – typically between 10,000 and 15,000 – and builds an array for the next stage. The implementation traverses a tree of spheres (prebuilt by our pipeline) and at each leaf we do bounding-box testing if the sphere is not fully inside.
Occlusion Cull. Finally, this is where visibility testing against the z-buffer happens. We firstly project the bounding-box of the mesh to screen-space and calculate its 2D area. If this is smaller than a certain value – determined on a per mesh basis – it will be immediately discarded (i.e, contribution culled).
Then, for the actual test against the z-buffer, we take the minimum distance from the camera to the bounding-box and compare it against the z-buffer over the whole screen-space rectangle. This falls somewhere in between the approach of [Woodard 07] – which actually rasterises occludees – and that of Conviction in terms of accuracy.
### 6.2 Performance
These timings reflect best-case parallelism over 5 SPUs and were measured in a typical scene. In practice, workloads between SPU jobs will vary slightly and may be intermixed with other jobs, so the overall time for visibility processing will be higher.
In this case we rasterised around 6000 occluder triangles (we normally observe 3000 to 5000), and performed around 3000 occlusion tests after frustum and extent culling.
Stage Time/SPU (ms) Triangle Setup 0.4 Rasterisation 1.0 Frustum Cull 0.6 Occlusion Cull 0.3 Total 2.3
Table 2: Performance timings
## 7. Future Development
### 7.1 Tools
Although artist-authored occluders are generally a good idea for performance reasons (particularly so with a software rasteriser), we encountered a couple of notable problems with this strategy on Conviction. Firstly, with a large team and therefore a number of people making changes to a particular map, there were a few cases where modifications to the layout of visual meshes would not be applied to the associated occluders. Even with the blueprint of a map largely locked down, cosmetic changes sometimes introduced significant errors and these tended to show up right at the end of testing when production was most stretched!
Secondly, some artists had a tendency to think of modelling occluders in the same way as collision meshes – when, in fact, occluders should always be flush with or inside of the visual meshes they represent – or they did not feel that a small inaccuracy would be that important. This simply was not the case: time and again, testers would uncover these problems, particularly in scope mode where the reduced field of view can magnify these subtle differences up to half of the screen, causing large chunks of the world to disappear.
These errors would also show up as “shadow acne” due to the requirement that shadow occluders – those used for culling casters during shadow map visibility – had to cast shadows themselves. Sometimes, it would have made more sense to have just used these visual meshes directly as occluders, instead of creating separate occluder meshes.
While checks can be added in the editor to uncover a lot of these issues, another option could be to automatically weld together, simplify and chunk up existing visual meshes flagged by artists.
At the root of it all, the primary concern is correctness; there is no such thing as “pretty looking” visibility, so one could argue that it is not the best use of an artist’s time to be modelling occluders if we can generate them automatically for the most part, particularly if a human element can introduce errors. This is definitely something we would like to put to the test going forward.
### 7.2 Optimisations
One trivial optimisation for the GPU solution would be to add a pre-pass, testing a coarse subdivision of the scene (e.g. regular grid) to perform an earlier, high-level cull – just like in Battlefield, but using the occlusion system too. We chose not do this as performance was already within our budget, but it would certainly allow the approach to scale up to larger environments (e.g. “open world”).
Additionally, a less accurate object-level pre-pass – for instance, 4 HZB samples using the bounding sphere, as with [Shopf et al. 08] – could lead to a speed-up wherever there is a reasonable amount of occlusion (which by necessity is a common case). Equally, a finer-grained final pass (e.g. 8x8 HZB samples) could improve culling of larger occluders.
In a similar vein, another easy win for the SPU version would be using a hierarchical z-buffer either for early rejection or as a replacement for a complete loop over the screen bounds. As earlier numbers showed, however, the main hotspot performance-wise is occluder rasterisation. In that instance we might gain again, this time from hierarchical rasterisation as in [Abrash 09], although at the cost of increased implementation complexity. Frustum culling could also be sped up by switching to a different data structure (e.g. grid) to improve load balancing on SPUs as well as memory access patterns.
Although the accuracy versus performance trade-off from the HZB was almost always beneficial for Conviction, we did encounter a couple of instances where we could have profited from better culling of large, structural geometry. We believe that the biggest factor here was the lack of varying z over the occludee (see Figure 6) when testing against the HZB, not the number of tests (beyond 4x4) or the base resolution.
Figure 6: A single screen-space z value for occludees
can lead to conservative acceptance in some cases
On Xbox 360, we investigated directly hardware-rasterising occludee bounds as a proof-of-concept for overcoming this, but we ran out of time and there were some performance pitfalls with memory export. We hope to pick up where we left off in future.
Conviction’s shadow caster culling proved to be a significant optimisation for cascaded shadow maps. One potential avenue of future development would be to try to adapt the idea of frustum subdivision coupled with caster-receiver intersection testing, as presented in [Diamand 10], with similarities to [Lloyd et al. 04]. [Eisemann and Décoret 05] and [Décoret 05] also build on the latter.
We would also like to extend culling to local shadow lights in future. As we already cache10 casters per shadow light, we could directly evaluate shadow-visibility for this subset of the scene. This would avoid the higher fixed overhead of processing all objects in the map as we do for the main view or shadow cascades, which is important since we can have up to 8 active shadow lights per camera. These updates could either happen every frame or whenever the list changes.
### 7.3 Future Hardware
The jury is out on exactly what sort of future we face when it comes to the convergence of increasingly multi-core CPUs and more programmable GPUs and when, or indeed if, it will happen. Larrabee is an interesting example, showing that even fixed-function rasterisation hardware is potentially on the way out [Abrash 09] and while a CPU solution could be considered a safe long-term bet, the most efficient method going forward may be closer to the way hardware works than a traditional scan-line approach.
[Andersson 10] describes two possible future scenarios for visibility processing: either a progression of the GPU approach we already described but with lower latency, or having the ability for the GPU to feed itself commands. A killer application for the latter could be shadow map rendering, where visibility (as earlier) and subsequent draw calls would happen entirely on the GPU, thereby avoiding any CPU synchronisation, processing and dispatch. This is almost possible today and potentially so on current consoles, but existing APIs are a roadblock.
### 7.4 General
In Conviction, although arbitrary occlusion tests could be issued by the main thread – to accelerate other systems, in much the same way as Battlefield – we had to restrict their use in the end due to the need for deterministic behavior during co-operative play. This was primarily an issue for PC as we could not ensure matching results between GPUs from different IHVs, or indeed across generations from the same vendor. For the next title, we hope to find other applications for exploiting our system where this is not a problem.
Were we to generate a min-max depth hierarchy, we could also return more information about the state of occlusion, which may open up more applications. By testing the z-range of objects, we can determine one or more states: completely visible or occluded (all tests pass conclusively), partially occluded (tests pass conclusively as fully visible or occluded), potentially occluded (some tests are inclusive: i.e. z-range overlap with the HZB).
## 8. Conclusion
Whatever the future, experimenting with solutions like these is a good investment; in our experience, we gained significantly from employing these fast yet straightforward visibility systems, both in development and production terms.
The GPU implementation in particular is trivial to add – demonstrated by the fact that our initial version was developed and integrated in a matter of days – and comes with a very reasonable overhead.
## 9. Acknowledgements
We would like to thank Don Williamson, Steven Tovey, Nick Darnell, Christian Desautels, and Brian Karis for their insightful feedback or correspondence, as well as the authors of all cited papers and presentations for considerable inspiration.
## 10. References
[Abrash 96] Michael Abrash, “Inside Quake: Visible-Surface Determination”. In Dr. Dobb’s Sourcebook, January/February 1996.
[Abrash 09] Michael Abrash. “Rasterization on Larrabee”. Game Deveoper’s Conference, 2009.
[Andersson 10] Johan Andersson. “Parallel Futures of a Game Engine v2.0”. STHLM Game Developer Forum, 2010.
[Blinn 96] Jim Blinn. “Calculating Screen Coverage”. In IEEE CG&A, v16:3, 1996.
[Bittner et al. 09] Jiří Bittner, Oliver Mattausch, and Michael Wimmer. “Game Engine Friendly Occlusion Culling”. In ShaderX^7, Charles River Media, 2009.
[Diamand 10] Ben Diamand. “Shadows In God of War III”. Game Developer’s Conference, 2010.
[Décoret 05] Xavier Décoret. “N-Buffers for efficient depth map query”. Eurographics, 2005.
[Eisemann and Décoret 05] Elmar Eisemann and Xavier Décoret. “Fast Scene Voxelization and Applications”. ACM SIGGRAPH Symposium on Interactive 3D Graphics and Games, 2006.
[Greene et al. 93] Ned Greene, Michael Kass, and Gavin Miller. “Hierarchical Z-buffer Visibility”. SIGGRAPH, 1993.
[Hastings 07] Al Hastings. “Occlusion Systems”, 2007.
[Hill 10] Stephen Hill. “Rendering with Conviction”. Game Developer’s Conference, 2010.
[Lloyd et al. 04] Brandon Lloyd, Jeremy Wendt, Naga Govindaraju, and Dinesh Manocha. “CC Shadow Volumes”. Eurographics Symposium on Rendering (EGSR), 2004.
[Möller et al. 08] Tomas Akenine-Möller, Eric Haines, and Naty Hoffman, “Real-Time Rendering”, 3rd Edition. AK Peters, 2008.
[Redon et al. 02] Stephane Redon, Abderrahmane Kheddar, and Sabine Coquillart. “Fast Continuous Collision Detection between Rigid Bodies”. Eurographics 2002.
[Shopf et al. 08] Jeremy Shopf, Joshua Barczak, Christopher Oat, and Natalya Tatarchuk. “March of the Froblins: Simulation and Rendering Massive Crowds of Intelligent and Detailed Creatures on GPU”. SIGGRAPH 2008 Classes.
[Soininen 08] Teppo Soininen. “Visibility Optimization for Games”. Gamefest 2008.
[Woodard 07] Bruce Woodard. “SPU Occlusion Culling”. SCEA PS3 Graphics Seminar, 2007.
1. Of the order of 10 hours in some cases [Hastings 07].
2. Predicated rendering is one indirect and limited alternative on Xbox 360.
3. A more accurate extrusion should take into account rotational as well as spatial velocity, as with continuous collision detection [Redon et al. 02].
4. These are often a simplified version of the union of several adjoining, structural meshes.
5. This is approximately a quarter of the resolution of our main camera in single player mode.
6. We choose to use the object’s bounding sphere for rotational invariance.
7. But we could adapt this type of testing to cull more. See Section 7, Future Development.
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2019-02-23 07:52:39
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https://socratic.org/questions/how-do-you-find-the-vertex-and-intercepts-for-y-x-2-8x-7-1#235797
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# How do you find the vertex and intercepts for y=x^2+8x-7?
Vertex is at $\left(- 4 , - 23\right)$ Y intercept is at $\left(0 , - 7\right)$ X-intercepts are at $\left(0.796 , 0\right)$ and $\left(- 8.796 , 0\right)$
$y = {x}^{2} + 8 x - 7 = {x}^{2} + 8 x + 16 - 23 = {\left(x + 4\right)}^{2} - 23$ So vertex is at $\left(- 4 , - 23\right)$
y-intercept : putting x=0 in the equation we get $y = - 7$
x-intercept : Putting y=0 we get ${x}^{2} = 8 x - 7 = 0$ solving the quadratic equation we get $x = 0.796$ and $x = - 8.796$ graph{x^2+8x-7 [-80, 80, -40, 40]}[Answer]
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2022-01-22 20:05:07
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https://docs.wavesenterprise.com/en/latest/description/consensus/PoA.html
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Technical description of the platform
# PoA consensus algorithm¶
In a private blockchain, tokens are not always needed. For example, a blockchain can be used to store hashes of documents exchanged by organizations. In this case, in the absence of tokens and fees from transactions, a solution based on the PoS consensus algorithm is redundant. The Waves Enterprise Blockchain Platform offers the option of a Proof of Authority (PoA) consensus algorithm. Mining permission is issued centrally in the PoA algorithm, which simplifies the decision-making compared to the PoS algorithm. The PoA model is based on a limited number of block validators, which makes it scalable. Blocks and transactions are verified by pre-approved participants who act as moderators of the system.
## Algorithm description¶
An algorithm determining the miner of the current block is formed on the basis of the parameters stated below. The parameters of the consensus are specified in the consensus block of the node configuration file.
• t - the duration of a round in seconds (the parameter of the node configuration file: round-duration).
• ts - the duration of a synchronization period, calculated as t*0.1, but not more than 30 seconds (the parameter of the node configuration file: sync-duration).
• Nban - a number of missed consecutive rounds for issuing the ban for the miner (the parameter of the node configuration file: warnings-for-ban);
• Pban - a maximum percentage of banned miners, from 0 to 100 (the parameter of the node configuration file: max-bans-percentage);
• tban - the duration of the miner ban in blocks (the parameter of the node configuration file: ban-duration-blocks).
• T0 - unix timestamp of genesis block creation.
• TH - unix timestamp of creation of the H block — the NG key block.
• r - round number, calculated as (TCurrent -T0 ) div (t+ ts ).
• Ar - the leader of the round r, which is entitled to create key blocks and microblocks for NG in the round r.
• H – blockchain height, at that the NG key block and microblocks are created. The Ar round leader is entitled to generate the block.
• MH - the miner which creates a block at the H height.
• QH - the queue of active miners at the H height.
The QH queue consists of addresses that have the miner permission. In the same time, the miner permission should not be removed from the addresses before the H height or expiry before the TH time.
The queue is sorted by the time stamp of the mining rights transaction. The node which was granted the rights earlier will be higher in the queue. To keep the network consistent, this queue will be the same on each node.
A new block is generated during each r round. A duration of a round is t seconds. Each round is followed with ts seconds for network data synchronization. During the synchronization, microblocks and key blocks are not generated. Each round has a leader Ar , which is entitled to generate a block in this round. A leader can be defined at each network node with the same result.
The round leader is defined as follows:
1. The miner MH-1 is defined, which has created a previous block at the H-1 height.
2. The queue of active miners QH is calculated.
3. Inactive miners are excluded from the queue (see Exclusion of inactive miners).
4. If the miner of the H-1 (MH-1 ) block is in the QH queue, a next miner in the queue becomes the leader of the Ar round.
5. If the miner H-1 (MH-1 ) block is not in the QH queue, the miner next to the miner of the H-2(MH-2 ) block becomes a leader of the Ar round, and so on.
6. If the moners of the (H-1..1) blocks are not in the queue, the first miner in the queue becomes the round leader.
This algorithm identifies and checks the miner, which creates each block of the chain by calculating the list of authorized miners for each moment of time. If the block was not created by the designated leader within the allotted time, no blocks are generated within that round, and the round is skipped. Leaders who skip block generation are temporarily excluded from the queue by the algorithm described in the paragraph Exclusion of inactive miners.
The block generated by the leader Ar with the time of the block TH from the half-interval (T0 +(r-1)*(t+ts ); T0 +(r-1)*(t+ts )+t] is determined to be valid. The block created by the miner out of its turn or not in time is considered invalid. After a round of t duration, the network synchronizes the data for ts . The leader Ar has ts seconds to propagate the validation block over the network. If any node of the network during ts has not received a block from the leader Ar , this node recognizes the round as ‘skipped’ and expects a new H block in the next round r+1, from the following leader Ar+1 .
The consensus parameters t and ts are configured in the node configuration file. The parameter T should be the same for all network participants, otherwise the network will fork.
## Synchronization of time between network hosts¶
Each host should synchronize the application time with a trusted NTP server at the beginning of each round. The server address and port are specified in the node configuration file. The server must be available to each network node.
## Exclusion of inactive miners¶
If any miner misses generation of a block Nban times in a row, this miner is excluded from the queue for tban of next blocks (the ban-duration-blocks parameter in the node configuration file). Each node excludes an inactive miner on its own based on the calculated queue QH nd information about the H block and the MH miner. The Pban parameter specifies the maximum percentage of excluded miners in the network in comparison with all active miners at any moment. If the Nban of misses is achieved by a miner, but in the same time the Pban is also achieved, this miner will not be excluded from the queue.
## Monitoring¶
The PoA consensus monitoring helps to identify how non-valid blocks are created and distributed, as well as how miners skip the queue. Network administrators perform additional troubleshooting and blocking of malicious nodes.
To monitor the process of generating blocks using the PoA algorithm, the following details are entered in InfluxDB:
• Active list of miners sorted by the timestamp of granting of mining rights.
• Scheduled round timestamp.
• Actual round timestamp.
• Current miner.
## Changing consensus settings¶
The consensus parameters (round time and synchronization period) are changed on the basis of the node configuration file at the from-height of the blockchain. If any node does not specify new parameters, the blockchain will fork.
Configuration example:
// specifying inside of the blockchain parameter
consensus {
type = poa
sync-duration = 10s
round-duration = 60s
ban-duration-blocks = 100
changes = [
{
from-height = 18345
sync-duration = 5s
round-duration = 60s
},
{
from-height = 25000
sync-duration = 10s
round-duration = 30s
}]
}
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2021-10-21 15:20:51
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http://www.gradesaver.com/textbooks/math/algebra/intermediate-algebra-6th-edition/chapter-11-section-11-2-arithmetic-and-geometric-sequences-exercise-set-page-646/23
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# Chapter 11 - Section 11.2 - Arithmetic and Geometric Sequences - Exercise Set: 23
$a_{9}= 20$
#### Work Step by Step
$a_{n}$ of the arithmetic progression is $a_{n} = a_{1} + (n-1)d$ Second term of arithmetic progression is $a_{2} =-1$ $a_{2} = a_{1} + (2-1)d$ $a_{2} = a_{1} + d$ $a_{1} + d =-1$ Equation $(1)$ Fourth term of arithmetic progression is $a_{4} =5$ $a_{4} = a_{1} + (4-1)d$ $a_{4} = a_{1} + 3d$ $a_{1} +3d =5$ Equation $(2)$ Subtract Equation $(1)$ from Equation $(2)$ $a_{1} +3d -(a_{1} + d ) = 5 - (-1)$ $a_{1} +3d -a_{1} - d = 5 +1$ $2d=6$ $d=3$ Substituting $d$ value in Equation $(1)$ $a_{1} + d =-1$ $a_{1} + 3 =-1$ $a_{1} =-1-3$ $a_{1} =-4$ Using $a_{1}$ , $d$ values and $n=9$ , $a_{9} = a_{1} + (9-1)d$ $a_{9} = -4 + (8)3$ $a_{9} =-4+24$ $a_{9} = 20$
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.
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2017-11-18 08:39:54
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http://www.seas.upenn.edu/~ese171/vhdl/vhdl_primer.html
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Jan Van der Spiegel
University of Pennsylvania
Department of Electrical and Systems Engineering
VHDL Tutorial
1. Introduction
2. Levels of representation and abstraction
3. Basic Structure of a VHDL file
Behavioral model
Concurrency
Structural description
4. Lexical Elements of VHDL
5. Data Objects: Signals, Variables and Constants
Constant
Variable
Signal
6. Data types
Integer types
Floating-point types
Physical types
Array Type
Record Type
Signal attributes
Scalar attributes
Array attributes
7. Operators
8. Behavioral Modeling: Sequential Statements
Basic Loop statement
While-Loop statement
For-Loop statement
9. Dataflow Modeling – Concurrent Statements
10. Structural Modeling
Appendix: IEEE Standard Package STD_LOGIC_1164
________________________________________________________________________
This tutorial gives a brief overview of the VHDL language and is mainly intended as a companion for the Digital Design Laboratory. This writing aims to give the reader a quick introduction to VHDL and to give a complete or in-depth discussion of VHDL. For a more detailed treatment, please consult any of the many good books on this topic. Several of these books are listed in the reference list.
# 1. Introduction
VHDL stands for VHSIC (Very High Speed Integrated Circuits) Hardware Description Language. In the mid-1980’s the U.S. Department of Defense and the IEEE sponsored the development of this hardware description language with the goal to develop very high-speed integrated circuit. It has become now one of industry’s standard languages used to describe digital systems. The other widely used hardware description language is Verilog. Both are powerful languages that allow you to describe and simulate complex digital systems. A third HDL language is ABEL (Advanced Boolean Equation Language) which was specifically designed for Programmable Logic Devices (PLD). ABEL is less powerful than the other two languages and is less popular in industry. This tutorial deals with VHDL, as described by the IEEE standard 1076-1993.
Although these languages look similar as conventional programming languages, there are some important differences. A hardware description language is inherently parallel, i.e. commands, which correspond to logic gates, are executed (computed) in parallel, as soon as a new input arrives. A HDL program mimics the behavior of a physical, usually digital, system. It also allows incorporation of timing specifications (gate delays) as well as to describe a system as an interconnection of different components.
# 2. Levels of representation and abstraction
A digital system can be represented at different levels of abstraction [1]. This keeps the description and design of complex systems manageable. Figure 1 shows different levels of abstraction.
Figure 1: Levels of abstraction: Behavioral, Structural and Physical
The highest level of abstraction is the behavioral level that describes a system in terms of what it does (or how it behaves) rather than in terms of its components and interconnection between them. A behavioral description specifies the relationship between the input and output signals. This could be a Boolean expression or a more abstract description such as the Register Transfer or Algorithmic level. As an example, let us consider a simple circuit that warns car passengers when the door is open or the seatbelt is not used whenever the car key is inserted in the ignition lock At the behavioral level this could be expressed as,
Warning = Ignition_on AND ( Door_open OR Seatbelt_off)
The structural level, on the other hand, describes a system as a collection of gates and components that are interconnected to perform a desired function. A structural description could be compared to a schematic of interconnected logic gates. It is a representation that is usually closer to the physical realization of a system. For the example above, the structural representation is shown in Figure 2 below.
Figure 2: Structural representation of a “buzzer” circuit.
VHDL allows one to describe a digital system at the structural or the behavioral level. The behavioral level can be further divided into two kinds of styles: Data flow and Algorithmic. The dataflow representation describes how data moves through the system. This is typically done in terms of data flow between registers (Register Transfer level). The data flow model makes use of concurrent statements that are executed in parallel as soon as data arrives at the input. On the other hand, sequential statements are executed in the sequence that they are specified. VHDL allows both concurrent and sequential signal assignments that will determine the manner in which they are executed. Examples of both representations will be given later.
# 3. Basic Structure of a VHDL file
A digital system in VHDL consists of a design entity that can contain other entities that are then considered components of the top-level entity. Each entity is modeled by an entity declaration and an architecture body. One can consider the entity declaration as the interface to the outside world that defines the input and output signals, while the architecture body contains the description of the entity and is composed of interconnected entities, processes and components, all operating concurrently, as schematically shown in Figure 3 below. In a typical design there will be many such entities connected together to perform the desired function.
Figure 3: A VHDL entity consisting of an interface (entity declaration) and a body (architectural description).
VHDL uses reserved keywords that cannot be used as signal names or identifiers. Keywords and user-defined identifiers are case insensitive. Lines with comments start with two adjacent hyphens (--) and will be ignored by the compiler. VHDL also ignores line breaks and extra spaces. VHDL is a strongly typed language which implies that one has always to declare the type of every object that can have a value, such as signals, constants and variables.
The entity declaration defines the NAME of the entity and lists the input and output ports. The general form is as follows,
entity NAME_OF_ENTITY is [ generic generic_declarations);]
port (signal_names: mode type;
signal_names: mode type;
:
signal_names: mode type);
end [NAME_OF_ENTITY] ;
An entity always starts with the keyword entity, followed by its name and the keyword is. Next are the port declarations using the keyword port. An entity declaration always ends with the keyword end, optionally [] followed by the name of the entity.
· The NAME_OF_ENTITY is a user-selected identifier
· signal_names consists of a comma separated list of one or more user-selected identifiers that specify external interface signals.
· mode: is one of the reserved words to indicate the signal direction:
o in – indicates that the signal is an input
o out – indicates that the signal is an output of the entity whose value can only be read by other entities that use it.
o buffer – indicates that the signal is an output of the entity whose value can be read inside the entity’s architecture
o inout – the signal can be an input or an output.
· type: a built-in or user-defined signal type. Examples of types are bit, bit_vector, Boolean, character, std_logic, and std_ulogic.
o bit – can have the value 0 and 1
o bit_vector – is a vector of bit values (e.g. bit_vector (0 to 7)
o std_logic, std_ulogic, std_logic_vector, std_ulogic_vector: can have 9 values to indicate the value and strength of a signal. Std_ulogic and std_logic are preferred over the bit or bit_vector types.
o boolean – can have the value TRUE and FALSE
o integer – can have a range of integer values
o real – can have a range of real values
o character – any printing character
o time – to indicate time
· generic: generic declarations are optional and determine the local constants used for timing and sizing (e.g. bus widths) the entity. A generic can have a default value. The syntax for a generic follows,
generic (
constant_name: type [:=value] ;
constant_name: type [:=value] ;
:
constant_name: type [:=value] );
For the example of Figure 2 above, the entity declaration looks as follows.
-- comments: example of the buzzer circuit of fig. 2 entity BUZZER is port (DOOR, IGNITION, SBELT: in std_logic; WARNING: out std_logic); end BUZZER;
The entity is called BUZZER and has three input ports, DOOR, IGNITION and SBELT and one output port, WARNING. Notice the use and placement of semicolons! The name BUZZER is an identifier. Inputs are denoted by the keyword in, and outputs by the keyword out. Since VHDL is a strongly typed language, each port has a defined type. In this case, we specified the std_logic type. This is the preferred type of digital signals. In contrast to the bit type that can only have the values ‘1’ and ‘0’, the std_logic and std_ulogic types can have nine values. This is important to describe a digital system accurately including the binary values 0 and 1, as well as the unknown value X, the uninitialized value U, “-” for don’t care, Z for high impedance, and several symbols to indicate the signal strength (e.g. L for weak 0, H for weak 1, W for weak unknown - see section on Enumerated Types). The std_logic type is defined in the std_logic_1164 package of the IEEE library. The type defines the set of values an object can have. This has the advantage that it helps with the creation of models and helps reduce errors. For instance, if one tries to assign an illegal value to an object, the compiler will flag the error.
A few other examples of entity declarations follow
Four-to-one multiplexer of which each input is an 8-bit word.
entity mux4_to_1 is
port (I0,I1,I2,I3: in std_logic_vector(7 downto 0);
SEL: in std_logic_vector (1 downto 0);
OUT1: out std_logic_vector(7 downto 0));
end mux4_to_1;
An example of the entity declaration of a D flip-flop with set and reset inputs is
entity dff_sr is
port (D,CLK,S,R: in std_logic;
Q,Qnot: out std_logic);
end dff_sr;
The architecture body specifies how the circuit operates and how it is implemented. As discussed earlier, an entity or circuit can be specified in a variety of ways, such as behavioral, structural (interconnected components), or a combination of the above.
The architecture body looks as follows,
architecture architecture_name of NAME_OF_ENTITY is
-- Declarations
-- components declarations
-- signal declarations
-- constant declarations
-- function declarations
-- procedure declarations
-- type declarations
:
begin
-- Statements
:
end architecture_name;
## Behavioral model
The architecture body for the example of Figure 2, described at the behavioral level, is given below,
architecture behavioral of BUZZER is
begin
WARNING <= (not DOOR and IGNITION) or (not SBELT and IGNITION);
end behavioral;
The header line of the architecture body defines the architecture name, e.g. behavioral, and associates it with the entity, BUZZER. The architecture name can be any legal identifier. The main body of the architecture starts with the keyword begin and gives the Boolean expression of the function. We will see later that a behavioral model can be described in several other ways. The “<= ” symbol represents an assignment operator and assigns the value of the expression on the right to the signal on the left. The architecture body ends with an end keyword followed by the architecture name.
A few other examples follow. The behavioral description of a two-input AND gate is shown below.
entity AND2 is
port (in1, in2: in std_logic;
out1: out std_logic);
end AND2;
architecture behavioral_2 of AND2 is
begin
out1 <= in1 and in2;
end behavioral_2;
An example of a two-input XNOR gate is shown below.
entity XNOR2 is
port (A, B: in std_logic;
Z: out std_logic);
end XNOR2;
architecture behavioral_xnor of XNOR2 is
-- signal declaration (of internal signals X, Y)
signal X, Y: std_logic;
begin
X <= A and B;
Y <= (not A) and (not B);
Z <= X or Y;
End behavioral_xnor;
The statements in the body of the architecture make use of logic operators. Logic operators that are allowed are: and, or, nand, nor, xor, xnor and not. In addition, other types of operators including relational, shift, arithmetic are allowed as well (see section on Operators). For more information on behavioral modeling see section on Behavioral Modeling.
## Concurrency
It is worth pointing out that the signal assignments in the above examples are concurrent statements. This implies that the statements are executed when one or more of the signals on the right hand side change their value (i.e. an event occurs on one of the signals). For instance, when the input A changes, the internal signals X and Y change values that in turn causes the last statement to update the output Z. There may be a propagation delay associated with this change. Digital systems are basically data-driven and an event which occurs on one signal will lead to an event on another signal, etc. The execution of the statements is determined by the flow of signal values. As a result, the order in which these statements are given does not matter (i.e., moving the statement for the output Z ahead of that for X and Y does not change the outcome). This is in contrast to conventional, software programs that execute the statements in a sequential or procedural manner.
## Structural description
The circuit of Figure 2 can also be described using a structural model that specifies what gates are used and how they are interconnected. The following example illustrates it.
architecture structural of BUZZER is
-- Declarations
component AND2
port (in1, in2: in std_logic;
out1: out std_logic);
end component;
component OR2
port (in1, in2: in std_logic;
out1: out std_logic);
end component;
component NOT1
port (in1: in std_logic;
out1: out std_logic);
end component;
-- declaration of signals used to interconnect gates
signal DOOR_NOT, SBELT_NOT, B1, B2: std_logic;
begin
-- Component instantiations statements
U0: NOT1 port map (DOOR, DOOR_NOT);
U1: NOT1 port map (SBELT, SBELT_NOT);
U2: AND2 port map (IGNITION, DOOR_NOT, B1);
U3: AND2 port map (IGNITION, SBELT_NOT, B2);
U4: OR2 port map (B1, B2, WARNING);
end structural;
Following the header is the declarative part that gives the components (gates) that are going to be used in the description of the circuits. In our example, we use a two- input AND gate, two-input OR gate and an inverter. These gates have to be defined first, i.e. they will need an entity declaration and architecture body (as shown in the previous example). These can be stored in one of the packages one refers to in the header of the file (see Library and Packages below). The declarations for the components give the inputs (e.g. in1, in2) and the output (e.g. out1). Next, one has to define internal nets (signal names). In our example these signals are called DOOR_NOT, SBELT_NOT, B1, B2 (see Figure 2). Notice that one always has to declare the type of the signal.
The statements after the begin keyword gives the instantiations of the components and describes how these are interconnected. A component instantiation statement creates a new level of hierarchy. Each line starts with an instance name (e.g. U0) followed by a colon and a component name and the keyword port map. This keyword defines how the components are connected. In the example above, this is done through positional association: DOOR corresponds to the input, in1 of the NOT1 gate and DOOR_NOT to the output. Similarly, for the AND2 gate where the first two signals (IGNITION and DOOR_NOT) correspond to the inputs in1 and in2, respectively, and the signal B1 to the output out1. An alternative way is to use explicit association between the ports, as shown below.
label: component-name port map (port1=>signal1, port2=> signal2,… port3=>signaln);
U0: NOT1 port map (in1 => DOOR, out1 => DOOR_NOT);
U1: NOT1 port map (in1 => SBELT, out1 => SBELT_NOT);
U2: AND2 port map (in1 => IGNITION, in2 => DOOR_NOT, out1 => B1);
U3: AND2 port map (in1 => IGNITION, in2 => SBELT_NOT, B2);
U4: OR2 port map (in1 => B1, in2 => B2, out1 => WARNING);
Notice that the order in which these statements are written has no bearing on the execution since these statements are concurrent and therefore executed in parallel. Indeed, the schematic that is described by these statements is the same independent of the order of the statements.
Structural modeling of design lends itself to hierarchical design, in which one can define components of units that are used over and over again. Once these components are defined they can be used as blocks, cells or macros in a higher level entity. This can significantly reduce the complexity of large designs. Hierarchical design approaches are always preferred over flat designs. We will illustrate the use of a hierarchical design approach for a 4-bit adder, shown in Figure 4 below. Each full adder can be described by the Boolean expressions for the sum and carry out signals,
sum = (A Å B) Å C
carry = AB + C(A Å B)
Figure 4: Schematic of a 4-bit adder consisting of full adder modules.
In the VHDL file, we have defined a component for the full adder first. We used several instantiations of the full adder to build the structure of the 4-bit adder. We have included the library and use clause as well as the entity declarations.
Notice that the same input names a and b for the ports of the full adder and the 4-bit adder were used. This does not pose a problem in VHDL since they refer to different levels. However, for readability, it may be easier to use different names. We needed to define the internal signals c(4:0) to indicate the nets that connect the output carry to the input carry of the next full adder. For the first input we used the input signal Cin. For the last carry we defined c(4) as an internal signal since the last carry is needed as the input to the xor gate. We could not use the output signal Cout since VHDL does not allow the use of outputs as internal signals! For this reason we had to define the internal carry c(4) and assign c(4) to the output carry signal Cout.
c. Library and Packages: library and use keywords
A library can be considered as a place where the compiler stores information about a design project. A VHDL package is a file or module that contains declarations of commonly used objects, data type, component declarations, signal, procedures and functions that can be shared among different VHDL models.
We mentioned earlier that std_logic is defined in the package ieee.std_logic_1164 in the ieee library. In order to use the std_logic one needs to specify the library and package. This is done at the beginning of the VHDL file using the library and the use keywords as follows:
library ieee;
use ieee.std_logic_1164.all;
The .all extension indicates to use all of the ieee.std_logic_1164 package.
The Xilinx Foundation Express comes with several packages.
ieee Library:
• std_logic_1164 package: defines the standard datatypes
• std_logic_arith package: provides arithmetic, conversion and comparison functions for the signed, unsigned, integer, std_ulogic, std_logic and std_logic_vector types
• std_logic_unsigned
• std_logic_misc package: defines supplemental types, subtypes, constants and functions for the std_logic_1164 package.
To use any of these one must include the library and use clause:
library ieee;
use ieee.std_logic_1164.all;
use ieee.std_logic_arith.all;
use ieee.std_logic_unsigned.all;
In addition, the synopsis library has the attributes package:
library SYNOPSYS;
use SYNOPSYS.attributes.all;
One can add other libraries and packages. The syntax to declare a package is as follows:
-- Package declaration
package name_of_package is
package declarations
end package name_of_package;
-- Package body declarations
package body name_of_package is
package body declarations
end package body name_of_package;
For instance, the basic functions of the AND2, OR2, NAND2, NOR2, XOR2, etc. components need to be defined before one can use them. This can be done in a package, e.g. basic_func for each of these components, as follows:
-- Package declaration
library ieee;
use ieee.std_logic_1164.all;
package basic_func is
-- AND2 declaration
component AND2
generic (DELAY: time :=5ns);
port (in1, in2: in std_logic; out1: out std_logic);
end component;
-- OR2 declaration
component OR2
generic (DELAY: time :=5ns);
port (in1, in2: in std_logic; out1: out std_logic);
end component;
end package basic_func;
-- Package body declarations
library ieee;
use ieee.std_logic_1164.all;
package body basic_func is
-- 2 input AND gate
entity AND2 is
generic (DELAY: time);
port (in1, in2: in std_logic; out1: out std_logic);
end AND2;
architecture model_conc of AND2 is
begin
out1 <= in1 and in2 after DELAY;
end model_conc;
-- 2 input OR gate
entity OR2 is
generic (DELAY: time);
port (in1, in2: in std_logic; out1: out std_logic);
end OR2;
architecture model_conc2 of AND2 is
begin
out1 <= in1 or in2 after DELAY;
end model_conc2;
end package body basic_func;
Notice that we included a delay of 5 ns. However, it should be noticed that delay specifications are ignored by the Foundation synthesis tool. We made use of the predefined type std_logic that is declared in the package std_logic_1164. We have included the library and use clause for this package. This package needs to be compiled and placed in a library. Lets call this library my_func. To use the components of this package one has to declare it using the library and use clause:
library ieee, my_func;
use ieee.std_logic_1164.all, my_func.basic_func.all;
One can concatenate a series of names separated by periods to select a package. The library and use statements are connected to the subsequent entity statement. The library and use statements have to be repeated for each entity declaration.
One has to include the library and use clause for each entity as shown for the example of the four-bit adder above.
# 4. Lexical Elements of VHDL
Identifiers are user-defined words used to name objects in VHDL models. We have seen examples of identifiers for input and output signals as well as the name of a design entity and architecture body. When choosing an identifier one needs to follow these basic rules:
· May contain only alpha-numeric characters (A to Z, a to z, 0-9) and the underscore (_) character
· The first character must be a letter and the last one cannot be an underscore.
· An identifier cannot include two consecutive underscores.
· An identifier is case insensitive (ex. And2 and AND2 or and2 refer to the same object)
· An identifier can be of any length.
Examples of valid identifiers are: X10, x_10, My_gate1.
Some invalid identifiers are: _X10, my_gate@input, gate-input.
The above identifiers are called basic identifiers. The rules for these basic identifiers are often too restrictive to indicate signals. For example, if one wants to indicate an active low signal such as an active low RESET, one cannot call it /RESET. In order to overcome these limitations, there are a set of extended identifier rules which allow identifiers with any sequence of characters.
· An extended identifier is enclosed by the backslash, “\”, character.
· An extended identifier is case sensitive.
· An extended identifier is different from reserved words (keywords) or any basic identifier (e.g. the identifier \identity\ is allowed)
· Inside the two backslashes one can use any character in any order, except that a backslash as part of an extended identifier must be indicated by an additional backslash. As an example, to use the identifier BUS:\data, one writes: \BUS:\data\
· Extended identifiers are allowed in the VHDL-93 version but not in VHDL-87
Some examples of legal identifiers are:
Input, \Input\, \input#1\, \Rst\\as\
b. Keywords (Reserved words)
Certain identifiers are used by the system as keywords for special use such as specific constructs. These keywords cannot be used as identifiers for signals or objects we define. We have seen several of these reserved words already such as in, out, or, and, port, map, end, etc. Keywords are often printed in boldface, as is done in this tutorial. For a list of all the keywords click on complete keyword list. Extended identifiers can make use of keywords since these are considered different words (e.g. the extended identifier \end\ is allowed.
The default number representation is the decimal system. VHDL allows integer literals and real literals. Integer literals consist of whole numbers without a decimal point, while real literals always include a decimal point. Exponential notation is allowed using the letter “E” or “e”. For integer literals the exponent must always be positive. Examples are:
Integer literals: 12 10 256E3 12e+6
Real literals: 1.2 256.24 3.14E-2
The number –12 is a combination of a negation operator and an integer literal.
To express a number in a base different from the base “10”, one uses the following convention: base#number#. A few examples follow.
Base 2: 2#10010# (representing the decimal number “18”)
Base 16: 16#12#
Base 8: 8#22#
Base 2: 2#11101# (representing the decimal number “29”)
Base 16: 16#1D#
Base 8: 8#35#
To make the readability of large numbers easier, one can insert underscores in the numbers as long as the underscore is not used at the beginning or the end.
2#1001_1101_1100_0010#
215_123
d. Characters, Strings and Bit Strings
To use a character literal in a VHDL code, one puts it in a single quotation mark, as shown in the examples below:
‘a’, ‘B’, ‘,’
On the other hand, a string of characters are placed in double quotation marks as shown in the following examples:
“This is a string”,
“To use a double quotation mark inside a string, use two double quotation marks”
“This is a “”String””.”
Any printing character can be included inside a string.
A bit-string represents a sequence of bit values. In order to indicate that this is a bit string, one places the ‘B’ in front of the string: B”1001”. One can also use strings in the hexagonal or octal base by using the X or O specifiers, respectively. Some examples are:
Binary: B”1100_1001”, b”1001011”
Hexagonal: X”C9”, X”4b”
Octal: O”311”, o”113”
Notice that in the hexadecimal system, each digit represents exactly 4 bits. As a result, the number b”1001011” is not the same as X”4b” since the former has only 7 bits while the latter represents a sequence 8 bits. For the same reason, O”113” (represents 9 bits) is not the same sequence as X”4b” (represents 8 bits).
# 5. Data Objects: Signals, Variables and Constants
A data object is created by an object declaration and has a value and type associated with it. An object can be a Constant, Variable, Signal or a File. Up to now we have seen signals that were used as input or output ports or internal nets. Signals can be considered wires in a schematic that can have a current value and future values, and that are a function of the signal assignment statements. On the other hand, Variables and Constants are used to model the behavior of a circuit and are used in processes, procedures and functions, similarly as they would be in a programming language. Following is a brief discussion of each class of objects.
## Constant
A constant can have a single value of a given type and cannot be changed during the simulation. A constant is declared as follows,
constant list_of_name_of_constant: type [ := initial value] ;
where the initial value is optional. Constants can be declared at the start of an architecture and can then be used anywhere within the architecture. Constants declared within a process can only be used inside that specific process.
constant RISE_FALL_TME: time := 2 ns;
constant DELAY1: time := 4 ns;
constant RISE_TIME, FALL_TIME: time:= 1 ns;
constant DATA_BUS: integer:= 16;
## Variable
A variable can have a single value, as with a constant, but a variable can be updated using a variable assignment statement. The variable is updated without any delay as soon as the statement is executed. Variables must be declared inside a process (and are local to the process). The variable declaration is as follows:
variable list_of_variable_names: type [ := initial value] ;
A few examples follow:
variable CNTR_BIT: bit :=0;
variable VAR1: boolean :=FALSE;
variable SUM: integer range 0 to 256 :=16;
variable STS_BIT: bit_vector (7 downto 0);
The variable SUM, in the example above, is an integer that has a range from 0 to 256 with initial value of 16 at the start of the simulation. The fourth example defines a bit vector or 8 elements: STS_BIT(7), STS_BIT(6),… STS_BIT(0).
A variable can be updated using a variable assignment statement such as
Variable_name := expression;
As soon as the expression is executed, the variable is updated without any delay.
## Signal
Signals are declared outside the process using the following statement:
signal list_of_signal_names: type [ := initial value] ;
signal SUM, CARRY: std_logic;
signal CLOCK: bit;
signal TRIGGER: integer :=0;
signal DATA_BUS: bit_vector (0 to 7);
signal VALUE: integer range 0 to 100;
Signals are updated when their signal assignment statement is executed, after a certain delay, as illustrated below,
SUM <= (A xor B) after 2 ns;
If no delay is specified, the signal will be updated after a delta delay. One can also specify multiple waveforms using multiple events as illustrated below,
signal wavefrm : std_logic;
wavefrm <= ‘0’, ‘1’ after 5ns, ‘0’ after 10ns, ‘1’ after 20 ns;
It is important to understand the difference between variables and signals, particularly how it relates to when their value changes. A variable changes instantaneously when the variable assignment is executed. On the other hand, a signal changes a delay after the assignment expression is evaluated. If no delay is specified, the signal will change after a delta delay. This has important consequences for the updated values of variables and signals. Lets compare the two files in which a process is used to calculate the signal RESULT [7].
Example of a process using Variables architecture VAR of EXAMPLE is signal TRIGGER, RESULT: integer := 0; begin process variable variable1: integer :=1; variable variable2: integer :=2; variable variable3: integer :=3; begin wait on TRIGGER; variable1 := variable2; variable2 := variable1 + variable3; variable3 := variable2; RESULT <= variable1 + variable2 + variable3; end process; end VAR
Example of a process using Signals architecture SIGN of EXAMPLE is signal TRIGGER, RESULT: integer := 0; signal signal1: integer :=1; signal signal2: integer :=2; signal signal3: integer :=3; begin process begin wait on TRIGGER; signal1 <= signal2; signal2 <= signal1 + signal3; signal3 <= signal2; RESULT <= signal1 + signal2 + signal3; end process; end SIGN;
In the first case, the variables “variable1, variable2 and variable3” are computed sequentially and their values updated instantaneously after the TRIGGER signal arrives. Next, the RESULT, which is a signal, is computed using the new values of the variables and updated a time delta after TRIGGER arrives. This results in the following values (after a time TRIGGER): variable1 = 2, variable2 = 5 (=2+3), variable3= 5. Since RESULT is a signal it will be computed at the time TRIGGER and updated at the time TRIGGER + Delta. Its value will be RESULT=12.
On the other hand, in the second example, the signals will be computed at the time TRIGGER. All of these signals are computed at the same time, using the old values of signal1, 2 and 3. All the signals will be updated at Delta time after the TRIGGER has arrived. Thus the signals will have these values: signal1= 2, signal2= 4 (=1+3), signal3=2 and RESULT=6.
# 6. Data types
Each data object has a type associated with it. The type defines the set of values that the object can have and the set of operations that are allowed on it. The notion of type is key to VHDL since it is a strongly typed language that requires each object to be of a certain type. In general one is not allowed to assign a value of one type to an object of another data type (e.g. assigning an integer to a bit type is not allowed). There are four classes of data types: scalar, composite, access and file types. The scalar types represent a single value and are ordered so that relational operations can be performed on them. The scalar type includes integer, real, and enumerated types of Boolean and Character. Examples of these will be given further on.
a. Data Types defined in the Standard Package
VHDL has several predefined types in the standard package as shown in the table below. To use this package one has to include the following clause:
library std, work;
use std.standard.all;
Types defined in the Package Standard of the std Library Type Range of values Example bit ‘0’, ‘1’ signal A: bit :=1; bit_vector an array with each element of type bit signal INBUS: bit_vector(7 downto 0); boolean FALSE, TRUE variable TEST: Boolean :=FALSE’ character any legal VHDL character (see package standard); printable characters must be placed between single quotes (e.g. ‘#’) variable VAL: character :=’$’; file_open_kind* read_mode, write_mode, append_mode file_open_status* open_ok, status_error, name_error, mode_error integer range is implementation dependent but includes at least –(231 – 1) to +(231 – 1) constant CONST1: integer :=129; natural integer starting with 0 up to the max specified in the implementation variable VAR1: natural :=2; positive integer starting from 1 up the max specified in the implementation variable VAR2: positive :=2; real* floating point number in the range of –1.0 x 1038 to +1.0x 1038 (can be implementation dependent. Not supported by the Foundation synthesis program. variable VAR3: real :=+64.2E12; severity_level note, warning, error, failure string array of which each element is of the type character variable VAR4: string(1 to 12):= “@$#ABC*()_%Z”; time* an integer number of which the range is implementation defined; units can be expressed in sec, ms, us, ns, ps, fs, min and hr. . Not supported by the Foundation synthesis program variable DELAY: time :=5 ns;
* Not supported by the Foundation synthesis program
b. User-defined Types
One can introduce new types by using the type declaration, which names the type and specifies its value range. The syntax is
type identifier is type_definition;
Here are a few examples of type definitions,
## Integer types
type small_int is range 0 to 1024;
type my_word_length is range 31 downto 0;
subtype data_word is my_word_length range 7 downto 0;
A subtype is a subset of a previously defined type. The last example above illustrates the use of subtypes. It defines a type called data_word that is a sybtype of my_word_length of which the range is restricted from 7 to 0. Another example of a subtype is,
subtype int_small is integer range -1024 to +1024;
## Floating-point types
type cmos_level is range 0.0 to 3.3;
type pmos_level is range -5.0 to 0.0;
type probability is range 0.0 to 1.0;
subtype cmos_low_V is cmos_level range 0.0 to +1.8;
Note that floating point data types are not supported by the Xilinx Foundation synthesis program.
## Physical types
The physical type definition includes a units identifier as follows,
type conductance is range 0 to 2E-9
units
mho;
mmho = 1E-3 mho;
umho = 1E-6 mho;
nmho = 1E-9 mho;
pmho = 1E-12 mho;
end units conductance;
Here are some object declarations that use the above types,
variable BUS_WIDTH: small_int :=24;
signal DATA_BUS: my_word_length;
variable VAR1: cmos_level range 0.0 to 2.5;
constant LINE_COND: conductance:= 125 umho;
Notice that a space must be left before the unit name.
The physical data types are not supported by the Xilinx Foundation Express synthesis program.
In order to use our own types, we need either to include the type definition inside an architecture body or to declare the type in a package. The latter can be done as follows for a package called “my_types”.
package my_types is
type small_int is range 0 to 1024;
type my_word_length is range 31 downto 0;
subtype data_word is my_word_length is range 7 downto 0;
type cmos_level is range 0.0 to 3.3;
type conductance is range 0 to 2E-9
units
mho;
mmho = 1E-3 mho;
umho = 1E-6 mho;
nmho = 1E-9 mho;
pmho = 1E-12 mho;
end units conductance;
end package my_types;
c. Enumerated Types
An enumerated type consists of lists of character literals or identifiers. The enumerated type can be very handy when writing models at an abstract level. The syntax for an enumerated type is,
type type_name is (identifier list or character literal);
Here are some examples,
type my_3values is (‘0’, ‘1’, ‘Z’);
type hex_digit is (‘0’, ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, ‘6’, ‘7’, 8’, ‘9’, ‘A’, ‘B’, ‘C’, ‘D’, ‘E’, ‘F’);
type state_type is (S0, S1, S2, S3);
Examples of objects that use the above types:
signal SIG1: my_3values;
variable ALU_OP: pc_oper;
variable first_digit: hex_digit :=’0’;
signal STATE: state_type :=S2;
If one does not initialize the signal, the default initialization is the leftmost element of the list.
Enumerated types have to be defined in the architecture body or inside a package as shown in the section above.
An example of an enumerated type that has been defined in the std_logic_1164 package is the std_ulogic type, defined as follows
type STD_ULOGIC is (
‘U’, -- uninitialized
‘X’, -- forcing unknown
‘0’, -- forcing 0
‘1’, -- forcing 1
‘Z’, -- high impedance
‘W’, -- weak unknown
‘L’, -- weak 0
‘H’. -- weak 1
‘-‘); -- don’t care
In order to use this type one has to include the clause before each entity declaration.
library ieee; use ieee.std_logic_1164.all;
It is possible that multiple drivers are driving a signal. In that case there could be a conflict and the output signal would be undetermined. For instance, the outputs of an AND gate and NOT gate are connected together into the output net OUT1. In order to resolve the value of the output, one can call up a resolution function. These are usually a user-written function that will resolve the signal. If the signal is of the type std_ulogic and has multiple drivers, one needs to use a resolution function. The std_logic_1164 package has such a resolution function, called RESOLVED predefined. One can then use the following declaration for signal OUT1
signal OUT1: resolved: std_ulogic;
If there is contention, the RESOLVED function will be used to intermediate the conflict and determine the value of the signal. Alternatively, one can declare the signal directly as a std_logic type since the subtype std_logic has been defined in the std_logic_1164 package.
signal OUT1: std_logic;
d. Composite Types: Array and Record
Composite data objects consist of a collection of related data elements in the form of an array or record. Before we can use such objects one has to declare the composite type first.
## Array Type
An array type is declared as follows:
type array_name is array (indexing scheme) of element_type;
type MY_WORD is array (15 downto 0) of std_logic;
type YOUR_WORD is array (0 to 15) of std_logic;
type VAR is array (0 to 7) of integer;
type STD_LOGIC_1D is array (std_ulogic) of std_logic;
In the first two examples above we have defined a one-dimensional array of elements of the type std_logic indexed from 15 down to 0, and 0 up to 15, respectively. The last example defines a one-dimensional array of the type std_logic elements that uses the type std_ulogic to define the index constraint. Thus this array looks as follows:
Index: ‘U’ ‘X’ ‘0’ ‘1’ ‘Z’ ‘W’ ‘L’ ‘H’ ‘-‘
Element:
We can now declare objects of these data types. Some examples are given
signal DATA_WORD: YOUR_WORD := B“1101100101010110”;
constant SETTING: VAR := (2,4,6,8,10,12,14,16);
In the first example, the signal MEM_ADDR is an array of 16 bits, initialized to all ‘0’s. To access individual elements of an array we specify the index. For example, MEM_ACCR(15) accesses the left most bit of the array, while DATA_WORD(15) accesses the right most bit of the array with value ‘0’. To access a subrange, one specifies the index range, MEM_ADDR(15 downto 8) or DATA_WORD(0 to 7).
Multidimensional arrays can be declared as well by using a similar syntax as above,
type MY_MATRIX3X2 is array (1 to 3, 1 to 2) of natural;
type YOUR_MATRIX4X2 is array (1 to 4, 1 to 2) of integer;
type STD_LOGIC_2D is array (std_ulogic, std_ulogic) of std_logic;
variable DATA_ARR: MY_MATRIX :=((0,2), (1,3), (4,6), (5,7));
The variable array DATA_ARR will then be initialized to,
0 2
1 3
4 6
5 7
To access an element one specifies the index, e.g. DATA_ARR(3,1) returns the value 4.
The last example defines a 9x9 array or table with an index the elements of the std_ulogic type.
Sometimes it is more convenient not to specify the dimension of the array when the array type is declared. This is called an unconstrained array type. The syntax for the array declaration is,
type array_name is array (type range <>) of element_type;
Some examples are
type MATRIX is array (integer range <>) of integer;
type VECTOR_INT is array (natural range <>) of integer;
type VECTOR2 is array (natural range <>, natural range <>) of std_logic;
The range is now specified when one declares the array object,
variable MATRIX8: MATRIX (2 downto -8) := (3, 5, 1, 4, 7, 9, 12, 14, 20, 18);
variable ARRAY3x2: VECTOR2 (1 to 4, 1 to 3)) := ((‘1’,’0’), (‘0’,’-‘), (1, ‘Z’));
## Record Type
A second composite type is the records type. A record consists of multiple elements that may be of different types. The syntax for a record type is the following:
type name is
record
identifier :subtype_indication;
:
identifier :subtype_indication;
end record;
As an example,
type MY_MODULE is
record
RISE_TIME :time;
FALL_TIME : time;
SIZE : integer range 0 to 200;
DATA : bit_vector (15 downto 0);
end record;
signal A, B: MY_MODULE;
To access values or assign values to records, one can use one of the following methods:
A.RISE_TIME <= 5ns;
A.SIZE <= 120;
B <= A;
Since VHDL is a strongly typed language one cannot assign a value of one data type to a signal of a different data type. In general, it is preferred to the same data types for the signals in a design, such as std_logic (instead of a mix of std_logic and bit types). Sometimes one cannot avoid using different types. To allow assigning data between objects of different types, one needs to convert one type to the other. Fortunately there are functions available in several packages in the ieee library, such as the std_logic_1164 and the std_logic_arith packages. As an example, the std_logic_1164 package allows the following conversions:
###### Function
std_ulogic to bit
to_bit(expression)
std_logic_vector to bit_vector
to_bitvector(expression)
std_ulogic_vector to bit_vector
to_bitvector(expression)
bit to std_ulogic
To_StdULogic(expression)
bit_vector to std_logic_vector
To_StdLogicVector(expression)
bit_vector to std_ulogic_vector
To_StdUlogicVector(expression)
std_ulogic to std_logic_vector
To_StdLogicVector(expression)
std_logic to std_ulogic_vector
To_StdUlogicVector(expression)
The IEEE std_logic_unsigned and the IEEE std_logic_arith packages allow additional conversions such as from an integer to std_logic_vector and vice versa.
An example follows.
port (A, B: in bit_vector(3 downto 0);
out4: out std_logic_vector (3 downto 0));
begin
out4 <= to_StdLogicVector(A and B);
end behavioral_2;
The expression “A and B” which is of the type bit_vector has to be converted to the type std_logic_vector to be of the same type as the output signal out4.
The syntax of a type conversion is as follows:
type_name (expression);
In order for the conversion to be legal, the expression must return a type that can be converted into the type type_name. Here are the conditions that must be fulfilled for the conversion to be possible.
· Type conversions between integer types or between similar array types are possible
· Conversion between array types is possible if they have the same length and if they have identical element types or convertible element types.
· Enumerated types cannot be converted.
f. Attributes
VHDL supports 5 types of attributes. Predefined attributes are always applied to a prefix such as a signal name, variable name or a type. Attributes are used to return various types of information about a signal, variable or type. Attributes consist of a quote mark (‘) followed by the name of the attribute.
## Signal attributes
The following table gives several signal attributes.
Attribute Function signal_name’event returns the Boolean value True if an event on the signal occurred, otherwise gives a False signal_name’active returns the Boolean value True there has been a transaction (assignment) on the signal, otherwise gives a False signal_name’transaction returns a signal of the type “bit” that toggles (0 to 1 or 1 to 0) every time there is a transaction on the signal. signal_name’last_event returns the time interval since the last event on the signal signal_name’last_active returns the time interval since the last transaction on the signal signal_name’last_value gives the value of the signal before the last event occurred on the signal signal_name’delayed(T) gives a signal that is the delayed version (by time T) of the original one. [T is optional, default T=0] signal_name’stable(T) returns a Boolean value, True, if no event has occurred on the signal during the interval T, otherwise returns a False. [T is optional, default T=0] signal_name’quiet(T) returns a Boolean value, True, if no transaction has occurred on the signal during the interval T, otherwise returns a False. [T is optional, default T=0]
An example of an attribute is
if (CLOCK’event and CLOCK=’1’) then
This expression checks for the arrival of a positive clock edge. To find out how much time has passed since the last clock edge, one can use the following attribute:
CLOCK’last_event
## Scalar attributes
Several attributes of a scalar type, scalar-type, are supported. The following table shows some of these attributes.
Attribute Value scalar_type’left returns the first or leftmost value of scalar-type in its defined range scalar_type’right returns the last or rightmost value of scalar-type in its defined range scalar_type’low returns the lowest value of scalar-type in its defined range scalar_type’high returns the greatest value of scalar-type in its defined range scalar_type’ascending True if T is an ascending range, otherwise False scalar_type’value(s) returns the value in T that is represented by s (s stands for string value).
Here are a few examples.
type conductance is range 1E-6 to 1E3
units mho;
end units conductance;
type my_index is range 3 to 15;
type my_levels is (low, high, dontcare, highZ);
conductance’right returns: 1E3
conductance’high 1E3
conductance’low 1E-6
my_index’left 3
my_index’value(5) “5”
my_levels’left low
my_levels’low low
my_levels’high highZ
my_levels’value(dontcare) “dontcare”
## Array attributes
By using array attributes one can return an index value corresponding to the array range.
The following attributes are supported.
Attribute Returns MATRIX‘left(N) MATRIX’right(N) MATRIX’high(N) MATRIX’low(N) MATRIX’length(N) MATRIX’range(N) MATRIX’reverse_range(N) MATRIX’ascending(N) left-most element index right-most index upper bound lower bound the number of elements range reverse range a Boolean value TRUE if index is an ascending range, otherwise FALSE
The number N between parentheses refers to the dimension. For a one-dimensional array, one can omit the number N as shown in the examples below. Lets assume the following arrays, declared as follows:
type MYARR8x4 is array (8 downto 1, 0 to 3) of boolean;
type MYARR1 is array (-2 to 4) of integer;
MYARR1’left returns: -2
MYARR1’right 4
MYARR1’high 4
MYARR1’reverse_range 4 downto to -2
MYARR8x4’left(1) 8
MYARR8x4’left(2) 0
MYARR8x4’right(2) 3
MYARR8x4’high(1) 8
MYARR8x4’low(1) 1
MYARR8x4’ascending(1) False
# 7. Operators
VHDL supports different classes of operators that operate on signals, variables and constants. The different classes of operators are summarized below.
Class 1. Logical operators and or nand nor xor xnor 2. Relational operators = /= < <= > >= 3. Shift operators sll srl sla sra rol ror 4.Addition operators + = & 5. Unary operators + - 6. Multiplying op. * / mod rem 7. Miscellaneous op. ** abs not
The order of precedence is the highest for the operators of class 7, followed by class 6 with the lowest precedence for class 1. Unless parentheses are used, the operators with the highest precedence are applied first. Operators of the same class have the same precedence and are applied from left to right in an expression. As an example, consider the following std_ulogic_vectors, X (=’010’), Y(=’10’), and Z (‘10101’). The expression
not X & Y xor Z rol 1
is equivalent to ((not X) & Y) xor (Z rol 1) = ((101) & 10) xor (01011) =(10110) xor (01011) = 11101. The xor is executed on a bit-per-bit basis.
The logic operators (and, or, nand, nor, xor and xnor) are defined for the “bit”, “boolean”, “std_logic” and “std_ulogic” types and their vectors. They are used to define Boolean logic expression or to perform bit-per-bit operations on arrays of bits. They give a result of the same type as the operand (Bit or Boolean). These operators can be applied to signals, variables and constants.
Notice that the nand and nor operators are not associative. One should use parentheses in a sequence of nand or nor operators to prevent a syntax error:
X nand Y nand Z will give a syntax error and should be written as (X nand Y) nand Z.
b. Relational operators
The relational operators test the relative values of two scalar types and give as result a Boolean output of “TRUE” or “FALSE”.
Operator Description Operand Types Result Type = Equality any type Boolean /= Inequality any type Boolean < Smaller than scalar or discrete array types Boolean <= Smaller than or equal scalar or discrete array types Boolean > Greater than scalar or discrete array types Boolean >= Greater than or equal scalar or discrete array types Boolean
Notice that symbol of the operator “<=” (smaller or equal to) is the same one as the assignment operator used to assign a value to a signal or variable. In the following examples the first “<=” symbol is the assignment operator. Some examples of relational operations are:
variable STS : Boolean;
constant A : integer :=24;
constant B_COUNT : integer :=32;
constant C : integer :=14;
STS <= (A < B_COUNT) ; -- will assign the value “TRUE” to STS
STS <= ((A >= B_COUNT) or (A > C)); -- will result in “TRUE”
STS <= (std_logic (‘1’, ‘0’, ‘1’) < std_logic(‘0’, ‘1’,’1’));--makes STS “FALSE”
type new_std_logic is (‘0’, ‘1’, ‘Z’, ‘-‘);
variable A1: new_std_logic :=’1’;
variable A2: new_std_logic :=’Z’;
STS <= (A1 < A2); will result in “TRUE” since ‘1’ occurs to the left of ‘Z’.
For discrete array types, the comparison is done on an element-per-element basis, starting from the left towards the right, as illustrated by the last two examples.
c. Shift operators
These operators perform a bit-wise shift or rotate operation on a one-dimensional array of elements of the type bit (or std_logic) or Boolean.
Operator Description Operand Type Result Type sll Shift left logical (fill right vacated bits with the 0) Left: Any one-dimensional array type with elements of type bit or Boolean; Right: integer Same as left type srl Shift right logical (fill left vacated bits with 0) same as above Same as left type sla Shift left arithmetic (fill right vacated bits with rightmost bit) same as above Same as left type sra Shift right arithmetic (fill left vacated bits with leftmost bit) same as above Same as left type rol Rotate left (circular) same as above Same as left type ror Rotate right (circular) same as above Same as left type
The operand is on the left of the operator and the number (integer) of shifts is on the right side of the operator. As an example,
variable NUM1 :bit_vector := “10010110”;
NUM1 srl 2;
will result in the number “00100101”.
When a negative integer is given, the opposite action occurs, i.e. a shift to the left will be a shift to the right. As an example
NUM1 srl –2 would be equivalent to NUM1 sll 2 and give the result “01011000”.
Other examples of shift operations are for the bit_vector A = “101001”
variable A: bit_vector :=”101001”; A sll 2 results in “100100” A srl 2 results in “001010” A sla 2 results in “100111” A sra 2 results in “111010” A rol 2 results in “100110” A ror 2 results in “011010”
The addition operators are used to perform arithmetic operation (addition and subtraction) on operands of any numeric type. The concatenation (&) operator is used to concatenate two vectors together to make a longer one. In order to use these operators one has to specify the ieee.std_logic_unsigned.all or std_logic_arith package package in addition to the ieee.std_logic_1164 package.
Operator Description Left Operand Type Right Operand Type Result Type + Addition Numeric type Same as left operand Same type - Subtraction Numeric type Same as left operand Same type & Concatenation Array or element type Same as left operand Same array type
An example of concatenation is the grouping of signals into a single bus [4].
signal MYBUS :std_logic_vector (15 downto 0);
signal STATUS :std_logic_vector (2 downto 0);
signal RW, CS1, CS2 :std_logic;
signal MDATA :std_logic_vector ( 0 to 9);
MYBUS <= STATUS & RW & CS1 & SC2 & MDATA;
Other examples are
MYARRAY (15 downto 0) <= “1111_1111” & MDATA (2 to 9);
NEWWORD <= “VHDL” & “93”;
The first example results in filling up the first 8 leftmost bits of MYARRAY with 1’s and the rest with the 8 rightmost bits of MDATA. The last example results in an array of characters “VHDL93”.
e. Unary operators
The unary operators “+” and “-“ are used to specify the sign of a numeric type.
Operator Description Operand Type Result Type + Identity Any numeric type Same type - Negation Any numeric type Same type
f. Multiplying operators
The multiplying operators are used to perform mathematical functions on numeric types (integer or floating point).
Operator Description Left Operand Type Right Operand Type Result Type * Multiplication Any integer or floating point Same type Same type Any physical type Integer or real type Same as left Any integer or real type Any physical type Same as right / Division Any integer or floating point Any integer or floating point Same type Any physical type Any integer or real t ype Same as left Any physical type Same type Integer mod Modulus Any integer type Same type rem Remainder Any integer type Same type
The multiplication operator is also defined when one of the operands is a physical type and the other an integer or real type.
The remainder (rem) and modulus (mod) are defined as follows:
A rem B = A –(A/B)*B (in which A/B in an integer)
A mod B = A – B * N (in which N is an integer)
The result of the rem operator has the sign of its first operand while the result of the mod operators has the sign of the second operand.
Some examples of these operators are given below.
11 rem 4 results in 3
(-11) rem 4 results in -3
9 mod 4 results in 1
7 mod (-4) results in –1 (7 – 4*2 = -1).
g. Miscellaneous operators
These are the absolute value and exponentation operators that can be applied to numeric types. The logical negation (not) results in the inverse polarity but the same type.
Operator Description Left Operand Type Right Operand Type Result Type ** Exponentiation Integer type Integer type Same as left Floating point Integer type Same as left abs Absolute value Any numeric type Same type not Logical negation Any bit or Boolean type Same type
Delays or timing information
Packages (list standard, 1164 packages).
# 8. Behavioral Modeling: Sequential Statements
As discussed earlier, VHDL provides means to represent digital circuits at different levels of representation of abstraction, such as the behavioral and structural modeling. In this section we will discuss different constructs for describing the behavior of components and circuits in terms of sequential statements. The basis for sequential modeling is the process construct. As you will see, the process construct allows us to model complex digital systems, in particular sequential circuits.
a. Process
A process statement is the main construct in behavioral modeling that allows you to use sequential statements to describe the behavior of a system over time. The syntax for a process statement is
[process_label:] process [ (sensitivity_list) ] [is]
[ process_declarations]
begin
list of sequential statements such as:
signal assignments
variable assignments
case statement
exit statement
if statement
loop statement
next statement
null statement
procedure call
wait statement
end process [process_label];
An example of a positive edge-triggered D flip-flop with asynchronous clear input follows.
library ieee;
use ieee.std_logic_1164.all;
entity DFF_CLEAR is
port (CLK, CLEAR, D : in std_logic;
Q : out std_logic);
end DFF_CLEAR;
architecture BEHAV_DFF of DFF_CLEAR is
begin
DFF_PROCESS: process (CLK, CLEAR)
begin
if (CLEAR = ‘1’) then
Q <= ‘0’;
elsif (CLK’event and CLK = ‘1’) then
Q <= D;
end if;
end process;
end BEHAV_DFF;
A process is declared within an architecture and is a concurrent statement. However, the statements inside a process are executed sequentially. Like other concurrent statements, a process reads and writes signals and values of the interface (input and output) ports to communicate with the rest of the architecture. One can thus make assignments to signals that are defined externally (e.g. interface ports) to the process, such as the Q output of the flip-flop in the above example. The expression CLK’event and CLK = ‘1’ checks for a positive clock edge (clock event AND clock high).
The sensitivity list is a set of signals to which the process is sensitive. Any change in the value of the signals in the sensitivity list will cause immediate execution of the process. If the sensitivity list is not specified, one has to include a wait statement to make sure that the process will halt. Notice that one cannot include both a sensitivity list and a wait statement. Variables and constants that are used inside a process have to be defined in the process_declarations part before the keyword begin. The keyword begin signals the start of the computational part of the process. The statements are sequentially executed, similarly as a conventional software program. It should be noted that variable assignments inside a process are executed immediately and denoted by the “:=” operator. This is in contrast to signal assignments denoted by “<=” and which changes occur after a delay. As a result, changes made to variables will be available immediately to all subsequent statements within the same process. For an example that illustrates the difference between signal and variable assignments see the section on Data Types (difference between signals and variables).
The previous example of the D flip-flop illustrates how to describe a sequential circuit with the process statement. Although the process is mainly used to describe sequential circuits, one can also describe combinational circuits with the process construct. The following example illustrates this for a Full Adder, composed of two Half Adders. This example also illustrates how one process can generate signals that will trigger other processes when events on the signals in its sensitivity list occur [3]. We can write the Boolean expression of a Half Adder and Full Adder as follows:
S_ha = (AÅB) and C_ha = AB
Sum = (AÅB)ÅCin = S_ha ÅCin
Cout = (AÅB)Cin + AB = S_ha.Cin + C_ha
Figure 5 illustrates how the Full Adder has been modeled.
Figure 5: Full Adder composed of two Half Adders, modeled with two processes P1 and P2.
library ieee;
use ieee.std_logic_1164.all;
port (A, B, Cin : in std_logic;
Sum, Cout : out std_logic);
signal int1, int2, int3: std_logic;
begin
-- Process P1 that defines the first half adder
P1: process (A, B)
begin
int1<= A xor B;
int2<= A and B;
end process;
-- Process P2 that defines the second half adder and the OR -- gate
P2: process (int1, int2, Cin)
begin
Sum <= int1 xor Cin;
int3 <= int1 and Cin;
Cout <= int2 or int3;
end process;
end BEHAV_FA;
Of course, one could simplify the behavioral model significantly by using a single process.
b. If Statements
The if statement executes a sequence of statements whose sequence depends on one or more conditions. The syntax is as follows:
if condition then
sequential statements
[elsif condition then
sequential statements ]
[else
sequential statements ]
end if;
Each condition is a Boolean expression. The if statement is performed by checking each condition in the order they are presented until a “true” is found. Nesting of if statements is allowed. An example of an if statement was given earlier for a D Flip-flop with asynchronous clear input. The if statement can be used to describe combinational circuits as well. The following example illustrates this for a 4-to-1 multiplexer with inputs A, B, C and D, and select signals S0 and S1. This statement must be inside a process construct. We will see that other constructs, such as the Conditional Signal Assignment (“When-else”) or “Select” construct may be more convenient for these type of combinational circuits.
entity MUX_4_1a is
port (S1, S0, A, B, C, D: in std_logic;
Z: out std_logic);
end MUX_4_1a;
architecture behav_MUX41a of MUX_4_1a is
begin
P1: process (S1, S0, A, B, C, D)
begin
if (( not S1 and not S0 )=’1’) then
Z <= A;
elsif (( not S1 and S0) = ‘1’) then
Z<=B;
elsif ((S1 and not S0) =’1’) then
Z <=C;
else
Z<=D;
end if;
end process P1;
end behav_MUX41a;
A slightly different way of modeling the same multiplexer is shown below,
if S1=’0’ and S0=’0’ then
Z <= A;
elsif S1=’0’ and S0=’1’ then
Z <= B;
elsif S1=’1’ and S0=’0’ then
Z <= C;
elsif S1=’1’ and S0=’1’ then
Z <= D;
end if;
If statements are often used to implement state diagrams. For an example of a Mealy machine see Example Mealy Machine later on.
c. Case statements
The case statement executes one of several sequences of statements, based on the value of a single expression. The syntax is as follows,
case expression is
when choices =>
sequential statements
when choices =>
sequential statements
-- branches are allowed
[ when others => sequential statements ]
end case;
The expression must evaluate to an integer, an enumerated type of a one-dimensional array, such as a bit_vector. The case statement evaluates the expression and compares the value to each of the choices. The when clause corresponding to the matching choice will have its statements executed. The following rules must be adhered to:
• no two choices can overlap (i.e. each choice can be covered only once)
• if the “when others" choice is not present, all possible values of the expression must be covered by the set of choices.
An example of a case statement using an enumerated type follows. It gives an output D=1 when the signal GRADES has a value between 51 and 60, C=1 for grades between 61 and 70, the when others covers all the other grades and result in an F=1.
library ieee;
use ieee.std_logic_1164.all;
entity GRD_201 is
port(VALUE: in integer range 0 to 100;
A, B, C, D: out bit);
end GRD_201;
architecture behav_grd of GRD_201 is
begin
process (VALUE)
A <= ’0’;
B <= ’0’;
C <= ’0’;
D <= ’0’;
F <= ’0’;
begin
case VALUE is
when 51 to 60 =>
D <= ’1’;
when 61 to 70 | 71 to 75 =>
C <= ’1’;
when 76 to 85 =>
B <= ’1’;
when 86 to 100 =>
A <= ’1’;
when others =>
F <= ‘1’;
end case;
end process;
end behav_grd;
We used the vertical bar ( | ) which is equivalent to the “or” operator, to illustrate how to express a range of values. This is a useful operator to indicate ranges that are not adjacent (e.g. 0 to 4 | 6 to 10).
Another example using the case construct is a 4-to-1 MUX.
entity MUX_4_1 is
port ( SEL: in std_logic_vector(2 downto 1);
A, B, C, D: in std_logic;
Z: out std_logic);
end MUX_4_1;
architecture behav_MUX41 of MUX_4_1 is
begin
PR_MUX: process (SEL, A, B, C, D)
begin
case SEL is
when “00” => Z <= A;
when “01” => Z <= B;
when “10” => Z <= C;
when “11” => Z <= D;
when others => Z <= ‘X’;
end case;
end process PR_MUX;
end behav_MUX41;
The “when others” covers the cases when SEL=”0X”, “0Z”, “XZ”, “UX”, etc. It should be noted that these combinational circuits can be expressed in other ways, using concurrent statements such as the “With – Select” construct. Since the case statement is a sequential statement, one can have nested case statements.
d. Loop statements
A loop statement is used to repeatedly execute a sequence of sequential statements. The syntax for a loop is as follows:
[ loop_label :]iteration_scheme loop
sequential statements
[next [label] [when condition];
[exit [label] [when condition];
end loop [loop_label];
Labels are optional but are useful when writing nested loops. The next and exit statement are sequential statements that can only be used inside a loop.
• The next statement terminates the rest of the current loop iteration and execution will proceed to the next loop iteration.
• The exit statement skips the rest of the statements, terminating the loop entirely, and continues with the next statement after the exited loop.
There are three types of iteration schemes:
· basic loop
· while … loop
· for … loop
## Basic Loop statement
This loop has no iteration scheme. It will be executed continuously until it encounters an exit or next statement.
[ loop_label :] loop
sequential statements
[next [label] [when condition];
[exit [label] [when condition];
end loop [ loop_label];
The basic loop (as well as the while-loop) must have at least one wait statement. As an example, lets consider a 5-bit counter that counts from 0 to 31. When it reaches 31, it will start over from 0. A wait statement has been included so that the loop will execute every time the clock changes from ‘0’ to ‘1’.
Example of a basic loop to implement a counter that counts from 0 to 31 entity COUNT31 is port ( CLK: in std_logic; COUNT: out integer); end COUNT31; architecture behav_COUNT of COUNT31 is begin P_COUNT: process variable intern_value: integer :=0; begin COUNT <= intern_value; loop wait until CLK=’1’; intern_value:=(intern_value + 1) mod 32; COUNT <= intern_value; end loop; end process P_COUNT; end behav_COUNT;
We defined a variable intern_value inside the process because output ports cannot be read inside the process.
## While-Loop statement
The while … loop evaluates a Boolean iteration condition. When the condition is TRUE, the loop repeats, otherwise the loop is skipped and the execution will halt. The syntax for the while…loop is as follows,
[ loop_label :] while condition loop
sequential statements
[next [label] [when condition];
[exit [label] [when condition];
end loop[ loop_label ];
The condition of the loop is tested before each iteration, including the first iteration. If it is false, the loop is terminated.
## For-Loop statement
The for-loop uses an integer iteration scheme that determines the number of iterations. The syntax is as follows,
[ loop_label :] for identifier in range loop
sequential statements
[next [label] [when condition];
[exit [label] [when condition];
end loop[ loop_label ];
• The identifier (index) is automatically declared by the loop itself, so one does not need to declare it separately. The value of the identifier can only be read inside the loop and is not available outside its loop. One cannot assign or change the value of the index. This is in contrast to the while-loop whose condition can involve variables that are modified inside the loop.
• The range must be a computable integer range in one of the following forms, in which integer_expression must evaluate to an integer:
• integer_expression to integer_expression
• integer_expression downto integer_expression
e. Next and Exit Statement
The next statement skips execution to the next iteration of a loop statement and proceeds with the next iteration. The syntax is
next [label] [when condition];
The when keyword is optional and will execute the next statement when its condition evaluates to the Boolean value TRUE.
The exit statement skips the rest of the statements, terminating the loop entirely, and continues with the next statement after the exited loop. The syntax is as follows:
exit [label] [when condition];
The when keyword is optional and will execute the next statement when its condition evaluates to the Boolean value TRUE.
Notice that the difference between the next and exit statement, is that the exit statement terminates the loop.
The wait statement will halt a process until an event occurs. There are several forms of the wait statement,
wait until condition;
wait for time expression;
wait on signal;
wait;
The Xilinx Foundation Express has implemented only the first form of the wait statement. The syntax is as follows,
wait until signal = value;
wait until signal’event and signal = value;
wait until not signal’stable and signal = value;
The condition in the “wait until” statement must be TRUE for the process to resume. A few examples follow.
wait until CLK=’1’;
wait until CLK=’0’;
wait until CLK’event and CLK=’1’;
wait until not CLK’stable and CLK=’1’;
For the first example the process will wait until a positive-going clock edge occurs, while for the second example, the process will wait until a negative-going clock edge arrives. The last two examples are equivalent to the first one (positive-edge or 0-1 transitions). The hardware implementation for these three statements will be identical.
It should be noted that a process that contains a wait statement can not have a sensitivity list. If a process uses one or more wait statements, the Foundation Express synthesizer will use sequential logic. The results of the computations are stored in flip-flops.
g. Null statement
The null statement states that no action will occur. The syntax is as follows,
null;
It can be useful in a case statement where all choices must be covered, even if some of them can be ignored. As an example, consider a control signal CNTL in the range 0 to 31. When the value of CNTL is 3 or 15, the signals A and B will be xor-ed, otherwise nothing will occur.
entity EX_WAIT is
port ( CNTL: in integer range 0 to 31;
A, B: in std_logic_vector(7 downto 0);
Z: out std_logic_vector(7 downto 0) );
end EX_WAIT;
architecture arch_wait of EX_WAIT is
begin
P_WAIT: process (CNTL)
begin
Z <=A;
case CNTL is
when 3 | 15 =>
Z <= A xor B;
when others =>
null;
end case;
end process P_WAIT;
end arch_wait;
h. Example of a Mealy Machine
The sequence following detector recognizes the input bit sequence X: "1011". The machine will keep checking for the proper bit sequence and does not reset to the initial state after it recognizes the string. In case we are implementing a Mealy machine, the output is associated with the transitions as indicated on the following state diagram (Figure 6).
Figure 6: Sequence detector (1011), realized as a Mealy Machine.
The VHDL file is given below.
VHDL file for a sequence detector (1011) implemented as a Mealy Machine library ieee; use ieee.std_logic_1164.all; entity myvhdl is port (CLK, RST, X: in STD_LOGIC; Z: out STD_LOGIC); end; architecture myvhdl_arch of myvhdl is -- SYMBOLIC ENCODED state machine: Sreg0 type Sreg0_type is (S1, S2, S3, S4); signal Sreg0: Sreg0_type; begin --concurrent signal assignments Sreg0_machine: process (CLK) begin if CLK'event and CLK = '1' then if RST='1' then Sreg0 <= S1; else case Sreg0 is when S1 => if X='0' then Sreg0 <= S1; elsif X='1' then Sreg0 <= S2; end if; when S2 => if X='1' then Sreg0 <= S2; elsif X='0' then Sreg0 <= S3; end if; when S3 => if X='1' then Sreg0 <= S4; elsif X='0' then Sreg0 <= S1; end if; when S4 => if X='0' then Sreg0 <= S3; elsif X='1' then Sreg0 <= S2; end if; when others => null; end case; end if; end if; end process; -- signal assignment statements for combinatorial outputs Z_assignment: Z <= '0' when (Sreg0 = S1 and X='0') else '0' when (Sreg0 = S1 and X='1') else '0' when (Sreg0 = S2 and X='1') else '0' when (Sreg0 = S2 and X='0') else '0' when (Sreg0 = S3 and X='1') else '0' when (Sreg0 = S3 and X='0') else '0' when (Sreg0 = S4 and X='0') else '1' when (Sreg0 = S4 and X='1') else '1'; end myvhdl_arch;
# 9. Dataflow Modeling – Concurrent Statements
Behavioral modeling can be done with sequential statements using the process construct or with concurrent statements. The first method was described in the previous section and is useful to describe complex digital systems. In this section, we will use concurrent statements to describe behavior. This method is usually called dataflow modeling. The dataflow modeling describes a circuit in terms of its function and the flow of data through the circuit. This is different from the structural modeling that describes a circuit in terms of the interconnection of components.
Concurrent signal assignments are event triggered and executed as soon as an event on one of the signals occurs. In the remainder of the section we will describe several concurrent constructs for use in dataflow modeling.
a. Simple Concurrent signal assignments.
We have discussed several concurrent examples earlier in the tutorial. In this section we will review the different types of concurrent signal assignments.
A simple concurrent signal assignment is given in the following examples,
Sum <= (A xor B) xor Cin;
Carry <= (A and B);
Z <= (not X) or Y after 2 ns;
The syntax is as follows:
Target_signal <= expression;
in which the value of the expression transferred to the target_signal. As soon as an event occurs on one of the signals, the expression will be evaluated. The type of the target_signal has to be the same as the type of the value of the expression.
Another example is given below of a 4-bit adder circuit. Notice that we specified the package: IEEE.std_logic_unsigned in order to be able to use the “+” (addition) operator.
Example of a Four bit Adder using concurrent/behavioral modeling library ieee; use IEEE.std_logic_1164.all; use IEEE.std_logic_unsigned.all; entity ADD4 is port ( A: in STD_LOGIC_VECTOR (3 downto 0); B: in STD_LOGIC_VECTOR (3 downto 0); CIN: in STD_LOGIC; SUM: out STD_LOGIC_VECTOR (3 downto 0); COUT: out STD_LOGIC ); end ADD4; architecture ADD4_concurnt of ADD4 is -- define internal SUM signal including the carry signal SUMINT: STD_LOGIC_VECTOR(4 downto 0); begin -- <> SUMINT <= ('0' & A) + ('0' & B) + ("0000" & CIN); COUT <= SUMINT(4); SUM <= SUMINT(3 downto 0); end ADD4_concurnt;
b. Conditional Signal assignments
The syntax for the conditional signal assignment is as follows:
Target_signal <= expression when Boolean_condition else
expression when Boolean_condition else
:
expression;
The target signal will receive the value of the first expression whose Boolean condition is TRUE. If no condition is found to be TRUE, the target signal will receive the value of the final expression. If more than one condition is true, the value of the first condition that is TRUE will be assigned.
An example of a 4-to-1 multiplexer using conditional signal assignments is shown below.
entity MUX_4_1_Conc is
port (S1, S0, A, B, C, D: in std_logic;
Z: out std_logic);
end MUX_4_1_Conc;
architecture concurr_MUX41 of MUX_4_1_Conc is
begin
Z <= A when S1=’0’ and S0=’0’ else
B when S1=’0’ and S0=’1’ else
C when S1=’1’ and S0=’0’ else
D;
end concurr_MUX41;
The conditional signal assignment will be re-evaluated as soon as any of the signals in the conditions or expression change. The when-else construct is useful to express logic function in the form of a truth table. An example of the same multiplexer as above is given below in a more compact form.
entity MUX_4_1_funcTab is
port (A, B, C, D: in std_logic;
SEL: in std_logic_vector (1 downto 0);
Z: out std_logic);
end MUX_4_1_ funcTab;
architecture concurr_MUX41 of MUX_4_1_ funcTab is
begin
Z <= A when SEL = ”00” else
B when SEL = ”01” else
C when SEL = “10” else
D;
end concurr_MUX41;
Notice that this construct is simpler than the If-then-else construct using the process statement or the case statement. An alternative way to define the multiplexer is the case construct inside a process statement, as discussed earlier.
The selected signal assignment is similar to the conditional one described above. The syntax is as follows,
with choice_expression select
target_name <= expression when choices,
target_name <= expression when choices,
:
target_name <= expression when choices;
The target is a signal that will receive the value of an expression whose choice includes the value of the choice_expression. The expression selected is the first with a matching choice. The choice can be a static expression (e.g. 5) or a range expression (e.g. 4 to 9). The following rules must be followed for the choices:
• No two choices can overlap
• All possible values of choice_expression must be covered by the set of choices, unless an others choice is present.
An example of a 4-to-1 multiplexer is given below.
entity MUX_4_1_Conc2 is
port (A, B, C, D: in std_logic;
SEL: in std_logic_vector(1 downto 0);
Z: out std_logic);
end MUX_4_1_Conc2;
architecture concurr_MUX41b of MUX_4_1_Conc2 is
begin
with SEL select
Z <= A when “00”,
B when “01”,
C when “10”,
D when “11”;
end concurr_MUX41b;
The equivalent process statement would make use of the case construct. Similarly to the when-else construct, the selected signal assignment is useful to express a function as a truth table, as illustrated above.
The choices can express a single value, a range or combined choices as shown below.
target <= value1 when “000”,
value2 when “001” | “011” | “101” ,
value3 when others;
In the above example, all eight choices are covered and only once. The others choice must the last one used.
Notice that the Xilinx Foundation Express does not allow a vector as choice_expression such as std_logic_vector’(A,B,C).
As an example, lets consider a full adder with inputs A, B and C and outputs sum and cout,
port (A, B, C: in std_logic;
sum, cout: out std_logic);
--define internal signal: vector INS of the input signals
signal INS: std_logic_vector (2 downto 0);
begin
--define the components of vector INS of the input signals
INS(2) <= A;
INS(1) <= B;
INS(0) <= C;
with INS select
(sum, cout) <= std_logic_vector’(“00”) when “000”,
std_logic_vector’(“10”) when “001”,
std_logic_vector’(“10”) when “010”,
std_logic_vector’(“01”) when “011”,
std_logic_vector’(“10”) when “100”,
std_logic_vector’(“01”) when “101”,
std_logic_vector’(“01”) when “110”,
std_logic_vector’(“11”) when “111”,
std_logic_vector’(“11”) when others;
Notice: In the example above we had to define an internal vector INS(A,B,C) of the input signals to use as part of the with-select-when statement. This was done because the Xilinx Foundation does not support the construct std_logic_vector’(A,B,C).
# 10. Structural Modeling
Structural modeling was described briefly in the section Structural Modeling in “Basic Structure of a VHDL file”. A structural way of modeling describes a circuit in terms of components and its interconnection. Each component is supposed to be defined earlier (e.g. in package) and can be described as structural, a behavioral or dataflow model. At the lowest hierarchy each component is described as a behavioral model, using the basic logic operators defined in VHDL. In general structural modeling is very good to describe complex digital systems, though a set of components in a hierarchical fashion.
A structural description can best be compared to a schematic block diagram that can be described by the components and the interconnections. VHDL provides a formal way to do this by
· Declare a list of components being used
· Declare signals which define the nets that interconnect components
· Label multiple instances of the same component so that each instance is uniquely defined.
The components and signals are declared within the architecture body,
architecture architecture_name of NAME_OF_ENTITY is
-- Declarations
component declarations
signal declarations
begin
-- Statements
component instantiation and connections
:
end architecture_name;
a. Component declaration
Before components can be instantiated they need to be declared in the architecture declaration section or in the package declaration. The component declaration consists of the component name and the interface (ports). The syntax is as follows:
component component_name [is]
[port (port_signal_names: mode type;
port_signal_names: mode type;
:
port_signal_names: mode type);]
end component [component_name];
The component name refers to either the name of an entity defined in a library or an entity explicitly defined in the VHDL file (see example of the four bit adder).
The list of interface ports gives the name, mode and type of each port, similarly as is done in the entity declaration.
A few examples of component declaration follow:
component OR2
port (in1, in2: in std_logic;
out1: out std_logic);
end component;
component PROC
port (CLK, RST, RW, STP: in std_logic;
ADDRBUS: out std_logic_vector (31 downto 0);
DATA: inout integer range 0 to 1024);
port(a, b, c: in std_logic;
sum, carry: out std_logic);
end component;
As mentioned earlier, the component declaration has to be done either in the architecture body or in the package declaration. If the component is declared in a package, one does not have to declare it again in the architecture body as long as one uses the library and use clause.
b. Component Instantiation and interconnections
The component instantiation statement references a component that can be
• Previously defined at the current level of the hierarchy or
• Defined in a technology library (vendor’s library).
The syntax for the components instantiation is as follows,
instance_name : component name
port map (port1=>signal1, port2=> signal2,… port3=>signaln);
The instance name or label can be any legal identifier and is the name of this particular instance. The component name is the name of the component declared earlier using the component declaration statement. The port name is the name of the port and signal is the name of the signal to which the specific port is connected. The above port map associates the ports to the signals through named association. An alternative method is the positional association shown below,
port map (signal1, signal2,…signaln);
in which the first port in the component declaration corresponds to the first signal, the second port to the second signal, etc. The signal position must be in the same order as the declared component’s ports. One can mix named and positional associations as long as one puts all positional associations before the named ones. The following examples illustrates this,
component NAND2
port (in1, in2: in std_logic;
out1: out std_logic);
end component;
signal int1, int2, int3: std_logic;
architecture struct of EXAMPLE is
U1: NAND2 port map (A,B,int1);
U2: NAND2 port map (in2=>C, in2=>D, out1=>int2);
U3: NAND3 port map (in1=>int1, int2, Z);
…..
Another example is the Buzzer circuit of Figure 2.
# 11. References
1. D. Gajski and R. Khun, “Introduction: New VLSI Tools,” IEEE Computer, Vol. 16, No. 12, pp. 11-14, Dec. 1983.
2. M. Mano and C. Kime, “Logic and Computer Design Fundamentals,” 2nd Edition, Prentice Hall, Upper Saddle River, 2001.
3. S. Yalamanchili, “VHDL Starter’s Guide,” Prentice Hall, Upper Saddle River, 1998.
4. J. Bhasker, “VHDL Primer,” 3rd Edition, Prentice Hall, Upper Saddle River, 1998.
5. P. J. Ashenden, “The Student’s Guide to VHDL,” Morgan Kaufmann Publishers, Inc, San Francisco, 1998.
6. A. Dewey, “Analysis and Design of Digital Systems,” PWS Publishing Company, New York, 1997.
7. C. H. Roth, “Digital System Design using VHDL”, PWS Publishing Company, New York, 1998.
8. D. Pellerin and D. Taylor, “VHDL Made Easy!”, ,” Prentice Hall, Upper Saddle River, 1997.
9. VHDL Reference Guide, Xilinx, Inc., 1999 (available on line: http://toolbox.xilinx.com/docsan/ (select Foundation Series)
Copyright 2001; Created by Jan Van der Spiegel, Sept. 28, 2001; Updated August 6, 2006
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2014-11-01 00:35:18
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https://www.physicsforums.com/threads/killer-word-problem-spacing.86819/
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# Killer word problem-spacing
1. Aug 30, 2005
### TonyC
Killer word problem--spacing
The area of a parking lot is 1590 square meters. A car requires 6 square meters and a bus requires 32 square meters of space. There can be at most 200 vehicles parked at one time. If the cost to park a car is $2.00 and a bus is$6.00, how many buses should be in the lot to maximize income?
2. Aug 30, 2005
### morry
This sounds like a linear programming q. Have you learnt about the simplex algorithm? I would not know how to tackle this without simplex.
3. Aug 30, 2005
### TonyC
No I haven't. What is the algorithm? Maybe I can attempt it using it.
4. Aug 30, 2005
### morry
Google simplex. I would never be able to understand it without going through the lectures.
So a graphical method may be better for you.
What you first must do is write the above stuff as constraints. ie z= 2x +6y (For money)
6x +32y <(or equalto) 1590 and x + y<(or equalto)200. Youll have to graph these two equations (The ones on this line).
So when you have a graph, keep in mind that the optimal solution will lie on one of the vertices. There shouldnt be too many in this case. So plug stuff into the equations and you should get your maximum profit.
Hope that helped.
Last edited: Aug 30, 2005
5. Aug 30, 2005
### TonyC
Can you please break it down further?
I am still perplexed.
How?
6. Aug 30, 2005
### morry
Ok. So youre given all that stuff right? Ill try and explain why I chose those 3 equations.
z= 2x +6y . This is the money equation. The money taken will be $2 for every car and$6 for every bus. Thus money = 2x +6y. Where x and y are the number of cars and buses, respectively.
6x +32y <(or equalto) 1590 This equation is for the space in the car park. Since each car takes up 6 m and a bus 32 and the total space is 1590. So the sum of all the cars and buses must take up less than 1590.
x + y<(or equalto)200 It says that the total number of buses and cars must be les than 200. Hopefully you can start to see what these equations mean.
Then, graph the last two equations as you normally would. Think about the contraints, the solution will be bounded by the lines. The optimal solution will be at the vertex of those two lines.
The graph should look similar to this one: http://www.egwald.com/operationsresearch/images/lpgraph_primal_1.php [Broken]
Last edited by a moderator: May 2, 2017
7. Aug 30, 2005
### TD
Coïncidentally, the system of the two conditions gives an integer solution:
$$\left\{ \begin{gathered} c + b = 200 \hfill \\ 6c + 32b = 1590 \hfill \\ \end{gathered} \right. \Leftrightarrow \left\{ \begin{gathered} c = 185 \hfill \\ b = 15 \hfill \\ \end{gathered} \right$$
8. Aug 30, 2005
### TonyC
Now I see....thank you :0
9. Aug 30, 2005
### morry
haha, even easier.
10. Aug 30, 2005
### HallsofIvy
Staff Emeritus
What do you see? Do you know what the answer to this problem is? TD told you that the two equations are both satisfied when the number of cars is 15 and the number of buses is 185. In other words, that is one possible number of cars and buses that will fit on the lot. Do you have any reason to believe that that will give maximum income?
That is, in fact, the correct answer but you be able to prove it. The point of "linear programming" (you don't really need the "symplex method") is that when the set of "feasible" solutions (here the number of cars and buses that you can fit on the lot) is convex polygon and the "object function" (here the income) is linear, then object function takes on a maximum or a minimum only at a vertex of the polygon (imagine moving the straight line graph of the object function parallel to itself {increasing or decreasing its value}. The line will "leave" the polygon at a vertex.).
It's easy to see that the "feasible region" here is a polygon bounded by (taking c for number of cars, b for number of buses) b=0, c= 0; b= 0, c= 200 (where b+ c= 200 crosses the c-axis); c= 0, b= 49.68 (where the 6c+ 32b= 1590 crosses the b-axis);and c= 15, b= 185 (where the two lines cross). Now evaluate the object function 2c+ 6b at each of those to find the maximum value.
Last edited: Aug 30, 2005
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2017-05-28 22:52:01
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https://www.mathtrench.com/statistics-t-test-71/
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# Statistics: T-test – #71
Question: Suppose the objective of a study is to determine the differences in effectiveness of Pravastatin and Lovastatin in reducing cholesterol levels of patients with a cardiovascular incident(s) and high lipid levels. A two-sample t-test was computed and the resulting p-value was 0.0426. Use the objective of the study and the results of the t-test answer the following questions:
a) State the null and alternative hypotheses for the study
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2019-06-24 09:59:00
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https://labs.tib.eu/arxiv/?author=Frank%20Haberl
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• ### Effects of Interstellar Dust Scattering on the X-ray Eclipses of the LMXB AX J1745.6-2901 in the Galactic Center(1802.00637)
April 1, 2018 astro-ph.HE
AX J1745.6-2901 is an eclipsing low mass X-ray binary (LMXB) in the Galactic Centre (GC). It shows significant X-ray excess emission during the eclipse phase, and its eclipse light curve shows an asymmetric shape. We use archival XMM-Newton and Chandra observations to study the origin of these peculiar X-ray eclipsing phenomena. We find that the shape of the observed X-ray eclipse light curves depends on both photon energy and the shape of the source extraction region, and also shows differences between the two instruments. By performing detailed simulations for the time-dependent X-ray dust scattering halo, as well as directly modelling the observed eclipse and non-eclipse halo profiles of AX J1745.6-2901, we obtained solid evidence that its peculiar eclipse phenomena are indeed caused by the X-ray dust scattering in multiple foreground dust layers along the line-of-sight (LOS). The apparent dependence on the instruments is caused by different instrumental point-spread-functions. Our results can be used to assess the influence of dust scattering in other eclipsing X-ray sources, and raise the importance of considering the timing effects of dust scattering halo when studying the variability of other X-ray sources in the GC, such as Sgr A*. Moreover, our study of halo eclipse reinforces the existence of a dust layer local to AX J1745.6-2901 as reported by Jin et al. (2017), as well as identifying another dust layer within a few hundred parsecs to Earth, containing up to several tens of percent LOS dust, which is likely to be associated with the molecular clouds in the Solar neighbourhood. The remaining LOS dust is likely to be associated with the molecular clouds located in the Galactic disk in-between.
• ### Probing the Interstellar Dust towards the Galactic Centre: Dust Scattering Halo around AX J1745.6-2901(1703.05179)
Aug. 20, 2017 astro-ph.HE
AX J1745.6-2901 is an X-ray binary located at only 1.45 arcmin from Sgr A*, showcasing a strong X-ray dust scattering halo. We combine Chandra and XMM-Newton observations to study the halo around this X-ray binary. Our study shows two major thick dust layers along the line of sight (LOS) towards AX J1745.6-2901. The LOS position and $N_{H}$ of these two layers depend on the dust grain models with different grain size distribution and abundances. But for all the 19 dust grain models considered, dust Layer-1 is consistently found to be within a fractional distance of 0.11 (mean value: 0.05) to AX J1745.6-2901 and contains only (19-34)% (mean value: 26%) of the total LOS dust. The remaining dust is contained in Layer-2, which is distributed from the Earth up to a mean fractional distance of 0.64. A significant separation between the two layers is found for all the dust grain models, with a mean fractional distance of 0.31. Besides, an extended wing component is discovered in the halo, which implies a higher fraction of dust grains with typical sizes $\lesssim$ 590 \AA\ than considered in current dust grain models. Assuming AX J1745.6-2901 is 8 kpc away, dust Layer-2 would be located in the Galactic disk several kpc away from the Galactic Centre (GC). The dust scattering halo biases the observed spectrum of AX J1745.6-2901 severely in both spectral shape and flux, and also introduces a strong dependence on the size of the instrumental point spread function and the source extraction region. We build Xspec models to account for this spectral bias, which allow us to recover the intrinsic spectrum of AX J1745.6-2901 free from dust scattering opacity. If dust Layer-2 also intervenes along the LOS to Sgr A* and other nearby GC sources, a significant spectral correction for the dust scattering opacity would be necessary for all these GC sources.
• ### Supernova Remnants in M33: X-ray Properties as Observed by XMM-Newton(1708.01239)
Aug. 3, 2017 astro-ph.HE
We have carried out a study of the X-ray properties of the supernova remnant (SNR) population in M33 with XMM-Newton, comprising deep observations of 8 fields in M33 covering all of the area within the D$_{25}$ contours, and with a typical luminosity of 7.1$\times$10$^{34}$ erg s$^{-1}$ (0.2-2.0 keV) . Here we report our work to characterize the X-ray properties of the previously identified SNRs in M33, as well as our search for new X-ray detected SNRs. With our deep observations and large field of view we have detected 105 SNRs at the 3$\sigma$ level, of which 54 SNRs are newly detected in X-rays, and three are newly discovered SNRs. Combining XMM-Newton data with deep Chandra survey data allows detailed spectral fitting of 15 SNRs, for which we have measured temperatures, ionization timescales, and individual abundances. This large sample of SNRs allows us to construct an X-ray luminosity function, and compare its shape to luminosity functions from host galaxies of differing metallicities and star formation rates to look for environmental effects on SNR properties. We conclude that while metallicity may play a role in SNR population characteristics, differing star formation histories on short timescales, and small-scale environmental effects appear to cause more significant differences between X-ray luminosity distributions. In addition, we analyze the X-ray detectability of SNRs, and find that in M33 SNRs with higher [SII]/H$\alpha$ ratios, as well as those with smaller galactocentric distances, are more detectable in X-rays.
• ### Deep Chandra Survey of the Small Magellanic Cloud. II. Timing Analysis of X-ray Pulsars(1705.09733)
May 26, 2017 astro-ph.HE
We report the timing analysis results of X-ray pulsars from a recent deep Chandra survey of the Small Magellanic Cloud (SMC). We have analyzed a total exposure of 1.4 Ms from 31 observations over a 1.2 deg$^2$ region in the SMC under a Chandra X-ray Visionary Program. Using the Lomb-Scargle and epoch folding techniques, we have detected periodic modulations from 20 pulsars and a new candidate pulsar. The survey also covers 11 other pulsars with no clear sign of periodic modulation. The 0.5-8 keV X-ray luminosity ($L_X$) of the pulsars ranges from $10^{34}$ to $10^{37}$ erg s$^{-1}$ at 60 kpc. All the Chandra sources with $L_X$ $\gtrsim 4 \times 10^{35}$ erg s$^{-1}$ exhibit X-ray pulsations. The X-ray spectra of the SMC pulsars (and high mass X-ray binaries) are in general harder than those of the SMC field population. All but SXP~8.02 can be fitted by an absorbed power-law model with a photon index of $\Gamma$ $\lesssim$ 1.5. The X-ray spectrum of the known magnetar SXP~8.02 is better fitted with a two-temperature blackbody model. Newly measured pulsation periods of SXP~51.0, SXP~214 and SXP~701 are significantly different from the previous XMM-Newton and RXTE measurements. This survey provides a rich data set for energy-dependent pulse profile modeling. Six pulsars show an almost eclipse-like dip in the pulse profile. Phase-resolved spectral analysis reveals diverse spectral variation during pulsation cycle: e.g., for an absorbed power-law model, some exhibit an (anti)-correlation between absorption and X-ray flux, while others show more intrinsic spectral variation.
• ### Discovery of a 26.2 day period in the long-term X-ray light curve of SXP 1323: a very short orbital period for a long spin period pulsar(1704.07646)
April 25, 2017 astro-ph.HE
Context. About 120 Be/X-ray binaries (BeXBs) are known in the Small Magellanic Cloud (SMC); about half of them are pulsating with periods from a few to hundreds of seconds. SXP 1323 is one of the longest-period pulsars known in this galaxy. Aims. SXP 1323 is in the field of view of a large set of calibration observations that we analyse systematically, focusing on the time analysis, in search of periodic signals. Methods. We analyse all available X-ray observations of SXP 1323 from Suzaku, XMM-Newton, and Chandra, in the time range from 1999 to the end of 2016. We perform a Lomb-Scargle periodogram search in the band 2.5-10 keV on all observations to detect the neutron star spin period and constrain its long-term evolution. We also perform an orbital period search on the long-term light curve, merging all datasets. Results. We report the discovery of a 26.188+-0.045 d period analysing data from Suzaku, XMM-Newton, and Chandra, which confirms the optical period derived from the Optical Gravitational Lensing Experiment (OGLE) data. If this corresponds to the orbital period, this would be very short with respect to what is expected from the spin/orbital period relationship. We furthermore report on the spin period evolution in the last years. The source is spinning-up with an average rate of Pdot/P of 0.018 yr-1, decreasing from 1340 to 1100 s, in the period from 2006 to the end of 2016, which is also extreme with respect to the other Be/X-ray pulsars. From 2010 to the end of 2014, the pulse period is not clearly detectable, although the source was still bright. Conclusions. SXP 1323 is a peculiar BeXB due to its long pulse period, rapid spin-up for several years, and short orbital period. A continuous monitoring of the source in the next years is necessary to establish the long-term behaviour of the spin period.
• ### H{\alpha} imaging for BeXRBs in the Small Magellanic Cloud(1702.04606)
The Small Magellanic Cloud (SMC) hosts a large number of high-mass X-ray binaries, and in particular of Be/X-ray Binaries (BeXRBs; neutron stars orbiting OBe-type stars), offering a unique laboratory to address the effect of metalicity. One key property of their optical companion is H{\alpha} in emission, which makes them bright sources when observed through a narrow-band H{\alpha} filter. We performed a survey of the SMC Bar and Wing regions using wide-field cameras (WFI@MPG/ESO and MOSAIC@CTIO/Blanco) in order to identify the counterparts of the sources detected in our XMM-Newton survey of the same area. We obtained broad-band R and narrow-band H{\alpha} photometry, and identified ~10000 H{\alpha} emission sources down to a sensitivity limit of 18.7 mag (equivalent to ~B8 type Main Sequence stars). We find the fraction of OBe/OB stars to be 13% down to this limit, and by investigating this fraction as a function of the brightness of the stars we deduce that H{\alpha} excess peaks at the O9-B2 spectral range. Using the most up-to-date numbers of SMC BeXRBs we find their fraction over their parent population to be ~0.002-0.025 BeXRBs/OBe, a direct measurement of their formation rate.
• ### Statistical Analysis of Supernova Remnants in the Large Magellanic Cloud(1703.02676)
March 23, 2017 astro-ph.HE
We construct the most complete sample of supernova remnants (SNRs) in any galaxy - the Large Magellanic Cloud (LMC) SNR sample. We study their various properties such as spectral index ($\alpha$), size and surface-brightness. We suggest an association between the spatial distribution, environment density of LMC SNRs and their tendency to be located around supergiant shells. We find evidence that the 16 known type Ia LMC SNRs are expanding in a lower density environment compared to the Core-Collapse (CC) type. The mean diameter of our entire population (74) is 41 pc, which is comparable to nearby galaxies. We didn't find any correlation between the type of SN explosion, ovality or age. The $N(<D)$ relationship of $a={0.96}$ implies that the randomised diameters are readily mimicking such an exponent. The rate of SNe occurring in the LMC is estimated to be $\sim$1 per 200 yr. The mean $\alpha$ of the entire LMC SNR population is $\alpha=-0.52$, which is typical of most SNRs. However, our estimates show a clear flattening of the synchrotron $\alpha$ as the remnants age. As predicted, our CC SNRs sample are significantly brighter radio emitters than the type Ia remnants. We also estimate the $\Sigma - D$ relation for the LMC to have a slope $\sim3.8$ which is comparable with other nearby galaxies. We also find the residency time of electrons in the galaxy ($4.0-14.3$ Myr), implying that SNRs should be the dominant mechanism for the production and acceleration of CRs.
• ### XMM-Newton observation of the nearby pulsar B1133+16(1701.02554)
Jan. 10, 2017 astro-ph.HE
We constrain the X-ray properties of the nearby $(360\,{\rm pc})$, old ($5\,{\rm Myr}$) pulsar B1133+16 with $\sim 100\,{\rm ks}$ effective exposure time by {\it XMM-Newton}. The observed pulsar flux in the 0.2-3 keV energy range is $\sim 10^{-14} \, {\rm erg \, cm}^{-2} \, {\rm s}^{-1}$, which results in the recording of $\sim 600$ source counts with the EPIC pn and MOS detectors. The X-ray radiation is dominated by nonthermal radiation and is well described by both a single power-law model (PL) and a sum of blackbody and power-law emission (BB+PL). The BB+PL model results in a spectral photon index $\Gamma=2.4^{+0.4}_{-0.3}$ and a nonthermal flux in the 0.2-3 keV energy range of $(7\pm 2) \times 10^{-15}\, {\rm erg \, cm}^{-2} \, {\rm s}^{-1}$. The thermal emission is consistent with the blackbody emission from a small hot spot with a radius of $R_{\rm pc} \approx 14^{+7}_{-5} \, {\rm m}$ and a temperature of $T_{\rm s} = 2.9^{+0.6}_{-0.4} \, {\rm MK}$. Assuming that the hot spot corresponds to the polar cap of the pulsar, we can use the magnetic flux conservation law to estimate the magnetic field at the surface $B_{\rm s} \approx 3.9 \times 10^{14} \, {\rm G}$. The observations are in good agreement with the predictions of the partially screened gap model, which assumes the existence of small-scale surface magnetic field structures in the polar cap region.
• ### SXP214, an X-ray Pulsar in the Small Magellanic Cloud, Crossing the Circumstellar Disk of the Companion(1605.03672)
May 12, 2016 astro-ph.HE
Located in the Small Magellanic Cloud (SMC), SXP214 is an X-ray pulsar in a high mass X-ray binary system with a Be-star companion. A recent survey of the SMC under a Chandra X-ray Visionary program found the source in a transition when the X-ray flux was on a steady rise. The Lomb-Scargle periodogram revealed a pulse period of 211.49 +/- 0.42 s, which is significantly (>5sigma) shorter than the previous measurements with XMM-Newton and RXTE. This implies that the system has gone through sudden spin-up episodes recently. The pulse profile shows a sharp eclipse-like feature with a modulation amplitude of >95%. The linear rise of the observed X-ray luminosity from <~2x to 7x10^35 erg s^-1 is correlated with steady softening of the X-ray spectrum, which can be described by the changes in the local absorption from N_H ~ 10^24 to <~10^20 cm^-2 for an absorbed power-law model. The soft X-ray emission below 2 keV was absent in the early part of the observation when only the pulsating hard X-ray component was observed, whereas at later times both soft and hard X-ray components were observed pulsating. A likely explanation is that the neutron star was initially hidden in the circumstellar disk of the companion, and later came out of the disk with the accreted material that continued fueling the observed pulsation.
• ### Results from DROXO IV. EXTraS discovery of an X-ray flare from the Class I protostar candidate ISO-Oph 85(1510.06286)
Dec. 4, 2015 astro-ph.SR
X-ray emission from Young Stellar Objects (YSOs) is crucial to understand star formation. A very limited amount of X-ray results is available for the protostellar (ClassI) phase. A systematic search of transient X-ray phenomena combined with a careful evaluation of the evolutionary stage offer a widely unexplored window to our understanding of YSOs X-ray properties. Within the EXTraS project, a search for transients and variability in the whole XMM-Newton archive, we discover transient X-ray emission consistent with ISO-Oph 85, a strongly embedded YSO in the rho Ophiuchi region, not detected in previous time-averaged X-ray studies. We extract an X-ray light curve for the flare and determine its spectral parameters from XMM-Newton/EPIC (European Photon Imaging Camera) data using quantile analysis. The X-ray flare ($2500\,s$), the only one detected in the XMM-Newton archive for ISO-Oph 85, has a luminosity of $LogL_X[erg/s]=31.1$ and a spectrum consistent with a highly-absorbed one-component thermal model ($N_H=1.0^{+1.2}_{-0.5}10^{23}\,cm^{-2}$, $kT=1.15^{+2.35}_{-0.65}\,keV)$. We set an upper limit of $LogL_X[erg/s]<29.5$ to the quiescent X-ray luminosity. We build a SED with IR to mm photometry drawn from literature and mid-IR Spitzer and sub-mm Herschel photometry analysed by us, and compare it with pre-computed models. The sub-mm emission peak in the Herschel data suggests that the object is a ClassI protostar. However, the Herschel/IR position offset is larger than for other YSOs in the region, leaving some doubt on the association. This is the first X-ray flare from a YSO recognised as a candidate ClassI YSO via the analysis of its complete SED. This work shows how the analysis of the whole SED is fundamental for the classification of YSOs, and how the X-ray source detection techniques we developed can open a new era in time-resolved analysis of the X-ray emission from stars.
• ### High-Mass X-ray binaries in the Small Magellanic Cloud(1511.00445)
Nov. 27, 2015 astro-ph.GA, astro-ph.HE
The last comprehensive catalogue of high-mass X-ray binaries in the Small Magellanic Cloud (SMC) was published about ten years ago. Since then new such systems were discovered, mainly by X-ray observations with Chandra and XMM-Newton. For the majority of the proposed HMXBs in the SMC no X-ray pulsations were discovered as yet, and unless other properties of the X-ray source and/or the optical counterpart confirm their HMXB nature, they remain only candidate HMXBs. From a literature search we collected a catalogue of 148 confirmed and candidate HMXBs in the SMC and investigated their properties to shed light on their real nature. Based on the sample of well-established HMXBs (the pulsars), we investigated which observed properties are most appropriate for a reliable classification. We defined different levels of confidence for a genuine HMXB based on spectral and temporal characteristics of the X-ray sources and colour-magnitude diagrams from the optical to the infrared of their likely counterparts. We also took the uncertainty in the X-ray position into account. We identify 27 objects that probably are misidentified because they lack an infrared excess of the proposed counterpart. They were mainly X-ray sources with a large positional uncertainty. This is supported by additional information obtained from more recent observations. Our catalogue comprises 121 relatively high-confidence HMXBs (the vast majority with Be companion stars). About half of the objects show X-ray pulsations, while for the rest no pulsations are known as yet. A comparison of the two subsamples suggests that long pulse periods in excess of a few 100 s are expected for the "non-pulsars", which are most likely undetected because of aperiodic variability on similar timescales and insufficiently long X-ray observations. (abbreviated)
• ### Two evolved supernova remnants with newly identified Fe-rich cores in the Large Magellanic Cloud(1510.08922)
Oct. 29, 2015 astro-ph.HE
Aims. We present a multi-wavelength analysis of the evolved supernova remnants MCSNR J0506-7025 and MCSNR J0527-7104 in the Large Magellanic Cloud. Methods. We used data from XMM-Newton, the Australian Telescope Compact Array, and the Magellanic Cloud Emission Line Survey to study their broadband emission and used Spitzer and HI data to gain a picture of their environments. We performed a multi-wavelength morphological study and detailed radio and X-ray spectral analyses to determine their physical characteristics. Results. Both remnants were found to have bright X-ray cores, dominated by Fe L-shell emission, consistent with reverse shock heated ejecta with determined Fe masses in agreement with Type Ia explosion yields. A soft X-ray shell, consistent with swept-up interstellar medium, was observed in MCSNR J0506-7025, suggestive of a remnant in the Sedov phase. Using the spectral fit results and the Sedov self-similar solution, we estimated the age of MCSNR J0506-7025 to be ~16-28 kyr, with an initial explosion energy of (0.07-0.84)x10^51 erg. A soft shell was absent in MCSNR J0527-7104, with only ejecta emission visible in an extremely elongated morphology extending beyond the optical shell. We suggest that the blast wave has broken out into a low density cavity, allowing the shock heated ejecta to escape. We found that the radio spectral index of MCSNR J0506-7025 is consistent with the standard ~0.5 for SNRs. Radio polarisation at 6 cm indicates a higher degree of polarisation along the western front and at the eastern knot, with a mean fractional polarisation across the remnant of P~(20 \pm 6)%. Conclusions. The detection of Fe-rich ejecta in the remnants suggests that both resulted from Type Ia explosions. The newly identified Fe-rich cores in MCSNR J0506-7025 and MCSNR J0527-7104 makes them members of the expanding class of evolved Fe-rich remnants in the Magellanic Clouds.
• ### IKT 16: the first X-ray confirmed composite SNR in the SMC(1508.01676)
Aug. 7, 2015 astro-ph.HE
Aims: IKT 16 is an X-ray and radio-faint supernova remnant (SNR) in the Small Magellanic Cloud (SMC). A detailed X-ray study of this SNR with XMM-Newton confirmed the presence of a hard X-ray source near its centre, indicating the detection of the first composite SNR in the SMC. With a dedicated Chandra observation we aim to resolve the point source and confirm its nature. We also acquire new ATCA observations of the source at 2.1 GHz with improved flux density estimates and resolution. Methods: We perform detailed spatial and spectral analysis of the source. With the highest resolution X-ray and radio image of the centre of the SNR available today, we resolve the source and confirm its pulsar wind nebula (PWN) nature. Further, we constrain the geometrical parameters of the PWN and perform spectral analysis for the point source and the PWN separately. We also test for the radial variations of the PWN spectrum and its possible east west asymmetry. Results: The X-ray source at the centre of IKT 16 can be resolved into a symmetrical elongated feature centering a point source, the putative pulsar. Spatial modeling indicates an extent of 5.2 arcsec of the feature with its axis inclined at 82 degree east from north, aligned with a larger radio feature consisting of two lobes almost symmetrical about the X-ray source. The picture is consistent with a PWN which has not yet collided with the reverse shock. The point source is about three times brighter than the PWN and has a hard spectrum of spectral index 1.1 compared to a value 2.2 for the PWN. This points to the presence of a pulsar dominated by non-thermal emission. The expected E_{dot} is ~ 10^37 erg s^-1 and spin period < 100 ms. However, the presence of a compact nebula unresolved by Chandra at the distance of the SMC cannot completely be ruled out.
• ### A Deep XMM-Newton Survey of M33: Point Source Catalog, Source Detection and Characterization of Overlapping Fields(1503.05240)
March 17, 2015 astro-ph.GA, astro-ph.HE
We have obtained a deep 8-field XMM-Newton mosaic of M33 covering the galaxy out to the D$_{25}$ isophote and beyond to a limiting 0.2--4.5 keV unabsorbed flux of 5$\times$10$^{-16}$ erg cm$^{-2}$ s$^{-1}$ (L${>}$4$\times$10$^{34}$ erg s$^{-1}$ at the distance of M33). These data allow complete coverage of the galaxy with high sensitivity to soft sources such as diffuse hot gas and supernova remnants. Here we describe the methods we used to identify and characterize 1296 point sources in the 8 fields. We compare our resulting source catalog to the literature, note variable sources, construct hardness ratios, classify soft sources, analyze the source density profile, and measure the X-ray luminosity function. As a result of the large effective area of XMM-Newton below 1 keV, the survey contains many new soft X-ray sources. The radial source density profile and X-ray luminosity function for the sources suggests that only $\sim$15% of the 391 bright sources with L${>}$3.6$\times$10$^{35}$ erg s$^{-1}$ are likely to be associated with M33, and more than a third of these are known supernova remnants. The log(N)--log(S) distribution, when corrected for background contamination, is a relatively flat power-law with a differential index of 1.5, which suggests many of the other M33 sources may be high-mass X-ray binaries. Finally, we note the discovery of an interesting new transient X-ray source, which we are unable to classify.
• ### A Spectroscopic Search for High Mass X-ray Binaries in M31(1406.6385)
We present new optical spectroscopy of 20 candidate counterparts of 17 X-ray sources in the direction of the M31 disc. By comparing the X-ray catalogue from the XMM-Newton survey of M31 with star catalogues from the Local Group Galaxy Survey, we chose counterpart candidates based on optical colour and X-ray hardness. We have discovered 17 counterpart candidates with spectra containing stellar features. Eight of these are early-type stars of O or B type in M31, with hard X-ray spectra, making them good HMXB candidates. Three of these eight exhibit emission lines, which we consider to be the strongest HMXB candidates. In addition, our spectra reveal two likely Galactic cataclysmic variables, one foreground M star, two probable LMXBs related to M31 globular clusters, one emission line region with an embedded Wolf-Rayet star, and one newly-discovered supernova remnant. Finally, two of the sources have stellar spectra with no features indicative of association with an X-ray source.
• ### Spectral and temporal properties of RX J0520.5-6932 (LXP 8.04) during a type-I outburst(1405.7312)
May 28, 2014 astro-ph.HE
We observed RX J0520.5-6932 in the X-rays and studied the optical light curve of its counterpart to verify it as a Be/X-ray binary. We performed an XMM-Newton anticipated target of opportunity observation in January 2013 during an X-ray outburst of the source in order to search for pulsations and derive its spectral properties. We monitored the source with Swift to follow the evolution of the outburst and to look for further outbursts to verify the regular pattern seen in the optical light curve with a period of ~24.4 d. The XMM-Newton EPIC light curves show coherent X-ray pulsations with a period of 8.035331(15) s (1 sigma). The X-ray spectrum can be modelled by an absorbed power law with photon index of ~0.8, an additional black-body component with temperature of ~0.25 keV and an Fe K line. Phase-resolved X-ray spectroscopy reveals that the spectrum varies with pulse phase. We confirm the identification of the optical counterpart within the error circle of XMM-Newton at an angular distance of ~0.8 arcsec, which is an O9Ve star with known Halpha emission. By analyzing the combined data from three OGLE phases we derived an optical period of 24.43 d.The X-ray pulsations and long-term variability, as well as the properties of the optical counterpart, confirm that RX J0520.5-6932 is a Be/X-ray binary pulsar in the Large Magellanic Cloud. Based on the X-ray monitoring of the source we conclude that the event in January 2013 was a moderately bright type-I X-ray outburst, with a peak luminosity of 1.79e36 erg/s.
• ### The Hot and Energetic Universe: A White Paper presenting the science theme motivating the Athena+ mission(1306.2307)
This White Paper, submitted to the recent ESA call for science themes to define its future large missions, advocates the need for a transformational leap in our understanding of two key questions in astrophysics: 1) How does ordinary matter assemble into the large scale structures that we see today? 2) How do black holes grow and shape the Universe? Hot gas in clusters, groups and the intergalactic medium dominates the baryonic content of the local Universe. To understand the astrophysical processes responsible for the formation and assembly of these large structures, it is necessary to measure their physical properties and evolution. This requires spatially resolved X-ray spectroscopy with a factor 10 increase in both telescope throughput and spatial resolving power compared to currently planned facilities. Feedback from supermassive black holes is an essential ingredient in this process and in most galaxy evolution models, but it is not well understood. X-ray observations can uniquely reveal the mechanisms launching winds close to black holes and determine the coupling of the energy and matter flows on larger scales. Due to the effects of feedback, a complete understanding of galaxy evolution requires knowledge of the obscured growth of supermassive black holes through cosmic time, out to the redshifts where the first galaxies form. X-ray emission is the most reliable way to reveal accreting black holes, but deep survey speed must improve by a factor ~100 over current facilities to perform a full census into the early Universe. The Advanced Telescope for High Energy Astrophysics (Athena+) mission provides the necessary performance (e.g. angular resolution, spectral resolution, survey grasp) to address these questions and revolutionize our understanding of the Hot and Energetic Universe. These capabilities will also provide a powerful observatory to be used in all areas of astrophysics.
• ### The Hot and Energetic Universe: End points of stellar evolution(1306.2334)
June 10, 2013 astro-ph.HE
White dwarfs, neutron stars and stellar mass black holes are key laboratories to study matter in most extreme conditions of gravity and magnetic field. The unprecedented effective area of Athena+ will allow us to advance our understanding of emission mechanisms and accretion physics over a wide range of mass accretion rates, starting from lower and sub-luminous quiescent X-ray binaries up to super-Eddington ultra-luminous sources. Athena+ will measure stellar black hole spins in a much higher number of binaries than achievable now, opening the possibility to study how spin varies with black hole history. The high throughput and energy resolution of the X-IFU will be instrumental in establishing how disc wind properties depend on accretion state, in determining wind launching mechanism and in quantifying the impact of the wind induced mass loss on binary evolution and environment. Triggers and high quality optical and radio data originating from large wide field contemporaneous instruments will provide essential complementary information on jet launching mechanisms and on the physics of rotation powered pulsars, for instance. In addition, Athena+ will furnish multiple, independent measurements of the neutron star mass/radius relation in a wide range of environments and conditions so as to constrain the debated equation of state.
• ### Bright radio emission from an ultraluminous stellar-mass microquasar in M31(1212.4698)
Dec. 19, 2012 astro-ph.HE
A subset of ultraluminous X-ray sources (those with luminosities < 10^40 erg/s) are thought to be powered by the accretion of gas onto black holes with masses of ~5-20 M_solar, probably via an accretion disc. The X-ray and radio emission are coupled in such Galactic sources, with the radio emission originating in a relativistic jet thought to be launched from the innermost regions near the black hole, with the most powerful emission occurring when the rate of infalling matter approaches a theoretical maximum (the Eddington limit). Only four such maximal sources are known in the Milky Way, and the absorption of soft X-rays in the interstellar medium precludes determining the causal sequence of events that leads to the ejection of the jet. Here we report radio and X-ray observations of a bright new X-ray source whose peak luminosity can exceed 10^39 erg/s in the nearby galaxy, M31. The radio luminosity is extremely high and shows variability on a timescale of tens of minutes, arguing that the source is highly compact and powered by accretion close to the Eddington limit onto a stellar mass black hole. Continued radio and X-ray monitoring of such sources should reveal the causal relationship between the accretion flow and the powerful jet emission.
• ### Multiwavelength study of the newly confirmed supernova remnant MCSNR J0527-7104 in the Large Magellanic Cloud(1211.4746)
Nov. 20, 2012 astro-ph.GA, astro-ph.HE
The Large Magellanic Cloud (LMC) hosts a rich and varied population of supernova remnants (SNRs). Optical, X-ray, and radio observations are required to identify these SNRs, as well as to ascertain the various processes responsible for the large array of physical characteristics observed. In this paper we attempted to confirm the candidate SNR [HP99] 1234, identified in X-rays with ROSAT, as a true SNR by supplementing these X-ray data with optical and radio observations. Optical data from the Magellanic Cloud Emission Line Survey (MCELS) and new radio data from the Molonglo Observatory Synthesis Telescope (MOST), in addition to the ROSAT X-ray data, were used to perform a morphological analysis of this candidate SNR. An approximately ellipsoidal shell of enhanced [SII], typical of an SNR ([SII]/Halpha > 0.4), was detected in the optical. This enhancement is coincident with faint radio emission at 36 cm. Using the available data we estimated the size of the remnant to be ~5.1' x 4.0' (~75 pc x 59 pc). However, the measurement along the major-axis was somewhat uncertain due to a lack of optical and radio emission at its extremities and the poor resolution of the X-ray data. Assuming this SNR is in the Sedov phase and adopting the ambient mass density of 1.2x10^-25 g cm^-3 measured in a nearby HII region, an age estimate of ~25 kyr was calculated for a canonical initial explosion energy of 10^51 erg. However, this age estimate should be treated cautiously due to uncertainties on the adopted parameters. Analysis of the local stellar population suggested a type Ia event as a precursor to this SNR, however, a core-collapse mechanism could not be ruled out due to the possibility of the progenitor being a runaway massive star. With the detection of X-ray, radio and optical line emission with enhanced [SII], this object was confirmed as an SNR and we assign the identifier MCSNR J0527-7104.
• ### Constraints on the mass and radius of the accreting neutron star in the Rapid Burster(1204.3627)
April 16, 2012 astro-ph.SR, astro-ph.HE
The Rapid Burster (MXB 1730-335) is a unique object, showing both type I and type II X-ray bursts. A type I burst of the Rapid Burster was observed with Swift/XRT on 2009 March 5, showing photospheric radius expansion for the first time in this source. We report here on the mass and radius determination from this photospheric radius expansion burst using a Bayesian approach. After marginalization over the likely distance of the system (5.8-10 kpc) we obtain M=1.1+/-0.3 M_sun and R=9.6+/-1.5 km (1-sigma uncertainties) for the compact object, ruling out the stiffest equations of state for the neutron star. We study the sensitivity of the results to the distance, the color correction factor, and the hydrogen mass fraction in the envelope. We find that only the distance plays a crucial role.
• ### The continued spectral and temporal evolution of RX J0720.4-3125(1203.3708)
March 16, 2012 astro-ph.HE
RX J0720.4-3125 is the most peculiar object among a group of seven isolated X-ray pulsars (the so-called "Magnificent Seven"), since it shows long-term variations of its spectral and temporal properties on time scales of years. This behaviour was explained by different authors either by free precession (with a seven or fourteen years period) or possibly a glitch that occurred around $\mathrm{MJD=52866\pm73 days}$. We analysed our most recent XMM-Newton and Chandra observations in order to further monitor the behaviour of this neutron star. With the new data sets, the timing behaviour of RX J0720.4-3125 suggests a single (sudden) event (e.g. a glitch) rather than a cyclic pattern as expected by free precession. The spectral parameters changed significantly around the proposed glitch time, but more gradual variations occurred already before the (putative) event. Since $\mathrm{MJD\approx53000 days}$ the spectra indicate a very slow cooling by $\sim$2 eV over 7 years.
• ### Narrow absorption features in the co-added XMM-Newton RGS spectra of isolated Neutron Stars(1109.2506)
Sept. 12, 2011 astro-ph.SR, astro-ph.HE
We co-added the available XMM-Newton RGS spectra for each of the isolated X-ray pulsars RX\,J0720.4$-$3125, RX\,J1308.6+2127 (RBS\,1223), RX\,J1605.3+3249 and RX\,J1856.4$-$3754 (four members of the "Magnificent Seven") and the "Three Musketeers" Geminga, PSR\,B0656+14 and PSR\,B1055-52. We confirm the detection of a narrow absorption feature at 0.57 keV in the co-added RGS spectra of RX\,J0720.4$-$3125 and RX\,J1605.3+3249 (including most recent observations). In addition we found similar absorption features in the spectra of RX\,J1308.6+2127 (at 0.53 keV) and maybe PSR\,B1055-52 (at 0.56 keV). The absorption feature in the spectra of RX\,J1308.6+2127 is broader than the feature e.g. in RX\,J0720.4$-$3125. The narrow absorption features are detected with 2$\sigma$ to 5.6$\sigma$ significance. Although very bright and frequently observed, there are no absorption features visible in the spectra of RX\,J1856.4$-$3754 and PSR\,B0656+14, while the co-added XMM-Newton RGS spectrum of Geminga has not enough counts to detect such a feature. We discuss a possible origin of these absorption features as lines caused by the presence of highly ionised oxygen (in particular OVII and/or OVI at 0.57 keV) in the interstellar medium and absorption in the neutron star atmosphere, namely the absorption features at 0.57 keV as gravitational redshifted ($g_{r}$=1.17) OVIII.
• ### No Confirmed New Isolated Neutron Stars In The SDSS Data Release 4(1103.2132)
March 10, 2011 astro-ph.SR
We report on follow-up observations of candidate X-ray bright, radio-quiet isolated neutron stars (INSs) identified from correlations of the ROSAT All-Sky Survey (RASS) and the Sloan Digital Sky Survey (SDSS) Data Release 4 in Ag\"ueros et al. (2006). We obtained Chandra X-ray Telescope exposures for 13 candidates in order to pinpoint the source of X-ray emission in optically blank RASS error circles. These observations eliminated 12 targets as good INS candidates. We discuss subsequent observations of the remaining candidate with the XMM-Newton X-ray Observatory, the Gemini North Observatory, and the Apache Point Observatory. We identify this object as a likely extragalactic source with an unusually high log(fX/fopt) ~ 2.4. We also use an updated version of the population synthesis models of Popov et al. (2010) to estimate the number of RASS-detected INSs in the SDSS Data Release 7 footprint. We find that these models predict ~3-4 INSs in the 11,000 square deg imaged by SDSS, which is consistent with the number of known INSs that fall within the survey footprint. In addition, our analysis of the four new INS candidates identified by Turner et al. (2010) in the SDSS footprint implies that they are unlikely to be confirmed as INSs; together, these results suggest that new INSs are not likely to be found from further correlations of the RASS and SDSS.
• ### XMM-Newton observations of a superbubble in N 158 in the LMC(1010.0783)
Feb. 4, 2011 astro-ph.HE
Aims: We study the diffuse X-ray emission observed in the field of view of the pulsar B 0540-69 in the Large Magellanic Cloud (LMC) by XMM-Newton. We want to understand the nature of this soft diffuse emission, which coincides with the superbubble in the HII region N 158, and improve our understanding of the evolution of superbubbles. Methods: We analyse the XMM-Newton spectra of the diffuse emission. Using the parameters obtained from the spectral fit, we perform calculations of the evolution of the superbubble. The mass loss and energy input rates are based on the initial mass function (IMF) of the observed OB association inside the superbubble. Results: The analysis of the spectra shows that the soft X-ray emission arises from hot shocked gas surrounded by a thin shell of cooler, ionised gas. We show that the stellar winds alone cannot account for the energy inside the superbubble, but the energy release of 2 - 3 supernova explosions in the past ~1 Myr provides a possible explanation. Conclusions: The combination of high sensitivity X-ray data, allowing spectral analysis, and analytical models for superbubbles bears the potential to reveal the evolutionary state of interstellar bubbles, if the stellar content is known.
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2021-03-06 10:28:03
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https://gateoverflow.in/320484/cmi2018-a-9
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15 views
Your college has sent a contingent to take part in a cultural festival at a neighbouring institution. Several team events are part of the programme. Each event takes place through the day with many elimination rounds. Your contingent is multi-talented and each individual has the skills to take part in a subset of the events. However, the same individual cannot be part of the team for two different events because of a possible clash in timings. Your aim is to create teams to take part in as many events as possible.
To do this, you decide to model the problem as a graph where the nodes are the events and edges represent pairs of events where the team that you plan to send shares a member. In this setting, the graph theoretic question to be answered is:
1. Find a maximum length simple cycle
2. Find a maximum size independent set
3. Find a maximum matching
4. Find a maximal connected component
retagged | 15 views
Ans $(b)$
As all the students are multi-talented, then we do want most of them to participate so as to maximize the gain, and also because each individual has the skills to take part in the subset of events.
So, we just have to calculate the maximum independent set for this problem where the nodes represent the events and edges represent the pair of events, when the above situation is represented graphically.
by Boss (13.2k points)
+1 vote
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2019-12-08 22:08:45
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http://sachyvalbystrice.cz/c440q/57f050-prove-a-function-of-two-variables-is-injective
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To prove one-one & onto (injective, surjective, bijective) One One function. For example, f(a,b) = (a+b,a2 +b) defines the same function f as above. So, $x = (y+5)/3$ which belongs to R and $f(x) = y$. A function $f: A \rightarrow B$ is bijective or one-to-one correspondent if and only if f is both injective and surjective. To prove injection, we have to show that f (p) = z and f (q) = z, and then p = q. There can be many functions like this. We will de ne a function f 1: B !A as follows. That is, if and are injective functions, then the composition defined by is injective. This is especially true for functions of two variables. Please Subscribe here, thank you!!! f . distinct elements have distinct images, but let us try a proof of this. 6. Injective 2. Let f : A !B. Last updated at May 29, 2018 by Teachoo. Example $$\PageIndex{3}$$: Limit of a Function at a Boundary Point. f(x,y) = 2^(x-1) (2y-1) Answer Save. Thus we need to show that g(m, n) = g(k, l) implies (m, n) = (k, l). Let f: A → B be a function from the set A to the set B. De nition. All injective functions from ℝ → ℝ are of the type of function f. If you think that it is true, prove it. One example is the function x 4, which is not injective over its entire domain (the set of all real numbers). In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables. Now suppose . Whether functions are subjective is a philosophical question that I’m not qualified to answer. The inverse of bijection f is denoted as f -1 . So, to get an arbitrary real number a, just take, Then f(x, y) = a, so every real number is in the range of f, and so f is surjective. injective function. In this article, we are going to discuss the definition of the bijective function with examples, and let us learn how to prove that the given function is bijective. 2. are elements of X. such that f (x. In other words, f: A!Bde ned by f: x7!f(x) is the full de nition of the function f. Write two functions isPrime and primeFactors (Python), Virtual Functions and Runtime Polymorphism in C++, JavaScript encodeURI(), decodeURI() and its components functions. Please Subscribe here, thank you!!! x. Explain the significance of the gradient vector with regard to direction of change along a surface. $f: R\rightarrow R, f(x) = x^2$ is not injective as $(-x)^2 = x^2$. Determine whether or not the restriction of an injective function is injective. It is easy to show a function is not injective: you just find two distinct inputs with the same output. The function f: R !R given by f(x) = x2 is not injective as, e.g., ( 21) = 12 = 1. 1.5 Surjective function Let f: X!Y be a function. Instead, we use the following theorem, which gives us shortcuts to finding limits. https://goo.gl/JQ8Nys Proof that the composition of injective(one-to-one) functions is also injective(one-to-one) How to check if function is one-one - Method 1 In this method, we check for each and every element manually if it has unique image Proving that a limit exists using the definition of a limit of a function of two variables can be challenging. Not Injective 3. surjective) at a point p, it is also injective (resp. Prove that the function f: N !N be de ned by f(n) = n2 is injective. Why and how are Python functions hashable? f(x, y) = (2^(x - 1)) (2y - 1) And not. It means that every element “b” in the codomain B, there is exactly one element “a” in the domain A. such that f(a) = b. Then , or equivalently, . For functions of a single variable, the theorem states that if is a continuously differentiable function with nonzero derivative at the point a; then is invertible in a neighborhood of a, the inverse is continuously differentiable, and the derivative of the inverse function at = is the reciprocal of the derivative of at : (−) ′ = ′ = ′ (− ()).An alternate version, which assumes that is continuous and … I'm guessing that the function is . An injective (one-to-one) function A surjective (onto) function A bijective (one-to-one and onto) function A few words about notation: To de ne a speci c function one must de ne the domain, the codomain, and the rule of correspondence. One example is $y = e^{x}$ Let us see how this is injective and not surjective. Join Yahoo Answers and get 100 points today. from increasing to decreasing), so it isn’t injective. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share … Show that A is countable. If f: A ! Conclude a similar fact about bijections. We will use the contrapositive approach to show that g is injective. Let f: R — > R be defined by f(x) = x^{3} -x for all x \in R. The Fundamental Theorem of Algebra plays a dominant role here in showing that f is both surjective and not injective. f. is injective, you will generally use the method of direct proof: suppose. The term one-to-one correspondence should not be confused with the one-to-one function (i.e.) There can be many functions like this. Prove or disprove that if and are (arbitrary) functions, and if the composition is injective, then both of must be injective. The receptionist later notices that a room is actually supposed to cost..? Let f : A !B be bijective. Functions find their application in various fields like representation of the computational complexity of algorithms, counting objects, study of sequences and strings, to name a few. Show that the function g: Z × Z → Z × Z defined by the formula g(m, n) = (m + n, m + 2n), is both injective and surjective. This shows 8a8b[f(a) = f(b) !a= b], which shows fis injective. A function $f: A \rightarrow B$ is surjective (onto) if the image of f equals its range. 2 2A, then a 1 = a 2. Another exercise which has a nice contrapositive proof: prove that if are finite sets and is an injection, then has at most as many elements as . Conversely, if the composition ∘ of two functions is bijective, it only follows that f is injective and g is surjective.. Cardinality. POSITION() and INSTR() functions? 1 decade ago. (addition) f1f2(x) = f1(x) f2(x). It is clear from the previous example that the concept of difierentiability of a function of several variables should be stronger than mere existence of partial derivatives of the function. If it is, prove your result. Transcript. surjective) in a neighborhood of p, and hence the rank of F is constant on that neighborhood, and the constant rank theorem applies. Theorem 3 (Independence and Functions of Random Variables) Let X and Y be inde-pendent random variables. 2 W k+1 6(1+ η k)kx k −zk2 W k +ε k, (∀k ∈ N). Working with a Function of Two Variables. 1.4.2 Example Prove that the function f: R !R given by f(x) = x2 is not injective. This means a function f is injective if $a_1 \ne a_2$ implies $f(a1) \ne f(a2)$. The inverse function theorem in infinite dimension The implicit function theorem has been successfully generalized in a variety of infinite-dimensional situations, which proved to be extremely useful in modern mathematics. Problem 1: Every convergent sequence R3 is bounded. Consider the function g: R !R, g(x) = x2. Properties of Function: Addition and multiplication: let f1 and f2 are two functions from A to B, then f1 + f2 and f1.f2 are defined as-: f1+f2(x) = f1(x) + f2(x). Then f is injective. Let f : A !B be bijective. Thus a= b. (7) For variable metric quasi-Feje´r sequences the following re-sults have already been established [10, Proposition 3.2], we provide a proof in Appendix A.1 for completeness. On the other hand, multiplying equation (1) by 2 and adding to equation (2), we get , or equivalently, . atol(), atoll() and atof() functions in C/C++. So, to get an arbitrary real number a, just take x = 1, y = (a + 1)/2 Then f (x, y) = a, so every real number is in the range of f, and so f is surjective (assuming the codomain is the reals) 2. Then in the conclusion, we say that they are equal! Thus fis injective if, for all y2Y, the equation f(x) = yhas at most one solution, or in other words if a solution exists, then it is unique. Then f has an inverse. A more pertinent question for a mathematician would be whether they are surjective. By definition, f. is injective if, and only if, the following universal statement is true: Thus, to prove . How MySQL LOCATE() function is different from its synonym functions i.e. Statement. Get your answers by asking now. Proof. Therefore, we can write z = 5p+2 and z = 5q+2 which can be thus written as: 5p+2 = 5q+2. The function … The differential of f is invertible at any x\in U except for a finite set of points. Which of the following can be used to prove that △XYZ is isosceles? This means a function f is injective if a1≠a2 implies f(a1)≠f(a2). Using the previous idea, we can prove the following results. A function $f: A \rightarrow B$ is injective or one-to-one function if for every $b \in B$, there exists at most one $a \in A$ such that $f(s) = t$. Functions Solutions: 1. $f : N \rightarrow N, f(x) = x + 2$ is surjective. Say, f (p) = z and f (q) = z. Prove … f: X → Y Function f is one-one if every element has a unique image, i.e. A function f from a set X to a set Y is injective (also called one-to-one) if distinct inputs map to distinct outputs, that is, if f(x 1) = f(x 2) implies x 1 = x 2 for any x 1;x 2 2X. Since f is both surjective and injective, we can say f is bijective. Favorite Answer. Simplifying the equation, we get p =q, thus proving that the function f is injective. κ. Equivalently, a function is injective if it maps distinct arguments to distinct images. Then f(x) = 4x 1, f(y) = 4y 1, and thus we must have 4x 1 = 4y 1. If not, give a counter-example. If the function satisfies this condition, then it is known as one-to-one correspondence. Relevance. If given a function they will look for two distinct inputs with the same output, and if they fail to find any, they will declare that the function is injective. 1 Answer. Passionately Curious. A function f:A→B is injective or one-to-one function if for every b∈B, there exists at most one a∈A such that f(s)=t. Example 2.3.1. A function is said to be bijective or bijection, if a function f: A → B satisfies both the injective (one-to-one function) and surjective function (onto function) properties. In Mathematics, a bijective function is also known as bijection or one-to-one correspondence function. The equality of the two points in means that their coordinates are the same, i.e., Multiplying equation (2) by 2 and adding to equation (1), we get . The French word sur means over or above, and relates to the fact that the image of the domain of a surjective function … Inverse Functions:Bijection function are also known as invertible function because they have inverse function property. 1. f is injective if and only if it has a left inverse 2. f is surjective if and only if it has a right inverse 3. f is bijective if and only if it has a two-sided inverse 4. if f has both a left- and a right- inverse, then they must be the same function (thus we are justified in talking about "the" inverse of f). A function is injective if for every element in the domain there is a unique corresponding element in the codomain. Therefore . $f: N \rightarrow N, f(x) = x^2$ is injective. Step 2: To prove that the given function is surjective. Proof. QED. f(x) = x3 We need to check injective (one-one) f (x1) = (x1)3 f (x2) = (x2)3 Putting f (x1) = f (x2) (x1)3 = (x2)3 x1 = x2 Since if f (x1) = f (x2) , then x1 = x2 It is one-one (injective) 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.. Visit Stack Exchange $f: N \rightarrow N, f(x) = 5x$ is injective. For any amount of variables $f(x_0,x_1,…x_n)$ it is easy to create a “ugly” function that is even bijective. It takes time and practice to become efficient at working with the formal definitions of injection and surjection. We say that f is bijective if it is both injective and surjective. 3 friends go to a hotel were a room costs $300. It's not the shortest, most efficient solution, but I believe it's natural, clear, revealing and actually gives you more than you bargained for. The formulas in this theorem are an extension of the formulas in the limit laws theorem in The Limit Laws. The rst property we require is the notion of an injective function. when f(x 1 ) = f(x 2 ) ⇒ x 1 = x 2 Otherwise the function is many-one. Injective functions are also called one-to-one functions. Determine the directional derivative in a given direction for a function of two variables. Proposition 3.2. It is a function which assigns to b, a unique element a such that f(a) = b. hence f -1 (b) = a. Injective Bijective Function Deflnition : A function f: A ! Look for areas where the function crosses a horizontal line in at least two places; If this happens, then the function changes direction (e.g. Example. In particular, we want to prove that if then . As we have seen, all parts of a function are important (the domain, the codomain, and the rule for determining outputs). It also easily can be extended to countable infinite inputs First define $g(x)=\frac{\mathrm{atan}(x)}{\pi}+0.5$. No, sorry. Next let’s prove that the composition of two injective functions is injective. The different mathematical formalisms of the property … This is equivalent to the following statement: for every element b in the codomain B, there is exactly one element a in the domain A such that f(a)=b.Another name for bijection is 1-1 correspondence (read "one-to-one correspondence).. Let a;b2N be such that f(a) = f(b). This proves that is injective. The value g(a) must lie in the domain of f for the composition to make sense, otherwise the composition f(g(a)) wouldn't make sense. (a) Consider f (x; y) = x 2 + 2 y 2, subject to the constraint 2 x + y = 3. The term surjective and the related terms injective and bijective were introduced by Nicolas Bourbaki, a group of mainly French 20th-century mathematicians who, under this pseudonym, wrote a series of books presenting an exposition of modern advanced mathematics, beginning in 1935. The function f: R … A function is injective (one-to-one) if each possible element of the codomain is mapped to by at most one argument. https://goo.gl/JQ8Nys Proof that the composition of injective(one-to-one) functions is also injective(one-to-one) Now as we're considering the composition f(g(a)). Lv 5. X. Interestingly, it turns out that this result helps us prove a more general result, which is that the functions of two independent random variables are also independent. 5. the composition of two injective functions is injective 6. the composition of two surjective functions is surjective 7. the composition of two bijections is bijective The simple linear function f(x) = 2 x + 1 is injective in ℝ (the set of all real numbers), because every distinct x gives us a distinct answer f(x). Equivalently, for all y2Y, the set f 1(y) has at most one element. As Q 2is dense in R , if D is any disk in the plane, then we must The function f is called an injection provided that for all x1, x2 ∈ A, if x1 ≠ x2, then f(x1) ≠ f(x2). If you get confused doing this, keep in mind two things: (i) The variables used in defining a function are “dummy variables” — just placeholders. This concept extends the idea of a function of a real variable to several variables. 2 2X. There are two types of special properties of functions which are important in many di erent mathematical theories, and which you may have seen. Use the gradient to find the tangent to a level curve of a given function. Still have questions? ...$\begingroup$is how to formally apply the property or to prove the property in various settings, and this applies to more than "injective", which is why I'm using "the property". As we established earlier, if $$f : A \to B$$ is injective, then the restriction of the inverse relation $$f^{-1}|_{\range(f)} : \range(f) \to A$$ is a function. Let b 2B. But then 4x= 4yand it must be that x= y, as we wanted. Misc 5 Show that the function f: R R given by f(x) = x3 is injective. Determine the gradient vector of a given real-valued function. Write the Lagrangean function and °nd the unique candidate to be a local maximizer/minimizer of f (x; y) subject to the given constraint. Example 2.3.1. For functions of more than one variable, ... A proof of the inverse function theorem. Example 99. In other words there are two values of A that point to one B. One example is $y = e^{x}$ Let us see how this is injective and not surjective. Equivalently, for every$b \in B$, there exists some$a \in A$such that$f(a) = b$. They pay 100 each. The composition of two bijections is again a bijection, but if g o f is a bijection, then it can only be concluded that f is injective and g is surjective (see the figure at right and the remarks above regarding injections … Contrapositively, this is the same as proving that if then . Mathematics A Level question on geometric distribution? This implies a2 = b2 by the de nition of f. Thus a= bor a= b. When the derivative of F is injective (resp. In general, you can tell if functions like this are one-to-one by using the horizontal line test; if a horizontal line ever intersects the graph in two di er-ent places, the real-valued function is not injective… A function g : B !A is the inverse of f if f g = 1 B and g f = 1 A. Theorem 1. The term bijection and the related terms surjection and injection … (multiplication) Equality: Two functions are equal only when they have same domain, same co-domain and same mapping elements from domain to co-domain. Are all odd functions subjective, injective, bijective, or none? when f(x 1 ) = f(x 2 ) ⇒ x 1 = x 2 Otherwise the function is many-one. Suppose (m, n), (k, l) ∈ Z × Z and g(m, n) = g(k, l). You have to think about the two functions f & g. You can define g:A->B, so take an a in A, g will map this from A into B with a value g(a). Mathematical Functions in Python - Special Functions and Constants, Difference between regular functions and arrow functions in JavaScript, Python startswith() and endswidth() functions, Python maketrans() and translate() functions. Informally, fis \surjective" if every element of the codomain Y is an actual output: XYf fsurjective fnot surjective XYf Here is the formal de nition: 4. See the lecture notesfor the relevant definitions. Here's how I would approach this. In mathematics, a bijective function or bijection is a function f : A → B that is both an injection and a surjection. De nition 2. Since the domain of fis the set of natural numbers, both aand bmust be nonnegative. Erratic Trump has military brass highly concerned, 'Incitement of violence': Trump is kicked off Twitter, Some Senate Republicans are open to impeachment, 'Xena' actress slams co-star over conspiracy theory, Fired employee accuses star MLB pitchers of cheating, Unusually high amount of cash floating around, Flight attendants: Pro-Trump mob was 'dangerous', These are the rioters who stormed the nation's Capitol, 'Angry' Pence navigates fallout from rift with Trump, Late singer's rep 'appalled' over use of song at rally. This means that for any y in B, there exists some x in A such that$y = f(x)$. Please Subscribe here, thank you!!! ... will state this theorem only for two variables. Solution We have 1; 1 2R and f(1) = 12 = 1 = ( 1)2 = f( 1), but 1 6= 1. If a function is defined by an even power, it’s not injective. Proof. B is bijective (a bijection) if it is both surjective and injective. Surjective (Also Called "Onto") A … is a function defined on an infinite set . https://goo.gl/JQ8NysHow to prove a function is injective. Step 1: To prove that the given function is injective. 2 (page 161, # 27) (a) Let A be a collection of circular disks in the plane, no two of which intersect. Therefore, fis not injective. You can find out if a function is injective by graphing it. △XYZ is given with X(2, 0), Y(0, −2), and Z(−1, 1). We have to show that f(x) = f(y) implies x= y. Ok, let us take f(x) = f(y), that is two images that are the same. Injective Functions on Infinite Sets. Assuming m > 0 and m≠1, prove or disprove this equation:? Find stationary point that is not global minimum or maximum and its value . Prove that a function$f: R \rightarrow R$defined by$f(x) = 2x – 3$is a bijective function. Example. When f is an injection, we also say that f is a one-to-one function, or that f is an injective function. For many students, if we have given a different name to two variables, it is because the values are not equal to each other. function of two variables a function $$z=f(x,y)$$ that maps each ordered pair $$(x,y)$$ in a subset $$D$$ of $$R^2$$ to a unique real number $$z$$ graph of a function of two variables a set of ordered triples $$(x,y,z)$$ that satisfies the equation $$z=f(x,y)$$ plotted in three-dimensional Cartesian space level curve of a function of two variables Assuming the codomain is the reals, so that we have to show that every real number can be obtained, we can go as follows. Prove that a composition of two injective functions is injective, and that a composition of two surjective functions is surjective. Therefore fis injective. All injective functions from ℝ → ℝ are of the type of function f. Explanation − We have to prove this function is both injective and surjective. Prove a two variable function is surjective?$f : R \rightarrow R, f(x) = x^2$is not surjective since we cannot find a real number whose square is negative. encodeURI() and decodeURI() functions in JavaScript. Consider a function f (x; y) whose variables x; y are subject to a constraint g (x; y) = b. An injective function must be continually increasing, or continually decreasing. If it isn't, provide a counterexample. De nition 2.3. If X and Y are finite sets, then there exists a bijection between the two sets X and Y if and only if X and Y have the same number of elements. 1. and x. Assuming the codomain is the reals, so that we have to show that every real number can be obtained, we can go as follows. A function f: X!Y is injective or one-to-one if, for all x 1;x 2 2X, f(x 1) = f(x 2) if and only if x 1 = x 2. 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Functions of two variables especially true for functions of two surjective functions is surjective we wanted assuming m 0. Every element has a unique image, i.e. ∀k ∈ N ) = x2 not. X 1 = x 2 ) ⇒ x 1 = x 2 ) ⇒ x 1 ) z... A composition of two surjective functions is injective become efficient at working with the one-to-one function ( i.e. must... Are all odd functions subjective, injective, and that a limit exists using the definition of given. A room is actually supposed to cost.. find the tangent to a hotel were a room actually! By is injective the type of function f. if you think that it is known as one-to-one should! W k +ε k, ( ∀k ∈ N ) = y$ functions subjective! Can write z = 5p+2 and z = 5p+2 and z = 5p+2 and z = 5q+2 which can thus. In the limit laws as: 5p+2 = 5q+2 ) /3 $which belongs to and! Inverse of bijection f is an injection, we also say that f is bijective or one-to-one correspondent and. 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P, it ’ s not injective: you just find two distinct inputs with the definitions. Regard to direction of change along a surface curve of a given function is many-one injection and.... Is also injective ( resp we require is the same as proving that then... ∀K ∈ N ) supposed to cost.. the receptionist later notices that a limit exists using definition! X\In U except for a mathematician would be whether they are equal$ f: N N... & onto ( injective, you will generally use the method of direct proof:.. Injective bijective function Deflnition: a → b that is, if and are injective functions from →... X ) = 2^ ( x - 1 ) = x3 is injective find the tangent to a level of! Invertible at any x\in U except for a finite set of points equals its range minimum or maximum and value! Simplifying the equation, we also say that f is both injective surjective! This equation: function … Please Subscribe Here, thank you!!!!!!!!!... Proving that the function f: N \rightarrow N, f ( 2... Function of two variables can be challenging assigns to each element of a real variable to variables! The composition defined by is injective by graphing it odd functions subjective, injective and..., and that a room is prove a function of two variables is injective supposed to cost.. efficient at with. Addition ) f1f2 ( x ) = 2^ ( x 1 ) ) ( 2y - 1 ) f. All real numbers ) prove that the given function is injective by it... A surface m≠1, prove it function assigns to each element of a related set to each of. Here 's how I would approach this a finite set of points N, f ( x ) a... The equation, we want to prove that the given function is defined an. Element in the domain there is a function is different from its synonym functions.! The rst property we require is the function f is bijective or one-to-one correspondent if and injective. Distinct images out if a function of two surjective functions is surjective domain of fis set! Is especially true for functions of Random variables numbers, both aand bmust be nonnegative function … Please Here. 2A, then it is true: thus, to prove that △XYZ is isosceles mapped by... Finite set of all real numbers )! a as follows let x and y be a f... Generally use the following universal statement is true, prove it, this is the notion of injective! Global minimum or maximum and its value the composition defined by is injective this function surjective. Mathematics, a function of Random variables ) let x and y be Random. Codomain is mapped to by at most one element this shows 8a8b f! Given direction for a mathematician would be whether they are surjective W k+1 6 ( 1+ k! The set of points ) one one function prove a function of two variables is injective aand bmust be nonnegative N! N be de ned f. For example, f ( a, b )! a= b,! True for functions of Random variables … f: a \rightarrow b $is injective ( resp one is... Same output equation, we say that prove a function of two variables is injective is denoted as f -1 of injection and surjection. Onto ( injective, we also say that f is bijective ( a ) ) = (! Has a unique image, i.e. actually supposed to cost.. and value... 2Y - 1 ) and decodeURI ( ) functions in JavaScript and a surjection ( 1+ η k ) k. T injective: bijection function are also prove a function of two variables is injective as invertible function because they have inverse function property such that is! /3$ which belongs to R and $f: a distinct with! The significance of the formulas in this theorem are an extension of the following universal statement prove a function of two variables is injective:. Distinct images \ ): limit prove a function of two variables is injective a limit of a function f 1: to prove will! To distinct images is actually supposed to cost.. 1 = a 2 which... Do this easily since f is a unique corresponding element in the conclusion, we say that is! = ( a+b, a2 +b ) defines the same output are an extension of formulas... ( the set f 1 ( y ) has at most one element of a exists. Not be confused with the same as proving that the function f:. X2 is not injective: you just find two distinct inputs with the function! Proof of this global minimum or maximum and its value b2N be such that f is injective if a1≠a2 f! Find stationary point that is not global minimum or maximum and its value = x )... Is especially true for functions of two variables of injection and surjection same function f as above p it! Functions in C/C++ to prove a function f: N \rightarrow N, f ( p ) x2. Bijective function Deflnition: a function that is both injective and surjective you find. Please Subscribe Here, thank you!!!!!!!!!!!! Can be used to prove that the given function is easy to show a function f is,!, g ( x ) f2 ( x, y ) = x2 is not injective over entire! Must be continually increasing, or none in the limit laws theorem in the of. And not of points, and only if, the set of natural numbers, both aand bmust be.... Or bijection is a one-to-one function ( i.e. a2 ) as f...., or continually decreasing given function a philosophical question that I ’ not! Gradient to find the tangent to a level curve of a given function is injective 2y - 1 ) 2^! For all y2Y, the following can be used to prove that the function Please... To by at most one element de nition of f. thus a= bor a= b theorem the! Global minimum or maximum and its value or one-to-one correspondent if and are injective functions surjective... And the related terms surjection and injection … Here 's how I approach... Rst property we require is the function g: R R given f..., as we wanted they are equal a1 ) ≠f ( a2 prove a function of two variables is injective of Random variables in a direction. Disprove this equation: the inverse of bijection f is an injective.! At May 29, 2018 by Teachoo which shows fis injective be inde-pendent Random variables ) x! If for every element has a unique image, i.e. let x y! Determine the directional derivative in a given function is surjective and functions of Random variables ) let x y... Room costs$ 300 at May 29, 2018 by Teachoo be confused with same.
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2022-06-30 06:59:45
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https://www.physicsforums.com/threads/silly-question-but-uhh.139255/
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# Silly question but uhh
1. Oct 20, 2006
### Hollysmoke
How can I calculate cos ^2 (53)?
2. Oct 20, 2006
### Staff: Mentor
What don't you understand? I assume you have a calculator and you realize that cos ^2 (53) = [cos(53)]squared.
3. Oct 20, 2006
### andrevdh
Take the cos of the angle, $\cos$, then square the value obtained, $x^2$.
4. Oct 20, 2006
### Hollysmoke
oh okay. Thanks.
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2018-03-22 16:46:48
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https://homework.cpm.org/category/CC/textbook/cca/chapter/6/lesson/6.2.3/problem/6-89
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### Home > CCA > Chapter 6 > Lesson 6.2.3 > Problem6-89
6-89.
1. Given the sequence 2, 10, 50, 250, … complete parts (a) through (c) below. Homework Help ✎
1. What kind of sequence is it?
2. Describe the shape of the graph.
3. Give an explicit equation for the sequence.
How do you get from one term to the next?
The shape of the graph is curved.
What is t(0)? What is the multiplier?
$t(n)=\frac{2}{5}(5)^{n}$
Make sure you know why this is the answer.
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2019-08-22 07:34:44
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https://worldbuilding.stackexchange.com/questions/103348/is-there-a-technological-difference-between-going-half-light-speed-and-near-ligh/103402
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# Is there a technological difference between going half light speed and near light speed?
Assuming a civilization has the capacity to build space vessels designed to travel from one solar system to another, what is the technological difference between traveling at 50% light speed and traveling at 100% light speed (or near)? And then, what kind of technological leap is required to go beyond light speed? The idea is not to have "hyperjumps" but that there is a constant speed most ships can go. So traveling 4 light years takes 4 years at light speed. Takes 8 years at 50% light speed. you get the idea.
I am trying to decide how technologically advanced humans in my space-travel-based universe are. Would it make sense to say "We are only advanced enough to go x% of light speed"? Or is Light-speed the real barrier here? What are the limiting factors to going very fast (subluminal)? Assuming light speed is the real barrier, would anything really stop anyone going near light speed given enough fuel and distance to reach that speed?
• You’re looking at this in small manageable numbers, but 50% light speed and 100% light speed are phenomenally different. Just take a look at the difference between going half the speed of sound vs breaking the sound barrier for example. – JustSnilloc Jan 27 '18 at 21:48
• @JustSnilloc That's not a good analogy. There's nothing fundamental about travelling faster than sound in a particular medium: the difficulties with breaking the sound barrier are purely aerodynamic. Further, there's not a huge difference between travelling at half the speed of sound and travelling at, say, 90% of the speed of sound, which commercial airliners do all the time. – David Richerby Jan 28 '18 at 13:55
• @PremierBromanov at near light speed the near vacuum of interstellar space is like standing in the beam of a particle accelerator. – Dan is Fiddling by Firelight Jan 28 '18 at 15:17
• i must say that @JustSnilloc 's comment is very confusing and raises totally unrelated issues. (A) In fact, there's no difference whatsoever between a plane or car that can go 500 mph and 700 mph (it uses "more fuel" and you need "stronger windows"). If you put a huge engine in your Toyota Avalon it could trivially go over the sound barrier. (B) absolutely trivial engineering issues like "going fast in atmosphere" have just no connection at all to "faster than light?" physics issues. – Fattie Jan 28 '18 at 15:42
• My point is that all the differences that you would find between half SoS and full SoS will be exponentially amplified when you consider the differences between half SoL and full SoL. More than “simply” going faster, there are a whole host of other things to consider. – JustSnilloc Jan 28 '18 at 17:29
Assuming known physics, there's no way to go 100% of the speed of light ($c$), but (in principle) you can get as close to it as you want. So let's compare $0.5c$ (50% the speed of light) with $0.95c$ (95% the speed of light).
There are a couple of big differences between travelling at these speeds. The first is the amount of energy needed to reach them. In space it doesn't take energy to keep moving at speed - if you don't do anything you just keep coasting at whatever speed you're moving - but you need to use energy to speed up and slow down. Let's calculate how much energy it takes to move at the speeds mentioned above.
The kinetic energy of an object moving at relativistic speeds is
$$E_k = m\gamma c^2 - mc^2 = \frac{mc^2}{\sqrt{1 - v^2/c^2}} - mc^2$$
(from Wikipedia), where $m$ is the mass of the object and $v$ is its velocity. Let's use units where $c=1$ and let's assume $m=1$ as well for simplicity. Now an object travelling at $0.5c$ has a kinetic energy of about $0.15$, while an object at $0.95c$ has an energy of about $2.2$. This measures the amount of energy you need to get up to speed, assuming the mass of your spaceship doesn't change. You can see that getting up to $0.95c$ takes 14 times more energy than getting to $0.5c$.
However, it's likely to be much worse than that in reality. For most methods of propulsion you will need to take more fuel with you to get to a higher speed, and that means more mass, which means more energy. These feedbacks combine in an explosive way, so that travelling just a bit faster usually requires an exponentially larger amount of fuel. This is called the tyranny of the rocket equation, and is generally not your friend. Don't forget that it takes energy to slow down too, since you definitely don't want to be travelling near the speed of light when you reach your destination.
If you want to go even closer to $c$ you will have to spend even more energy. Travelling at $0.99c$ requires about $6.1$ energy units, and $0.999c$ requires $21$. As you get closer to $c$ you'll need more and more energy for smaller and smaller gains. Accelerating to $c$ itself would require an infinite amount of energy, which is why you can't do it.
The other big difference between $0.5c$ and $0.95c$ is collisions with space dust and other particles. Space is almost empty, but if you run into even a tiny piece of dust grain of sand at $0.5c$ it will hit like a nuclear bomb tonne of TNT.1 A larger object, with mass around 1kg, would be comparable to a nuclear bomb. At $0.95c$ it will hit with 14 times the energy, due once again to the higher kinetic energy. Such collisions are inevitable on a journey between stars, and so most serious concepts for interstellar travel have a huge bulky shield in front of them, to protect against this. The closer you get to c the more protection you need from collisions, which adds more mass, which again requires exponentially more fuel due to the rocket equation.
In conclusion, everything you say in your question is basically right. Nothing stops you from going as fast as you want given enough time, fuel and distance, but these practical considerations mean there's a huge difference in the amount of technology and cost between travelling between stars $0.5c$ and $0.95c$.
1My initial guess was way off, my apologies. Wolfram|alpha is a useful tool for doing these kinds of calculations, and I should have run it through that in the first place. Although the energies involved are smaller than I expected, colliding with dust grains at relativistic speeds will release a cascade of subatomic particles, and the radiation from this is probably more dangerous than the initial release of energy. I am not an expert on this stuff, though.
• Your calculation for the energy collision assumes the particle comes to a stop, and that ALL kinetic energy is released. – Justin Thyme Jan 28 '18 at 4:50
• @JustinThyme that is correct. One would expect this to be the case. The only way it wouldn't be is if the particle passes all the way through the spacecraft and out the other side. One would hope the spacecraft is designed so that that wouldn't happen. – Nathaniel Jan 28 '18 at 4:58
• @JustinThyme sure, that's what I'm doing: treat the spacecraft as if it were at rest, and the particle as if it were moving at 0.5c. The point is that even a tiny speck of dust moving at 0.5c would do a huge amount of damage - it definitely wouldn't pass through without doing any damage. See for example what-if.xkcd.com/1 for what happens when matter collides with matter at relativistic speeds. – Nathaniel Jan 28 '18 at 6:16
• @JustinThyme "Also a particle traveling at you at a velocity equivalent to c would be showing the relativistic effects, not you" -- in the reference frame of the particle, yes, it's the starship that shows relativistic effects. This is the origin of the 'twin paradox'. – LSerni Jan 28 '18 at 21:33
• @JustinThyme: "It is the assumption that all speeds are relative and not absolute that produces the paradox. If you throw out that assumption, there is no paradox." You're basically saying "if you stop saying that special relativity works, then special relativity doesn't work". Yes, that's true. But since special relativity has been observed and there is a multitude of evidence that it works, you can't just deny reality because you don't like where it leads. – Nicol Bolas Jan 28 '18 at 23:43
What percent of the speed of light you go is not really a function of how "advanced" you are. So long as you have reaction mass for thrust (or whatever your particular method of acceleration is), you can get arbitrarily close to the speed of light. Obviously, you need some minimum tech level to be able to fly in space and navigate over long-distances at all.
The limit on how fast you go is therefore based primarily on your particular engine design, any external motive systems, and how much reaction mass you carry, all of which is relative to the overall mass of the ship you're using. But these elements of technology don't map to the practical speed of a ship.
So you can't look at a ship that travels 75% of the speed of light and judge anything about the tech level of the people who made it based solely on that. Maybe they had a stationary magnetic accelerator in their launch system and are relying on high-impulse propulsion to slow them down. That's not particularly higher of technology that someone who uses low-impulse propulsion over a long duration to achieve the same speed.
• @PyRulez: My point is that you can't "really" know. If you see a ship going 0.75c, that alone tells you almost nothing about how they got it there, relative to if you see a ship going 0.25c. For all you know, the latter could be more advanced than the former, but the former was willing to use more brute-force/inefficient methods to do so. There are enough low-tech solutions to get high velocities that you cannot tell one way or the other just from its speed. – Nicol Bolas Jan 28 '18 at 3:17
• In particular, if you can accelerate at 1g for a little under a year, you're travelling at the speed of light. – David Richerby Jan 28 '18 at 13:58
• The original Voyager spacecraft were developed at a period of low technology compared to today, but they are going extremely fast compared to rockets launched from earth using current modern technology. Point taken. – Justin Thyme Jan 28 '18 at 16:32
• @DavidRicherby False. – wizzwizz4 Jan 28 '18 at 18:22
• If you are under a constant acceleration using the same technology, you will NEVER approach cee. The closer to cee you get, the more the acceleration you need to go faster. That is to say, the method and technology you use to accelerate at, say, 5 m/s/s if you are travelling at normal earthly velocities, will NOT accelerate you at 5 m/s/s if you are going at point 8 cee. At point 8 cee, if you add 5 m/s to your velocity, you are going considerably less than point 8 cee plus 5 m/s.Velocities are not purely additive at speeds approaching cee. – Justin Thyme Jan 28 '18 at 22:45
When you add more energy with any thruster (assuming abundant reaction mass or bonkers Isp) as you get closer to light speed less energy is going into your relative velocity and more is bleeding over into time dilation effects. From the chart it looks like you start seeing some serious losses in Δv above 0.3c. Above 0.9c most of the energy from continued thrusting is going toward time dilation and not toward getting anywhere any faster - and then you'll have to decelerate which equates to a whole lot of wasted fuel.
So above 0.8-0.9c there's no advantage to trying to go any faster. Any limit below that is going to strictly be limited by the amount of fuel you can carry (or find, if you are going the ramscoop direction where you use a magnetic inlet to capture and fuse interstellar hydrogen), the efficiency of your engines, and the relationship between acceleration and distance between start and end points. For example, you could have very high efficiency but very low thrust engines for interstellar travel, so you may need several lightyears to get up to 0.8c. In this case you're average speed would be lower for "short" hops like from Sol to Alpha Centari, and approach the 0.8c cruising speed as you make very long journeys.
As a plot device, any sort of race in the 0.8-0.99c range where it's worth it to burn insane amounts of resources to gain a few days or hours on the competition could be interesting.
Faster than light is the big jump because with our current physics, no one knows how to do it. With any known propulsion method, we would just lose acceleration and speed to the time dilation effect. Any FTL method is going to have to abandon the Science and lean on the Fiction.
• "less energy is going into your relative velocity and more is bleeding over into time dilation effects" The time dilation effects makes the trip shorter from your point of view though. For many applications, perceived time is what is important, not actual time. – PyRulez Jan 28 '18 at 2:48
• @PyRulez Don't disagree at all. You get this fun situation where time is a resource and it enters the trade space with fuel consumption. You also get the interesting scenario where limiting the passage of perceived time is not really desirable - how much scifi has been written about the struggle associated with taking a few short trips and watching your loved ones age and die? – MParm Jan 28 '18 at 3:12
• @PyRulez: The important question is what is the actual time? It's purely (if you'll excuse the pun) relative: to someone aboard the near-lightspeed ship, their time is every bit as real as the slowed-down time of the rest of the universe. – jamesqf Jan 28 '18 at 4:53
• @jamesqf From the point of view of the ship, length contraction is happening, resulting in an overall shorter trip. Regardless of point of view, they will have "aged" the same (i.e., less than if they/the universe was moving slower). – PyRulez Jan 28 '18 at 4:57
• @jamesqf For sure. Have you read Hyperion? - Very Highly recommend if you haven't. It's an anthology (but very well done, not usually a fan of anthologies) and the Consul's story has a lot to do with relativistic time effects and is a real tear jerker. – MParm Jan 28 '18 at 5:03
I assume when you refer to speed, you mean relative to earth or some other planet, as all speed is relative. There is no huge difference between getting to different sub-light speeds, more thrust is simply required to go faster.
However, do keep in mind that going near light speed, the effects of time dilation get very noticeable. A journey of four light years might take a few years for the people on your ship, but centuries for everyone else on the planet from which they launched. Nothing can actually go faster than light, as this would mean going at a theoretically infinite speed and cause you to go back in time. You might however want to look into the Alcubierre drive, a theoretical warp drive which creates a bubble of spacetime, contracting space in front of it and expanding it behind. This means that the ship technically isn't moving at all, and would allow the it to travel at any speed with no time dilation. There are of course many problems with it, such as energy requirements and radiation, but it could work for your story.
Basically, the biggest technological difference is whether or not your civilization has discovered a way to go faster than light.
You bet there's a difference
• In 1804 the first steam rail locomotive could scream along at 5 mph.
• Steam improved by 1830 when the Stephenson Rocket hit an earth shattering 30 mph.
• In 1848 steam — or should I say, rail — had hit 60 mph. It took nearly 100 years to get to 100 mph. All this time, the technology to move the mail was changing and improving. Steam reached its peak in 1938 with 126 mph.
• Then the technology changed and diesel was introduced. In 1936 diesel hit 127 mph. By 1980 it was up to 152 mph.
• Then the technology changed again, and today we have mag-lev trains that top out at 375 mph.
My point is, there is a HUGE technological difference between 0.5c and 1.0c.
I'm ignoring completely today's understanding of physics. World history has proven over and over that "today's" understanding imposes few actual limits. Said limits tend to be overcome by "tomorrow's" understanding. Once humanity can build a ship that can reach 0.5c it's altogether likely that we'll have figured out the physics behind getting to 1.0c. Anyone who tells you "...can't be done, because..." is forgetting that people 100 years ago were saying the same thing about many of the technologies we enjoy today.
However, when you ask, "...what is the technological difference...," that's a question no one here can answer. You're asking us to postulate the operation of technology that doesn't exist in our wildest dreams, and then extrapolate from that ignorance whether or not light speed represents an insurmountable barrier.
Remember! Scientists actually thought the sound barrier was insurmountable until we figured out how to do it and Chuck Yeager actually did it. Today, we can't see how to overcome the light-speed barrier ... but we've walked across a barrier once before. I wouldn't be at all surprised that we do it again. It just takes a better understanding of the problem than we have today. Regrettably, it's the habit of science-oriented people to believe that what we understand today is all there is and all there will ever be. History has proven them wrong time and time again... but they believe it anyway.
So, you'll be inventing the "technology" that your story needs to accomodate space travel, but to answer your title question, yes! It makes reasonable sense to say, "that species can only reach 0.25c." as a reference to their general technology level. Indeed, this kind of reference has already been used in Star Trek where some species are only capable of "warp 4" while others are capable of "warp 7" and it's hands-off non-warp-capable species because Clarkian Magic would make you look like gods and that's considered poor sportsmanship.
• I have oft said 'If the physics book is thick enough. And we are doubling its thickness every decade.' Upvote for that. Proof in point, 150 years ago we didn't even have the technology to get into space. Constant acceleration does not cut it, as any acceleration we have today has a limitation in thrust and velocity, and once we reach that limit, greater acceleration is not possible. To go from point 5 cee to point 8 cee, it's not just a matter of a constant acceleration, but of an increasing acceleration. – Justin Thyme Jan 28 '18 at 18:29
• ctd Velocities are not purely additive at speeds approaching cee. The closer to cee, the greater the acceleration needed to go 'faster'. It is this 'greater acceleration' that is the technological barrier. – Justin Thyme Jan 28 '18 at 18:32
• @JustinThyme, that's absolutely true... according to how we understand the physics today. Most readers of Jules Verne's books were delighted with what they perceived as the pure fantasy of his stories. They couldn't imagine anything like what he described being possible. As with all fiction, most proved unobtainable, some proved wonderously possible. As we understand light speed today, we need an accelerating acceleration. But that's just a snapshot. Perhaps it will prove to be the end-all understanding, perhaps not. Cool, that. – JBH Jan 28 '18 at 19:06
Assuming a civilization has the capacity to build space vessels designed to travel from one solar system to another, what is the technological difference between traveling at 50% light speed and traveling at 100% light speed (or near)?
I'd say, pretty significant. To achieve a speed of X, you need to gain a kinetic energy of mX2 and that energy, whatever your propulsion system, ultimately comes from fuel. But since you need to have the fuel with you, that's more mass that you need to have with you when you start. In the end, it's a matter of energy density.
Then, relativistic speeds offer two important challenges that your technology must overcome:
• anything in space - dust, grit, stray protons, gas molecules, junk - in your trajectory becomes a projectile hitting at relativistic speeds. You need to be able to either locate such obstacles far enough, and maybe manoeuver fast enough, to avoid them, or survive the smaller impacts.
• at relativistic speeds, your ship-clock time slows down. This means that you have even less time to detect obstacles, less time to react, less time to manoeuver.
At 99% c, you send out a pulse at the speed of light towards a half-kilo pebble floating one million kilometers in front of you. The pulse takes 3 seconds to reach the pebble; in those three seconds you've covered about 895,000 km and are at 105,000 km from the pebble. The pulse goes back, and you detect it when you're at less than 10,000 km from the pebble. To move a space of s = 50 meters off from your route, hold the relativistic slow-down, you have around t = 0.03 seconds. Given that $s = \frac{1}{2}at^2$, this gives $a=\frac{2s}{t^2}$ = nine thousand gravities.
So: you either have technology to survive accelerations two orders of magnitude above lethal, and detection technology capable of locating position and speed of a pebble one million kilometers away; or a detection range proportionately higher; or the capability to survive impact, and a half-kilo pebble at .99c has the same effect of a multimegaton-range fusion bomb.
And then, what kind of technological leap is required to go beyond light speed?
The impossible kind, for all that we know. It's a sort of Chinese Corridor race: every technological leap you do will halve the distance separating you from light speed. So you go from 50%c to 75%, to 87.5%, 93.75%... but you will never reach c (the Engineer's response in the joke is "Yeah, mate, but I only need to get close enough).
So traveling 4 light years takes 4 years at light speed.
Welllll... actually, 4 light years at light speed takes no time at all, if you're aboard the ship. Time contraction again. That might be an advantage.
Of course, reaching near enough the speed of light takes time.
Would it make sense to say "We are only advanced enough to go x% of light speed"?
Yes, it makes a lot of sense.
would anything really stop anyone going near light speed given enough fuel and distance to reach that speed?
At a certain point, exotic effects become observable and begin kicking in. The most relevant is probably the Doppler-Zatsepin effect, whereby you observe the ubiquitous microwave background blue-shifted towards higher energetic levels. In other words, wherever you look you see a gamma-ray laser firing at you point-blank with energy enough to photodisintegrate the ship. This phenomenon limits the distance traveled by a fast-enough particle to what is called the GZK limit. Accelerating further will expose you to a different but equally nasty effect: the temperature of the vacuum will appear to increase.
So, relativistic travel is hot, but wearing :-)
There is one crucial term in your question that perhaps needs exploring. You do not ask in terms of 'anything' but in terms of 'anyone'. That is, can a HUMAN travel that fast?
We really have absolutely no data on how any biological process would function at that speed, let alone a human. The trick is, we have to ACCELERATE to that speed. We know that space flight has repercussions on the human body, and on biology. We DON'T know if these effects are cumulative.
As an analogy, consider a change in temperature. Frogs will freeze to death at a slow drop in temperature, without sensing it. Humans, on the other hand, show physiological reactions in order to maintain a specific body temperature. Could, somehow, constant acceleration to a faster and faster speed have a biological effect? We don't know. No human has yet accelerated to such a speed.
We know almost certainly that biology depends upon quantum effects. Quantum tunneling, for instance, in electrolyte transport through the cell, and in photosynthesis. Will the quantum effects be somehow altered?
So what happens to human biology, or biology in general, if the organism is subjected to a constant acceleration that results in a speed approaching that of a massless particle? Are humans adapted to operate optimally in an environment of an acceleration and velocity range typical of earth, and would we have extreme difficulty in adapting to any other environment?
So, in answer to your question, yes it is possible that humans (not things) might have limitations on going that fast, and these limitations would have to be addressed by technology beyond that which we currently have.
EDIT
I found the reference that, in part, addresses this.
Speed kills: Highly relativistic spaceflight would be fatal for passengers and instruments
Unfortunately, as spaceship velocities approach the speed of light, interstellar hydrogen H, although only present at a density of approximately 1.8 atoms/cm3, turns into intense radiation that would quickly kill passengers and destroy electronic instrumentation. In addition, the energy loss of ionizing radiation passing through the ship’s hull represents an increasing heat load that necessitates large expenditures of energy to cool the ship.
• There were also back in the early 19th century people who said railway travelling was unhealty because the human body was not suitable for high speeds. – Karl Jan 28 '18 at 17:24
• @Karl Point taken, until you ride a roller coaster. Some people can handle it, others can't. It's not just the pure g forces, it is the acceleration. – Justin Thyme Jan 28 '18 at 17:32
• Äh, g force is acceleration. ;-) And if you're prepared to travel for decades, you can also take another half year to gain cruise speed. – Karl Jan 28 '18 at 17:51
• @Karl Okay, more specifically, the CHANGE in acceleration, and the TYPE of acceleration. Car sickness is real, and it has its basis in our vestibular system. It has adapted to a constant centripetal acceleration as we rotate with the earth. We are always going around in circles. Slow, but constant centripetal acceleration. Yet we are unaware of it. Our body has adapted to it. Change that to faster or slower, and some of us are in trouble. Change that to constant linear vs constant centripetal, we haven't experienced that yet. Even our growth has adapted to centripetal acceleration. – Justin Thyme Jan 28 '18 at 18:18
Assuming light speed is the real barrier, would anything really stop anyone going near light speed given enough fuel and distance to reach that speed?
I'm pretty sure the answer to the spirit of your question is very simply "no".
1. Say you are going any speed, whatsoever. Any speed. To go faster, you simply attach a rocket at the back and light a match. Once again, no matter what speed you are going, to go faster you just fire a rocket. There is utterly no difference whatsoever, at all, in the fundamentals.
2. Regarding travel at light speed, like a photon (or faster than light speed). This is simply utterly impossible, based on our current deepest understanding of mathematics.
Regarding point 1, of course - obviously - you might need staggeringly big rockets and other astounding engineering difficulties. (You may well need fusion! or anti-matter! engines to make huge amounts of electricity - whatever. You would surely need some sort of astounding laser technology to blast out of the way any micro-particles in front of you - etc etc.)
Once again, thanks Einstein - any speed at all, whatsoever, is identical to no speed at all. There is absolutely no difference between speed and no speed.
(Note that indeed our planet (indeed, our galactic group) is whipping along at an astounding speed; when we take off to the moon we just "add speed" - the "original" (staggering) speed of the planet means absolutely nothing.)
# Speed and no-speed are the same.
In contrast - point 2 - traveling at light speed (or higher) is utterly and totally different, requiring utterly new base mathematical concepts, totally and completely unknown to us.
• Your first point is not quite accurate. If you are accelerating from earth, and escaping gravity, then your rocket strapped to your back would also need enough thrust to allow you to reach escape velocity, otherwise you fall back to earth. Since gravity is everywhere, and everything is basically escaping from or being drawn to something under the effects of gravity, there is a minimum thrust required to overcome some gravitational effect. So you need to add 'CONSTANT unaccelerated' before speed. And maybe change 'speed' to 'velocity' (scalar to vector). There are advantages to inertia. – Justin Thyme Jan 28 '18 at 17:23
• Hey @JustinThyme - lift off from Earth is uninvolved in this question. – Fattie Jan 28 '18 at 18:51
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2020-01-29 03:19:49
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https://www.hpmuseum.org/forum/thread-3142-post-28135.html#pid28135
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HP35s RPN Series # 3 [ENTER]
02-18-2015, 08:24 PM (This post was last modified: 02-18-2015 08:30 PM by MarkHaysHarris777.)
Post: #1
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
HP35s RPN Series # 3 [ENTER]
The classic HP style [ENTER] key is an RPN conundrum; an inconsistent and illogical relic dating back to the earliest of RPN calculators, yet 'beloved' by all HP classic RPN users. What is the [ENTER] key, what is it for, how does it work? First a bold proclamation: the HP35s calculator (in fact all RPN calculators) may be used effectively for all purposes without the user ever touching the [ENTER] key-! (We have already seen this at work in the ten-key emulation method cf. #2 Entry)
As stated earlier the stack is the heart and sole of the RPN methodology; broadly stated, the [ENTER] key is the RPN primary stack manipulation key among others: [x↔y] , [R↓] , [←] , [R↑] & [CLSTK].
Contrary to its name, its purpose is not 'entry,' nor 'input,' rather its primary purpose is stack (register) manipulation, something more than mere 'entry' and nuanced by the subtleties of how and when it affects stack 'lift'; however, as is the case for unary and binary operators the [ENTER] key also shares the property of terminating numeric keying into the X stack register.
Before we get to the [ENTER] key, per se, let's perform a multiplication and let us NOT touch the [ENTER] button; to demonstrate the idea that [ENTER] is not required for 'entry,' which is important for this discussion. In order for us to find the product of two multiplicands using a 'postfix' methodology like classic RPN, we first must get the multiplicands into memory (into the X and Y registers) so that the [X] binary operator may do its job. It is important to note that it does not matter in the slightest 'how' the multiplicands get into their respective registers, only that they get there-! Consider the following key sequence: [3] [x↔y] [←] [4] [X]
The [x↔y] key terminates the [3] keying and swaps the X register with the Y register. The [←] key clears X but primarily is used to cancel automatic stack 'lift' (discussed later) in preparation for [4] keying. The [X] key terminates [4] keying and operates (multiplication) on the operands in the X and Y registers (initiating automatic stack 'drop') and leaving our product in the X register. Voilà! Notice that the [ENTER] key was not touched with this method. How many ways are there to manipulate the stack registers to accomplish the same purpose? Remember it is not important how the operands get into X and Y necessarily, only that they get there. Try this one:
[4] [R↓] [←] [3] [R↑] [X] (or) [4] [R↑] [←] [3] [X] (or) [CLSTK] [4] [+] [3] [X]
The above key stroke sequences work to multiply (4 X 3) and no one would actually do this in practice; however, this example illustrates the point that 'entry' is about controlling the stack by the use of stack manipulators (not necessarily by use of the [ENTER] key)!
Let us now return to our conundrum. The [ENTER] key is primarily a stack|register manipulator. Its purposes might be listed (below) in no particular order:
1) Initiate manual stack 'lift' replicating X into Y
2) Terminate X register keying (also initiates 'lift' and replicate, nuance #1)
3) Push a value into Y (nuance on #1)
4) Prepare X for entry (nuance on #3, and #1)
What makes [ENTER] a conundrum?
[ENTER] causes confusion because its called 'ENTER' and because it really doesn't enter anything. Primarily the [ENTER] key forces stack 'lift' and replicates X into Y; also canceling automatic 'lift' for the 'next' keying operation! (which may be leveraged in a number of interesting ways). Secondarily, [ENTER] terminates X register keying, as do most unary and binary operators; however, [ENTER] does not use an input buffer in classic style, and [ENTER] does not 'enter' X (it only terminates numeric keying of a value 'already' in the X register. Of course, [ENTER] doesn't 'equal' anything either. The [=] key does not exist on 'real' classic RPN calculators; [ENTER] has nothing to do with [=]. Well, there you have it, a conundrum; well beloved and highly useful! (if not logical, nor consistent)
Sidebar: I can't prove the following conjecture (but I believe it non the less). The [ENTER] key and its quirky behavior are an oversight, or bug, left over from the early design and test of the HP35. The [ENTER] key IMHO was not designed (it evolved) and when the dust settled the engineering team left it alone because they found uses for the accident. What makes me believe this to be true are three observations (and I go back to the era personally): 1) other programmable calculators of the era (Wang 700, others) had register manipulators, but no [ENTER] key (certainly nothing like the HP RPN [ENTER]), and 2) the [ENTER] key is not necessary using consistent entry methods [+] with other register manipulators, and 3) in a modern sense users typically often want 'entry' RPN; a style whereby [ENTER] enters a value from an input buffer into the X register-- actually 'enters' something. Neither here nor there... just historical speculation (not a theological challenge)
Conclusion: Regardless how the [ENTER] key came into existence, and regardless being a conundrum, the [ENTER] is here to stay; important for register manipulation certainly. But also important as an icon of cultural expression worthy of preservation and appreciation – just for the beauty of it. Voilà !
Cheers,
marcus
Kind regards,
marcus
02-18-2015, 08:36 PM (This post was last modified: 02-18-2015 08:36 PM by Don Shepherd.)
Post: #2
Don Shepherd Senior Member Posts: 745 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
Mark, that's quite a writeup on the ENTER key!
What seems to be lost in all of this, however, is the basic purpose of the ENTER key on an RPN calculator: it separates the two numbers in any arithmetic operation. If you don't have an equal key to deliver an answer, you need an alternative. All a casual (or new) RPN user needs to remember to operate his/her calculator successfully is that you separate your two numbers with the ENTER key, and press the desired operation key last.
Of course, RPN calculator programmers realize what the ENTER key does, but your average Joe is not a programmer and doesn't care about all that. There is just something "elegant" (shall I say) about separating your two numbers with the ENTER key and then specifying what you want to do with them.
Don
02-18-2015, 10:04 PM
Post: #3
Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 08:24 PM)MarkHaysHarris777 Wrote: 1) other programmable calculators of the era (Wang 700, others) had register manipulators, but no [ENTER] key (certainly nothing like the HP RPN [ENTER])
Using the Wang 700 Programmable Calculator Simulator I have the impression that the [↑] key pretty much does what the [ENTER↑] key does: copy the number from the x register to the y register. I assume that's similar to how the 3-level stack of the HP-9100 worked:
Quote:Keying numbers into the stack did not cause the automatic stack lift that occurred on later calculators. For example, to calculate sqrt(25)+5, the user would press 2 5 [sqrt] [Enter] 5 +. The Enter wouldn't be needed on later RPN calculators. (Since calculator displayed the entire stack, the user always knew exactly where each number was and whether it needed to be copied up with Enter.)
When later calculators used a one line display, leaving results in an invisible stack register would have been a nuisance so RPN was altered. This later form of RPN popped the result down to the only visible register and then automatically pushed it back into Y when the user continued to enter data. When later HP models again used larger displays, the stack lift behavior was altered again.
Stack manipulation keys included an enter key (labeled only with an upward arrow), a drop key (labeled with a downward arrow) as well as ROLL keys for both directions and an X and Y exchange key. (X<->Y.)
With the one line display of the HP-35 the result of a calculation (i.e. what was the accumulator in register y) had to be displayed. But then this result shouldn't be overwritten with the next entry. Thus the number in display is moved to register y when a new number is entered. This is fine except immediately after the [ENTER↑] key. In this case what we call now stack-lift is disabled.
The HP-engineers came up with a clever solution for this problem.
Quote:2) the [ENTER] key is not necessary using consistent entry methods [+] with other register manipulators
Sooner or later you want to duplicate a number. You may call it what ever you like: [↑], [ENTER↑] or [DUP]. But the [+] key doesn't help here.
Cheers
Thomas
02-18-2015, 10:54 PM (This post was last modified: 02-18-2015 10:55 PM by MarkHaysHarris777.)
Post: #4
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 08:36 PM)Don Shepherd Wrote: There is just something "elegant" (shall I say) about separating your two numbers with the ENTER key and then specifying what you want to do with them.
Yes, I agree. I've explained it that way in the past, as well. The problem comes up though that 'infix' calculators do that too: 4 + 3 = 7 ... the (+) separates the two numbers just fine. What's the difference (I'm speaking tongue in cheek, devil's advocate). Well, obviously, the stack is the difference. Its not that 'postfix' is better; its that RPN uses a stack, and stack manipulators (like the [ENTER] key) make for more efficient control of arithmetic in a hand-held calculator.
Most of our students today frankly don't know enough about what's going on in their calculator to appreciate the RPN stack (usually). The TI and Casio systems with 'pretty print' and AOS, CAS, etc, are making that worse. <sigh>
Cheers,
marcus
Kind regards,
marcus
02-18-2015, 11:07 PM (This post was last modified: 02-18-2015 11:11 PM by MarkHaysHarris777.)
Post: #5
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 10:04 PM)Thomas Klemm Wrote:
(02-18-2015 08:24 PM)MarkHaysHarris777 Wrote: 1) other programmable calculators of the era (Wang 700, others) had register manipulators, but no [ENTER] key (certainly nothing like the HP RPN [ENTER])
Using the Wang 700 Programmable Calculator Simulator I have the impression that the [↑] key pretty much does what the [ENTER↑] key does: copy the number from the x register to the y register.
Yes; but without all of the [ENTER] key baggage. The Wang did not have a stack. It had a rich set of register manipulators, and again, if you could figure out a way to get your numbers into the X and Y registers you could do some maths on them!
(02-18-2015 10:04 PM)Thomas Klemm Wrote: I assume that's similar to how the 3-level stack of the HP-9100 worked:
I never got the pleasure of using the HP-9100; I believe it had a three level stack, but I cannot offer any clue how it worked, sadly.
(02-18-2015 10:04 PM)Thomas Klemm Wrote: The HP-engineers came up with a clever solution for this problem.
Oh, no doubt; very clever (as they say, the rest is history)
(02-18-2015 10:04 PM)Thomas Klemm Wrote: Sooner or later you want to duplicate a number. You may call it what ever you like: [↑], [ENTER↑] or [DUP]. But the [+] key doesn't help here.
I disagree. The truth is, if you'll be honest about it with yourself, you 'want' to duplicate a number with the [ENTER] key because you 'can,' not because its necessary. Well, on the surface, if you want to duplicate a number:
[2] (auto stack lift) [X] (auto stack drop) {problem solved}
I agree with you that the [ENTER] key (and its quirks) may be leveraged in many interesting ways (as I stated in my article), but its not necessary. In other words, there are alternate ways of manipulating the stack and registers without using the [ENTER] key.
Having said that, the only reason I point out the [ENTER] conundrum is to help new users (and new programmers) to understand what is really happening behind the RPN stack and [ENTER] methodology.
PS Thanks for pointing me into the Wang emulator again... brings back many fond memories (almost chokes me up to see it again).
Cheers,
marcus
Kind regards,
marcus
02-18-2015, 11:25 PM
Post: #6
Don Shepherd Senior Member Posts: 745 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 10:54 PM)MarkHaysHarris777 Wrote: Most of our students today frankly don't know enough about what's going on in their calculator
I'm sure that's true. My math students don't use calculators (middle school). I want them to learn how to add, subtract, multiply, and divide the way I learned it 50 years ago. Call me old-fashioned, I wear that badge proudly.
02-18-2015, 11:37 PM
Post: #7
Sanjeev Visvanatha Member Posts: 267 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 08:24 PM)MarkHaysHarris777 Wrote: What makes [ENTER] a conundrum?
[ENTER] causes confusion because its called 'ENTER' and because it really doesn't enter anything.
It enters the X register value into the Y register. I have always thought of it as "STO Y". This is what it does in its simplest sense. The named function of STOring to a stack register did not exist at the time the earliest HP RPN machines came out.
-- Sanjeev Visvanatha
02-19-2015, 12:02 AM
Post: #8
Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 11:07 PM)MarkHaysHarris777 Wrote: The truth is, if you'll be honest about it with yourself, you 'want' to duplicate a number with the [ENTER] key because you 'can,' not because its necessary.
Evaluating a polynomial $$p(x)$$ comes to my mind. Sure, I'm just lazy and don't want to key in $$x$$ multiple times.
02-19-2015, 12:16 AM
Post: #9
Thomas Klemm Senior Member Posts: 1,447 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 11:07 PM)MarkHaysHarris777 Wrote: I never got the pleasure of using the HP-9100; I believe it had a three level stack, but I cannot offer any clue how it worked, sadly.
No problem: Dave has already given a description in the link HP-9100 I provided.
02-19-2015, 06:30 AM
Post: #10
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 11:37 PM)Sanjeev Visvanatha Wrote:
(02-18-2015 08:24 PM)MarkHaysHarris777 Wrote: What makes [ENTER] a conundrum?
[ENTER] causes confusion because its called 'ENTER' and because it really doesn't enter anything.
It enters the X register value into the Y register. I have always thought of it as "STO Y". This is what it does in its simplest sense. The named function of STOring to a stack register did not exist at the time the earliest HP RPN machines came out.
Yes, many think of it that way (which is kinda my point)... that is NOT what it does. The [ENTER] key initiates 'stack lift' (which is way more baggage than STO Y. The T reg is lost, Z is copied into T, Y is copied into Z, and X is replicated (copied) into Y; automated stack lift is canceled (for the next keying) and the X keying is terminated. whew. Goes a lot further than, STO Y. Of course moderns want an input buffer, and they want the [ENTER] key to STO X basically (leaving the stack alone). I am not in favor of this, actually. I configure my Droid virtual RPN calc (RealCalc) to use a traditional [ENTER] and XYZT four level stack.
Cheers,
marcus
Kind regards,
marcus
02-19-2015, 06:37 AM (This post was last modified: 02-19-2015 06:37 AM by MarkHaysHarris777.)
Post: #11
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
Greetings, as I was fixing my overlay and button stickers on my latest WP34s (20b unit) tonight I noticed the [ENTER] key-- has a little vertical white arrow along with the word ENTER. This is an improvement, actually. If I had designed the HP I would have called the [ENTER] key the [STACK] key, and I would have put a little vertical arrow on it. See pic:
Eric, if you're listening out there in Texas, I received the caps, crystals, and overlays tonight (frozen solid of course). I had dinner while they thawed out and got to work (for dessert!).
The 20b came out nicely; it is quickly becoming my favorite WP34s (of the five units I've successfully repurposed. Thanks much bubba!
Cheers,
marcus
Kind regards,
marcus
02-19-2015, 08:37 AM
Post: #12
Tugdual Senior Member Posts: 756 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
(02-19-2015 06:37 AM)MarkHaysHarris777 Wrote: Greetings, as I was fixing my overlay and button stickers on my latest WP34s (20b unit) tonight I noticed the [ENTER] key-- has a little vertical white arrow along with the word ENTER. This is an improvement, actually. If I had designed the HP I would have called the [ENTER] key the [STACK] key, and I would have put a little vertical arrow on it. See pic:
Eric, if you're listening out there in Texas, I received the caps, crystals, and overlays tonight (frozen solid of course). I had dinner while they thawed out and got to work (for dessert!).
The 20b came out nicely; it is quickly becoming my favorite WP34s (of the five units I've successfully repurposed. Thanks much bubba!
Cheers,
marcus
Oh wow brand new 34s is looking good.
Mine is really in poor condition now, mainly because of stickers, to the point I moved to a 35s which is far less powerfull but good enough on a daily base and far better casing.
02-19-2015, 09:13 AM
Post: #13
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
(02-19-2015 08:37 AM)Tugdual Wrote: Oh wow brand new 34s is looking good.
Mine is really in poor condition now, mainly because of stickers, to the point I moved to a 35s which is far less powerfull but good enough on a daily base and far better casing.
The WP34s is soooo needing to be commercially marketed; photo spreads, posters, chick appeal, the whole nine yards... it needs a real case (actually, the case is fine, very solid, just needs real buttons). I love the 35s, really, but its case (well made as it is) is just a 'tad' too big... with a case that big it should have had a four line display, IMHO.
The WP43s will hopefully have a real case, real buttons, four line display (all points addressable) and be the same size as the WP34s... I hope.
Cheers,
marcus
Kind regards,
marcus
02-19-2015, 08:53 PM
Post: #14
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
(02-18-2015 11:37 PM)Sanjeev Visvanatha Wrote:
(02-18-2015 08:24 PM)MarkHaysHarris777 Wrote: What makes [ENTER] a conundrum?
[ENTER] causes confusion because its called 'ENTER' and because it really doesn't enter anything.
It enters the X register value into the Y register. I have always thought of it as "STO Y". This is what it does in its simplest sense. The named function of STOring to a stack register did not exist at the time the earliest HP RPN machines came out.
I've been thinking about your comment today, also in light of the discussion going on in the WP34s forum regarding allowing 'entry' RPN as a configurable alternative. Of course, I don't have any idea how the engineers of the HP35s implemented [ENTER] precisely, because it is not an open platform. The WP34s, on the other hand, is an open platform and we can take a look at some of its code:
Code:
/* Decode and process the specials. These are niladic functions and * commands with non-standard stack operation. */ static void specials(const opcode op) { int opm = argKIND(op); switch (opm) { case OP_0: case OP_1: case OP_2: case OP_3: case OP_4: case OP_5: case OP_6: case OP_7: case OP_8: case OP_9: case OP_A: case OP_B: case OP_C: case OP_D: case OP_E: case OP_F: digit(opm - OP_0); break; case OP_DOT: if (is_intmode()) break; . . . {code snipped here for clarity} case OP_ENTER: <======== this is what we're interested in process_cmdline(); lift(); clr_lift(); break;
You will notice that OP_ENTER does the three things I noted in my article: 1) process the command line {parsing, error checking, terminates keyboard numeric entry}, 2) initiate stack lift {this is the hefty work of [ENTER]}, and 3) clear the 'lift' state {cancels lift for the next keyboard command line activity}
This switch-case statement is handling (partially) commands that have non standard stack operations (and there are quite a few which I have snipped away to simplify things here). This is what makes [ENTER] a conundrum for RPN methodology. It really doesn't DO what its name implies, and it DOES do things that the user does not understand... even if they can observe them and describe them... each person comes away with their own interpretation of what [ENTER] means (for them, and for the system!)
Cheers,
marcus
Kind regards,
marcus
02-20-2015, 02:19 AM
Post: #15
Sanjeev Visvanatha Member Posts: 267 Joined: Dec 2013
RE: HP35s RPN Series # 3 [ENTER]
If you look at the older manuals, there was an entire chapter devoted to stack mechanics and the Enter key. Something so complex requires a simple designation on the keypad, IMO. The user has to read the manual, experiment, and gain confidence in what the machine is doing. It doesn't take long for a technically minded person to master it.
You had mentioned the "=" key earlier. Well, "=" is also in the same boat by your logic. It doesn't equal anything unless the user understands OOP and the use of parenthesis.
-- Sanjeev Visvanatha
02-20-2015, 05:34 AM (This post was last modified: 02-20-2015 05:38 AM by MarkHaysHarris777.)
Post: #16
MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s RPN Series # 3 [ENTER]
(02-20-2015 02:19 AM)Sanjeev Visvanatha Wrote: You had mentioned the "=" key earlier. Well, "=" is also in the same boat by your logic. It doesn't equal anything unless the user understands OOP and the use of parenthesis.
hi Sanjeev, sorry to be argumentative (because I enjoy dialoguing with you) but I must disagree again; and here is why... and it's important! The primary difference between the calculation methodology of classic HP RPN, and algebraic systems like TI's AOS, for instance, and others, is that RPN stacks ONLY the data. Algebraic systems necessarily stack BOTH the data AND the operators (and in fact, must stack the operators in some fashion with nested levels of parenthesis according to a complex set of 'algebraic hierarchy' or order of precedence of operations). This 'requires' necessarily and absolutely an 'equals' key. Now, for semantics, you may call the key [=], [Solve], [Resolve], [Approximate], or [GO], but hey, it necessarily must be there; equals actually and really means 'equals'. Something must tell the system to unstack the data (and the 'infix' operators) according to algebraic usage; the stack must be 'unwound' if you will. This is entirely different from the RPN methodology of [ENTER], and its semantics|baggage, whereby only the data are stacked and the user handles all of the policy of precedence and execution dynamics-- what 'postfix' calculation strategy of RPN is all about!
By the way, I do not really believe that the HP engineers in the beginning were really all fired up about Jan Łukasiewicz' PN, nor the elegance of 'postfix' methodology from some kind of intellectual pedestal (or anything like that, no one will ever convince me). That is just HP revisionist history to justify the paradigm. The real issue in 1972 was memory and speed. Why use valuable onboard memory (or complicated policy, programming) within the calculator when the user is better suited for the purpose of precedence and policy... when the calculator requires EVERY 'bit' (pun intended) of memory for the actual algorithms? Postfix methodology works well with a stack, and that's what Hewlett needed! The method may have come from Jan Łukasiewicz (at some level) but the mother-of-invention (primarily) involved the idea that logic of that era was 'slow' and memory was difficult and expensive.
Thanks for the dialogue.
Cheers,
marcus
Kind regards,
marcus
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2021-12-08 13:44:41
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https://answers.ros.org/answers/234142/revisions/
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# Revision history [back]
Hi schultza,
the extracted obstacles are published as Marker type from the teb_local_planner on topic teb_markers. Just add the marker display to your rviz configuration.
Note, the conversion algorithms are still experimental. I implemented them "quickly" in spare-time. So if you observe some issues or if you have some suggestions or better default parameter sets, please let me know :-). Also I need to perform some benchmarks in the future between the different algorithms.
According to your console output, the converter is indeed loaded properly. You can tune some of the parameters using rqt_reconfigure. By the way, better start with a convex hull or line algorithm since calculating concave hulls takes much more time and is often not required.
1 Hz is indeed slow. I recently added a FAQ section to the tutorials with some hints about parameters and their influences on computation time: Link
Hi schultza,
the extracted obstacles are published as Marker type from the teb_local_planner on topic teb_markers. Just add the marker display to your rviz configuration.
Note, the conversion algorithms are still experimental. I implemented them "quickly" in spare-time. So if you observe some issues or if you have some suggestions or better default parameter sets, please let me know :-). Also I need to perform some benchmarks in the future between the different algorithms.
According to your console output, the converter is indeed loaded properly. You can tune some of the parameters using rqt_reconfigure. By the way, better start with a convex hull or line algorithm since calculating concave hulls takes much more time and is often not required.
1 Hz is indeed slow. I recently added a FAQ section to the tutorials with some hints about parameters and their influences on computation time: Link
EDIT #1:
After trying to reproduce your parameter setting I recognized, that the planner wasn't loading the correct parameter namespace. Instead of namespace /.../TebLocalPlannerROS/costmap_converter/CostmapTo* it tried to access /.../TebLocalPlannerROS/CostmapTo*. Consequently, your parameters (even in rqt_reconfigure) did not changed anything. I fixed that in the source code and it is included in the new release I am going to push later today).
Regarding your rviz output: Each occupied cell (lethal obstacle, yellow cell) is transformed into a single point. No conversions are performed at all. The reason is that you are using a low costmap resolution (large resolution value >0.5?), but I configured the default values for resolution of 0.1 meters. Note, the default value of parameter cluster_max_distance is too low. Maybe I can change the default parameters such that they scale better with the resolution of the costmap in the future. However, in my opinion your resolution is way too high. The costmap raytrace algorithm marks a lot of free space in your map as obstacles. This could also make navigating through narrow doors nearly impossible. Additionally, after some tests with the converter and a resolution of 0.5, I am not really satisfied with the results of the current implementation.
I am really interested in your computer specs, if the planner runs with just 1 Hz for you?
Hi schultza,
the extracted obstacles are published as Marker type from the teb_local_planner on topic teb_markers. Just add the marker display to your rviz configuration.
Note, the conversion algorithms are still experimental. I implemented them "quickly" in spare-time. So if you observe some issues or if you have some suggestions or better default parameter sets, please let me know :-). Also I need to perform some benchmarks in the future between the different algorithms.
According to your console output, the converter is indeed loaded properly. You can tune some of the parameters using rqt_reconfigure. By the way, better start with a convex hull or line algorithm since calculating concave hulls takes much more time and is often not required.
1 Hz is indeed slow. I recently added a FAQ section to the tutorials with some hints about parameters and their influences on computation time: Link
EDIT #1:
After trying to reproduce your parameter setting I recognized, that the planner wasn't loading the correct parameter namespace. Instead of namespace /.../TebLocalPlannerROS/costmap_converter/CostmapTo* it tried to access /.../TebLocalPlannerROS/CostmapTo*. Consequently, your parameters (even in rqt_reconfigure) did not changed anything. I fixed that in the source code and it is included in the new release I am going to push later today).
Regarding your rviz output: Each occupied cell (lethal obstacle, yellow cell) is transformed into a single point. No conversions are performed at all. The reason is that you are using a low costmap resolution (large resolution value >0.5?), but I configured the default values for resolution of 0.1 meters. Note, the default value of parameter cluster_max_distance is too low. low. Try to change all parameters with rqt_reconfigure first. Maybe I can change the default parameters such that they scale better with the resolution of the costmap in the future. However, in my opinion your resolution is way too high. The costmap raytrace algorithm marks a lot of free space in your map as obstacles. This could also make navigating through narrow doors nearly impossible. Additionally, after some tests with the converter and a resolution of 0.5, I am not really satisfied with the results of the current implementation.
I am really interested in your computer specs, if the planner runs with just 1 Hz for you?
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2022-05-26 11:27:03
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https://www.nature.com/articles/s41598-021-82882-1?error=cookies_not_supported&code=9d1d6967-1d8b-49b6-a6dc-1e84285d66bb
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## Introduction
Gravity is greatly simplified in oceanography from a three-dimensional vector field [g = (gλ, gφ, gz)] with (λ, φ, z) being the (longitude, latitude, height) and (i, j, k) being the corresponding unit vectors with eastward positive for i, northward positive for j, and upward positive (in the Earth radial direction) for k to a vertical vector (−g0k) with the uniform gravity g0 = 9.81 m/s2. The feasibility of such a practice has never been challenged because the horizontal components (gλ, gφ) are much smaller (5–6 orders of magnitudes) than the vertical component gz and the deviation of the magnitude of gz to g0 is also very small. However, similar situation also occurs with the three-dimensional pressure gradient force: the horizontal pressure gradient force is much smaller (5–6 orders of magnitudes) than the vertical pressure gradient force in large-scale oceanic motion. The horizontal pressure gradient forces are considered important in oceanic motion for any scales. Thus, the feasibility to neglect the horizontal gravity components (gλ, gφ) against the vertical gravity (gz) needs to be investigated. The correct approach is to compare the horizontal gravity with the horizontal forces such as the Coriolis force or the horizontal pressure gradient force.
### Reference coordinate systems
The polar spherical coordinates (more popular) and oblate spherical coordinates (less popular, see Appendix) are the reference coordinate system used in the Earth science. In all the fields of the Earth science such as meteorology, oceanography, and geodesy, the horizontal component of any vector A is on the spherical surface if the polar spherical coordinates are used or on the ellipsoidal surface if the oblate spherical coordinates are used,
$${\mathbf{A}} = {\mathbf{A}}_{h} + A_{z} {\mathbf{k}}, \, {\mathbf{A}}_{h} = A_{\lambda } {\mathbf{i}} + A_{\varphi } {\mathbf{j}}$$
(1)
no matter the variable is evaluated on the geoid, isobaric, isopycnal, or topographic-following surfaces. Ocean numerical models have several representations of the vertical (i.e., the radial) coordinate such as z-coordinate1,2, isopycnal coordinate3,4, topographic-following coordinate (i.e., sigma-coordinate)5,6. However, the horizontal component of the vector A is always given by (1).
### Three forms of the gravity
Three forms of gravity exist in geodesy and oceanography: the real gravity g(λ, φ, z), the normal gravity [−g(φ)k], and the uniform gravity (−g0k, g0 = 9.81 m/s2). The real gravity (g) is a three-dimensional vector field, which is decomposed into
$${\mathbf{g}} = {\mathbf{g}}_{h} + g_{z} {\mathbf{k}}, \, {\mathbf{g}}_{h} = g_{\lambda } {\mathbf{i}} + g_{\varphi } {\mathbf{j}}$$
(2)
where gh is the horizontal gravity component; and (gzk) is the vertical gravity component. The normal gravity vector [−g(φ)k] (vertical vector) is associated with a mathematically modeled Earth (i.e., a rigid and geocentric ellipsoid) called the normal Earth. The normal Earth is a spheroid (i.e., an ellipsoid of revolution), has the same total mass and angular velocity as the Earth, and coincides its minor axis with the mean rotation of the Earth7. Similar to g(λ, φ, z), the normal gravity [−g(φ)k] is the sum of the gravitational and centrifugal accelerations exerted on the water particle by the normal Earth. Its intensity g(φ) is called the normal gravity and determined analytically. For example, the World Geodetic System 1984 uses the Somiglina equation to represent g(φ)8
$$g(\varphi ) = g_{e} \left[ {\frac{{1 + \kappa \sin^{2} \varphi }}{{\sqrt {1 - e^{2} \sin^{2} \varphi } }}} \right], \, e^{2} = \frac{{a^{2} - b^{2} }}{{a^{2} }}{, }\kappa = \frac{{bg_{p} - ag_{e} }}{{ag_{e} }}$$
(3)
where (a, b) are the equatorial and polar semi-axes; a is used for the Earth radius, R = a = 6.3781364 × 106 m; b = 6.3567523 × 106 m; e is the spheroid’s eccentricity; ge = 9.780 m/s2, is the gravity at the equator; and gp = 9.832 m/s2 is the gravity at the poles. The uniform gravity (−g0k) is commonly used in oceanography.
### Real and normal gravity potential
Let (P, Q) be the Newtonian gravitational potential of the (real Earth, normal Earth) and PR $$( = \Omega^{2} r^{2} \cos^{2} \varphi /2)$$) be the potential of the Earth’s rotation. Let V = P + PR be the gravity potential of the real Earth (associated with real gravity g) and E = Q + PR be the gravity potential of the normal Earth [associated with the normal gravity -g(φ)k]. The potential of the normal gravity [−g(φ)k] is given by
$$E(\varphi ,z) = - g(\varphi )z$$
(4)
The gravity disturbance is the difference between the real gravity g(λ, φ, z) and the normal gravity [−g(φ)k] at the same point9. The potential of the gravity disturbance (called the disturbing gravity potential) is given by
$$T = V - E = P - Q.$$
(5)
Consequently, the centrifugal effect disappears and the disturbing gravity potential (T) can be considered a harmonic function. With the disturbing gravity potential T, the real gravity g (= gh + gzk) is represented by
$${\mathbf{g}}_{h} = \nabla_{h} T, \, g_{z} = - g(\varphi ) + \frac{\partial T}{{\partial z}}$$
(6)
where $$\nabla_{h}$$ is the horizontal vector differential operator. The geoid height relative to the normal Earth (i.e., reference spheroid) is given by Bruns’ formula10
$$N(\lambda ,\varphi ) = \frac{T(\lambda ,\varphi ,0)}{{g_{0} }}$$
(7)
Equations (5), (6), (7) clearly show that the fluctuation of the marine geoid is independent of the Earth rotation and dependent on the disturbing gravity potential (T) evaluated at z = 0 only.
The disturbing static gravity potential (T) outside the Earth masses in the spherical coordinates with the spherical expansion is given by11
$$T(r,\lambda ,\varphi ) = \frac{GM}{r}\sum\limits_{l = 2}^{\infty } {\sum\limits_{m = 0}^{l} {\left( \frac{R}{r} \right)} }^{l} \left[ {\left( {C_{l,m} - C_{l,m}^{el} } \right)\cos m\lambda + S_{l,m} \sin m\lambda } \right]P_{l,m} (\sin \varphi ),$$
(8)
where G = 6.674 × 10−11m3kg−1 s−2, is the gravitational constant; M = 5.9736 × 1024 kg, is the mass of the Earth; r is the radial distance with z = rR; $$P_{l,m} (\sin \varphi )$$ are the Legendre associated functions with (l, m) the degree and order of the harmonic expansion; $$(C_{l,m} ,C_{l,m}^{el} ,S_{l,m} )$$ are the harmonic geopotential coefficients (Stokes parameters with $$C_{l,m}^{el}$$ belonging to the reference ellipsoid.
From Eqs. (4) and (5) the potential of the real gravity is given by
$$V = T - g(\varphi )z.$$
(9)
From Eq. (6) the real gravity is represented by
$${\mathbf{g}}(\lambda ,\varphi ,z) = \nabla_{h} T + \left[ {\frac{\partial T}{{\partial z}} - g(\varphi )} \right]{\mathbf{k}}$$
(10)
The horizontal gravity component at the reference ellipsoid surface (z = 0) is obtained using (7) and (10)12,13
$${\mathbf{g}}_{h} (\lambda ,\varphi ,0) = \nabla_{h} T = g_{0} \nabla_{h} N$$
(11)
### An approximate 3D gravity field for oceanography
According to Eq. (8) (i.e., the spectral of the disturbing static gravity potential T), the ratio between T(λ, φ, z) to T(λ, φ, 0) through the water column can be roughly estimated by
$$\left| {\frac{T(\lambda ,\varphi ,z)}{{T(\lambda ,\varphi ,0)}}} \right| \approx \frac{R}{(R + z)} \approx 1,\quad 0 \ge z \ge - H(\lambda ,\varphi )$$
(12)
where H is the water depth. Since R is the radius of the Earth and more than 3 orders of magnitude larger than the water depth H. This leads to the first approximation that the surface disturbing gravity potential T(λ, φ, 0) is used for the whole water column,
$$T(\lambda ,\varphi ,z) \approx T(\lambda ,\varphi ,0),\quad 0 \ge z \ge - H(\lambda ,\varphi )$$
(13)
Since the deviation of the vertical component of the gravity (gz) to a constant (−g0) is 3–4 orders of magnitude smaller than g0, it leads to the second approximation
$$g_{z} \approx - g_{0}$$
(14)
With the two approximations, the near real gravity in the water column is given by
$$g_{x} (\lambda ,\varphi ,z) \approx g_{0} \frac{\partial N}{{\partial x}}, \, g_{y} (\lambda ,\varphi ,z) \approx g_{0} \frac{\partial N}{{\partial y}}, \, g_{z} (\lambda ,\varphi ,z) \approx - g_{0}$$
(15)
Correspondingly, the potential of the real gravity is approximately given by
$$V(\lambda ,\varphi ,z) \approx g_{0} \left[ {N(\lambda ,\varphi ) - z} \right]$$
(16)
where Eq. (9) is used.
### Unexpectedly large horizontal gravity component
For simplicity, the local coordinates (x, y, z) are used from now on to replace the polar spherical coordinates with x representing longitude (eastward positive) and y representing latitude (northward positive). The local and spherical coordinate systems are connected by
$$\frac{\partial }{\partial x} = \frac{1}{R\cos \varphi }\frac{\partial }{\partial \lambda }{, }\frac{\partial }{\partial y} = \frac{1}{R}\frac{\partial }{\partial \varphi }, \, \frac{\partial }{\partial z} = \frac{\partial }{\partial r}$$
(17)
The EIGEN-6C4 model14,15, listed on the website http://icgem.gfz-potsdam.de/home, was developed jointly by the GFZ Potsdam and GRGS Toulouse up to degree and order 2190 to produce global static geoid height (N) dataset. Following the instruction, the author ran the EIGEN-6C4 model in 1° × 1° resolution for 17 s to get the global N (Fig. 1) with mean value of 30.57 m, minimum value of -106.20 m, and maximum of 85.83 m. Two locations on the marine geoid are identified with NA = − 99.76 m at A (80° W, 3° N) in the Indian Ocean, and NB = 65.38 m at B (26° W, 45° N) in the North Atlantic Ocean, i.e., |ΔN|AB = 165.14 m. The big circle distance between A and B is about ΔL = 7920 km. Equation (11) shows that the corresponding |gh| at z = 0 is computed by
$$\left| {{\mathbf{g}}_{h} } \right|_{AB} = g_{0} \frac{{\left| {\Delta N} \right|_{AB} }}{\Delta L} = 9.81{\text{ m/s}}^{2} \times \frac{{165.14{\text{ m}}}}{{7.920 \times 10^{6} {\text{ m}}}} = 20.45{\text{ mGal}}$$
(18)
With the geoid height data obtained from the EIGEN-6C4, N(x, y), the horizontal gravity components gx (Fig. 2a) and gy (Fig. 2b) at z = 0 are computed using Eq. (11). The magnitude of the horizontal gravity vector is calculated by
$$\left| {{\mathbf{g}}_{h} (x,y)} \right| = \sqrt {\left[ {g_{x} (x,y)} \right]^{2} + \left[ {g_{y} (x,y)} \right]^{2} } ,$$
(19)
as shown in Fig. 2c. The histogram of |gh| (Fig. 2d) indicates a positively skewed distribution with a long tail extending to values larger than 100 mGal (1 mGal = 10−5 m s−2). The statistical characteristics of |gh| are 20.84 mGal as the mean, 15.89 mGal as the standard deviation, 3.11 as the skewness, and 21.63 as the kurtosis. The statistical estimate of the mean intensity of the horizontal gravity |gh| (20.84 mGal) is coherent with the simple calculation of |gh|AB between points A and B (20.45 mGal). The two values (20.84 mGal, 20.45 mGal) are unexpectedly large.
### C number to identify importance of the horizontal gravity
The importance of the horizontal gravity can be identified by a non-dimensional C number16 from the analysis of horizontal gravity versus the Coriolis force,
$$C(x,y,z) = \frac{{\left| {{\mathbf{g}}_{h} } \right|}}{\left| f \right|U}$$
(20)
where f = 2Ωsinφ, is the Coriolis parameter; and U is the speed of the horizontal current. With Eq. (11) the C number at z = 0 is given by
$$C_{0} (x,y) \equiv C(x,y,0) = \frac{{g_{0} \left| {\Delta N} \right|}}{\left| f \right|U\Delta L}$$
(21)
where ΔL is the horizontal scale of the motion.
The Ocean Surface Current Analysis Real-time (OSCAR) third degree resolution 5-day mean surface current vectors17 on 26 February 2020 (Fig. 3a) was downloaded from the website https://podaac-tools.jpl.nasa.gov/drive/files/allData/oscar/ and the data at the same 1° × 1° grid points as the EIGEN-6C4 data were used. The data represent vertically averaged surface currents over the top 30 m of the upper ocean, which consist of a geostrophic component with a thermal wind adjustment using satellite sea surface height, and temperature and a wind-driven ageostrophic component using satellite surface winds. The histogram of the OSCAR current speed U(x, y) (Fig. 3b) indicates a positively skewed distribution with a long tail extending to values larger than 0.4 m/s. The statistical characteristics of U are 0.1397 m/s as the mean, 0.1414 m/s as the standard deviation, 3.013 as the skewness, and 21.01 as the kurtosis. The histogram of the corresponding Coriolis force $$|f|U(x,y)$$ (Fig. 3c) also shows a positively skewed distribution with a long tail extending to values larger than 2.5 mGal. The statistical characteristics of $$|f|U$$ are 0.8815 mGal as the mean, 1.029 mGal as the standard deviation, 3.379 as the skewness, and 20.24 as the kurtosis. Comparison between Figs. 2d and 3c leads to the fact that the mean intensity of horizontal gravity component $$|{\mathbf{g}}_{h} |$$ (= 20.84 mGal) is nearly 24 times as large as the mean intensity of the Coriolis force identified from the OSCAR surface currents on 26 February 2020. Such unexpectedly large horizontal gravity component is also shown in the world ocean distribution of (1/C0) values (Fig. 4a). The histogram of (1/C0) (Fig. 4b) indicates a positively skewed distribution with a long tail extending to values larger than 0.18. The statistical characteristics of (1/C0) are 0.04238 as the mean, 0.04108 as the standard deviation, 1.447 as the skewness, and 4.481 as the kurtosis. Thus, the global mean of C0 is about 23.6, which is coherent with the rough estimate given above using the geoid height data at the two points A and B (near 24).
### New equations with the real gravity
Application of the Newton’s second law of motion into the ocean for the large-scale motions with the Boussinesq approximation leads to
$$\rho_{0} \left[ {\frac{{D{\mathbf{U}}}}{Dt} + 2{{\varvec{\Omega}}} \times {\mathbf{U}}} \right] = - \nabla p + \rho \nabla V + \rho_{0} {\mathbf{F}}$$
(22)
if the pressure gradient force, gravitation, and friction are the only real forces. Here, $${{\varvec{\Omega}}} = \Omega \left( {{\mathbf{j}}\cos \varphi + {\mathbf{k}}\sin \varphi } \right)$$, is the Earth rotation vector with Ω = 2π/(86,400 s) the Earth rotation rate; ρ is the density; ρ0 = 1028 kg/m3, is the characteristic density; U = (u, v), is the horizontal velocity vector; $$\nabla$$ is the three dimensional vector differential operator; and D/Dt is the total time rate of change; F = (Fx, Fy), is the frictional force and usually represented using vertical eddy viscosity K,
$$F_{x} = \frac{\partial }{\partial z}\left( {K\frac{\partial u}{{\partial z}}} \right), \, F_{y} = \frac{\partial }{\partial z}\left( {K\frac{\partial v}{{\partial z}}} \right)$$
(23)
The continuity equation is given by
$$\nabla _h \cdot {\mathbf{U}} + \frac{\partial w}{{\partial z}} = 0$$
(24)
where w is the vertical velocity. Substitution of (16) into (22) leads to
$$\rho_{0} \left[ {\frac{{D{\mathbf{U}}}}{Dt} + 2{{\varvec{\Omega}}} \times {\mathbf{U}}} \right] = - \nabla p + \rho g_{0} \nabla_{h} N - g_{0} {\mathbf{k}} + \rho_{0} {\mathbf{F}}$$
(25)
Equation (25) can be easily used by any ocean numerical model with just adding the horizontal gravity component represented by $$(\rho g_{0} \nabla_{h} N)$$.
### Hydrostatic balance
Large-scale oceanic motion is hydrostatically balanced,
$$- \frac{\partial p}{{\partial z}} + \rho \frac{\partial V}{{\partial z}} = 0 \, \Rightarrow \, dp = \rho dV$$
(26)
Vertical integration of this equation from the marine geoid (i.e., V = 0) to any equipotential surface V leads to the integral form of the hydrostatic balance
$$p = \int\limits_{ - V(x,y,z)}^{0} {\rho d\tilde{V}} + \rho_{0} g_{0} (S - N)$$
(27)
where S is the sea surface height; and the marine geoid surface (N) is the coincidence of the equipotential and isobaric surfaces (i.e., balance of the 3D pressure gradient force and gravity on N).
### Equipotential (-V) coordinate system
The hydrostatic Eq. (27) clearly shows that a single valued monotonic relationship exists between gravitational potential and the depth in each vertical water column. Thus, we may use (-V) as the independent vertical coordinate. The negative sign is due to the vertical component of the gravity is defined positive downward. The total derivative is expanded as
\begin{aligned} \frac{D}{Dt} &= \frac{\partial }{\partial t} + \frac{Dx}{{Dt}}\frac{\partial }{\partial x} + \frac{Dy}{{Dt}}\frac{\partial }{\partial y} + \frac{D( - V)}{{Dt}}\frac{\partial }{\partial ( - V)} \\ &= \frac{\partial }{\partial t} + u\frac{\partial }{\partial x} + v\frac{\partial }{\partial y} + \omega \frac{\partial }{\partial V} \\ \end{aligned}
(28)
The continuity Eq. (24) becomes
$$\nabla _h\cdot {\mathbf{U}} + \frac{\partial \omega }{{\partial V}} = 0$$
(29)
here,
$$\omega \equiv \frac{dV}{{dt}} = {\mathbf{U}} \cdot \nabla _h V + w\frac{\partial V}{{\partial z}}$$
(30)
where ω is the “vertical velocity” in the V-coordinate. Note that V is the static gravitational potential such that ∂V/∂t = 0.
### Dynamic equations in the equipotential coordinate system
The horizontal pressure gradients can be computed from (27),
\begin{aligned} \frac{\partial p}{{\partial x}} & = \rho \frac{\partial V}{{\partial x}} + \int\limits_{ - V}^{0} {\frac{\partial \rho }{{\partial x}}d\tilde{V} + \rho_{0} g_{0} \frac{\partial (S - N)}{{\partial x}}} , \\ \frac{\partial p}{{\partial y}} & = \rho \frac{\partial V}{{\partial y}} + \int\limits_{ - V}^{0} {\frac{\partial \rho }{{\partial y}}d\tilde{V}} + \rho_{0} g_{0} \frac{\partial (S - N)}{{\partial y}} \\ \end{aligned}
(31)
Substitution of (31) into (22) leads to the horizontal momentum equations
$$\frac{Du}{{Dt}} - fv = - \frac{1}{{\rho_{0} }}\int\limits_{ - V}^{0} {\frac{\partial \rho }{{\partial x}}d\tilde{V}} - g_{0} \frac{\partial (S - N)}{{\partial x}} + F_{x}$$
(32a)
$$\frac{Dv}{{Dt}} + fu = - \frac{1}{{\rho_{0} }}\int\limits_{ - V}^{0} {\frac{\partial \rho }{{\partial y}}d\tilde{V}} - g_{0} \frac{\partial (S - N)}{{\partial y}} + F_{y}$$
(32b)
### Extended geostrophic equilibrium and thermal wind relation
For steady state (no total derivative) without friction, Eqs. (32a) and (32b) become the extended equations for the geostrophic currents
$$- fv_{G} = - \frac{1}{{\rho_{0} }}\int\limits_{ - V}^{0} {\frac{\partial \rho }{{\partial x}}d\tilde{V}} - g_{0} \frac{\partial (S - N)}{{\partial x}}$$
(33a)
$$fu_{G} = - \frac{1}{{\rho_{0} }}\int\limits_{ - V}^{0} {\frac{\partial \rho }{{\partial y}}d\tilde{V}} - g_{0} \frac{\partial (S - N)}{{\partial y}}$$
(33b)
Vertical derivative of (33a) and (33b) leads to the extended thermal wind relation
$$- f\frac{{\partial v_{G} }}{\partial z} = \frac{{g_{0} }}{{\rho_{0} }}\frac{\partial \rho }{{\partial x}} - \frac{1}{{\rho_{0} }}\int\limits_{ - V}^{0} {\frac{{\partial^{2} \rho }}{\partial x\partial z}d\tilde{V}}$$
(34a)
$$f\frac{{\partial u_{G} }}{\partial z} = \frac{{g_{0} }}{{\rho_{0} }}\frac{\partial \rho }{{\partial y}} - \frac{1}{{\rho_{0} }}\int\limits_{ - V}^{0} {\frac{{\partial^{2} \rho }}{\partial y\partial z}d\tilde{V}}$$
(34b)
where the vertical differentiation of lower limit (-V) of the integrals of the righthand side of (33a) and (33b)
$$\frac{\partial V}{{\partial z}} = g_{z} \approx - g_{0}$$
(35)
is used.
### Vorticity equation
Subtraction of the differentiation of the longitudinal component of Eq. (25) with respect to y from the differentiation of the latitudinal component of Eq. (25) with respect to x leads to the vorticity equation,
\begin{aligned} \frac{\partial \zeta }{{\partial t}} & = - {\mathbf{U}} \cdot \nabla _h\zeta - \omega \frac{\partial \zeta }{{\partial V}} + \beta v - (\zeta + f)\nabla _h \cdot {\mathbf{U}} + {\mathbf{k}} \cdot \left( {\frac{{\partial {\mathbf{U}}}}{\partial V} \times \nabla_h \omega } \right) \\ &\quad + \frac{{g_{0} }}{{\rho_{0} }}J(\rho ,N) + \left( {\frac{{\partial F_{y} }}{\partial x} - \frac{{\partial F_{x} }}{\partial y}} \right) \\ \end{aligned}
(36)
where $$J(\rho ,N) = (\partial \rho /\partial x)(\partial N/\partial y) - (\partial \rho /\partial y)(\partial N/\partial x)$$, is the Jacobian; $$\beta = df/dy$$ is the latitudinal change of the Coriolis parameter; and $$\zeta = \partial v/\partial x - \partial u/\partial y$$ is the vertical vorticity.
## Conclusion
The non-dimensional C number is used to identify relative importance of the horizontal gravity and the Coriolis force using the geoid height data (N) provided by the EIGEN-6C4 gravity model, and the Ocean Surface Current Analysis Real-time (OSCAR) surface current vectors on 26 February 2020. Unexpectedly large value of the C number (global mean around 24) may surprise both oceanographic and geodetic communities. It is very hard for my oceanographic colleagues to accept such strong horizontal gravity (at z = 0), which is an order of magnitude lager that the Coriolis force. Thus, in situ measurement of gravity may be needed for oceanography in addition to the routine hydrographic and current meter measurements.
A geodesist may also be surprised that the horizontal gravity (z = 0) associated with the geoid height (N) varying between -106.20 m to 85.83 m (well accepted by the geodetic community), which was produced by a community gravity model (EIGEN-64C), generates the ocean currents with the intensity nearly 24 times as large as the currents identified from the ocean surface current analysis real-time (OSCAR) (oceanographic community product).
How to resolve such incoherency between the two communities on this issue becomes urgent. The new ocean dynamic equations including the horizontal gravity may provide a theoretical framework to resolve the incoherency since the potential of the real gravity (V) obtained from a geodetic gravity model is explicitly in the dynamical equations. Besides, use of the real gravity in the ocean dynamics may ultimately resolve some fundamental problems in oceanography such as reference level, and absolute geostrophic current calculation. A new dynamic system for large-scale oceanic motion with the real gravity is presented such as hydrostatic balance, geostrophic equilibrium, thermal wind, equipotential coordinate system, and the vorticity equation. Close collaboration between the oceanographic and geodetic communities helps the use of the real gravity in oceanography and the verification of the gravity model in geodesy with oceanographic data.
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2022-09-25 12:59:24
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https://www.gradesaver.com/textbooks/math/algebra/college-algebra-11th-edition/chapter-r-test-page-78/17
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## College Algebra (11th Edition)
$2m(4m+3)(3m-4)$
$\bf{\text{Solution Outline:}}$ To factor the given expression, $24m^3-14m^2-24m ,$ factor first the $GCF.$ Then find two numbers whose product is $ac$ and whose sum is $b$ in the quadratic expression $ax^2+bx+c.$ Use these $2$ numbers to decompose the middle term of the given quadratic expression and then use factoring by grouping. $\bf{\text{Solution Details:}}$ The $GCF$ of the constants of the terms $\{ 24,-14,-24 \}$ is $2$ since it is the highest number that can divide all the given constants. The $GCF$ of the common variable/s is the variable/s with the lowest exponent. Hence, the $GCF$ of the common variable/s $\{ m^3,m^2,m \}$ is $m .$ Hence, the entire expression has $GCF= 2m .$ Factoring the $GCF= 2m ,$ the expression above is equivalent to \begin{array}{l}\require{cancel} 2m \left( \dfrac{24m^3}{2m}-\dfrac{14m^2}{2m}-\dfrac{24m}{2m} \right) \\\\= 2m \left( 12m^2-7m-12 \right) .\end{array} In the trinomial expression above the value of $ac$ is $12(-12)=-144$ and the value of $b$ is $-7 .$ The $2$ numbers that have a product of $ac$ and a sum of $b$ are $\left\{ 9,-16 \right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to \begin{array}{l}\require{cancel} 2m \left( 12m^2+9m-16m-12 \right) .\end{array} Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to \begin{array}{l}\require{cancel} 2m [(12m^2+9m)-(16m+12)] .\end{array} Factoring the $GCF$ in each group results to \begin{array}{l}\require{cancel} 2m [3m(4m+3)-4(4m+3)] .\end{array} Factoring the $GCF= (4m+3)$ of the entire expression above results to \begin{array}{l}\require{cancel} 2m [(4m+3)(3m-4)] \\\\= 2m(4m+3)(3m-4) .\end{array}
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2018-08-16 05:07:06
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https://math.stackexchange.com/questions/4032570/show-x-n1-1-sqrtx-n-is-upper-bounded-and-increasing/4032586
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# Show $x_{n+1} = 1 + \sqrt{x_n}$ is upper-bounded and increasing
Given $$x_1 = 1$$, it is clear that $$x_n \ge 1$$ for any $$n \in \Bbb{N}$$. I know that {$$x_n$$} is obviously increasing and limit as $$n \to \infty$$ is $$\frac{3 + \sqrt{5}}{2}$$, so {$$x_n$$} has an upper bound also. I seem to have trouble proving $$x_{n+1} / x_n \ge 1$$ and don't even have any idea on how to prove the sequence is upper-bounded. Can you guys give me some hints?
• You say that $(x_n)$ is “obviously” increasing, but you have trouble to prove that $x_{n+1} / x_n \ge 1$? Feb 20, 2021 at 4:06
• Well I just mean I could not prove it is increasing in an elegant manner. It is easy to notice, but what you notice is not a proof. Feb 20, 2021 at 4:13
## 3 Answers
From the recurrence , we can deduce that $$x_2 = 2$$ $$x_3 = 1 + \sqrt{2}$$ $$x_4 = 1 + \sqrt{1+\sqrt{2}}$$ $$x_5 = 1 + \sqrt{1+\sqrt{1+\sqrt{2}}}$$ You can continue . Let $$z = x_n$$ as $$n \to \infty$$ you can write $$z = 1 + \sqrt{z}$$ Solving you get that $$z = \frac{3 + \sqrt{5}}{2}$$ ($$z$$ is positive real) . Also to prove $$\frac{x_n}{x_{n-1}} \geq 1$$ You can write it as $$1 + \sqrt{x_n} \geq x_n$$ $$0 \geq x_n^2 -2x_n + 1$$ Which is true from the limit as let $$f(x) = x^2 -3x +1$$ You can write it as $$f(x) = \left(x - \frac{3 + \sqrt{5}}{2}\right)\left(x - \frac{3 - \sqrt{5}}{2}\right)$$ and for $$f(x) \leq 0$$ , $$x \in [\frac{3 - \sqrt{5}}{2} , \frac{3 + \sqrt{5}}{2}]$$ .
For boundedness from above just note that
$$x_n \leq 4\Rightarrow x_{n+1} = 1+\sqrt{x_n} \leq 1+\sqrt 4 =3 \leq 4$$
Now, the claim follows immediately by induction.
• I just came up with the simplest proof of {$x_n$} being increasing sequence: note if $x_n \le x_{n+1} => \sqrt{x_n} \le \sqrt{x_{n+1}} => 1+ \sqrt{x_n} \le 1 + \sqrt{x_{n+1}} => x_{n+1} \le x_{n+2}$ so by induction {$x_n$} is increasing Feb 20, 2021 at 4:15
• @Gerald I understood form your question that your problem was the boundedness from above. Feb 20, 2021 at 4:17
• That the sequence is increasing also follows by induction quickly just considering $$x_{n+1}-x_n = \left(1+\sqrt{x_n}\right)-\left(1+\sqrt{x_{n-1}}\right) = \sqrt{x_n}-\sqrt{x_{n-1}}$$ Feb 20, 2021 at 4:20
Let $$f(x)=1+\sqrt{x}$$, so $$f(\phi^2)=\phi^2$$ where $$\phi=(1+\sqrt{5})/2$$. Since $$f$$ is strictly increasing and $$x_1<\phi^2$$, it follows by induction that $$f(x_n) <\phi^2$$ for all $$n \ge 1$$. Also, since $$x_1, we infer by induction that $$x_n for all $$n \ge 1$$. The induction step is simply an application of $$f$$ to both sides.
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2022-06-27 19:12:11
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http://motls.blogspot.hr/
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## Saturday, October 01, 2016 ... /////
### Janet Yellen is right: central banks' purchase of stocks may be useful and justified
When Janet Yellen was being chosen as the boss of the Federal Reserve, I didn't really know who she was, what she knew, and I was somewhat skeptical that she was an extremely bright economist.
Larry Summers – whom I intimately (don't overstate this word, however) know as the former president of Harvard – was an example of a guy whom I often disagree with but whose thinking was expected to be more penetrating, impartial, rational to me than Yellen's. After all, I have known way too many examples in which a less qualified female was picked by the forces of affirmative action.
I must say that after I have watched several press conferences featuring Yellen, I have largely changed my mind. As far as I can say, she understands economics, the economy, and the forces and pressures that affect it. And she is remarkably rational and impartial when it comes to the evaluation of the relevant questions.
## Friday, September 30, 2016 ... /////
### Barry Barish deserves a LIGO Nobel prize, too
It's not certain at all that next Tuesday, the Nobel prize in physics will be given to the people associated with LIGO, the (double) L-shaped experiment that announced the detection of Einstein's gravitational waves in February 2016. Recall that the waves were actually detected on September 14th, 2015, a year ago, just four months after an interview where someone said that the detection would take place "within five years". Sometimes things are slower than expected but indeed, sometimes they are faster, too.
Despite the uncertainty about the 2016 Nobel, the LIGO possibility is reasonably likely by now. Rumors indicate that the January 31st deadline for the nominations didn't turn out to be a fatal obstacle for the LIGO-related candidates.
In February, I was afraid that there could be some politically correct folks who would want to reward the current leaders of the experiment – basically random politically chosen hires. But thankfully or hopefully, it seems that the probability of this scenario has decreased and the actual fathers of the LIGO success – which made the decisive steps decades ago – are more likely to win.
### In 61 days, a Slovak billionaire will monitor every single Czech cash transfer in real time
Millions of stupid and jealous Czech sheep embrace the new "1984"
Unless something unexpected happens – and I pray that it will – the first batch of 50,000 of Czech businesses, mainly restaurants and hotels etc., will be obliged to immediately report every single payment from a consumer to the ministry of finance led by the Slovak-born food industry billionaire, media mogul, a VIP ex-member of the communist party, and a former communist snitch Andrej Babiš (net worth over $3 billion). The consumer gets a receipt and he or she – an amateur snitch – will be able to send the receipt's ID to a server of the ministry and verify that the payment has been reported by the business. A motivation is that he may win a lottery for the amateur snitches. Andrej Babiš's former career of a snitch is seen in every aspect of this sick system. If the payment hasn't been reported, the businessman will immediately face existentially threatening fines and other punishments that the minister himself may decide about – or forgive. The law defining the EET things is a classic "rubber law" that may be bent by the executive power. It's a similar kind of a law that made Adolf Hitler the Führer. This system is meant to guarantee that the taxes from that payment – every payment – will be sent to the government. Andrej Babiš, a member of the very bottom of the Czechoslovak moral cesspool who would have been executed in late 1989 if we hadn't decided to make our revolution in the "velvet" way (for example, their dirty family disinherited a relative who "dared to emigrate" from the communist Czechoslovakia, to emphasize how deeply into the communist leaders' aßes they are willing to climb in order to keep their undeserved advantages), and a guy who already owns most of the largest newspapers, will have access to all the information about every single cash payment to every business on the territory of Czechia, at least after all businesses are included into the system in a coming year or so. ## Thursday, September 29, 2016 ... ///// ### Aspects of the Indian-Pakistani (so far) miniwar The British Empire has been in charge of the British India for some time. In 1947, that territory declared their independence and new countries, Pakistan and India, were created. Pakistan is some 98% Islamic. India is mostly Hinduist (Buddhism is below 1% these days) and only 15% Islamist (Christianity is over 2%, the third largest religion there). However, you may see that India is still the by far more diverse country among the two. I would surely say that India is the more "politically Western" country among the two. You could say that it's "ironic" given the Pakistani prime minister Nawaz Sharif's Western suit and "Aryan" skin color on the picture above with the visually darker and more folklore-dressed Indian prime minister Modi. But India's fights against the Islamic terrorists basically coincide with the logic of similar fights that sensible Western countries have to wage. There have been three conflicts between India and Pakistan. Most of the conflicts are linked to the most disputed part of the border, inside Kashmir. Kashmir is a territory in the Northern part of the Pakistani-Indian border, a cool region adjacent to the Himalayas. Both countries claim all of it. In practice, it's divided to two similarly large parts by the de facto (but internationally unrecognized) border, the so-called "Line of Control" (LoC). That's where the newest tension is concentrated, too. ### Rainer Weiss' birthday: from Slovakia to circuits, vinyl in Manhattan to LIGO Along with Kip Thorne and Ronald Drever, Rainer Weiss is one of the most likely "triplet" that can share the Nobel prize in physics next Tuesday. Weiss' key contribution already occurred in 1967 – see the history of LIGO – when he began to construct a laser interferometer and published a text pointing out its usefulness. WVXU, a BBC-linked news source, just released a fun biography: A physicist who proved Einstein right started by tinkering with the family record player Aside from fundamental physics, one of the additional reasons why this biography may be relevant on this blog are his family's links to Czechoslovakia. ## Wednesday, September 28, 2016 ... ///// ### 92% in unhealthy air? Another example of a boy who cries wolf By Václav Klaus, Czech ex-president Today in the morning, my smartphone beeped and informed me about the reports that "an overwhelming majority of the inhabitants of the planet, namely 92 percent, is living at places where the air pollution surpasses the limits defined by the World Health Organization". ## Tuesday, September 27, 2016 ... ///// ### Most Czech viewers: Trump won 1st debate Donald and Hillary met in the first presidential debate (90 minutes of video) at Hofstra University, New York. Lester Holt was the moderator. The host had the full control over the questions, the audience – partly students – was expected to remain silent and not to use cameras and phones. Hillary said "Hey Donald!" and he shook her hand, apparently confident in his immunity against pneumonia and other contagious diseases. Quite generally, I am sure it's right to say that they behaved in a much more friendly way towards each other than their voters. ;-) Concerning similar formalities and speaking strategies, Trump was attempting to interrupt Hillary more than 20 times but only succeeded once. She didn't try to interrupt him, with three failed exceptions. ## Sunday, September 25, 2016 ... ///// ### Civil casualties in Aleppo are sad but negligible I just listened to a rant by Samantha Power, the current U.S. ambassador to the U.N. Well, what a hateful woman – when it comes to anything that has a relationship with Russia. She has nothing to do with the America that we used to love and that was inspiring us. One of the reasons I would love Trump to win is that he could end this absolutely insane anti-Russian hysteria in the U.S. Among other things, he could help to fire this particular insufferable female talking head. But it's not just Samantha Power. Boris Johnson talks about Russian war crimes in Syria while The Telegraph shocks us with the Aleppo horror. From that paper, you may learn what has actually happened. In a hugely intense bombing of the anti-Assad forces in Aleppo, an operation masterminded by the Kremlin and Assad, "dozens" of civilians have been killed. That's sad. (Media close to the Kremlin dispute even these dozens of death but let me assume that these sad reports are true.) But is that unexpected? Is that a lot? ## Saturday, September 24, 2016 ... ///// ### Orbán wants to build a Hong Kong for Arabs and blacks in Libya Hungary's prime minister Viktor Orbán keeps on presenting creative proposals that actually make sense. Hungarian Prime Minister says EU should set up refugee city in Libya He wants to grab a piece of land outside the EU – most specifically, he mentioned a place in Libya – and build a large enough camp that should host a really, really large number of migrants or self-described refugees. I chose the term "Hong Kong" because there could be a million people over there; the terms "Liberland" or "Dachau" look too small for Orbán's project. Note that Hong Kong was liberated from the Japanese overlords in 1945 by a combination of Chinese and British troops. The latter players were enough to bring the place under the British control which meant a huge economic advantage. As previously negotiated, Hong Kong returned under the control of the People's Republic of China in 1997. So far, they haven't destroyed the place – because at least in the economic sense, the mainland China has largely embraced capitalism by itself. ### NASA-sponsored article makes millions of Ophiuchus-born women hysterical Every five years or so (see 2007 and 2011), I write a blog post about the 13rd zodiac sign, the Serpentarius (the Greek name Ophiuchus is preferred by many these days but not by me) – the wearer of the snakes – in which I was born, much like everyone whose birthday is between November 29th and December 17th or so (more dates). Fall 2016 just began and it was inevitable that someone makes sure that this insight shocks millions of people, especially women. And it's here. See the recent Ophiuchus articles on Google News. ### Europe has a chance to be "out" when Paris comes to force The Paris agreement is a recent meaningless remake of the 1997 meaningless Kyoto treaty that, like the predecessor, tries to "fight against the climate change". Err once, err twice... If you remember the Kyoto treaty, Al Gore signed it but the U.S. has never ratified it, and neither has Australia. Canada later withdrew from that pact. I think that the impact of this absence of the U.S. on the production of carbon dioxide – let alone the climate – was non-existent. In fact, the U.S. saw a greater decrease of "CO2 produced per dollar or capita" than the average Kyoto signatory. But because the U.S. stayed out, the American climate alarmists couldn't show their muscles as aggressively as their European counterparts. Even though conservative Americans love to imagine that their nation is always more conservative than the European nations, I think that it doesn't apply to the current U.S. administration that is more left-wing than most European governments. This has many manifestations but one of them concerns the climate hysteria. ## Friday, September 23, 2016 ... ///// ### Media downgrade Roger Penrose to an invisible appendix of crank Lee Smolin A week ago, Roger Penrose released his new book Fashion, Faith, and Fantasy. We already knew that he was writing a book of this name in 2009 and Penrose was actually giving lectures with this name in 2006 or earlier. So you may say that this book is something that Roger Penrose – and he's far from an average man – has been working on for something like one decade. Also, the book has almost 200 figures which are freely available. I wrote the clearest description of the book that is now out in 2014. Is the demand for this product of a decade-long effort by a famous thinker appropriate? Before we turn to this question, let me remind you about the content of the book or the meaning of the words in the title. The three words, fashion, faith, and fantasy, primarily refer to string theory, quantum mechanics, and inflation, respectively. Roger Penrose has some problems with all these three things – and others. So he invents slogans to dismiss all these three important theories. String theory is a bubble, quantum mechanics is a religious cult, and inflationary cosmology is a result of folks on drugs who see pink elephants around. (Penrose's explanations are less concise and less colorful than mine, he's no Motl.) As I have discussed in previous blog posts, his negative opinions on all these three theories are fundamentally wrong. ## Thursday, September 22, 2016 ... ///// ### Thomson Reuters: Nobel for Cohen, LIGO 3, or control theory We got used to the predictions of the Nobel prize winners by Thomson Reuters. The awards will be announced between October 3rd and 10th. The predictions are in the article Web of Science Predicts 2016 Nobel Prize Winners Let us spend less time with the disciplines different than physics. ## Wednesday, September 21, 2016 ... ///// ### Nanopoulos' and pals' model is back to conquer the throne Once upon a time, there was an evil witch-and-bitch named Cernette whose mass was $750\GeV$ and who wanted to become the queen instead of the beloved king. Fortunately, that witch-and-bitch has been killed and what we're experiencing is The Return of the King: No-Scale ${\mathcal F}$-$SU(5)$, Li, Maxin, and Nanopoulous point out. It's great news that the would-be $750\GeV$ particle has been liquidated. They revisited the predictions of their class of F-theory-based, grand unified, no-scale models and found some consequences that they surprisingly couldn't have told us about in the previous 10 papers and that we should be happy about, anyway. ## Tuesday, September 20, 2016 ... ///// ### Al Jazeera attempts a terrorist attack against the Czech gambling industry "No stronger retrograde force exists in the world. Far from being moribund, Mohammedanism is a militant and proselytising faith," Winston Churchill famously pointed out. We could have seen another example just five hours ago when Al Jazeera, a hybrid of written Mohammedanism and modern Western left-wing brainwashing outlets, picked a particular target, the Czech gambling industry: Czech Republic: A dangerous gambling addiction The author, an American living in Burma ($5,000 is the GDP per capita, PPP), described Czechia as a decaying society where 110,000 gamblers (over 1%) should probably be stored in a psychiatric asylum. (The number 110,000 was picked from some random government documents and compared with numbers from other governments – which obviously use completely different methods so he was comparing apples with oranges.)
He admitted that these industries were overregulated during communism (which doesn't mean that gambling was absent: the totto-lotto ["Sportka" existed during socialism] and betting on sports was alive and reasonably well ["Sazka" was the large company that did this business already during socialism], while avoiding the efficiency of capitalism) but he described the results of freedom in this business as catastrophic.
Slot machines, quizomats – machines that test the encyclopedic knowledge or IQ, betting on sports, and other things were all included in his picture of the Armageddon.
### Czech presidents would pick Trump
There are various people in the Europe – and even in Czechia – who have endorsed Hillary Clinton for the U.S. president. Well, even though the late Václav Havel could be one of these people if he were around, the Czech presidents who are alive beg to differ.
President Emeritus Václav Klaus believes (and so do his aides) that Hillary's reign would be a continuation of the ongoing tragic drift towards the PC post-democracy. He thinks that Trump is a natural political animal who is currently playing the role of a campaigner and who will behave differently, more responsibly, once he sits in the White House. However, Klaus often says that "unfortunately, Hillary will probably win".
Well, I actually think that Trump's victory is more likely.
Today, the current Czech president Miloš Zeman, the founder of the modern social democracy in Czechia, was interviewed by iDNES TV and its boss Jaroslav Plesl, a journalist owned by the billionaire Andrej Babiš.
The first half of the 15-minute interview is dedicated to the Czech regional elections (in October 2016), the Czech economy, budget deficits etc. The elections are less important than the parliamentary elections. Those things are totally boring for 98% of TRF voters. Let me jump to the foreign policy questions.
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2016-10-01 18:52:57
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https://math.gatech.edu/seminars-and-colloquia-by-series?series_tid=72&page=21
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## Seminars and Colloquia by Series
### The 15th International Conference on Random Structures and Algorithms
Series
Other Talks
Time
Tuesday, May 24, 2011 - 08:00 for 8 hours (full day)
Location
Emory University
Speaker
Conference on Random Structures and AlgorithmsEmory University
The 15th International Conference on Random Structures and Algorithms (RS&A) 2011 will be held at Emory University, May 24-28 (Tuesday-Saturday) 2011 and is co-organized by Emory University, Georgia Institute of Technology and Adam Mickiewicz University. The conference, organized biennially since 1983, brings together probabilists, discrete mathematicians and theoretical computer scientists working in probabilistic methods, random structures and randomized algorithms. The program will consist of one-hour plenary addresses by the invited speakers and parallel sessions of 25-minute contributed talks. It will begin on Tuesday morning and end on Saturday afternoon. The list of plenary speakers includes: Béla Bollobás [University of Cambridge and University of Memphis]; Jennifer Chayes [Microsoft Research New England, Cambridge]; Fan Chung [University of California, San Diego]; Jacob Fox [Massachusetts Institute of Technology]; David Gamarnik [Massachusetts Institute of Technology]; Jeff Kahn [Rutgers University]; Subhash Khot [Courant Institute]; Eric Vigoda [Georgia Institute of Technology]; Nick Wormald [University of Waterloo].
### SHARP MIXING TIME BOUNDS FOR SAMPLING RANDOM SURFACES
Series
Other Talks
Time
Monday, May 23, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
KLAUS 1116W
Speaker
Fabio MartinelliUniversity of Rome 3, Rome, Italy
We analyze the mixing time of a natural local Markov Chain (Gibbs sampler) for twocommonly studied models of random surfaces: (i) discrete monotone surfaces in Z3 with almostplanar" boundary conditions and (ii) the one-dimensional discrete Solid-on-Solid (SOS) model.In both cases we prove the first almost optimal bounds O(L^2 polylog(L)) where L is the natural size of the system. Our proof is inspired by the so-called mean curvature" heuristic: on a large scale, the dynamics should approximate a deterministic motion in which each point of the surface moves according to a drift proportional to the local inverse mean curvature radius. Key technical ingredients are monotonicity, coupling and an argument due to D.Wilson in the framework of lozenge tiling Markov Chains together with Kenyon's results on the free Gaussian field approximation of monotone surfaces. The novelty of our approach with respect to previous results consists in proving that, with high probability, the dynamics is dominated by a deterministic evolution which, apart from polylog(L) corrections, follows the mean curvature prescription. Our method works equally well for both models despite the fact that their equilibrium maximal deviations from the average height profile occur on very different scales (log(L) for monotone surfaces and L^{1/2} for the SOS model).This is work in collaboration with PIETRO CAPUTO and FABIO LUCIO TONINELLI
### Concentration of measure and optimal transport
Series
Other Talks
Time
Friday, May 20, 2011 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nathael GozlanUniversity of Paris, Marne La Vallee
The aim of this talk is to present recent results obtained in collaboration with C. L\'eonard, C. Roberto and P.M Samson. In the first part, I will give a necessary and sufficient condition for Talagrand's inequality on the real line. In the second part, I will explain the links between Talagrand's inequality and the dimension-free Gaussian concentration phenomenon. This will lead us to a new proof of Otto-Villani Theorem. Finally, in the third part, we will show that Talagrand's inequality is equivalent to a variant of the log-Sobolev inequality, called the inf-convolution log-Sobolev inequality. This theorem will enable us to prove a general perturbation result for Talagrand's inequality.
### Graduate Student Probability Conference 2011
Series
Other Talks
Time
Friday, April 29, 2011 - 09:00 for 8 hours (full day)
Location
Klaus 1116
Speaker
Graduate Students Probability ConferenceSchool of Mathematics, Georgia Tech
Please Note: Other organizers include: Ruoting Gong, Huy Huynh, Jinyong Ma, Ruodu Wang, and Linwei Xin.
Georgia Tech School of Mathematics will host the 5th Annual Graduate Student Probability Conference (GSPC) from April 29 - May 1, 2011. The conference is open to all graduate students and post-doctoral fellows interested in probability. We will host two keynote speakers: Professor Nathalie Eisenbaum (Université Pierre et Marie Curie) and Professor Philip Protter (Columbia University). The conference will begin at 9:00 AM Friday, April 29 and end at noon on Sunday May 1.
### Atlanta Lecture Series in Combinatorics and Graph Theory III
Series
Other Talks
Time
Saturday, April 16, 2011 - 13:00 for 4 hours (half day)
Location
Klaus 1456
Speaker
Atlanta Lecture SeriesSchool of Mathematics, Georgia Tech
Emory University, the Georgia Institute of Technology and Georgia State University will host a series of 9 mini-conferences from November, 2010 - April 2013. The conferences will stress a variety of areas and feature one prominent researcher giving 2 fifty minute lectures and 4 outstanding southern researchers each giving one fifty minute lecture. There will also be several 30 minute lecturers by young researchers or graduate students. The featured speaker is Maria Chudnovsky, Columbia University. The lectures begin at 1:00 PM Saturday, April 16 and end at noon on Sunday, April 17.
### FoSoM Panel Discussion
Series
Other Talks
Time
Thursday, April 14, 2011 - 16:00 for 3 hours
Location
Skiles 005
Speaker
Math AlumniSchool of Mathematics, Georgia Tech
Please Note: Refreshments will be served at 3:30.
The Friends of the School of Mathematics present a panel discussion on "Non-Academic Careers: Opportunities and Challenges for Students" A distinguished panel of alumni of the School will present their views on opportunities and challenges for students as they prepare for non-academic careers. The panelists will also answer questions from the audience. Graduate students and undergraduate majors in Mathematics are especially encouraged to attend.
### Club Math - From Flapping Birds to Space Telescopes - The Mathematics of Origami
Series
Other Talks
Time
Monday, April 11, 2011 - 17:00 for 1 hour (actually 50 minutes)
Location
Student Success Center, Clary Theater
Speaker
Robert LangAlamo, California
Please Note: Robert J. Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. With a Ph.D. in Applied Physics from Caltech, he has, during the course of work at NASA/Jet Propulsion Laboratory, Spectra Diode Laboratories, and JDS Uniphase, authored or co-authored over 80 papers and 45 patents in lasers and optoelectronics as well as authoring, co-authoring, or editing 9 books and a CD-ROM on origami. He is a full-time artist and consultant on origami and its applications to engineering problems but moonlights in physics: from 2007-2010 as the Editor-in-Chief of the IEEE Journal of Quantum Electronics.
The last decade of this past century has been witness to a revolution in the development and application of mathematical techniques to origami, the centuries-old Japanese art of paper-folding. The techniques used in mathematical origami design range from the abstruse to the highly approachable. In this talk, I will describe how geometric concepts led to the solution of a broad class of origami folding problems – specifically, the problem of efficiently folding a shape with an arbitrary number and arrangement of flaps, and along the way, enabled origami designs of mind-blowing complexity and realism, some of which you’ll see, too. As often happens in mathematics, theory originally developed for its own sake has led to some surprising practical applications. The algorithms and theorems of origami design have shed light on long-standing mathematical questions and have solved practical engineering problems. I will discuss examples of how origami has enabled safer airbags, Brobdingnagian space telescopes, and more. From 3:30pm-4:30pm, Informal Folding Session will take place in Skiles 236
### Robert J. Lang - Origami Informal Folding Session
Series
Other Talks
Time
Monday, April 11, 2011 - 15:30 for 1 hour (actually 50 minutes)
Location
Skiles 236
Speaker
Robert LangAlamo, California
Robert Lang is recognized as one of the foremost origami artists in the world as well as a pioneer in computational origami and the development of formal design algorithms for folding. Join him for an informal folding session before his presentation.
### Southeast Geometry Seminar
Series
Other Talks
Time
Sunday, April 10, 2011 - 09:00 for 8 hours (full day)
Location
Emory University
Speaker
Southeast Geometry SeminarEmory University
The Southeast Geometry Seminar is a series of semiannual one-day events focusing on geometric analysis. These events are hosted in rotation by the following institutions: The University of Alabama at Birmingham; The Georgia Institute of Technology; Emory University; The University of Tennessee Knoxville. The following five speakers will give presentations on topics that include geometric analysis, and related fields, such as partial differential equations, general relativity, and geometric topology. Borin Rubin (Louisiana State Univ); Joseph Fu (Univ of Georgia); Paul Yang (Princeton U); Robert Gulliver (Univ of Minnesota); Ken Stephenson (U of Tennessee).
### Research in Mathematics Educational Technology - Current Trends and Future Demands
Series
Other Talks
Time
Friday, April 8, 2011 - 10:30 for 1 hour (actually 50 minutes)
Location
CEISMC, 760 Spring St.
Speaker
Robert Ronau and Christopher RakesUniversity of Louisville and Institue for Education Sciences
This systematic review of mathematics educational technology literature identified 1356 manuscripts addressing the integration of educational technology into mathematics instruction. The manuscripts were analyzed using three frameworks (research design, teacher knowledge, and TPACK) and four supplementary lenses (Data sources, outcomes, NCTM Principles, and NCTM Standards) to produce a database to support future research syntheses and meta-analyses. Preliminary analyses of student and teacher outcomes (i.e., knowledge, cognition, affect, and performance) suggest that graphing calculator and dynamic geometry technologies have been abundantly studied, but the strength of the evidence measures (i.e., validity and reliability) may be lacking. More specifically, research on mathematics educational technology appears at first glance to be ubiquitous, the usefulness of this research to practitioners and researchers is limited by lack of attention to research design and validity, reliability, and threats to validity (Rakes et al., 2011). Additionally, much of the research appears to be unorganized, with topics such as graphing calculators studied often, while other topics such as virtual manipulatives understudied (Ronau et al., 2010).
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2022-09-27 11:34:09
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https://www.physicsforums.com/threads/tight-binding-fcc-structures.258276/
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# Tight binding (FCC structures)
1. Sep 22, 2008
### disclaimer
I'm reading my lectures on TBM and I don't understand the following thing:
$$\omega(\overrightarrow k)=\omega_0-4t\cdot[\cos(k_xa/2)\cos(k_ya/2)+...]$$
It's related to FCC structures, in which the number of Nearest Neighbors $$(Z)$$ of an atom is equal to 12. Basically the three dots at the end leave me puzzled. What are they supposed to mean? Any help appreciated.
2. Sep 22, 2008
### weejee
I guess just the cyclic permutation of (k_x, k_y, k_z)
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2017-05-27 00:54:59
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https://proxies123.com/tag/transforming/
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## MS Word: When transforming a photo, what causes the photo to have white transformation points versus gray transformation points?
For the photos shown, the same camera was used, but some transformation points (see photos) are white, while other photos have gray points. What causes the difference? What does the difference mean?
White transformation points allow users to select from prefabricated Correction options, where gray transformation points only allow users to change brightness directly
White transformation points
Gray transformation points
## Transforming an immutable binary tree without recursion
I am fighting for this. I have a Binary Decision Diagram, which is quite similar to a tree. Each node has a hi node and it. I need to resort to the tree, and if some conditions are the case, replace the node with a new node. The nodes are immutable. So, when I find something that I have to change, I have to return the new version of the node completely. Ultimately, the root changes. Specifically I am trying to implement the RESTRICT algorithm for ROBDD.
And I have! This works fine (C #, sorry?)
`````` Node Restrict(Node node, Func npoint)
{
if (node == context.Term0 || node == context.Term1)
return node;
// value has been restricted, replace with true or false path
if (npoint(node.Variable) is bool value)
return Restrict(value ? node.Hi : node.Lo, npoint);
var lo = Restrict(node.Lo, npoint);
var hi = Restrict(node.Hi, npoint);
return new Node(node.Variable, lo, hi);
}
``````
However, my diagram is quite large. And I'm running out of pile space.
So, I am trying to find a way to do this without recurrence. I have tried some things but I have not found anything that works. When I begin to expand it, it becomes quite complicated and I begin to lose track of things.
Can anyone point me any recourse on this?
## How smart contracts are transforming the e-commerce industry? – Corner of cryptocurrencies.
TThe blockchain technology has managed to attract the attention of the general public for a while. Although it was the popularity of bitcoins that essentially put blockchain on the roadmap to familiarity, blockchain technology has begun to revolutionize the way the e-commerce industry operates with the introduction of smart contracts.
The application of blockchain technology is best seen in the way smart contracts are designed. Smart contracts are basically agreements that are executed automatically when all the parties involved comply with the required terms and conditions. These agreements are stored in data blocks protected by cryptographic encryption.
Smart contracts have proven to be extremely important for e-commerce operations. When a user makes a purchase through an e-commerce platform, the smart contract is programmed to release the value of the purchase in the seller's wallet only after both the buyer and the seller have met the conditions required to comply with the transaction process. Until then, the amount is retained by the intelligent contract.
Another way in which an intelligent contract operates is by eliminating the intermediaries in the process of the transaction. By doing so, a large amount of money that is usually dedicated to transaction fees is reduced. The ease of making a transaction and the process faster are other side effects of transaction automation with the help of smart contracts.
Searching development of smart contracts Companies? Visit the Blockchain applications factory to obtain high-quality development services from smart contracts.
## post processing: the Gimp perspective tool is not really transforming
I have uploaded a screenshot below to illustrate the problem. I dragged a jpeg to Gimp, clicked on the perspective tool and then tried to use it … but as you can see, it's not really transforming the image. Why is this so?
Click to enlarge the image.
## Transforming ParametricFunction into expression depending on the parameter
As a result of resolving an ODE system using `ParametricNDSolveValue` I get 4 functions, each one of them. Parametric Function depending on the parameter specified in `ParametricNDSolveValue`.
Even though what I want seems "simple" to me, I have searched the documentation and this site without success, so here is my question:
Can I transform my solution? Parametric Function in an expression of some kind? The motivation is to manipulate this expression, and this may involve different software.
If that is not possible, is there any other way in Mathematics to solve a $$2 times 2$$ System of EDOs at a point with a free parameter? Here is the question where I first asked about that.
## opengl – Transforming a length into a trunk projection
How do I calculate the screen lengths of the position vectors aligned with the axis after a frustum projection transformation?
Background:
In Java I create a frustum projection matrix via
``````Matrix.frustumM (projMatrix, 0, left, right, top bottom, near, far);
``````
and a view matrix via
``````Matrix.setLookAtM (viewMatrix, 0,
0, 0, -2.5, // eye position
0, 0, 0 // search position
0, -1, 0); // address above
``````
I also know how many GL units of width and height is the screen of my device, let's say `width` Y `height`. If my game tokens are `dx` Y `dy` GL units in size, then for a spelling projection I can calculate `width / dx` Y `height / dy` to determine how many squares you should have horizontally and vertically (approximately).
But with a trunk projection, which basically is always looking down according to the previous definition, this does not give me the correct result.
(Keep in mind that my tiles are always placed in the `x / y` airplane in `z = -1`
Of course I understand why, this is because the further away from the camera the smaller lengths are made. But how do I transform my `dx` Y `dy` values to deal with this?
I have tried:
• divide my `dx` Y `dy` by `1 + 2.5 + 1 = 4.5` since that is the distance from the eye to the plane of the tile.
• Multiplying the projection and view matrices (and both together) by the vector (dx, 0, 0, 1) for example.
But these do not work.
I also hear that the projection matrix has a `w` component in the lower right part of the matrix, which may have something to do with the z-scale, but I'm not sure if it's on the right track.
Any advice welcome. I will continue investigating.
## – primaverabss – Transforming a FP into FA (Sales Documents)
Goodnight everyone,
I am trying to make the transformation of Sales Documents, in the case of a Pro-form in an Invoice, but it gives an error because the origin does not have Warehouse in the Lines.
How can I do to add the store I want?
I have the following code that works if you have Warehouse:
``````
On Error GoTo Error
Dim objDocOrigen The GcpBEDocumentoVenda
ObjDocOrigen = motor.Comercial.Vendientes.Edita ("000", cbOrigTipoDoc.Text, cbOrigSerie.Text, CInt (cbOrigDoc.Text))
Dim objDocDestino The GcpBedocumentoVenda
objDocDestino = New GcpBEDocumentoVenda
objDocDestino.Entity = objDocOrigen.Entity
objDocDestino.Tipodoc = cbDestTipoDoc.Text
objDocDestino.Serie = cbDestSerie.Text
objDocDestino.CondPag = objDocOrigem.CondPag
Dim Doc (0) As Object
Doc (0) = objDocOrigen
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2019-08-20 18:44:59
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|
https://openreview.net/forum?id=HygpgV2-bX
|
## Training a Network of Spiking Neurons with Equilibrium Propagation
Jun 15, 2018 Submission readers: everyone
• Keywords: credit-assignment, spiking, quantization
• TL;DR: How to do Equilibrium Propagation when your neurons can only communicate binary signals
• Abstract: Backpropagation is almost universally used to train artificial neural networks. However, there are several reasons that backpropagation could not be plausibly implemented by biological neurons. Among these are the facts that (1) biological neurons appear to lack any mechanism for sending gradients backwards across synapses, and (2) biological "spiking" neurons emit binary signals, whereas back-propagation requires that neurons communicate real numbers between one another. Recently (Scellier and Bengio, 2017), demonstrated an alternative to backpropagation, called Equilibrium Propagation, wherein gradients are implicitly computed by the dynamics of the neural network, so that neurons do not need an internal mechanism for backpropagation of gradients. This provides an interesting solution to problem (1). In this paper, we address problem (2) by proposing a way in which Equilibrium Propagation can be implemented with neurons which are constrained to just communicate binary values at each time step. We show that with appropriate step-size annealing, we can converge to the same fixed-point as a real-valued neural network, and that with predictive coding, we can make this convergence much faster. We demonstrate that the resulting model can be used to train a neural network using the update scheme from Equilibrium propagation.
0 Replies
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2020-05-29 01:32:30
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https://brainmass.com/math/complex-analysis/pg8
|
Explore BrainMass
# Complex Analysis
### Algebra & Complex Numbers : Amplitude Ratio
Make y the subject of the formula E = p(1-e^(y-1)) If the amplitude ratio, N in decibels is given by n = 10log(P0/P1) and the power is given by P=(V^2/R), show that for matched input and output resistances the output Vo is related to input voltage Vi by Vo = Vi 10^(N/20) If N is increase by 6 dB, show that output volta
1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). Questi
### Open mapping theorem. Complex Analysis
Let P : C -> R be defined by P(z) = Re z; show that P is an open map but it is not a closed map. ( Hint: Consider the set F = { z : Imz = ( Re z)^-1 and Re z doesn't equal to 0}.) Please explain every step and justify.
### Proof of absolute maximum and minimum
I would like help with the following problem: Find with proof the absolute maximum and minimum values of f(x) = x^4 + 2x^2 - 4 on the interval [0,3]. There's a hint saying that you can prove this using the mean value theorem. Thanks for all of your help.
### Average value on an interval
Find the average value of y=csc2xcot2x on the interval π/6 ≤ x ≤ π/4 I think I have to use substitution for the integration
### Imaginary Powers / Residues : Allowing Functions
1. Allowing z = x + iy, find all of the roots for z^i=-2i. 2. By evaluating residues only, solve integral (-infinity --> infinity) xsinx/(x2 -2x =2)^2 dx
### Applying Complex Analysis and Argument Principle
Suppose f is analytic on B(bar) (0;1) and satisfies |f(z)| < 1 for |z| = 1. Find the number of solutions (counting multiplicities) of the equation f(z) = z^n, where n is an integer larger than or equal to 1. Please justify every step and claim and refer to any theorems you use.
### Complex Analysis / Singularities / Argument Principle
Let f be meromorphic on the region G and not constant; show that neither the poles nor the zeros of f have a limit point in G. In your solution, please refer to theorems or certain lemmas. Justify your claims and steps. I want to learn not just have the right answer. Thanks.
### Complex Analysis / Singularities
One can classify isolated singularities by examining the equations: lim (z -> a) |z - a|^s |f(z)| = 0 lim(z -> a) |z - a|^s |f(z)| = infinity Now, prove that a function f has an essential singularity at z = a iff neither of the above holds for any real number s.
### Complex Analysis and Singularities : If f : G -> C ( C here is complex plane) is analytic except for poles show that the poles of f cannot have limit point in G.
If f : G -> C ( C here is complex plane) is analytic except for poles show that the poles of f cannot have limit point in G.
### Complex Cross Ratio : Evaluate cross ratio
Evaluate cross-ratio (infinity,0,i,1) give answer in the form a + ib where a,b in R.
### Complex / Entire Function : Let f be an entire function such that |f(z)| =<10|z+1| for all |z|>100. Show that f is a linear function, f(z)= pz + q.
Let f be an entire function such that |f(z)| =<10|z+1| for all |z|>100 Show that f is a linear function, f(z)= pz + q.
### Analytic functions complex
Let f = u + iv be an analytic function on an open connected set G in C ( C = complex plane) where u and v are its real and imaginary parts. assume u(z) >= u(a) for some a in G and all z in G. Prove that f is constant.
### Concept of squared variables in a system of equations
Kindly elaborate on the concept of squared variables in a system of equations by the sample that was given to me. See attached file for full problem description.
### Power series representation of analytic functions (Complex integrals)
Evaluate the following integrals: a). integral over gamma of e^(iz) / z^2 dz, where gamma(t) = e^(it), 0=<t=<2 pi ( e here is exponential function). Please use basic definitions and power series representation of analytic functions to do so. b). integral over gamma of sin(z)/z^3 dz ( same gamma and values of t as abo
### Root of the Problem Descriptions
(See attached file for full problem description with proper symbols and equations) --- First: solve this problem. Second: check my answer. Third: if my answer is wrong or incomplete explain why. Explain why cannot have more than one root. This is how I tried to solve it: I used the interval [-1,1] By the
### Let G be a region and suppose that f:G->C (C here is complex plane)is analytic and a in G such that |f(a)|=<|f(z)| for all z in G. Show that either f(a) = 0 or f is constant.
Let G be a region and suppose that f:G->C (C here is complex plane)is analytic and a in G such that |f(a)|=<|f(z)| for all z in G. Show that either f(a) = 0 or f is constant.
### Potential Flow Theory : Conformal Transformation and Velocity on the Surface of an Ellipse
A) Show that if b<a the conformal transformation....maps a circle of radius 'a' in the plane into an ellipse in the ...plane. b) Show that the velocity on the surface of an ellipse in a uniform horizontal flow of velocity U reaches a maximum when theta = 90 degrees and has a magnitude of... c) Determine the velocity on the sur
### Potential flow theory
(See attached file for full problem description) --- The complex potential of a two-dimensional motion is... ---
### Potential flow theory
(See attached file for full problem description) --- The complex potential for a flow over a body is given by... ---
### Show that SO(4) is isomorphic to the quotient
Show that SO(4) is isomorphic to the quotient of SU(2) X SU(2) by the subgroup generated by (-1,1).
### Radius of Convergence and Abel's Theorem in Complex Analysis
A) I want to prove that if sum of a_n(z-a)^n have radius of convergence 1 and if the sum a_n converges to A then lim (r -> 1- ) of the sum (a_n r^n) = A. ( I believe z here is a complex number). B) Using Abel's theorem, prove that log2 = 1 - 1/2 + 1/3 - ...
### I need help with these five algebra problems.
BACKGROUND INFORMATION: A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and fort
### Complex Analysis : Analytic Functions as Mappings
1). Let G be a region and suppose that f : G -> C ( C is complex plane) is analytic such that f(G) is a subset of a circle. Show that f is constant. 2). If Tz = (az + b)/(cz + d), find necessary and sufficient conditions that T(t) = t where t is the unit circle { z: |z| = 1}. My solution for number 2 is : T(t) = t , which
### Finding the side of base of a pyramid from surface area.
The surface area of the right squre pyramid is given by S=b square rt. b^2 + 4h^2. If the pyramid has height of 10 feet and surface area of 100 square feet, what is the length of a side b of its base?
### Complex Analysis : Mobius Transformation
1). Let D = {z: |z| < 1 } and find all Mobius transformations T such that T(D) = D. 2). Show that a Mobius transformation T satisfies T(0) = infinity and T ( infinity) = 0 if and only if Tz = az^-1 for some a in C ( C is complex plane).
### Complex Numbers : RSA Cipher and Summation
A=1,B=2,C=3,D=4,E=5,........X=24,Y=25,Z=26 It is enciphered using the rule 35 R (m)=m (mod 91) 35 The resulting ciphertext is ( 73,14,23,73,23) Verify the rule given satisfy the condition for an RSA cipher. Using the repeated squaring technique decipher the ciphertext and find the message
### Polynomial Equations : Complex Solutions, Conjugates and Shift Operator
Prove that if p is a polynomial with real coefficients, and if is a (complex) solution of P(E)z = 0, then the conjugate of z, the real part of z, and the imaginary part of z are also solutions. Note: This is from a numerical analysis course, and here P(E) refers to a polynomial in E, the "shift operator" for a sequence.
### Forming Relationships between Variables
Please help! I cannot seem to get this problem solved! (See attached file for full problem description)
### Analytic functions in complex plane
1). Determine the set A such that For r > 0 let A ={w, w = exp (1/z) where 0<|z|<r}. 2).Prove that there is no branch of the logarithm defined on G= C-{0}. ( C here is the complex plane). ( Hint: suppose such a branch exists and compare this with the principal branch). I want detailed proofs and please prove ever
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2021-05-10 02:04:18
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https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=131&t=5194&p=12822
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## Determining greater change in entropy!
$\Delta S = \frac{q_{rev}}{T}$
Regina Chi 2K
Posts: 51
Joined: Fri Sep 26, 2014 2:02 pm
### Determining greater change in entropy!
This is actually a question on the 2010 midterm practice exam. It is part B of the problem 4B. I also realize that this is a homework problem from chapter eight. It asks us which (house exterior or interior) has a greater change in entropy. However, they also mentioned that the temperature stays the same even though heat went into the house from the outside. They make the statement T (interior) > T (exterior) and therefore change in entropy for the interior of the house must be less than change in entropy of the outside of the house. I understand how this works because of the equation: change in entropy = q (heat) / T (temperature). However, how did they come up with the statement T (interior) > T (exterior)? Should we assume that the interior of the house would naturally be warmer than the exterior of the house?
Kayla Denton 1A
Posts: 106
Joined: Fri Sep 26, 2014 2:02 pm
### Re: Determining greater change in entropy!
The way I see it is pretty simplistic—the question initially says that the pump "extracts heat from the COLD outdoors and releases it into the WARM interior." It seems to specify an initial temperature difference!
Satvir Saggi 1I
Posts: 22
Joined: Fri Sep 26, 2014 2:02 pm
### Re: Determining greater change in entropy!
The question states that "the heat pump heats a house in winter by extracting heat from the cold outdoors and releasing it into the warm interior. Therefore, based off the statement, we can deduce that the temperature of the interior is greater than the temperature of the exterior.
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2020-06-04 02:58:41
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http://mathematica.stackexchange.com/questions/32730/find-if-element-exists-in-n-dimensional-array
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# Find if element exists in N-dimensional array
I was wondering if there was a more elegant way of finding whether an element exists in an N-dimensional array. The way I would do it is:
inArrayQ[a_,el_] := If[Length@Position[a,x_/;x==el]==0,False,True];
But this seems rather cumbersome. I am surprised there is no built-in Mathematica function that does this, but if not, is there a better way to write such a function?
-
check out MemberQ – Pinguin Dirk Sep 20 '13 at 20:07
D'oh, if only the documentation search was better...thanks. – Guillochon Sep 20 '13 at 20:08
@Guillochon If you search for MemberQ you get the answer right away ;) – belisarius Sep 20 '13 at 20:31
@Guillochon You can also use Position to determine where the element is. – RM1618 Sep 22 '13 at 10:40
Check out MemberQ, you should find all information there.
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2014-12-19 09:30:17
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http://compgroups.net/comp.sys.ibm.as400.misc/how-do-i-get-rid-of-the-folder-my-doc/1346779
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f
#### How do I get rid of the folder "\My Documents\IBM\Client Access"?
Client Access seems to create the folder "\My Documents\IBM\Client
Access" automatically.
If I move / delete the folder, it gets recreated following a Windows
restart.
If I change / delete the registry entry
"HKEY_CURRENT_USER\Software\IBM\Client Access
Express\CurrentVersion\(Default)", the entry gets reset and the folder
recreated following a Windows restart.
I am running:
IBM iSeries Access for Windows
Version 5
Release 3
Modification level 0
Service level SI23492
Anyone know how to get rid of it for good?
Even being able to move it to somewhere else would be good.
Thanks.
0
8/2/2006 8:46:24 AM
comp.sys.ibm.as400.misc 9219 articles. 4 followers.
2 Replies
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andyrobertsonuk@gmail.com wrote:
> Client Access seems to create the folder "\My Documents\IBM\Client
> Access" automatically.
>
> If I move / delete the folder, it gets recreated following a Windows
> restart.
>
> If I change / delete the registry entry
> "HKEY_CURRENT_USER\Software\IBM\Client Access
> Express\CurrentVersion\(Default)", the entry gets reset and the folder
> recreated following a Windows restart.
>
> I am running:
> IBM iSeries Access for Windows
> Version 5
> Release 3
> Modification level 0
> Service level SI23492
>
> Anyone know how to get rid of it for good?
> Even being able to move it to somewhere else would be good.
>
> Thanks.
>
Maybe I would try "Control Panel/iSeries Access for Windows" properties
in the PC5250 tab, selecting something different from "Documents" in
"PC5250 file path" section.
--
Dr.Ugo Gagliardelli,Modena,ItalyCertifiedUindoscrasherA�ejoAlcoolInside
Spaccamaroni andate a cagare/Spammers not welcome/Spammers v�o � merda
Spamers iros a la mierda/Spamers allez vous faire foutre/Spammers loop
schijten/Spammers macht Euch vom Acker/Spamerzy wypierdalac'
0
info1229 (187)
8/2/2006 11:59:11 AM
Dr.UgoGagliardelli wrote:
> Maybe I would try "Control Panel/iSeries Access for Windows" properties
> in the PC5250 tab, selecting something different from "Documents" in
> "PC5250 file path" section.
Thanks for the tip, but that didn't seem to do the trick. I'm still
stuck with the folder.
Andy
0
8/14/2006 7:18:48 PM
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Web resources about - How do I get rid of the folder "\My Documents\IBM\Client Access"? - comp.sys.ibm.as400.misc
Resources last updated: 3/15/2016 8:31:54 AM
|
2021-01-16 11:56:54
|
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http://www.whxb.pku.edu.cn/CN/abstract/abstract23179.shtml
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### 氢在多壁碳纳米管上吸附行为研究
1. 上海交通大学制冷与低温工程研究所，上海 200030
• 收稿日期:2002-05-07 修回日期:2002-09-11 发布日期:2003-02-15
• 通讯作者: 郑青榕 E-mail:qrzheng816@sina.com
### Theoretical Study on the Adsorbed Hydrogen Molecules on Multi-Walled Carbon Nanotubes
Zheng Qing-Rong;Gu An-Zhong;Lin Wen-Sheng;Li Ming;Lu Xue-Sheng
1. Institute of Refrigeration and Cryogenics, Shanghai Jiaotong University, Shanghai 200030
• Received:2002-05-07 Revised:2002-09-11 Published:2003-02-15
• Contact: Zheng Qing-Rong E-mail:qrzheng816@sina.com
Abstract: A general model for hydrogen adsorption is derived to discuss the compressibility of the hydrogen molecules on the adsorption surface caused by the strong adsorptive potential exerted by the carbon wall. The mono-layer capacity (see Table 1) inside the tube of the MWCNTs tested in our laboratory is evalued by the comparison studies on the adsorptive performance between the tubular pore and the slit-pore, the results show that better adsorptive performance can only be obtained when temperature is getting lower or the diameter of the tube is getting smaller (see Fig.1). From the model, the strong attraction to the surface may even cause hydrogen molecules to attain much higher densities than that of liquid hydrogen, and this will surely make adsorbed hydrogen molecules to behave as repulsion among each other. This phenomenon is discussed in terms of experimental data and the ascertained model (see Fig.3). A linear form of the model is applied to determine the interaction energy between hydrogen molecules in the adsorbed layer from the experimental data. Analysis of the experimental data of hydrogen adsorption over a wide range of pressure and temperature shows that the energies of hydrogen-hydrogen interactions in the adsorbed phase are positive in low temperature region(< 200 K) and obtain the highest value in the temperature range of 160～180 K, but will be negative when the temperature is above 230 K(see Fig.4), indicating the repulsions among the adsorbed hydrogen molecules are prominent in low temperature, however, the attractions among the adsorbed hydrogen molecules at higher temperature are hard to understand because the pressures are also high in those cases. Comments are made that the chemical adsorption should be included to interpret the experimental data at higher temperatures. The results presented here also show that the concept of ‘maximum capacity’ for hydrogen adsorption should differ from the density of the adsorbed hydrogen molecules.
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2022-01-23 19:00:49
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http://mathoverflow.net/questions/59245/what-relations-exist-among-quasi-modular-forms-of-different-levels/67001
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# What relations exist among (quasi-) modular forms of different levels?
Given a (quasi-) modular form $f(\tau)$ for some congruence subgroup (say) $\Gamma(k)$, we know that $f(N\tau)$ is a (quasi-) modular form for $\Gamma(N k)$. Is there anything known about when we can do a partial reverse, that is, when we can take linear combinations of (quasi-) modular forms for some higher level subgroup to obtain one of stricktly lower level?
An example is the following:
Let $E(q) = \sum_{k=0}^\infty \sigma_1(2k+1)q^{2k+1}$ and $A(q) = \sum_{k=1}^\infty \sigma_1(k)q^k$. Then $E(q)$ is modular with respect to a non-trivial character, and both $A(q^2)$ and $A(q^4)$ are quasi-modular of level 2 and 4, respectively (though not of pure weight).
However: it turns out that $$E(q) + 3A(q^2) - 2A(q^4) = A(q)$$ which shows that a linear combination of higher level terms (and one which is modular with respect to a non-trivial character) yields one of lower level.
Is this simply random chance? Are there known relations of this type?
-
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2016-05-02 23:59:28
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http://openstudy.com/updates/50be72dee4b0de4262a02eb3
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## henriquerb Group Title Someone knows how to integrate (x+sqrt(1-x²))dx? one year ago one year ago
1. Goten77
|dw:1354658992590:dw| hmm not sure if this is hyperbolic *which they really dont teach* but this method here works since sqrt(1+x2) is a identity or whatever it is http://www.wolframalpha.com/input/?i=integrate+x+%2B+sqrt%281%2Bx^2%29
2. Goten77
sqrt(x-x2) i meant
3. mukushla
u might use trig sub like this$x=\sin \theta$or even$x=\cos \theta$
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2014-10-25 16:01:30
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https://en.wikipedia.org/wiki/Isomorphism_of_categories
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# Isomorphism of categories
Jump to: navigation, search
In category theory, two categories C and D are isomorphic if there exist functors F : CD and G : DC which are mutually inverse to each other, i.e. FG = 1D (the identity functor on D) and GF = 1C. This means that both the objects and the morphisms of C and D stand in a one to one correspondence to each other. Two isomorphic categories share all properties that are defined solely in terms of category theory; for all practical purposes, they are identical and differ only in the notation of their objects and morphisms.
Isomorphism of categories is a very strong condition and rarely satisfied in practice. Much more important is the notion of equivalence of categories; roughly speaking, for an equivalence of categories we don't require that $FG$ be equal to $1_D$, but only naturally isomorphic to $1_D$, and likewise that $GF$ be naturally isomorphic to $1_C$.
## Properties
As is true for any notion of isomorphism, we have the following general properties formally similar to an equivalence relation:
• any category C is isomorphic to itself
• if C is isomorphic to D, then D is isomorphic to C
• if C is isomorphic to D and D is isomorphic to E, then C is isomorphic to E.
A functor F : CD yields an isomorphism of categories if and only if it is bijective on objects and on morphism sets. This criterion can be convenient as it avoids the need to construct the inverse functor G.
## Examples
Consider a finite group G, a field k and the group algebra kG. The category of k-linear group representations of G is isomorphic to the category of left modules over kG. The isomorphism can be described as follows: given a group representation ρ : G → GL(V), where V is a vector space over k, GL(V) is the group of its k-linear automorphisms, and ρ is a group homomorphism, we turn V into a left kG module by defining
$(\sum_{g\in G} a_g g) v = \sum_{g\in G} a_g \rho(g)(v)$
for every v in V and every element Σ ag g in kG. Conversely, given a left kG module M, then M is a k vector space, and multiplication with an element g of G yields a k-linear automorphism of M (since g is invertible in kG), which describes a group homomorphism G → GL(M). (There are still several things to check: both these assignments are functors, i.e. they can be applied to maps between group representations resp. kG modules, and they are inverse to each other, both on objects and on morphisms).
Every ring can be viewed as a preadditive category with a single object. The functor category of all additive functors from this category to the category of abelian groups is isomorphic to the category of left modules over the ring.
Another isomorphism of categories arises in the theory of Boolean algebras: the category of Boolean algebras is isomorphic to the category of Boolean rings. Given a Boolean algebra B, we turn B into a Boolean ring by using the symmetric difference as addition and the meet operation $\land$ as multiplication. Conversely, given a Boolean ring R, we define the join operation by a$\lor$b = a + b + ab, and the meet operation as multiplication. Again, both of these assignments can be extended to morphisms to yield functors, and these functors are inverse to each other.
Further, if C is a category with an initial object s, then the slice category (sC) is isomorphic to C. Dually, if t is a terminal object in C, the functor category (Ct) is isomorphic to C. Similarly, if 1 is the category with one object and only its identity morphism (in fact, 1 is the terminal category), and C is any category, then the functor category C1, with objects functors c: 1C, selecting an object c∈Ob(C), and arrows natural transformations f: cd between these functors, selecting a morphism f: cd in C, is again isomorphic to C.
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2015-06-30 05:31:36
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https://www.quantstart.com/articles/How-to-Learn-Advanced-Mathematics-Without-Heading-to-University-Part-2
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How to Learn Advanced Mathematics Without Heading to University - Part 2
In the last article in the series we looked at the foundational courses that are often taken in a four-year undergraduate mathematics course. We saw that the major courses were Linear Algebra, Ordinary Differential Equations, Real Analysis and Probability. In the "second year" of our self-study mathematics degree we'll be digging deeper into analysis and algebra, with discussions on the Riemann integral, abstract algebra, metric spaces and vector calculus.
In a formal setting the midpoint of Year 2 is where students begin to get a feel for whether they want to specialise in either pure or applied mathematics, and whether they wish to concentrate on analysis or algebra. Pure mathematics and algebra are quite synonymous, as are analysis and applied mathematics. The former, because advanced pure mathematics is often concerned with symmetry and relationships between disparate areas of mathematics (such as the pairing of algebra and geometry in algebraic geometry). The latter, because real-valued vector spaces are often the domain of partial differential equations, which represent spatio-temporaral physical phenomena such as electromagnetic fields, compressible fluids and deformable structures.
It is highly likely that as a prospective quant you will want to specialise in applied mathematics, leading to courses in Stochastic Analysis, Fourier Analysis, Partial Differential Equations, Statistics and Scientific Computing. However, this is not always the case. Many famous quants started in pure mathematics or theoretical physics backgrounds, including Jim Simons and Emanuel Derman.
This article will cover Year 2 while the previous article covered Year 1. At least two more articles will cover Years 3 and 4. Later articles will cover the broad syllabus for a Masters in Financial Engineering (MFE) style course.
### Year 2
As mentioned briefly above the second year of an undergraduate mathematics degree extends the discussion of analysis to the Riemann integral, which is the usual integral that is familiar from highschool, engineering and physics. This is in contrast to the Lebesgue integral, which is discussed in Measure Theory during the third year.
In addition further assumptions of structure are relaxed leading to the concept of metric spaces. These are sets that also possess a notion of "distance". Vector calculus extends differentiation and integration to vector spaces - highly applicable in the fields of electrodynamics, continuum mechanics and fluid dynamics.
Group theory is given more rigourous development via the introduction of rings as well as basic ideas of groups of matrices (Lie groups). Many courses also discuss non-Euclidean geometry in more depth. This includes spherical/elliptic geometry and hyperbolic geometry. These concepts eventually lead onto differential geometry and its application to the General Theory of Relativity.
The second year is also when basic stochastic processes are introduced, which are highly releveant for the quantitative finance professional. Another absolutely essential topic, which builds on the elementary probability discussed in Year 1, is statistics. Usually the statistics department of most universities will allow cross-over modules for mathematicians.
Also relevant to the quant, and usually offered as an option, is numerical analysis, which attempts to analyse algorithms that approximate problems in analysis such as with differential equations. Since many quant algorithms ultimately involve approximately computing values of functions, seeking eigenvalues, solving regression or optimisation problems (as in machine learning) it is highly worth studying as a module.
The courses found in a second year largely reflect the extension and consolidation of the topics introduced in the first year. The following areas of mathematics are considered:
Here is the course list for Year 1:
#### Real Analysis - Riemann Integral
The first year courses on real analysis tend to concentrate on sequences, series, functions of a single real variable (i.e. $f:\mathbb{R} \rightarrow \mathbb{R}$), continuity of those functions as well as properties and results related to their derivatives.
In the second year the focus transfers across to the Riemann integral, which is the "standard" integral that will be familiar from high-school, as well as the concepts of pointwise convergence and uniform convergence of sequences of functions. One of the most important concepts discussed is the Fundamental Theorem of Calculus, which governs how derivatives and integrals of a function are related to each other.
Studying the Riemann integral is absolutely necessary for the quant analyst who desires to work in derivatives pricing, as a large part of stochastic calculus and probability theory relies on measure theoretic concepts such as the Lebesgue integral, which is more general than the more familiar Riemann integral.
Real analysis is a prerequesite for further second year courses in Metric Spaces and Vector Calculus, the latter of which is highly relevant to certain areas of machine learning.
#### Metric Spaces
A course in Metric Spaces is often the first introduction to the more abstract ideas from the branch of mathematics known as topology. A metric space is a mathematical set along an associated function of two points within the set that defines a sense of "distance" or "metric" between them.
This idea of distance within a set allows interesting properties to be discussed such as openness, closedness, completeness, connectedness as well as varying forms of continuity of functions between metric spaces. These ideas build on the concepts studied in Real Analysis, including sequences, series and convergence, albeit in higher dimensional settings.
A very familiar example of a metric space is three-dimensional Euclidean space with the "standard" Euclidean metric ("distance as the crow flies") between two points. A more abstract example is given by the Levenshtein distance between two strings of text, which allows a numerical measure of how similar the strings are. I can personally attest that this is extremely useful in the field of Natural Language Processing.
##### Study Material
At university I made use of Sutherland's Introduction to Metric and Topological Spaces for my second year Metric Spaces course. However, I've also found in retrospect that the Springer Undergraduate Mathematics Series book Metric Spaces, by M. O'Searcoid, is worth studying too.
#### Vector Calculus
Vector calculus is one of the most practically relevant courses for a prospective quant to have studied. It deals with the concept of change in scalar and vector fields. Many concepts in mathematics, physics and quant finance can be modelled as fields and as such the machinery of vector calculus is highly applicable.
A course in vector calculus will introduce many useful tools such as the partial derivative, gradient, divergence, curl and Laplacian operators, as well as the key theorems of Gauss and Stokes, which are the building blocks of partial differential equations that ultimately model electromagnetic fields and fluid flows.
Partial derivatives and the gradient operator make strong appearances in the fields of statistical machine learning, particularly when it comes to optimising a solution over an optimisation surface as in the stochastic gradient descent algorithm.
Some university courses in vector calculus contain topics from the field of complex analysis. Although the majority of courses concentrate solely on physical applications of vector calculus methods such as electrodynamics, gravitation, continuum mechanics or fluid dynamics.
#### Ordinary Differential Equations - Non-linearity and Chaos
Differential equations are a large research area in their own right. Once beyond the first year material, which generally finishes up discussing second order linear ODE with constant coefficients, more interesting ODE found in real-life applications appear. These include the areas of mechanics, electronics and mathematical biology. Such ODE possess non-linear and chaotic behaviour.
There is quite a large jump in complexity when studying differential equations of this type. The focus becomes less about mechanical methods for obtaining solutions and more about understanding the bounds on behaviour of more complicated systems. Differential equations eventually lead onto the more advanced area of dynamical systems. However, these are not often studied properly until the third or fourth year of a mathematics degree.
Ordinary differential equations also lead onto stochastic differential equations (SDE), which are ODE that contain a random aspect. SDE are extremely relevant to the prospective quant who wishes to study derivatives pricing and time series analysis. The underlying models for stock price movements are often modelled as geometric random walks necessitating the use of SDE.
##### Study Material
As with first year ODE courses, there is no shortage of textbooks to learn undergraduate ordinary differential equations. The trick is to find a solid introductory text and then a text that goes a little deeper including discussions of control theory, non-linearity, chaos and modelling.
Springer and CUP have a relatively good set of textbooks on ODEs. In particular after looking at those I recommended in the previous article, you could consider the following:
#### Geometry - Non-Euclidean
The familiar geometry of everyday life is three-dimensional Euclidean geometry. In the second year students are often introduced to projective geometry, elliptic geometry and hyperbolic geometry. These geometries arise when Euclids "fifth postulate" is relaxed, which allows parallel lines to cross or diverge, unlike in Euclidean geometry.
These additional geometries play a large part in the physical sciences, particularly the study of relativity and cosmology, where Riemannian geometry is used to model space-time in general relativity. These geometries are also extremely interesting subjects to study in their own right.
The study of geometry is less applicable to the quant than other areas of mathematics. However, I did mention in the previous article that a solid understanding of trigonometric concepts was essential for the study of Fourier Analysis, which is very relevant to quants.
#### Abstract Algebra
In Part 1 we saw that students will often be exposed to abstract groups through a Foundations module. In Year 2 a more thorough treatment of abstract algebra is provided, which covers groups in depth and often leads onto the study of rings.
A ring is similar to a group except that it has two operations representing "addition" and "multiplication". A group only has a single operation. Perhaps the most common example of a ring is that of the integers ($\mathbb{Z}$) with addition and multiplication.
The majority of second year abstract algebra courses discuss isomorphisms, quotient groups, Lagrange's Theorem, Abelian groups, orbits and stabilisers. These are all essential topics for futher study of abstract algebra including Lie groups and Lie algebras.
As I made clear in Part 1 it is not necessary for a prospective quant to have a huge grasp of group theoretic concepts. These concepts are not generally applicable to the main areas of quantitative finance. However, groups and rings are fascinating areas of mathematics and will provide a lot of enjoyment for the autodidact choosing to study them for their own sake.
#### Stochastic Processes
Stochastic Processes is generally offered as an option module at university and as such is not "core". However it is clearly extremely relevant to quantitative finance particularly in the area of derivatives pricing.
Before studying stochastic calculus in depth, which requires an understand of the Lebesgue integral and other measure theoretic concepts, it is advisable to consider more elementary stochastic processes.
Such courses often begin with a review of probability theory, including a brief discussion on sigma-fields and probability measures (but without undue additional measure theoretic concepts). Attention then turns to processes such as discrete martingales and markov chains before introducing the continuous case.
Such a course naturally leads on to further study in stochastic analysis, which will introduce Ito calculus and ultimately options pricing.
#### Numerical Analysis
The main goal of Numerical Analysis is to introduce methods for solving equations via a numerical method, that is, using approximate methods rather than finding an analytic solution. The topic also introduces methods for understanding the errors introduced in the process as well as important concepts such as iterating equations, converge and stability.
Numerical analysis is extremely important to the solution of differential equations, which are pervasive in quantitative finance, fluid dynamics, gravitation, continuum mechanics and electrodynamics. Study of numerical analysis provides an understanding of when certain numerical techniques are applicable and when they can lead to excessive error.
As a quant it is likely that you will be using some form of numerical approximation, either Markov Chain Monte Carlo for Bayesian analysis or numerical integration for solving partial differential equations in derivatives pricing. Hence study of numerical analysis is a worthwhile endeavour to consider in order to avoid the common pitfalls.
#### Statistics
Statistics is probably the most sought after quantitative skill in the commercial sector that can be studied on a mathematics degree. It provides the basis for understanding uncertainty and measuring risk, both of which are absolutely crucial to practising quants.
In addition to its value as a risk management tool it also provides the foundations on which most of the major machine learning techniques are built. Hence it is imperative that prospective quant study statistics at the undergraduate level.
Statistics makes use of the theory of probability and then builds on it to discuss the concepts of probability distributions, expectation, correlation and covariance. Once these basic concepts are outlined the remainder of the material generally consists of explaining classical/frequentist hypothesis tests for data analysis.
These tests are incredibly pervasive in the commercial world - especially in quantitative finance. As a quant portfolio manager or risk analyst you will be using them frequently in real world settings. Hence it is worth becoming extremely familiar with these techniques.
A course in classical/frequentist statistics leads naturally to a course in Bayesian statistics. The latter has become popular in recent years due to the computational tractability of the underlying Markov Chain Monte Carlo algorithms.
## Next Steps
The second year of an undergraduate syllabus is all about consolidating and extending the ideas of the first year. For the autodidact it is a time to begin choosing modules that make sense for their own career trajectory.
I have outlined many courses above. Some of these are unimportant for the quant wishing to learn the "bare minimum" necessary for working on derivatives pricing, statistical machine learning or quantitative trading.
However it is important to realise that roles in quantitative finance are highly competitive. Having a well-rounded education in mathematics is just as important as knowing the prequisites for quantitative finance particularly when it comes to interview situations. One should not dismiss the more abstract courses such as Abstract Algebra or Non-Euclidean Geometry as results form these realms will often find their way into the more applied areas of mathematics and quantitative finance.
In the next article covering Year 3 we will look at more abstract areas of analysis, such as measure theory and functional analysis. The former is highly relevant for the study of probability and stochastic analysis. Many applied modules will be introduced such as Bayesian Statistics and Fluid Dynamics, both of which are great training grounds for teaching prospective quants how to perform data analysis and solve partial differential equations.
Read the next article in the series: How to Learn Advanced Mathematics Without Heading to University - Part 3
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2017-06-26 05:14:19
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https://www.esaral.com/q/the-ratio-in-which-the-x-axis-divides-the-segment-joining-3-6-and-12-3-is-32941/
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The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
Question:
The ratio in which the x-axis divides the segment joining (3, 6) and (12, −3) is
(a) 2: 1
(b) 1 : 2
(c) −2 : 1
(d) 1 : −2
Solution:
Let $P(x, 0)$ be the point of intersection of $x$-axis with the line segment joining $A(3,6)$ and $B(12,-3)$ which divides the line segment $A B$ in the ratio $\lambda: 1$.
Now according to the section formula if point a point $P$ divides a line segment joining $A\left(x_{1}, y_{1}\right)$ and $B\left(x_{2}, y_{2}\right)$ in the ratio $m$ : $n$ internally than,
$\mathrm{P}(x, y)=\left(\frac{m x_{1}+m x_{2}}{m+n}, \frac{n y_{1}+m y_{2}}{m+n}\right)$
Now we will use section formula as,
$(x, 0)=\left(\frac{12 \lambda+3}{\lambda+1}, \frac{-3 \lambda+6}{\lambda+1}\right)$
Now equate the y component on both the sides,
$\frac{-3 \lambda+6}{\lambda+1}=0$
On further simplification,
$\lambda=\frac{2}{1}$
So $x$-axis divides $A B$ in the ratio $\frac{2}{1}$
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2022-06-25 13:28:17
|
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https://www.esaral.com/q/mark-the-tick-against-the-correct-answer-in-the-following-74759
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Deepak Scored 45->99%ile with Bounce Back Crack Course. You can do it too!
# Mark the tick against the correct answer in the following:
Question:
Mark the tick against the correct answer in the following:
Let $A$ be the set of all points in a plane and let $O$ be the origin. Let $R=\{(P, Q): O P=Q Q\} .$ Then, $R$ is
A. reflexive and symmetric but not transitive
B. reflexive and transitive but not symmetric
C. symmetric and transitive but not reflexive
D. an equivalence relation
There is printing mistake in the question...
$\mathrm{R}$ should be $\mathrm{R}=\{(\mathrm{P}, \mathrm{Q}): \mathrm{OP}=\mathrm{OQ}\}$
Instead of $\mathrm{R}=\{(\mathrm{P}, \mathrm{Q}): \mathrm{OP}=\mathrm{QQ}\}$
Solution:
According to the question,
$\mathrm{O}$ is the origin
$\mathrm{R}=\{(\mathrm{P}, \mathrm{Q}): \mathrm{OP}=\mathrm{OQ}\}$
Formula
For a relation $R$ in set $A$
Reflexive
The relation is reflexive if $(a, a) \in R$ for every $a \in A$
Symmetric
The relation is Symmetric if $(a, b) \in R$, then $(b, a) \in R$
Transitive
Relation is Transitive if $(a, b) \in R \&(b, c) \in R$, then $(a, c) \in R$
Equivalence
If the relation is reflexive, symmetric and transitive, it is an equivalence relation.
Check for reflexive
Consider, $(P, P) \in R \Leftrightarrow O P=O P$
which is always true.
Therefore , R is reflexive ……. (1)
Check for symmetric
$(P, Q) \in R \Leftrightarrow O P=O Q$
$(Q, P) \in R \Leftrightarrow O Q=O P$
Both the equation are the same and therefore will always be true.
Therefore , R is symmetric ……. (2)
Check for transitive
$(P, Q) \in R \Leftrightarrow O P=O Q$
$(Q, R) \in R \Leftrightarrow O Q=O R$
On adding these both equations, we get , OP = OR
Also,
$(P, R) \in R \Leftrightarrow O P=O R$
$\therefore$ It will always be true
Therefore , R is transitive ……. (3)
Now, according to the equations $(1),(2),(3)$
Correct option will be (D)
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2023-01-27 01:15:41
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https://support.bioconductor.org/p/9142955/
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Cleaning GeneSets from GSEA
1
0
Entering edit mode
@0693d951
Last seen 5 weeks ago
Italy
Hi everyone,
I'm running a GSEA procedure on R (in particular I am using the GSVA package). I have downloaded the lists of genes composing the gene sets from the MSigDB using the package msigdbr.
Anyway, if I extract the gene symbols for a gene set from the downloaded object, they are not unique. It happens for example that genes with the same symbol and EntrezID have different EnsemblID, hence they are listed as different.
How should I deal with these when using the gsva function? I have gene symbols as rows in my expression matrix, thus I can't match the different EnsemblIDs. If I keep duplicates this would be a sort of increased weight for the considered genes, leading to a slightly skew distribution for the enrichment scores. Is it safe to delete duplicates or am I losing relevant information?
msigdb GSEABase GSVA • 135 views
1
Entering edit mode
Robert Castelo ★ 2.9k
@rcastelo
Last seen 49 minutes ago
Barcelona/Universitat Pompeu Fabra
This kind of question has been answered previously at least in two posts (this one and this other one). In essence, you need to stick to the annotations you used, or were used, to produce the gene expression data matrix that you are using and do the id mapping at the level of gene set. As you rightly suspect, if you duplicate the expresion profiles in your gene expression data matrix, you're going to introduce colinearities at gene level that, at the very least, are going to distort your inferences and more likely trigger some error during downstream calculations. Doing the id mapping at the level of gene set has the advantage that it doesn't matter much whether a gene set has 10 genes in terms of gene symbols, 8 in terms of Entrez and 15 in terms of Ensembl, because in all three cases, the gene set remains being the same gene set, just that its definition changes slightly depending on the gene nomenclature and most likely, with little impact in the actual calculations.
cheers,
robert.
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2022-06-27 08:47:19
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http://openstudy.com/updates/521f44b9e4b06211a67e5bbb
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• anonymous
Charge Q is applied to a circular disk of ebonite of radius a by rubbing it while it is rotating. in this way, the surface charge density becomes proportional to the radial distance from the center. Show that the electric field strength on the axis of the disk at an axial distance h from the center is $E=\frac{ 3Qh }{ 4\pi \epsilon_{0}a^{3} }\left[ \ln \frac{ a+\sqrt{a^2+h^2} }{ h }-\frac{ 1 }{\sqrt{a^2+h^2}} \right]a_{n}$
Mathematics
Looking for something else?
Not the answer you are looking for? Search for more explanations.
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2017-04-26 08:12:11
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https://www.khanacademy.org/economics-finance-domain/core-finance/stock-and-bonds/company-statements-capital-struc/v/market-value-of-assets
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In the last video, we saw that if Ben's Shoe Company's stock prices are trading at $21.50 per share, and if Ben's Shoe Company has 10,000 shares-- and we saw that over here on the left, if it had 10,000 shares. Actually both of the shoe companies have 10,000 shares. Then the market is essentially valuing the equity of Ben's Shoe Company at$215,000, even though the book value of the equity was $135,000. What I want to do in this video is think about what does that mean, or how should we perceive the market's value of the assets of Ben's Shoe Company. Then we can also think about Jason's Shoe Company. So remember, assets are equal to liabilities plus the shareholders' equity. So if all of a sudden the market value of the equity, the market capitalization for Ben's Shoe Company is$215,000, that's the equity part right over here, this is the equity. And the only liability that Ben's Shoe Company had was this $5,000 in accounts payable. So let me show you that right over here, he had this$5,000 in accounts payable, also depicted over there. So the only liability is this $5,000. So the liabilities plus the equity, in the case of Ben's company, is$215,000 plus $5,000. So this piece right over here is$220,000. Now, you might remember from previous videos that the book value of the assets in Ben's company are only $140,000.$20,000 of cash, $100,000 of inventory,$20,000-- this isn't equity, this is equipment, I should call it-- $20,000 of equipment. So The question is, what makes up the gap here, when we think about the market value of the equity? Because remember, this piece right here only adds up to$140,000. But our total assets-- or the market's perception of the total assets of the company-- are essentially what it's willing to pay for the equity plus the liability. So the market is saying that Ben's assets, the assets in that company, are worth $220,000. So what makes the difference? And even better, let's assume that Ben has actually done a good job of saying the market value of his inventory, the market value of his equipment. Well, what the market's saying in this situation-- and this is actually what tends to happen in general, the market value of a company's equity tends to be higher than the book value-- is that this company has some type of intangibles. Things that you really can't put a finger on, or touch, or feel, or hold. But it makes this company's assets-- or this company has more than just the sum of its parts. There's more to this company than just the equipment, the inventory, and the cash. It might be Ben's management expertise. It might be a certain way they have of doing business. It might be a certain location they have. It might be their assortment. Who knows what it has, but the market is saying that the combination of this plus all of the expertise and how the business is organized means that it actually has more assets than are on the books. And the same thing is true of Jason's company, when they assign a$120,000 market cap there. This is the $120,000 in equity-- market value of equity. He has another$105,000 in liabilities. So the market's valuing their equity plus liabilities at $225,000. Is that right? 120 plus 100 plus 5. So 225,000. So once again, they're valuing all of the assets at$225,000, because assets are equal to liabilities-- these are the liabilities right here-- plus equity. So once again, you're saying there's something above and beyond the \$140,000 that makes this company special. And an interesting thing to think about-- and we'll address it in the next video-- is which one is a better deal, considering that these companies are pretty similar?
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2017-10-22 06:35:02
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http://yingtongli.me/blog/tag/encryption/
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• ### Broken Uno house rules; or, the importance of systems thinking, rather than ‘reasoning by Lego’
House rules are a staple of card and board games, and Uno is no exception. Recently with friends, we played some games of Uno, observing a common house rule:
House Rule 1. A player who incorrectly calls ‘Uno’ must draw two cards.1 (Each player
»
## Background
This post concerns a DRM system used in an online ebook platform, released circa 2018. Users of the platform can purchase ebooks and either view them online, or download them for offline viewing using a proprietary Android/iOS app.
As usual, the particular DRM system… »
## Sony PlayStation 3 ECDSA random number reuse
The Sony PlayStation 3 (2006) uses Elliptic Curve DSA (ECDSA) to sign executable binaries.
ECDSA takes a private key $$d_A$$ and a random number $$k$$ with public parameters $$G$$, $$n$$ and public key $$Q_A = d_A G$$, and… »
• ### Investigating an early-2010s gaming DRM system: Part 4
Last time, we investigated how an early-2010s gaming DRM system approached machine-based licensing. This time, we'll investigate exactly how the DRM system interacts with the game to accomplish its ends.
## Structure of the DRM system
Looking at the game binary, FooBarBazX.exe, for the… »
• ### Investigating an early-2010s gaming DRM system: Part 3
Last time, we investigated how an early-2010s gaming DRM system stored licences for games. This time, we'll investigate how those licences are tied to particular devices.
From last time, we know that the licence file contains an encrypted XML payload:
<?xml version="1.0" encoding="UTF-8" standalone="yes"?>
»
• ### Investigating an early-2010s gaming DRM system: Part 2
Last time, we investigated part of a gaming DRM system from the early-2010s, looking at some of the configuration files. This time, we'll investigate how the licences for these games are stored.
Is is known that the licence data for the games is stored… »
## Background
This post concerns a DRM system used in a PC gaming platform introduced in the early 2010s. The particular DRM system is not relevant and will not be identified, but will be familiar to many.
One function of the DRM system is to require… »
• ### Questionable crypto - Neal Asher's ‘Depature’
Last time, we investigated some questionable design choices in the TLS-like AF protocol from Autonomous. Today's unfortunate victim is a TOTP-like monstrosity from Neal Asher's The Departure. Near the end of the novel, the main character, Saul, commandeers a network of robots… »
• ### Questionable crypto in Annalee Newitz's ‘Autonomous’
Autonomous is a 2017 novel from former io9 editor Annalee Newitz. One of the viewpoint characters is a bot, Paladin, and during his first few pages, we are treated to the following exchange between him and another bot, Fang:
The mantis [Fang] beamed Paladin a
»
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2020-02-17 15:07:41
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http://mathoverflow.net/questions/111030/non-trivial-action-of-sl-n-mathbbz-on-a-simplicial-tree
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# Non-trivial action of $SL_n(\mathbb{Z} )$ on a simplicial tree
A group $G$ has Serre's property $FA$ if any isometric action of $G$ on a simplicial tree has a global fixed point. Let $n\geq 3$. It is well-known that $SL_n(\mathbb{Z} )$ has property $FA$. Now my question is that are there nontrivial group actions of $SL_n(\mathbb{Z} )$ on a simplicial tree by isometries? Here "nontrivial" means the fixed point set is NOT the whole tree.
-
Any non-trivial group $G$ has a non-trivial action on a "star" tree $T$ whose vertex set is $G\cup\{\infty\}$ (where $\infty\notin G$) and edges are $\{\infty,g\}$ for $g\in G$. Thus any group admits a faithful action on a tree.
Any residually finite countable group has a faithful action on a locally finite tree. If $(H_n)$ is a decreasing sequence of finite index subgroups with trivial intersection with $H_0=G$, this tree is the disjoint union of cosets $G/H_n$, with an edge between $gH_n$ and $gH_{n+1}$ for all $g$ and all $n$; the root is just the point $G/H_0$ and is fixed by the action. This applies to $\text{SL}_d(\mathbf{Z})$; in this precise case the $H_n$ can be chosen so that the index $H_n/H_{n+1}$ is bounded and thus the tree has bounded valency.
@Agol I see a generalization to any nested sequence of subgroups $(H_n)_{n\in K}$ with $K$ a convex subset of the chain $\mathbf{Z}$ such that $\bigcup_{n\in K} H_n=G$. But I can't guess which kind of generalization you have in mind even in the case of the action of $\mathbf{Z}$ on a linear tree. – YCor Oct 29 '12 at 22:54
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2016-05-05 05:05:59
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https://www.mathdoubts.com/unlike-algebraic-terms/
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# Unlike algebraic terms
The algebraic terms whose literal coefficients are not same, are called the unlike algebraic terms.
## Introduction
The unlikeness of two or more algebraic terms are actually determined by their literal coefficients. If the literal coefficients of two or more algebraic terms are not same, then the algebraic terms are looked dissimilar, and they are called as unlike algebraic terms. So, the property of the unlikeness is a key factor for determining the unlike algebraic terms in algebra.
#### Example
$5xy$ and $6x^2y$ are two algebraic terms.
Look at the two algebraic terms, and it seems they are dissimilar. It can be confirmed mathematically by determining the literal coefficients of them and it helps us to check the property of unlikeness of them mathematically.
$5xy = 5 \times xy$ and $6x^2y = 6 \times x^2y$
$xy$ is the literal coefficient of $5$ in the first algebraic term and $x^2y$ is the literal coefficient of $6$ in the second algebraic term. The literal coefficients of them are not same. Due to this reason, the two algebraic terms are looked dissimilar and they are called as unlike algebraic terms.
### Examples
Look at the following examples to understand unlike algebraic terms clearly.
$(1) \,\,\,$ $2a$, $6b$
$(2) \,\,\,$ $l^2$, $\dfrac{l^2m}{5}$, $-0.25l^2m^2$
$(3) \,\,\,$ $4m$, $4mn$, $4m^2n$, $4mn^2$
$(4) \,\,\,$ $-4p^3qr$, $10pq^2r^3$
$(5) \,\,\,$ $-x$, $x^2$, $3xy$, $6xz$, $-176xyz$
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Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.
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2021-06-19 18:21:26
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https://nivent.github.io/blog/surreal-numbers/
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# Surreal Numbers
When people talk about “numbers”, they usually mean real numbers or natural numbers. I like to think that when God talks about “numbers”, he means surreal numbers. Surreal numbers are a beautiful class of numbers with a simple construction with the surprising property that they include “All numbers great and small”.
# Construction
Definition
A surreal number form is an ordered pair $(L, R)$ of two sets of surreal number forms: the left set $L$ and the right side $R$.
That’s it. Maybe not all of it, but that’s pretty much it. It doesn’t look like much, and it may not be obvious that this is a valid definition, but it’s almost all there is to it. Let’s look at an example. To start with, there are no surreal number forms, the only possibility for $L$ and $R$ is the empty set. Hence, $(\emptyset, \emptyset)$ is our first surreal number form (Spoiler 1).
One thing to notice is that I am calling these things surreal number forms, and not just surreal numbers. There’s a reason for this. Not every surreal number form is a surreal number.
Definition
Given two surreal number forms $x=(X_L, X_R)$ and $y=(Y_L, Y_R)$, we say that $x\le y$ if there is no $y_R\in Y_R$ s.t. $y_R\le x$ and there is no $x_L\in X_L$ s.t. $y\le x_L$.
As we’ll see with the next couple of definitions, the intuition behind a surreal number is that it’s value lies between the values in its two sets. If $x$’s left set is $\{0, 1\}$ and its right set is $\{2, 3\}$, then whatever number $x$ is should be larger than $0$ and $1$, but smaller than $2$ and $3$. With that in mind, this definition says that $x\le y$ when $x$ is smaller than the things larger than $y$, and $y$ is larger than the things smaller than $x$.
Before moving on to the next definition, I want to fix some notation. Throughout this post, I will try to use lowercase variables $(x, y, z, \dots)$ for surreal number forms, and uppercase variables for sets of surreal number forms. The subscripts $L$ and $R$ will be used to differentiate left and right sets. The above definition gives examples of what I mean. Finally, instead of writing pairs completely explicitly (Ex. $(\{0, 1\}, \{2, 3\})$), I’ll write them as $\{L\mid R\}$ where $\mid$ separates the two sets, and the only curly braces appear on the outside (Ex. $\{0, 1\mid2, 3\}$).
Definition
A surreal number form $x=\{X_L|X_R\}$ is well-formed if no member of $X_R$ is lequal to a member of $X_L$. Symbolically2, $\forall x_L\in X_L\forall x_R\in X_R$ $x_R\not\le x_L$
Another quick aside. I’m likely going to be less formal later in this post than in the previous two definitions, so just remember that if you see something that looks like $x_L$, then its a member of some set $X_L$ that is the left set of some surreal number (form) $x$. I won’t always make this explicit.
Now that we’ve defined well-formed, we can finally define surreal numbers. First, note that since we have a definition for lequality, we automatically get natural defintions for grequality, equality, strict less than 3, and strict greater than as well. As an example $x=y\iff x\le y\text{ and }y\le x$.
Definition
The surreal numbers are the equivalence classes of the class4 of well-formed surreal number forms under the equivalence relation $x\sim y\iff x\le y\text{ and }y\le x$.
Now that we’ve finally gotten to this definition, I advise that you ignore it for the most part. It’s really not necessary it have it in mind for working with surreal numbers; it just serves to make things mathematically precise and well-defined. One thing that happens with well-formed surreal number forms is that numbers have multiple representations (Ex. $\{0,3,6\mid\}=\{2,6,1\mid\}$), but these representations are different under the normal interpretation of equality (equality as pairs of sets). While we are working with pairs of sets, we’re thinking of them as numbers and not as pairs, so we want to use a different type of equality and this is down by considering equivalence classes. This let’s us have different representations for a value, but only one object (its equivalence class). This is like how $\frac48$ and $\frac12$ are formally different, but still equal and refer to the same value.
For thinking about surreal numbers, you really only need to keep in mind the original definition of a surreal number form, and the fact that surreal numbers are well-formed (i.e. that the left set is strictly “smaller” than the right set).
# Making Sense of This
If you feel like the definition of surreal numbers makes complete sense, then skip this or just read the summary at the end of it.
So, a surreal number is two sets of surreal numbers, a left set and a right set. Every member of its left set is less than every member of its right set. One surreal number is less than another one if its less than the second’s right set and its left set is less than the second one.
Honestly, it’s not even obvious this makes sense. In the standard approach to constructing numbers, you have real numbers made from rational numbers, and ration numbers made from integers. Every type is constructed using previous types. Here, there is only one type, so isn’t it circular? 5
The thing to keep in mind is that concepts surrounding surreal numbers are defined in terms of other surreal numbers, but they’re only defined in terms of simpler surreal numbers! As you “unfold” these definitions, you will eventually reach the simplest surreal number of all $\{\mid\}$, and at this point you are done. Since there is nothing left to unfold (and members of the empty set satisfy all properties6), these definitions are perfectly fine. This actually has a nice side affect. If you want to prove a statement about the natural numbers, you can do so inductively. You show that it holds for 0, and that if it holds for some number $k$, then it also holds for $k+1$, and this shows that it’s true for all natural numbers 7. Surreal numbers have their own form of induction. If you want to prove a statement holds for all surreal numbers, it’s enough to show that if it holds for all members a number’s left and right sets, then it holds for that number; you don’t even need a base case! This is because the base case would be $\{\mid\}$ but everything holds for the empty set so its trivially satisfied.
To summarize, surreal number definitions make sense because everything is defined in terms of simpler numbers. A consequence of this is that statements can be proved inductively by showing that if a claim holds for all $x_L$ and all $x_R$, then it also holds for $x$. In my opinion, this second part is amazing. Surreal numbers contain far more values than the real numbers, but at the same time allow for induction that is arguably more simple than induction on natural numbers.
# Happy Birthday
Finally, all the set up is out of the way; we can start playing with these things. As I mentioned before, the first and simplest surreal number is $\{\mid\}$ which we’ll call $*$ for now. From this, we can create 4 possible new forms
The top-left one is just $*$ again so nothing new. The bottom right one is not well-formed so that’s not a surreal numbers. The other two however actually look like two new surreal numbers. We’ll call them $\{*\mid\}=\uparrow$ and $\{\mid*\}=\downarrow$. Before moving on, let’s verify that these actually are new numbers, and not just $*$ in disguise.
Theorem
$% $
We’ll prove this in 4 separate parts 8
Part 1: $\downarrow\le*$
We want to show that $\{\mid*\}\le\{\mid\}$, so we need to show that $\downarrow$ is less than everything in $*$'s right set and everything in $\downarrow$'s left set is less than $*$. Both of the sets in equation ($*_R$ and $\downarrow_L$) are empty, so both statements hold and we're done.
Part 2: $*\not\le\downarrow$
We want to show that $\{\mid\}\not\le\{\mid*\}$. This is the case since $*\le *$ and $*\in\downarrow_R$
I won’t bother doing the other two parts, but they work out as well and you can do them youself.$\square$
The above proof should seem misleading. Not because the theorem is false, but because I’m using things we haven’t proved yet. Namely, reflexivity and transitivity of $\le$. These properties hold for $\le_{\mathbb R}$, but we’re working with a different concept of lequality here. To calm our worries, in the next section, we will show that transitivity and reflexivity hold here as well. We’ll also recover some other familiar properties of “numbers”, and rename the 3 numbers we’ve created thus far.
Before that though, let’s introduce some useful terminology for talking about surreal numbers. From the three we’ve seen so far, it’s clear how the rest of the numbers will be constructed. Each step along the way, the $k$ numbers already construct form $4^k$ 9 candidate new surreal numbers, some (only few) of which will actually be new numbers. With this in mind, there’s a kind of order to the numbers separate from lequality: some are made before others. To capture this notion, we define the following
Definition
The ancestors of $x$ are all the numbers $x_L$ and all the numbers $x_R$
Definition
We say $\{\mid\}$ was born on day 0. In general, $x$ was born 1 day after the oldest of its ancestors (members of either $X_L$ or $X_R$). We call the day a number $x$ was born its birthday or birthday number.
Definition
We say $x$ is simpler than $y$ if $x$ was born before $y$
These definitions will give a nice way of identifying surreal numbers. In the next section, we will prove the following theorem
The Simplicity Theorem
Given any surreal number $y=\{Y_L\mid Y_R\}$, if $x$ is the simplest number such that $% $, then $x=y$.
The notation $% $ means that $% $. In generally, when a relation is applied to a set (of surreals), it is applied elementwise.
# Some Properties
The surreal numbers form what’s called an ordered Field. This means four things. You can add them, you can multiply, you can order them, and all these things play nicely with each other and generally behave as you would expect. We won’t show all of this here because it would be a lot and I don’t want to, but we’ll a thing or two about the ordering, define addition and multiplication, and then probably show some other stuff 10 11.
Theorem (Transitivity of $\le$)
If $x\le y$ and $y\le z$, then $x\le z$ 12
As I suggested before, the standard way for proving things about surreal numbers is induction. With that said, assume the theorem holds for any triple ($x', y', z')$ where $x'$ is an ancestor of $x$ and similarly for $y'$ and $z'$. Furthermore, assume $x\le y$ and $y\le z$. We need to show that $x$ is lequal to every $z_R$ and every $x_L$ is lequal to $z$. For the first condition, $x\le y$ and $y\le z_R$ (by assumption), and so $x\le z_R$ by induction (since $z_R$ is an ancestor of z). For the second condition, $x_L\le y\le z$ by assumption and so $x_L\le z$ (by induction). Hence, $x\le z$ and we are done. $\square$
We had this messy recursive definition of $\le$, and we just showed it was transitive using induction pretty simply without even needing a base case. Take some time to convince yourself that the above proof is actually correct and not just cheating13. I’ll wait. Now that we have transitivity, the natural thing to prove next is reflexivity, and then we’ll have shown that $\le$ is a partial order14. Instead of doing that here, I’ll leave that to you and prove something else.
Theorem
$% $. Possibly more clearly, $\forall x_L\in X_L\forall x_R\in X_R$ we have $% $
We start by showing that $x>X_L$. Fix any $x_L$, so we need to show that $x>x_L$. This follows from the definition since $x_L\le x_L$ ($x>x_L\iff x\not\le x_L$ and lequality requires no $x_L$ s.t. $x_L\le x_L$).
We now show that $x< X_R$. Fix any $x_R$, so we need to show that $x_R>x$ or equivalently that $x_R\not\le x$. This once again follows from the definition since $x_R\le x_R$. $\square$
The next theorem blew my mind the first time I saw it.
The Simplicity Theorem (Again)
Given any surreal number $y=\{Y_L\mid Y_R\}$, if $x$ is the simplest number such that $% $, then $x=y$.
Let $y$ be any surreal number, and let $x$ be the simplest number s.t. $Y_L< x < Y_R$. We first show that $x\le y$, which is the case iff $x < Y_R$ and $y > X_L$. The first inequality holds by assumption. For the second inequality, we use contradiction. Assume $y\le x_L$ for some $x_L$. Then, $Y_L < y \le x_L < x < Y_R$ which contradicts our assumption on $x$ being the simplest such number. Thus, $y > X_L$ and so $x\le y$. Similarly, it can be shown that $y\le x$ and so $x=y$. $\square$
This theorem (and the next one) is extremely useful for identifying surreal numbers. It can also be used to find an explicit formula for the number of surreals born on each day 15.
Theorem
$\{X_L\mid X_R\}=\{\max X_L\mid \min X_R\}$ when the maximum and minimum both exist.
Let’s move on to some arthmetic. What might we mean by $x+y$? One important property of addition of real numbers (important enough for it to be required of all ordered fields) is that $a\le b\iff a+c\le b+c$. With this in mind, we would want the following to hold in the case of surreals: $x+y_L\le x+y\le x+y_R$. Motivated by this, we make the following definition
Definition
$x+y=\{X_L+y,x+Y_L\mid X_R+y,x+Y_R\}$
This satisfies $x+y_L\le x+y\le x+y_R$ by construction and also satisfies other properties of addition that you would expect. For brevity, we will only prove communitivity here because it has a short proof.
Theorem
$x+y=y+x$
Using induction \begin{align*} x+y= \{X_L+y,x+Y_L\mid X_R+y,x+Y_R\}= \{y+X_L,Y_L+x\mid y+X_R,Y_R+x\}= y+x \end{align*} $\square$
Nice and simple. Another thing of note is the following
Theorem
$x+\{\mid\}=x$. That is, $\{\mid\}$ is the additive identity.
Note that $x+\emptyset=\emptyset$ since there is nothing to add to $x$. Assume the claim holds for all of $x$'s ancestors, and let $*=\{\mid\}$. Then, \begin{align*} x+* &= \{X_L+*,x+\emptyset\mid X_R+*,x+\emptyset\} \\ &= \{X_L+*\mid X_R+*\} \\ &= \{X_L\mid X_R\} \\ &= x \end{align*} $\square$
Awesome. We just found an additive identity, and we use this as justification to name $0=\{\mid\}$. Seeing that we have a $0$, the next natural question is to ask whether there are additive inverses, and if so, how to find them.
Definition
$-x=\{-X_R\mid-X_L\}$
It is up to the reader to verify that this actually is the additive inverse of $x$.
Next up is multiplication. Looking at field properties we might want satisfied, we see that $0\le a,0\le b\implies0\le ab$. It isn’t immediately obvious how we might use this discover the correct definition of multiplication, but replacing the $0$’s with variables gets us there
This (and similar considerations) motivates the next definition
Definition
$xy=x*y=\\\{X_L*y+x*Y_L-X_L*Y_L,X_R*y+x*Y_R-X_R*Y_R\mid\\ X_L*y+x*Y_R-X_L*Y_R,X_R*y+x*Y_L-X_R*Y_L\}$
Not gonna lie. This one is pretty ugly, and they only get uglier from here 16. On the bright side, they still behave nicely. For instance
Theorem
$0x=0=x0$ and $x*\{0|\}=x=\{0|\}*x$
Each sum involved in calculating $0x$ or $x0$ includes a term containing the left (or right) set of $0$. This is the empty set, so when you multiply it by something, you still get the empty set. When that resulting empty set is added to other sets, you still have the empty set so both the left and right sets of $0x$ or $x0$ are empty and hence $0x=0=x0$.
The other half of the theorem is easily seen. $\square$
Now that we have an additive inverse as well, we call $1=\{0\mid\}$. Furthermore, we note that, by definition, $-1=\{\mid-0\}=\{\mid0\}$, and so we finally have approriate names for all 3 surreal numbers we have constructed.
# All Numbers Great and Small
We have $0, 1$, and $-1$, but what about the rest of the numbers. First, note that $\{0\mid\}+\{0\mid\}=\{1\mid\}$ and that in general, letting $y=\{x\mid\}$, $y+1=\{x\mid\}+\{0\mid\}=\{x+1,y\mid\}$ 17. If you start with $y=0$, and keep adding 1 in this way you find that the usual natural numbers are embedded in the surreal via $n\mapsto\{n-1\mid\}$. You get the rest of the integers by considering their negatives: $-n\mapsto\{\mid-(n-1)\}$.
What about the rationals? First note that, letting $x=\{0\mid1\}$, $\{0\mid1\}+\{0\mid1\}=\{x\mid1+x\}=1$ by the simplicity theorem, and so we say $\{0\mid1\}=\frac12$. Similarly, we define $\{0\mid\frac12\}=\frac14$ and $\{\frac12\mid1\}=\frac34$.
We can combine these two observations into the following theorem
Theorem
Let $% $ be all the numbers born on some (finite) day $n$ or earlier. Then, the numbers born on day $n+1$ are the following where $0\le i\le m-1$ $% $
The proof of this theorem is omitted. Hint for proving it yourself, use the simplicity theorem and use $x=\frac12y\implies x+x=y$.
The above theorem classifies all numbers born on finite days. One thing to notice is that the integers get special treatment, and the dyadic rationals 18 get special treatment, but the reals and the rationals in general do not. In fact, on any finite day, the only numbers are integers and dyadic rationals. There’s no $\pi$, no $e$, nothing. Things don’t really get interesting until day $\omega$.
$\omega$ can be thought of as the number after all the natural numbers. In the surreals, we actually define $\omega=\{0,1,2,3,\dots\mid\}$ and this is a completely legitimate surreal number; it obeys all the same rules as the other surreals. It is born on day $\omega$, but is not the only number born on day $\omega$. You also get, for example,
$\varepsilon$ is an interesting number. It is larger than $0$, but smaller than any positive dyadic rational (and by extension, any positive real number). For this reason, it is called an infinitesimal.
Another interesting fact is that on day $\omega$, you get every real number. They can be constructed using a process similar to Dedekind cuts. This is nothing new, but what makes things interesting is that the fact that prior to day $\omega$ the only non-integers constructed are the dyadic rationals suggests a method of finding appropriate cuts for each real number. Consider any real number $x$ and write it out in binary 19 (Ex. $\pi=11.00100100001111110\dots_2$). To form the members of $X_L$, take substrings of $x$’s binary expansion that end in 1. To form the members of $X_R$, take substrings of $x$’s binary expansion that end in 0, execpt replace the final 0 with a 1. Doing this for real number yields its equivalent surreal number and shows that all real numbers are born by the end of day $\omega$. Ex.
So on day $\omega$ you have all the reals, an infinite number, and an infinitesimal. Of course, it doesn’t stop there. On day $\omega+1$, you get numbers like
By the time you reach day $2\omega$, you start seeing things like
From here, there is no limit. The surreals also contain strange numbers like
The amazing thing about this is not that these are actual constructible numbers, but that these are well-behaved numbers. Most notions of doing arithmetic with infinity that you come across either don’t work very well or are very limited. Here, you have infinities and infinitesimals behaving just like any other numbers. Everything is legitimate and well-definied, and the whole thing forms an ordered field! You can pick any two of the numbers above, and one is larger than the other, and that order is well-behaved. It plays nice with multiplication and addition and many other operations. Not only that, but you can do more than just arithmetic with surreal numbers. In his book On Numbers and Games, Conway takes the theory of surreals much farther than I touched on in this post. He studies 20 analysis, algebra, and number theory of surreals.
# There’s More
Unfortunately, this post got really long, really fast, and so I was not able to talk about everything I wanted to. In particular, I didn’t even touch on what’s maybe the most surprising property of surreal numbers: how they were discovered. Conway originally discovered surreal numbers while studying the board game Go. He found a way to represent Go positions as sums of smaller games, and evenetually realized that the games he was studying behaved like numbers. What I called a surreal number form in the beginning is more appropriately dubbed a Game. Games in general share many of the properties of surreal numbers (which are just a subclass of games), and there are many interesting games that are not well-formed. This post is too long as is to go into the details, but if you want learn more about the connection between surreal numbers and games, I recommend Winning Ways for Your Mathematical Plays.
In you just want more practice with surreals, Knuth has a nice book about them, told from the perspective of two people stranded on an island who find a rock with a couple definitions, and find they have way too much free time.
1. We’ll see later in this post that this number is 0. Technically, we can call this whatever we want. We’ll see that we want to call it 0
2. The upside-down A means “for all”. There’s also a backwards E that means “there exists”
3. I’m tempted to call this strict lequality, but the name sounds misleading. In case it’s not clear, I’m referring to < here
4. not set
5. Spoiler: no
6. That is, any statement of the form “for all x in A, blah” is true when A is empty
7. Truth for 0 implies truth for 1, truth for 1 implies truth for 2, etc. It’s like how if you line up a bunch of dominoes and knock over the first one, you know they’ll all fall because the first one falls and every one that falls knocks over the next one
8. I’m not sure how I feel about making the areas where the proof is stand out.
9. Try to see why (Hint: This upper bound is much larger than the true number, and much larger than other upper bounds you could come up with)
10. I will most likely end up using x_L to refer to different things at different times in the same proof (either as a specific member of X_L or any general member of X_L). Try to keep up.
11. Throughout this whole post, I’m talking about things in the order in which they pop into my head, so theorems and definitions do not necessarily appear in the most logical order. Keep that in mind.
12. If it’s not clear from reading the follow proof, I was not entirely sure how to formulate in the induction in a way that didn’t feel hand-wavy. What you see below is the result of me going back and forth between different formulations and between whether or not I should just ignore the specifics and hope no one notices. Honestly, no one reads this blog so I could have done that.
13. Probably worth mentioning that I haven’t been super strict/formal in setting up how induction on surreals works. Basically, given some tuple (x_1,…,x_n) of surreal numbers, you can consider the sum of their birthdays, and call one tuple simpler than another if its members have a lower bitherday sum than the other. Then you do induction on the birthday sum of tuples and you win.
14. Also show that if x is not lequal to y, then y is lequal to x to show that it is in fact a total order
15. Hint: It’s much less than the 4^k upper bound
16. Seriously, look up the definitions for 1/x and sqrt(x).
17. When y is an integer, x+1 >= y. For what other cases does this inequality hold?
18. rationals with denominator a power of 2
19. we use binary because writing a number in binary is equivalent to writing it as a sum of numbers of the form 1/2^n and so we are only using already constructed numbers
20. does? performs? What’s a good verb here?
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2023-02-09 03:02:19
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https://blender.stackexchange.com/questions/46566/aligning-plane-normal-vector-side-to-face-a-point-python
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Aligning plane normal vector side to face a point : Python
I have 2 points P1 = (x1, y1, z1) and P2 = (x2, y2, z2). The problem statement is some what like this.
Draw a plane at point P1 (any arbitrary point in 3D space). Rotate the plane to face point P2 (another arbitrary point in 3D space) such that the normal vector of plane at point P1 is facing point P2. Change the rotation of the plane such that it maintains it perpendicularity to point P2 as much it can while one of its X, Y or Z rotations is 0
So far, I've managed to draw the plane and make it face the point P2 using this code:
def align_plane_to_point(obj, point):
normal = obj.data.polygons[0].normal.xyz
mat_obj = obj.matrix_basis
mat_scale = mathutils.Matrix.Scale(1, 4, mat_obj.to_scale())
trans = mat_obj.to_translation()
mat_trans = mathutils.Matrix.Translation(trans)
point_trans = point - trans
q = normal.rotation_difference(point_trans)
mat_rot = q.to_matrix()
mat_rot.resize_4x4()
mat_obj = mat_trans * mat_rot * mat_scale
obj.matrix_basis = mat_obj
Calling this function with arguments obj = Plane at Point P1 and point = point P2, makes sure that the normal side is facing point P2.
Now I am not sure as to how to go about the last part of the problem. Maintaining perpendicularity to point P2 but making sure at least one of the rotations is 0.
Say for example the rotations (in degrees) are like so after executing the above function:
X: -40
Y: 60
Z: -80
Again how do I know (programmatically) which value can I set to 0, making sure plane is as much perpendicular as it can be. I don't mind changing the rest of the values as well as long as the normal is facing towards the point P2. Manually changing the values, I can see the rotation of the plane and thus decide, but using Python I don't know how to figure this out.
Any help is appreciated.
1. The function precisely for that is to_track_quat Works much like track to constraints. Gives more than rotation difference.
to_track_quat(track, up)
This uses the Vector to point with the specified track axis, (Z for normal) and a secondary "up" axis (x or y, never same ...).
Code would be:
def align_plane_to_point(obj, point):
dir = point - obj.location
return dir.to_track_quat("Z", "X").to_euler()
if obj:
obj.rotation_euler = align_plane_to_point(obj, point)
Of course you can extra check for obj rotation type, the function giving a quaternion, I convert it here to euler assuming the usual kind. Or may use it for rotation matrix, like:
rotMatrix = dir.to_track_quat("Z", "X").to_matrix().to_4x4()
(as quat to matrix produces a 3x3 matrix)
1. If u need more control, but more complicated, you can have the second dir (up be controlled by another vector) you may look into this, if it helps.
I build there the rotation matrix directly out of 1 vector and a second that is not necessarily perpendicular.
First I make the second/third vector perpendicular by the cross functions, with some exceptions. I'll not copy that here ... Then can build a 3x3 matrix (only rotation) by putting the 3 vecs into columns
mat3x3 = mathutils.Matrix().to_3x3()"
mat3x3.col[0], mat3x3.col[1], mat3x3.col[2] = mx, my, mz"
eulerRotation = mat3x3.to_euler()
where 3 vecs, mx, my, mz, mz would be the point - obj.location, the other 2 being determined as in the linked code
if u use directly such matrix (to 4x4 ok) you'll have some difficulty controlling the scale for some exceptional cases (may fall to 0 on some axes), so to euler or to quaternion is the way, even if u further convert back to a full matrix
• to_track_quat worked perfectly. Thanks a ton! :) :) – Kunal Aggarwal Feb 9 '16 at 16:44
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2020-09-18 14:41:52
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https://codeforces.com/problemset/problem/776/E
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E. The Holmes Children
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
The Holmes children are fighting over who amongst them is the cleverest.
Mycroft asked Sherlock and Eurus to find value of f(n), where f(1) = 1 and for n ≥ 2, f(n) is the number of distinct ordered positive integer pairs (x, y) that satisfy x + y = n and gcd(x, y) = 1. The integer gcd(a, b) is the greatest common divisor of a and b.
Sherlock said that solving this was child's play and asked Mycroft to instead get the value of . Summation is done over all positive integers d that divide n.
Eurus was quietly observing all this and finally came up with her problem to astonish both Sherlock and Mycroft.
She defined a k-composite function Fk(n) recursively as follows:
She wants them to tell the value of Fk(n) modulo 1000000007.
Input
A single line of input contains two space separated integers n (1 ≤ n ≤ 1012) and k (1 ≤ k ≤ 1012) indicating that Eurus asks Sherlock and Mycroft to find the value of Fk(n) modulo 1000000007.
Output
Output a single integer — the value of Fk(n) modulo 1000000007.
Examples
Input
7 1
Output
6
Input
10 2
Output
4
Note
In the first case, there are 6 distinct ordered pairs (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1) satisfying x + y = 7 and gcd(x, y) = 1. Hence, f(7) = 6. So, F1(7) = f(g(7)) = f(f(7) + f(1)) = f(6 + 1) = f(7) = 6.
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2022-05-20 00:59:00
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https://www.math.ucdavis.edu/research/seminars/?talk_id=2343
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# Mathematics Colloquia and Seminars
Let each site of the triangular lattice (or edge of the \Z^2 lattice) have an independent Poisson clock switching between open and closed. So, at any given moment, the configuration is just critical percolation. In particular, the probability of a left-right open crossing in an n*n box is roughly 1/2, and, on the infinite lattice, almost surely there are only finite open clusters. In the box, how long do we have to wait before we lose essentially all information about having a left-right open crossing? In the infinite lattice, are there random exceptional times when there are infinite clusters? In joint work with Christophe Garban and Oded Schramm, we gave quite complete answers: exceptional times do exist on both lattices, and the Hausdorff dimension of their set is computed to be 31/36 for the triangular lattice. The indicator function of a percolation crossing event is a function on the hypercube {-1,+1}^{sites or edges}, and thus it has a Fourier-Walsh expansion. Our proofs are based on giving sharp concentration results for the weight'' of the Fourier coefficients at different frequencies.
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2020-01-29 03:07:11
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https://labs.tib.eu/arxiv/?author=G.%20Collin
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• ProtoDUNE-SP is the single-phase DUNE Far Detector prototype that is under construction and will be operated at the CERN Neutrino Platform (NP) starting in 2018. ProtoDUNE-SP, a crucial part of the DUNE effort towards the construction of the first DUNE 10-kt fiducial mass far detector module (17 kt total LAr mass), is a significant experiment in its own right. With a total liquid argon (LAr) mass of 0.77 kt, it represents the largest monolithic single-phase LArTPC detector to be built to date. It's technical design is given in this report.
• This document presents the Conceptual Design Report (CDR) put forward by an international neutrino community to pursue the Deep Underground Neutrino Experiment at the Long-Baseline Neutrino Facility (LBNF/DUNE), a groundbreaking science experiment for long-baseline neutrino oscillation studies and for neutrino astrophysics and nucleon decay searches. The DUNE far detector will be a very large modular liquid argon time-projection chamber (LArTPC) located deep underground, coupled to the LBNF multi-megawatt wide-band neutrino beam. DUNE will also have a high-resolution and high-precision near detector.
• ### Sr$_2$IrO$_4$ magnetic phase diagram, from resistivity(1410.5726)
April 28, 2015 cond-mat.str-el
We show that, contrary to previous belief, the transition to the antiferromagnetic state of Sr$_2$IrO$_4$ in zero magnetic field does show up in the transverse resistivity. We attribute this to a change in transverse integrals associated to the magnetic ordering, which is evaluated considering hopping of the localized charge. The evolution of the resistivity anomaly associated to the magnetic transition under applied magnetic field is studied. It tracks the magnetic phase diagram, allowing to identify three different lines, notably the spin-flip line, associated with the reordering of the ferromagnetic component of the magnetization, and an intriguing line for field induced magnetism, also corroborated by magnetization measurements.
• The US neutrino community gathered at the Workshop on the Intermediate Neutrino Program (WINP) at Brookhaven National Laboratory February 4-6, 2015 to explore opportunities in neutrino physics over the next five to ten years. Scientists from particle, astroparticle and nuclear physics participated in the workshop. The workshop examined promising opportunities for neutrino physics in the intermediate term, including possible new small to mid-scale experiments, US contributions to large experiments, upgrades to existing experiments, R&D plans and theory. The workshop was organized into two sets of parallel working group sessions, divided by physics topics and technology. Physics working groups covered topics on Sterile Neutrinos, Neutrino Mixing, Neutrino Interactions, Neutrino Properties and Astrophysical Neutrinos. Technology sessions were organized into Theory, Short-Baseline Accelerator Neutrinos, Reactor Neutrinos, Detector R&D and Source, Cyclotron and Meson Decay at Rest sessions.This report summarizes discussion and conclusions from the workshop.
• ### Improved TPB-coated Light Guides for Liquid Argon TPC Light Detection Systems(1410.6256)
March 25, 2015 hep-ex, physics.ins-det
Scintillation light produced in liquid argon (LAr) must be shifted from 128 nm to visible wavelengths in light detection systems used for liquid argon time-projection chambers (LArTPCs). To date, LArTPC light collection systems have employed tetraphenyl butadiene (TPB) coatings on photomultiplier tubes (PMTs) or plates placed in front of the PMTs. Recently, a new approach using TPB-coated light guides was proposed. In this paper, we report on light guides with improved attenuation lengths above 100 cm when measured in air. This is an important step in the development of meter-scale light guides for future LArTPCs. Improvements come from using a new acrylic-based coating, diamond-polished cast UV transmitting acrylic bars, and a hand-dipping technique to coat the bars. We discuss a model for connecting bar response in air to response in liquid argon and compare this to data taken in liquid argon. The good agreement between the prediction of the model and the measured response in liquid argon demonstrates that characterization in air is sufficient for quality control of bar production. This model can be used in simulations of light guides for future experiments.
• ### The Effects of Dissolved Methane upon Liquid Argon Scintillation Light(1308.3658)
Jan. 17, 2014 hep-ex, physics.ins-det
In this paper we report on measurements of the effects of dissolved methane upon argon scintillation light. We monitor the light yield from an alpha source held 20 cm from a cryogenic photomultiplier tube (PMT) assembly as methane is injected into a high-purity liquid argon volume. We observe significant suppression of the scintillation light yield by dissolved methane at the 10 part per billion (ppb) level. By examining the late scintillation light time constant, we determine that this loss is caused by an absorption process and also see some evidence of methane-induced scintillation quenching at higher concentrations (50-100 ppb). Using a second PMT assembly we look for visible re-emission features from the dissolved methane which have been reported in gas-phase argon methane mixtures, and we find no evidence of visible re-emission from liquid-phase argon methane mixtures at concentrations between 10 ppb and 0.1%.
• ### LAr1-ND: Testing Neutrino Anomalies with Multiple LArTPC Detectors at Fermilab(1309.7987)
Nov. 5, 2013 hep-ex, physics.ins-det
This white paper describes LAr1-ND and the compelling physics it brings first in Phase 1 and next towards the full LAr1 program. In addition, LAr1-ND serves as a key step in the development toward large-scale LArTPC detectors. Its development goals will encompass testing existing and possibly innovative designs for LBNE while at the same time providing a training ground for teams working towards LBNE combining timely neutrino physics with experience in detector development.
• ### Whitepaper on the DAEdALUS Program(1307.2949)
July 11, 2013 hep-ex, physics.acc-ph
This whitepaper describes the status of the DAEdALUS program for development of high power cyclotrons as of the time of the final meeting of the Division of Particles and Fields 2013 Community Study ("Snowmass"). We report several new results, including a measurement capability between 4 and 12 degrees on the CP violating parameter in the neutrino sector. Past results, including the capability of the IsoDAR high Dm^2 antielectron neutrino disappearance search, are reviewed. A discussion of the R&D successes, including construction of a beamline teststand, and future plans are provided. This text incorporates short whitepapers written for subgroups in the Intensity Frontier and Frontier Capabilities Working Groups that are available on the Snowmass website.
• ### 23Na NMR study of sodium order in NaxCoO2 with 22K Neel temperature(1202.4254)
We report a systematic study of the $c$ lattice parameter in the Na$_{x}$CoO$_{2}$ phases versus Na content $x>0.5$, in which sodium always displays ordered arrangements. This allows us to single out the first phase which exhibits an AF magnetic order at a N\'eel temperature $T_{N}=$22 K which is found to occur for $x\approx 0.77(1)$. Pure samples of this phase have been studied both as aligned powders and single crystals. They exhibit identical $^{23}$Na NMR spectra in which three sets of Na sites could be fully resolved, and are found to display $T$ dependencies of their NMR shifts which scale with each other. This allows us to establish that the $T$ variation of the shifts is due to the paramagnetism of the Co sites with formal charge state larger than 3$^{+}$. The existence of a sodium site with axial charge symmetry and the intensity ratio between the sets of $^{23}$Na lines permits us to reveal that the 2D structure of the Na order corresponds to 10 Na sites on top of a 13 Co sites unit cell, that is with $x=10/13\approx 0.77$. This structure fits with that determined from local density calculations and involves triangles of 3 Na sites located on top of Co sites (so called Na1 sites). The associated ordering of the Na vacancies is quite distinct from that found for $x<0.75$.
• ### Spin correlations and cobalt charge states: A new phase diagram of sodium cobaltates(0807.3116)
July 19, 2008 cond-mat.str-el
Using 23Na NMR measurements on sodium cobaltates at intermediate dopings (0.44<=x<=0.62), we establish the qualitative change of behavior of the local magnetic susceptibility at x*=0.63-0.65, from a low x Pauli-like regime to the high x Curie-Weiss regime. For 0.5<=x<=0.62, the presence of a maximum T* in the temperature dependence of the susceptibility shows the existence of an x-dependent energy scale. T_1 relaxation measurements establish the predominantly antiferromagnetic character of spin correlations for x<x*. This contradicts the commonly assumed uncorrelated Pauli behavior in this x range and is at odds with the observed ferromagnetic correlations for x>x*. It is suggested that at a given x the ferromagnetic correlations might dominate the antiferromagnetic ones above T*. From 59Co NMR data, it is shown that moving towards higher x away from x=0.5 results in the progressive appearance of nonmagnetic Co3+ sites, breaking the homogeneity of Co states encountered for x<=0.5. The main features of the NMR-detected 59Co quadrupolar effects, together with indications from the powder x-ray diffraction data, lead us to sketch a possible structural origin for the Co3+ sites. In light of this ensemble of new experimental observations, a new phase diagram is proposed, taking into account the systematic presence of correlations and their x-dependence.
• ### Influence of charge order on the magnetic properties of Na$_{x}$CoO$_{2}$ for $x>0.65$(cond-mat/0703561)
We have synthesized and characterized the four different stable phases of Na ordered Na$_{x}$CoO$_{2}$, for $0.65<x\lesssim 0.75$. Above 100K they display similar Curie-Weiss spin susceptibilities as well as ferromagnetic $q=0$ spin fluctuations in the CoO$_{2}$ planes revealed respectively by $^{23}$Na NMR shift and spin lattice $T_{1}$ data. The Co disproportionate already above 300K into Co$^{3+}$ and $\approx$Co$^{3.5+}$ in all phases, which allows us to understand that magnetism is favoured. Below 100K the paramagnetic properties become quite distinct, and a 3D magnetic order sets in only for $x=0.75$, so that charge order has a subtle incidence on the low $T$ energy scales and transverse magnetic couplings.
• ### NMR study of the magnetic and metal-insulator transitions in Na0.5CoO2: a nesting scenario(cond-mat/0507514)
Co and Na NMR are used to probe the local susceptibility and charge state of the two Co sites of the Na-ordered orthorhombic Na0.5CoO2. Above T_N=86K, both sites display a similar T-dependence of the spin shift, suggesting that there is no charge segregation into Co3+ and Co4+ sites. Below T_N, the magnetic long range commensurate order found is only slightly affected by the metal-insulator transition (MIT) at T_MIT=51K. Furthermore, the electric field gradient at the Co site does not change at these transitions, indicating the absence of charge ordering. All these observations can be explained by successive SDW induced by two nestings of the Fermi Surface specific to the x=0.5 Na-ordering.
• ### Impurity induced Local Magnetism and Density of States in the superconducting state of YBa2Cu3O7(cond-mat/0504727)
Oxygen NMR is used to probe the local influence of nonmagnetic Zn and magnetic Ni impurities in the superconducting state of optimally doped high Tc YBa2Cu3O7. Zn and Ni induce a staggered paramagnetic polarization, similar to that evidenced above Tc, with a typical extension xi=3 cell units for Zn and xi>=3 for Ni. In addition, Zn is observed to induce a local density of states near the Fermi Energy in its neighbourhood, which also decays over about 3 cell units. Its magnitude decreases sharply with increasing temperature. This allows direct comparison with the STM observations done in BiSCO.
• ### Direct evidence for a dynamical ground state in the highly frustrated Tb$_2$Sn$_2$O$_7$ pyrochlore(cond-mat/0603434)
March 16, 2006 cond-mat.str-el
MuSR experiments have been performed on powder sample of the "ordered spin ice" Tb$_2$Sn$_2$O$_7$ pyrochlore compound. At base temperature (T=35mK) the muon relaxation is found to be of dynamical nature which demonstrates that strong fluctuations persist below the ferromagnetic transition (T_C=0.87K). Hints of long range order appear as oscillations of the muon polarization when an external field is applied and also as a hysteretic behavior below T_C. We propose a dynamical and strongly correlated scenario where dynamics results from fluctuation of large spin clusters with the "ordered spin ice" structure.
• ### Evidence of a single nonmagnetic Co3+ state in the Na1CoO2 cobaltate(cond-mat/0505668)
Macroscopic magnetization, muon spin rotation (muSR), and NMR measurements were carried out to study magnetism in the Na1CoO2 cobaltate. Using SQUID measurements, Na1CoO2 is shown to have a bulk magnetic susceptibility much lower and flatter than that of NaxCoO2 with x=0.7-0.9. In fact, muSR yields a signal of mostly nonmagnetic origin, which is attributed to the x=1 phase. The intrinsic cobalt spin susceptibility corresponding to this x=1 phase is measured using Na NMR. It is indeed found to be almost zero, in agreement with a low-spin 3+ charge state of all cobalt atoms. This single state of Co ions in CoO2 planes is confirmed by Co NMR, whose determination of cobalt shift and quadrupolar parameters allows us to give a reference value of the Co3+ orbital shift in cobaltates.
• ### Series of Bulk Magnetic Phase Transitions in NaxCoO2: a muSR study(cond-mat/0501203)
Jan. 10, 2005 cond-mat.str-el
Using muon spin rotation, well-defined bulk ~ 100% magnetic phases in NaxCoO2 are revealed. A novel magnetic phase is detected for x = 0.85 with the highest transition temperature ever observed for x >= 0.75. This stresses the diversity of x >=0.75 magnetic phases and the link between magnetic and structural degrees of freedom. For the charge-ordered x = 0.50 compound, a cascade of transitions is observed below 85 K. From a detailed analysis of our data, we conclude that the ordered moment varies continuously with temperature and suggest that the two secondary transitions at 48 K and 29 K correspond to a moderate reorientation of antiferromagnetically coupled moments.
• ### Antiferromagnetic properties of a water vapor-inserted $YBa_2Cu_3O_{6.5}$ compound studied by NMR, NQR and $\mu$ SR(cond-mat/0309698)
Aug. 24, 2004 cond-mat.supr-con
We present a detailed NQR, NMR and $\mu$SR study of a magnetic phase obtained during a topotactic chemical reaction of YBa$_{2}$Cu$_{3}$O$_{6.5}$ high- temperature superconductor with low-pressure water vapor. Our studies give straightforward evidence that the ''empty'' Cu(1) chains play the role of an easy water insertion channel. It is shown that the NQR spectrum of the starting material transforms progressively under insertion of water, and completely disappears when one H$_{2}$O molecule is inserted per unit cell. Similarly, a Cu ZFNMR signal characteristic of this water inserted material appears and grows with increasing water content, which indicates that the products of the reaction are non-superconducting antiferromagnetic phases in which the bilayers are ordered. These antiferromagnetic phases are felt by proton NMR which reveals two sites with static internal fields of 150 and about 15 Gauss respectively. Two muon sites are also evidenced with similar local fields which vanish at $T\approx 400$ K. This indicates that the magnetic phases have similar N\'{e}el temperatures as the other bilayer undoped compounds. An analysis of the internal fields on different sites of the structure suggests that they can be all assigned to a single magnetic phase at large water content in which the Cu(1) electron spins order with those of the Cu(2). It appears that even samples packed in Stycast epoxy resin heated moderately at a temperature (200$^{0}$C) undergo a reaction with epoxy decomposition products which yield the formation of the same final compound. It is then quite clear that such effects should be considered quite seriously and avoided in experiments attempting to resolve tiny effects in such materials, as those performed in some recent neutron scattering experiments.
• ### Determination and Control of Oxygen Stoichiometry in the Cuprate Bi2sr2cuo6+D(cond-mat/0301063)
The relatively low Tc of Bi2Sr2CuO6+D allows to study normal-state down to low temperatures and the non-substituted compound is intrinsically strongly overdoped. Hole concentration can be adjusted trough oxygen excess, but few data exist in the literature about the quantitative control of D. The synthesis, achieved in air by solid-state reaction, needs long-time annealing to obtain pure phase with stoichiometric cationic ratios. Thermogravimetric techniques were used to explore oxygen non-stoichiometry. Absolute oxygen content was determined by reduction with hydrogen, while the oxygen exchange was studied between 300 C and 670 C with different PO2. Oxygen excess varies between 0.14 and 0.18, with possibly two regimes of oxygen intercalation. These results are compared to Bi-2212.
• ### Failure of the empirical OCT law in the Bi2Sr2CuO6+d compound(cond-mat/0211135)
We have studied the evolution of the thermoelectric power S(T) with oxygen doping of single-layered Bi2Sr2CuO6+d thin films and ceramics in the overall superconducting (Tc, S290K) phase diagram. While the universal relation between the room-temperature thermopower S290K and the critical temperature is found to hold in the strongly overdoped region (d>0.14), a strong violation is observed in the underdoped part of the phase diagram. The observed behaviour is compared with other cuprates and the different scenarios are discussed.
• ### Absence of static phase separation in the high-Tc cuprate $YBa_{2}Cu_{3}O_{6+y}$(cond-mat/0203225)
We use 89Y NMR in $YBa_{2}Cu_{3}O_{6+y}$ in order to evaluate with high sensitivity the distribution of hole content p in the CuO2 planes. For y=1 and y=0.6, this hole doping distribution is found narrow with a full width at half maximum smaller than Delta p=0.025. This rules out any large static phase separation between underdoped and optimally doped regions in contrast with the one observed by STM in Bi2212 and by NQR in LaSrCuO. This establishes that static electronic phase separation is not a generic feature of the cuprates.
• ### Thermopower in Overdoped Region of Cuprates(cond-mat/0208483)
The thermoelectric power S(T) of single-layer Bi2Sr2CuO6+d is studied as a function of oxygen doping in the strongly overdoped region of the phase diagram (T, d). As other physical properties in this region, diffusion thermopower Sdiff(T) also shows an important deviation from conventional Fermi liquid behaviour. This departure from T-linear S(T) dependence together with the results of susceptibility on the same samples suggest that the origin of the observed non-metallic behaviour is the existence of a singularity in the density of states near the Fermi level. The doping and temperature dependence of themopower is compared with a tight-binding band model.
• ### Anomalous Electronic Susceptibility in Bi2sr2cuo6+d(cond-mat/0208489)
We report magnetic susceptibility performed on overdoped Bi2Sr2CuO6+d powders as a function of oxygen doping d and temperature T. The decrease of the spin susceptibility chis with increasing T is confirmed. At sufficient high temperature, chis presents an unusual linear temperature dependence chis=chis0 -chi1T . Moreover, a linear correlation between chi1 and chis0 for increasing hole concentration has been displayed. These non conventional metal features will be discussed in terms of a singular narrow-band structures.
• ### Anomalous electronic susceptibility in Bi2Sr2CuO6+d and comparison with other overdoped cuprates(cond-mat/0206313)
June 17, 2002 cond-mat.supr-con
We report magnetic susceptibility performed on overdoped Bi2Sr2CuO6+d powders as a function of oxygen doping d and temperature T. The decrease of the spin susceptibility with increasing T is confirmed. At sufficient high temperature, the spin susceptibility Chi_s presents an unusual linear temperature dependence Chi_s ~ Chi_s0 -Chi_1 T. Moreover, a linear correlation between Chi_1 and Chi_s0 for increasing hole concentration is displayed. A temperature Tchi, independent of hole doping characterizes this scaling. Comparison with other cuprates of the literature(LSCO, Tl-2201 and Bi-2212), over the same overdoped range, shows similarities with above results. These non conventional metal features will be discussed in terms of a singular narrow-band structure.
• ### Planar 17O NMR study of Pr_yY_{1-y}Ba_2Cu_3O_{6+x}(cond-mat/0201019)
We report the planar ^{17}O NMR shift in Pr substituted YBa_{2}Cu_{3}O_{6+x}, which at x=1 exhibits a characteristic pseudogap temperature dependence, confirming that Pr reduces the concentration of mobile holes in the CuO_{2} planes. Our estimate of the rate of this counterdoping effect, obtained by comparison with the shift in pure samples with reduced oxygen content, is found insufficient to explain the observed reduction of T_c. From the temperature dependent magnetic broadening of the ^{17}O NMR we conclude that the Pr moment and the local magnetic defect induced in the CuO_2 planes produce a long range spin polarization in the planes, which is likely associated with the extra reduction of T_c. We find a qualitatively different behaviour in the oxygen depleted Pr_yY_{1-y}Ba_2Cu_3O_{6.6}, i.e. the suppression of T$_c$ is nearly the same, but the magnetic broadening of the ^{17}O NMR appears weaker. This difference may signal a weaker coupling of the Pr to the planes in the underdoped compound, which might be linked with the larger Pr to CuO_2 plane distance, and correspondingly weaker hybridization.
• ### Thermopower in the strongly overdoped region of single-layer Bi2Sr2CuO6+d superconductor(cond-mat/0203515)
The evolution of the thermoelectric power S(T) with doping, p, of single-layer Bi2Sr2CuO6+d ceramics in the strongly overdoped region is studied in detail. Analysis in term of drag and diffusion contributions indicates a departure of the diffusion from the T-linear metallic behavior. This effect is increased in the strongly overdoped range (p~0.2-0.28) and should reflect the proximity of some topological change.
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2020-12-01 22:15:13
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https://en.m.wikisource.org/wiki/Popular_Science_Monthly/Volume_21/October_1882/Popular_Miscellany
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# Popular Science Monthly/Volume 21/October 1882/Popular Miscellany
POPULAR MISCELLANY.
A New Plan for Armored Vessels.—The Naval Committee of the United States House of Representatives has given favorable consideration to a new plan for building armored vessels which has been devised by a retired invalid engineer. The principal armorial application consists of a submerged "turtle-back," about four inches thick, and extending from side to side and from stem to stern of the vessel and below the waterline, so arranged that an enemy's shot from any direction can hit it only at a deflecting angle, so as to be thrown off rather than go through. The sides of the vessel above the turtle-back are filled in with cotton or cork, in which a breach made by the passage of a ball will be self-closed by the elastic action of the substance. They may, moreover, be shot to pieces without destroying the buoyant power of the ship. The guns are mounted upon heavy, impenetrable, centrally arranged, cylindrical armor, which extends to the bottom of the ship, and is there seated on an hydraulic cushion. The breech of the gun is also inclosed in an oval armor, so arranged as to deflect a ball, striking it from any point, in a harmless direction. The gun is operated by an hydraulic loading apparatus, which is worked by one gunner, and hydraulic buffers are provided to take up the recoil.
The Timber-Line of Mountains.—Mr. Henry Gannett, noticing, in "The American Journal of Science," Dr. Rothrock's statement that, as a whole, there is little or no increase in the altitude of the timber-line toward the equator in the Western hemisphere, south of the forty-first parallel of north latitude, observes that the height of the timber-line is purely a question of temperature, and that that is a function of the latitude, the elevation, and the mass, of the country in the neighborhood. A great mass of country, if raised to a considerable height above the sea, carries with it the isothermals. Therefore, in considering the height of the timber-line, "we must regard the mountain-ranges in connection with the plateaus on which they stand, their latitudes, heights, and masses, or what, in a measure, sums up these three, their temperatures, as it is by these that its height is determined." The actual elevation above sea-level of the timber-line in the Cordilleras of North America ranges from six or seven to twelve thousand feet. It is lowest in the Coast and Cascade Ranges of Washington Territory, and rises as we go southward through Oregon and California. On the high Sierras of Eastern-Central California, forests grow to 10,000 or 12,000 feet, while the ranges of Southern California do not reach the upper limits of forests Few of the ranges of Nevada reach the timber-line, which varies from the height of 9,000 feet in the northern to probably 11,000 feet in the southern part of the State. In Arizona, probably none of the mountains reach the timber-line except the San Francisco group and the Sierra Blanca, where the line is at 11,000 and 12,000 feet. In New Mexico, the line averages about 12,000 feet above sea-level, and the higher annual temperature of the southern part of the Territory is fully compensated for by the greater altitude of the plateau in the northern part. In Colorado, the line rises from 11,000 feet in the northern to 12,000 feet in the southern part of the State; in Wyoming, from 10,000 to 11,000 feet in the Wind River and Teton Ranges, to about 11,000 feet in the Park Range; in Montana and Idaho, it ranges at from 9,000 to 10,000 feet, and in the Uintah and Wahsatch Ranges of Utah it is at about 11,000 feet. It is evident, if these considerations hold good, that the upper limit of timber must have approximately the same mean annual temperature everywhere. This temperature can not be measured directly for different places, but may be estimated by calculation by taking the mean temperature at some base in the neighborhood, and allowing a degree of fall for every three hundred feet of additional elevation. A calculation made on this basis for thirteen mountains, including Mounts Washington and Marcy, and several Western peaks, gives a mean of 30.4°, the extremes being 28° and 33°.
The Soil and Scarlatina.—Dr. Eklund, of Stockholm, Sweden, has for several years devoted much time to the pathology and etiology of scarlatina, and has reached conclusions of high practical importance in the light they throw upon the connection between bad drainage and other insanitary conditions and outbreaks of that disease without actual infection. He has constantly found a prodigious number of discoid bodies in the urine-of persons suffering from scarlatina, and most positively asserts that he has also noticed those identical organisms in vast numbers in the soil and ground-water of the Isle of Skeppsholm; in mud from the trenches, dug for the watermains; and among the greenish molds of the walls of the old barracks, where scarlatina was most rife. He furthermore alleges cases of scarlatina occurring in children after drinking milk mixed with the ground water of the island, and one case which followed an immersion in one of these trenches, and the drying of the child's clothes in a small room. In still another case scarlatina broke out in a block immediately on the exposure of the ground-water by excavations around. These observations, however, and those of other persons who have found micrococci in the animal fluids in scarlatina, even if the organisms are observed to be invariably present, can not be held to prove that they are the cause of the disease till the fact has been directly verified by inoculation into a healthy body carefully isolated from all other sources of infection.
Lip-Teaching for the Deaf and Dumb.—Earl Granville, as President of the Association for the Oral Instruction of the Deaf and Dumb, had occasion recently, at a meeting in behalf of the system, to remark upon the satisfactory progress that had been made in lip-teaching, by which the deaf were placed in a position to converse with their fellow-creatures without the aid of signs. The number of pupils in the association's school had increased, and favorable reports had been received from the class of the School Board of London. Except where idiocy or mental incapacity existed, this method of teaching was applicable to all cases. Its advantages had been acknowledged in a remarkable degree at a conference lately held, where a consensus of opinion was expressed in its favor. In evidence of the great benefits the system conferred upon persons trained under it, Earl Granville mentioned that several former pupils of the school were present who were now earning their living in positions which they would hardly have obtained had they been educated by the system of signs. An examination was afterward had of pupils of the training college and school, in which they showed that they understood, by watching a speaker's lips, what was said to them, and could make intelligible replies to it.
Chaldean Astronomy.—The invention of astronomy is ascribed to the Chaldeans by some ancient writers. It is said that a certain Zoroaster, King of Bactriana, was the first who observed the stars, about 1700 b. c.; although, according to Porphyry, Calisthenes found at Babylon and sent to Aristotle a series of observations going back to the earlier date of 1903 b. c. As yet, however, the Chaldean observations with which we are acquainted are reduced to the account of three eclipses of the moon that took place about 719 b. c. Hopes were entertained, when the discoveries of cuneiform tablets were made in the ruins of Babylonia and Nineveh, that trustworthy information of the real condition of astronomical science among the Chaldeans might be gathered from them; but it was some time before anything of this kind was realized. Messrs. Oppert and Sayce, it is true, found a few astronomical documents in the library of a king of Assyria, but they contained more astrology than astronomy, and were, moreover, too badly preserved to be of much use. Quite recently the Assyriologue, Father Strassmeyer, of the Society of Jesus, has found a few documents relative to astronomy in the Spartoli collection of the British Museum; and these have been carefully examined by Father Epping. They indicate that the Chaldeans had considerable knowledge of astronomy. Besides calculating the time of the new moon, and taking account of the thirds in their observations, they followed the courses of the planets, were acquainted with the retrograde movement of Mars, and referred the positions of the planets to those of the stars. If other results similar to these are at all extensively obtained from the immense amount of study yet to be made of the tablets, astronomers may hope to acquire materials of extreme value for the verification of their tables and the study of the system of the world.
Pedigree Selection in Food-Plants.—Major Hallett, in commending before the Brighton Health Congress his "pedigree system" for the improvement of food plants, takes notice of the immensely greater advantages in favor of systematic improvement afforded by plants over animals. A cow or ewe, he says, "produces at birth one (or two) only; a single grain of wheat has produced a plant the ears of which contained 8,000 grains, all capable of reproduction. Now, we can plant all of these, and of the resultant 8,000 plants reserve only the best one of all, to perpetuate the race, rejecting every other." The principle of Major Hallett's system consists in applying this rule, of reproducing only the best plants of each lot in successive years. "Can anything approaching such a choice as this," he says, "be afforded any breeder of cattle or sheep, no matter how extensive his herd or flock?" Cereals, improved by Hallett's system, have now been cultivated in more than forty different countries in Europe, Asia, Africa, America, and Australia, with complete success everywhere, so far as reports have been received. A parcel of pedigree wheat taken to Perth, Western Australia, in 1862, where the average crop was ten bushels to the acre, produced from twenty-nine to thirty-five bushels to the acre, with seventy-two as the largest number of heads on one stool, and one hundred and thirteen grains in the largest ear. In 1881 the same wheat, or its descendant, produced, in New Zealand, seventy-two bushels on one acre; with more than ninety ears, some of them containing as many as one hundred and thirty-two grains each, on single plants. The same return—seventy-two bushels to the acre—was reported cf three acres in Essex, England, in 1876, with one hundred and five ears, containing more than 8,000 grains, on one plant. Reports corresponding with this have been received from Brussieres, France; Linlithgow, Scotland; Russia, Hungary, Italy, Holland, Denmark, and Sweden. The Hallett wheat withstood the frosts of 1875 and 1876 in Belgium, when other varieties were killed. In India, Sir Seymour Fitzgerald, Governor of Bombay, in 1870, reported the crop from the pedigree wheat to be fifty per cent greater in quantity and fifty per cent more valuable in quality than that produced from the best other seed that could be bought in the market. The same success has been obtained with barley and oats cultivated after this system. A friend of Major Hallett's, in Italy, applied his system to the sugar-beet, with the result of obtaining, after seven years of improvement, three times as much sugar and wine from the same acreage of roots as he had been accustomed to get at first. Experimenting with the potato, Major Hallett has started each year, for fourteen years, with a single tuber, the best of the year, cultivating for freedom from disease and for productiveness. Dividing the first twelve years of the fourteen into periods of four years each, he obtained for the first period an average of sixteen tubers from each single best seed-tuber; for the second period, nineteen; and for the third period, twenty-seven, or nearly double the yield of the first period. This plan of selection is on trial, in India, for cotton, and the reports so far received show already a marked difference in its favor.
The Mound-Builders in Mexico.—Mr. F. F. Hilder, in a paper on "The Archæology of Missouri," summarizes the results of the efforts of Mr. S. B. Evans to follow the works of the mound-builders down the Mississippi Valley, and connect them with the ancient works in Mexico. Beginning in Minnesota, Mr. Evans has, by personal survey, found an unbroken chain of these works along the great river to the Gulf, with colonies on the principal tributaries traversing the States that border on that stream. "Mounds were found along the entire route, and on the shores of the Gulf. Crossing into Mexico, the chain, dropped in the sea at Galveston, was recovered near Vera Cruz. On the plain of Cholula is a mound that, if transferred to Cahokia, would fit the landscape, and appear in general keeping with the works. On the other hand, if the great mound of Cahokia were brought in presence of Popocatepetl, it would not be abashed, but would be a fit companion of the pyramid. The pyramids of the sun and moon at Teotlihuacan would be mounds in Virginia and Ohio; and the great mounds of Grave Creek and Selzertown might embellish the 'ancient city of the gods.' Excavations were made in Mexican mounds, as they were made in the United States, and substantially the results were the same."
Co-operation of Medical Officers and People in Sanitary Objects.—The Sanitary Aid Association of St. Leonard's and Hastings, England, during nine years of work among a population of thirty-five thousand, has secured a co-operation between the people and the sanitary officers, under which the spread of all infectious diseases has been effectually prevented. This it has done by tact in the exercise of its functions as a medium between the medical officers and the people. It seeks, first, to guard against popular jealousy of inquisitorial inspection. The teachers of the schools are expected to make weekly returns of all absentees, with the cause of absence if known; if the cause is not known, some fit person is deputed to make a friendly casual visit to the family, without any suggestion of suspicion of fever, and report the information received to whoever acts as sanitary manager. The case is then put into the hands of the health officer, and his endeavors are furthered by explaining to the mother that she shall receive, for the strict performance of the processes of disinfection taught her, assistance, to be allotted according to the circumstances of the family. The assistance may come in the form of a milk allowance, beef-tea, wine, or whatever may be ordered by the medical attendant, a nurse, or a person to do the washing, or, where no want exists, of little delicacies and comforts which may be given without offense. It should always be connected with Obedience, by the persons assisted, of the inspector's orders, and should be accompanied, through the period of illness, by the promise of suitable help at the end. The greatest difficulties the medical officers have to meet arise from the desire of the poor to conceal their cases, for fear of injuring their business; but, under the operation of this system, every family that enjoys the benefit of its application and finds out what help and relief it gives tells the neighbors, and so it is brought about that the medical officer becomes himself the poor man's accepted friend. The St. Leonard's and Hastings society has never incurred a failure during all the years of its working; yet so unobtrusive have been its operations that one who should go down to inquire at random about it, without having a list of its allies, would have difficulty in discovering its existence. By adhering to and avowing the principle that it has no more right to interfere with the persons it visits than they with its members, by using persuasion and sympathy instead of threats, it has reduced the number of unmanageable cases to one a year; and has always brought even these around by taking care in conversing with the persons to give full information respecting disinfection. Thereupon, they turn around and act upon the information they have gained, so as to show how well they can do without their visitors.
Number of Species of the Orang-Outang.—The number of species of the orangoutang has been placed variously at from one to four. The upholders of the one-species theory have doubted whether the characteristics that were regarded as indications of specific differences might not really have arisen from the examination of skulls of different ages. To contribute to a solution of this doubt, Mr. Frederick A. Lucas has examined the large collection of orangs of Professor Henry A. Ward, and compared the notes taken by Mr. William T. Hornaday, while collecting orangs, and has satisfied himself that the views of the advocates of one species are correct. He previously believed that there were two species. He adds to his notes on the subject the suggestion that "they point clearly to the fact that it is extremely dangerous to form a species from observations of one or two skulls," and that they render it very probable that many fossil species have been based on individual or sexual peculiarities.
The Law of Land Formation on our Globe.—Professor Richard Owen, of New Harmony, Indiana, has observed some coincidences in the arrangements of continental lines and in the location and direction of elevations and depressions of the surface of the earth, which have suggested to him a law. by which dry land shows itself above the ocean, which he believes to be of almost universal application to geographical and geological phenomena. The coincidences which he describes may be traced by any one on a globe or a large map. The law, as Professor Owen has stated it in a paper on the subject presented to the American Association last year, is, in general terms: "The land on our globe shows itself above the ocean-level in definite multiple proportions, by measurement; the unit is the angular difference between the axis of revolution and the axis of progression. For convenience, as that angle has been lessening for centuries, we might call it 24°. We then have:
Geographical and geological unit ${\displaystyle =}$ 24° ${\displaystyle =}$ 360°15 Greatest width and length of continents ${\displaystyle =}$ 3 x 24° ${\displaystyle =}$ 72° ${\displaystyle =}$ 360°5 Radius for continents ${\displaystyle =}$ 36° ${\displaystyle =}$ 360°10 Half radius " ${\displaystyle =}$ 18° ${\displaystyle =}$ 360°20
The measure for oceanic distances is the complement of 24° ${\displaystyle =}$ 66°. The ratio of land to water, as shown by Professor Dana, is as 100: 275. The ratio of 24°: 66°:: 100: 275. All measurements are to be estimated at the equator.
Regarding his law in detail, Professor Owen finds, first, that many longitudinal elevations and depressions on the earth's surface (the result apparently of cooling and contraction), especially near the greatest median—north and south—extension of each continent, coincide with some meridian. This shrinkage has caused a north and south continent to appear in each of the four quarters of the earth, going around on the equator. Minor north and south extensions can be traced at intervals, often of 412° or 9° apart all around the globe, alternating usually with trends which form with them angles of 2312°. In verification of this law, adjust the globe so that the poles shall be at the wooden horizon and the eastern extremity of Brazil at the brass meridian. Then we shall find the two Americas occupying one, Europe and Africa the second, Asia and Australia the third, and North and South Oceania the fourth, of the quarters into which the rules divide the globe. It will be found that great elevations are matched by depressions on the opposite side of the globe, as the Himalayas and Central Asiatic table-land with Hudson Bay, the American lakes, the Gulf of Mexico, and the deep southeastern Pacific at 180° from them. A second feature is that the outlines of continents form angles of about 2312° with meridians. If we examine the great continental outlines, we shall find in the circuit of the globe five eastern trends of great continents exactly 72°, or one fifth of 360°, apart. These trends mark belts of seismic force, or lines apparently where the crust has less thickness than under the median lines of continents. The rule of trends may be verified by lifting the north pole of the globe 2312° above the, wooden horizon and bringing the continental trends under the brass meridian. Professor Owen finds, third, that besides these two forces which exert their powers along lines parallel, respectively, to the axis of revolution and to that of progression, each continent has two foci nearly on its median line, concentric circles around which mark important additions to the land and orography of the continent, and pass, as they successively enlarge, through areas of consecutive geological periods from the older to the newer. One of the foci, and the dominant one in the northern continents, is near the Arctic Circle; the other is in the geographical center of the continent. The southern continents have only the latter. The foci for North America are in Boothia Felix, near longitude 96° west, and latitude 71° north, and near the height west of Lake Superior, longitude 94° west, and latitude 48° north. A radius of 24° from the northern focus reaches the southern limits of the archæan area near Lake Superior and its junction with the palæozoic; and one of 29° or 30° takes in the mesozoic of Kansas and the new red sandstone of Connecticut and Massachusetts, with a valley of erosion between. Drawing our circles from the west shore of Lake Superior, a radius of 11° or 12° gives us Silurian, lower and upper, from Niagara to near Springfield, Ohio, Lexington and Frankfort, Kentucky, and Nashville, Tennessee, dominating at least the eastern half of the circle, while the western part was still under water. A radius of 12° to 13° marks the Appalachian and other coal-fields; and of 15°, the mesozoic formation curving from the cretaceous of Utah and Colorado through the intermediate of Arkansas and Tennessee to that of New Jersey. A radius of from 18° to 24° takes in the marine tertiaries of the East and the West; one of 24° marks the main outlines of the continent; while one of 36° takes in the extreme points of the continent in all directions. The rule is applied with almost literal similarity to the other continents. Professor Owen furthermore maintains that the western Alps became a dynamic focus at about the beginning of the Cenozoic period, and that Monte Rosa is nearly the center of the dry land of the globe, whence a great circle of immense seismic activity may be traced nearly parallel with the Asiatic continental trend to the Himalayas and thence around to the Andes and the South American earthquake-region. Another great circle is nearly parallel to the North American trend, and includes the volcanoes of Central America and the geysers of Iceland, and incloses and probably aids to heat our Gulf Stream.
Value of Disinfectants.—Dr. George M. Sternberg, surgeon in the United States Army, has reported upon the results of experiments he has made with various disinfectants and vaccine virus, the conclusion drawn from which is that chlorine, nitrous acid (nitrogen dioxide), and sulphurous acid (sulphur dioxide), are reliable disinfectants in the proportion of one volume to one hundred volumes of air. Probably a considerably smaller proportion of these disinfectants would be efficient in destroying the potency of thin layers of virus in a moist state, or of virus exposed to the action of the disinfectant in an atmosphere saturated with moisture. Experiments with carbolic acid, on the other hand, "show that the popular idea, shared perhaps by some physicians, that an odor of carbolic acid in the sick-room or foul privy is evidence that the place is disinfected, is entirely fallacious, and, in fact, that the use of this agent as a volatile agent is impracticable, because of the expense of the pure acid and the enormous quantity required to produce the desired result."
A Selenium Photometer.—M. Léon Vidal has devised a photometric apparatus of selenium, for measuring the intensity of natural or artificial light by means of an action purely physical and mechanical, and in a manner analogous to that by which we measure the temperature and the amount of atmospheric pressure with the thermometer and the barometer. The difference in conductibility which results from the action of light on selenium produces deviations in the needle of the galvanometer which correspond in extent with the intensity of the luminous source. In this manner we may determine, at a glance, the intensity of light at any instant. The principle is applied to the construction of meteorological photometers, for which elements of selenium of equivalent conductibility are provided, to be substituted for each other as their molecular condition becomes modified; the plates may be restored to their normal condition by heating them, and used again. This instrument may be employed for the rapid and visible record of the instantaneous changes in luminous intensity, at all heights and depths, the observer reading the indications of the galvanometer at the place which may be most convenient for him.
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2020-07-05 16:40:53
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https://zbmath.org/?q=an:1235.15007
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# zbMATH — the first resource for mathematics
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A disjoint idempotent decomposition for linear combinations produced from two commutative tripotent matrices and its applications. (English) Zbl 1235.15007
A square matrix $A$ of order $n$ over a field $F$ is said to be tripotent if $A^3= A$. In this note, the author studies some linear algebra properties of the associative algebra generated by two commutative tripotent matrices $A$ and $B$. If Jordan canonical forms of $A$ and $B$ were used from the very beginning (note that $A$ and $B$ are diagonalizable), proofs would be much simplified. By the way the author claims that the linear combinations of two commutative tripotent elements and their products can produce $3^9= 19$, $683$ tripotent elements. This is not accurate. For example, if $A= B= I_n$, then there are only three such tripotent matrices.
##### MSC:
15A09 Matrix inversion, generalized inverses 15A24 Matrix equations and identities 15A27 Commutativity of matrices 15B57 Hermitian, skew-Hermitian, and related matrices
##### Keywords:
tripotent matrix; disjoint idempotent decomposition
Full Text:
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2016-05-05 16:16:09
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https://www.physicsforums.com/threads/epsilon-delta-proof-of-zero.580978/
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# Epsilon-Delta proof of zero?
1. Feb 24, 2012
### savtaylor2010
Epsilon-Delta proof of zero??
1. The problem statement, all variables and given/known data
Write an epsilon delta proof for the limx$\rightarrow$2 0 = 0.
3. The attempt at a solution
This is for my discrete math class. I know how to do limit proofs with a variable, like x or x2, but it seems that this is obvious that the limit approaching zero is zero. It is so easy, that it is hard for me to use epsilon and delta to prove. I don't know really where to start for this one. I would appreciate some hints and help!
2. Feb 24, 2012
### LCKurtz
Re: Epsilon-Delta proof of zero??
It might help to call f(x) = 0. Write down the definition as you would with f(x) and L and replace f(x) and L by 0.
3. Feb 24, 2012
### mtayab1994
Re: Epsilon-Delta proof of zero??
Start by choosing an epsilon maybe let epsilon equal something really close to 0 like 0.2
and assume that x-2< alpha . so that you can so that 0<ε .
4. Feb 24, 2012
### Deveno
Re: Epsilon-Delta proof of zero??
hint: the proof is eactly the same if you replace 0 by c, where c is any constant. that is, if you replace the function f(x) = 0 with g(x) = c, the same argument works for both (the "delta" is really easy to find, for any "epsilon").
5. Mar 1, 2012
### savtaylor2010
Re: Epsilon-Delta proof of zero??
Thank you guys for all of your help! I know I am really late responding back, but all of the feedback really helped!
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2017-11-20 13:51:50
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https://www.proofwiki.org/wiki/Definition:Real_Number_Plane_with_Euclidean_Metric
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# Definition:Euclidean Metric/Real Number Plane
## Definition
Let $\R^2$ be the real number plane.
The Euclidean metric on $\R^2$ is defined as:
$\ds \map {d_2} {x, y} := \sqrt {\paren {x_1 - y_1}^2 + \paren {x_2 - y_2}^2}$
where $x = \tuple {x_1, x_2}, y = \tuple {y_1, y_2} \in \R^2$.
## Also known as
The Euclidean metric is sometimes also referred to as the usual metric.
The real number plane with the Euclidean metric is also known as the Euclidean plane, but in the field of abstract geometry that term is used for a specific construct.
## Also see
• Results about the Euclidean metric can be found here.
## Source of Name
This entry was named for Euclid.
## Historical Note
Euclid himself did not in fact conceive of the Euclidean metric and its associated Euclidean space, Euclidean topology and Euclidean norm.
They bear that name because the geometric space which it gives rise to is Euclidean in the sense that it is consistent with Euclid's fifth postulate.
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2022-08-09 13:14:46
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https://cracku.in/81-if-5-of-the-dot-balls-had-been-hit-for-4s-and-if-t-x-xat-2012
|
### XAT 2012 Question 81
Instructions
The following pie chart shows the percentage distribution of runs scored by a batsman in a test innings.
Question 81
# If 5 of the dot balls had been hit for 4s, and if two of the shots for which the batsman scored 3 runs each had fetched him one run instead, what would have been the central angle of the sector corresponding to the percentage of runs scored in 4s? {Use data from the previous question}
Solution
Net increment in the number of runs due to 5 the dot balls resulting in 4s and two 3s resulting in two 1s = 4*5 - 2*2 = 16.
Therefore, the total number of runs scored by the batsman = 16 + 306 = 322 runs.
The number of runs scored by 4's = 132 + 20 = 152 {We know that batsman scored 132 runs from 4s alone}
The angle subtended by 4's = $$\dfrac{152}{322}\times 360$$ = 169.93 $$\approx$$ 170.
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2022-06-26 02:28:10
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https://physics.stackexchange.com/questions/193188/why-was-general-relativity-needed-to-explain-gravity
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# Why was general relativity needed to explain gravity?
I was thinking about this recently and I think this is a reasonable question to ask. SR can handle forces just like Newtonian physics can; the difference is that the four-force is defined a bit differently than the classical force.
So this made me wonder; what's the difference between that a body is experiencing a force, of let's say 5 newtons, due to electrostatic forces and that the same body is experiencing the same force due to gravity?
Can't we just treat the force due to gravity like any other four-force in SR when it comes to gravity? Why does the origin of the force matter? A force is still a force, so what exactly does SR fail at? Can't we just treat gravity as a four-force acting on a body, like any other force in SR?
• This is almost a duplicate, but when questions similar to this were marked as duplicates the "originals" to which they refer tend to be about the particle theory level description of gravity, which is somewhat orthogonal to what's being asked here. – DanielSank Jul 8 '15 at 23:22
• "Can't we just treat the force due to gravity like any other four-force in SR when it comes to gravity?" Briefly, (and I believe I've answered this similarly before here), if gravity were described by a four-force, gravitational waves would transport negative energy. Courtesy of Google Books and "Gravitation": [1]: i.stack.imgur.com/eyWKU.png – Alfred Centauri Jul 9 '15 at 0:29
• Well, general relativity doesn't treat gravity as a real force - it's an inertial/apparent force. That's a bit of a paradigm shift :) One of the key observations is that inertial mass is the same as gravitational mass - very suspicious. So GR redefined universe in a way where gravitation is an inertial force - and it works marvellously. Indeed, SR handles gravity-as-a-real-force just fine - GR throws this explanation out of the window, and in doing so, explains a few suspicious things, as well as some pretty annoying things - like "why would light bend in a gravitational field" :) – Luaan Jul 9 '15 at 10:16
• @AlfredCentauri If we described gravity as just an other four-force, then there would be no such thing as "gravitational waves" since GR would not even exist to begin with. – Madde Anerson Jul 9 '15 at 12:14
• @MaddeAnerson, you're assuming that, by gravitational waves, one means propagating disturbances in spacetime curvature. But that isn't the case. Since the context is SR, there is no instantaneous action at a distance and thus, gravitational 'influence' must propagate with finite speed regardless. – Alfred Centauri Jul 9 '15 at 13:34
While DanielSank's answer is correct, I don't think it is the complete story. Sure the equivalence principle naturally leads to a geometric description of gravity but it does not necessitate such a description in and of itself.
For example, Newtonian gravity can be described geometrically in a manner completely analogous to GR but at the same time this description is entirely equivalent to the usual Newtonian description of gravity-both respect the equivalence principle but the geometric description comes from a reinterpretation of inertial frames.
So there is more that needs to be said regarding your question. For example, coming back to SR, what if I posit a scalar field $\varphi$ for the gravitational field that obeys a Lorentz covariant linear field equation? It is easy to convince oneself that such a field equation would have to take the form $\square \varphi = -4\pi T$ where $T$ is the trace of the stress-energy tensor of the matter field coupled to gravity.
There are immediately two problems with this. The less problematic of the two is that this equation implies the gravitational field does not couple to itself since $\square$ is a flat space-time operator and $T$ knows nothing about gravity (remember, in SR the metric is non-dynamical). This can however be fixed by making the gravitational field equations non-linear. More importantly is the issue that $T =0$ for the electromagnetic field. This means light would not be deflected by gravity, which immediately contradicts experiment and throws a scalar theory of gravity out of the picture.
Let us now consider a 4-vector $A^{\mu}$ for the gravitational field. It is actually very easy to show that this route leads to a dead end because any relativistic classical field theory of a vector field will yield repulsive like charges (see reference below), and we know gravity is attractive.
We thus finally come to a dimensionless symmetric tensor field $h_{\mu\nu}$ on flat space-time (see reference below for why a symmetric tensor is sufficient). Here the story is much more subtle and rather detailed. If we assume the gravitational interaction is linear then a rather detailed and involved set of arguments (again see reference below) lead to the field equations $-\square \bar{h}^{\mu\nu}- \eta^{\mu\nu}\partial_{\alpha}\partial_{\beta}\bar{h}^{\alpha\beta} + 2\partial_{\alpha}\partial^{(\nu}\bar{h}^{\mu)\alpha} \propto T^{\mu\nu}$, where $\bar{h}_{\mu\nu}$ is the trace-reverse.
However the gauge freedom $h_{\mu\nu} \rightarrow h_{\mu\nu} - \partial_{\mu}\xi_{\nu} - \partial_{\nu}\xi_{\mu}$ of the equations of motion demands that $\partial_{\mu}T^{\mu\nu} = 0$. This can only hold approximately since one cannot have energy conservation in the matter fields when they interact dynamically with the gravitational field.
This can be fixed by instead considering a non-linear gravitational interaction obtained from the above equations of motion through reduction of order. However such an order reduction process requires additional input in order to get a unique, gauge-invariant result; one can in fact show that with the appropriate inputs this iteration can yield the Einstein equations but this requires us knowing GR beforehand which defeats the purpose.
Thus it is much easier and far more elegant to simply adopt Einstein's conceptual leap through the equivalence principle and consider a dynamical metric theory of gravity (metric due to its elegant coherence with the equivalence principle and dynamical due to background independence/diffeomorphism invariance).
Reference
"Gravitation: Foundations and Frontiers"-T.Padmanabhan, sections 2.8, 3.3.
• This is an interesting answer but OP really just asked why gravity can't be treated as a usual 4-force. I think the blatant contradictions between $F=ma$ and how gravity works given in my answer definitely answer that question. Again, I still think this answer is interesting and well written. – DanielSank Jul 9 '15 at 1:46
• This seems to be the only answer so far that addresses the original question of why SR is needed. I wonder if the scalar field theory you mentioned would be a reasonable “low field” approximation, and give more than Newtonian gravity (gravitational waves, precession of Mercury...). Or maybe this should be a separate question? – Edgar Bonet Jul 9 '15 at 7:35
• @DanielSank, fair point; I don't disagree with what you've said. – FenderLesPaul Jul 9 '15 at 17:40
• @Edgar Bonet, That might be good to ask separately. I would love to try and answer it if you do. – FenderLesPaul Jul 9 '15 at 17:41
As Einstein himself put it, "If a person falls freely he will not feel his own weight."
Consider yoruself sitting in your chair right now. You don't see to be accelerating, yet you feel a force on your butt. This is very strange because $F=ma$$^{[a]}$ would suggest that if you are under the influence of a force (the one on your butt) you should be accelerating. Something is strange.
Now suppose you jump of a cliff and are in free fall. Now you most certainly seem to be accelerating, yet you feel no forces at all. This, again, runs against what you'd expect based on $F=ma$.
The resolution of this is that what we normally think of as accelerating under the influence of gravity is not really acceleration. An object in free fall is moving along its most natural unperturbed trajectory. It's actually you, sitting on your chair, under the influence of gravity but not moving, that are being deflected from your natural trajectory. You are, in a real sense, being accelerated away from your geodesic path through space-time.
$[a]$: And the special relativistic extension.
• This argument proves too much. If you were sitting on a chair in space, and were being pulled down by electromagnetic forces rather than by gravity, you would "feel a force on your butt" despite the fact that you weren't accelerating. Similarly, if you took the chair away, you would start accelerating despite the fact that you don't feel any force. (I'm assuming here that the charge in your body is uniformly distributed.) Since that argument doesn't prove that the electromagnetic force is geometric in nature, it can't be used to prove that the gravitational force is either. – Harry Johnston Jul 9 '15 at 2:37
• (The observation that gravitation always behaves this way but electromagnetic forces only behave that way under specific circumstances suggests GR as an elegant solution - but does not prove that it is necessary. And at the time in question, I don't believe we had the experimental evidence necessary to rule out the possibility that the equivalence principle is only approximately true, or only true under certain circumstances.) – Harry Johnston Jul 9 '15 at 2:44
• @HarryJohnston isn't part of what makes gravity special that it does in fact act on all matter (and light) whereas things like electrical forces do not? Therefore doesn't my answer indeed address OP's question of why gravity cannot be treated like a usual force? I'm not claiming this answer is a complete motivation of geometrical space-time, just that it's sufficient to answer the original question. – DanielSank Jul 9 '15 at 17:41
• I don't read the question quite the same way. But my objection isn't that, it's that I think it misleading to suggest that there's something inherently mysterious about feeling a "force on your butt" when you're not accelerating - IMO, this description misses the point of the equivalence principle, and could cause a novice to become confused when dealing with classical mechanics. – Harry Johnston Jul 9 '15 at 21:59
• @HarryJohnston definitely see your point. – DanielSank Jul 10 '15 at 5:14
General relativity is not a replacement of special relativity because the latter fails with gravity, rather it is the extension of its kinematic and dynamical quantities to accelerated systems, which, in turn, correspond to writing down the same equations of motion but with a different (non-Euclidean) metric.
Why then accelerated systems are equivalent to gravitation fields is nothing that concerns general relativity but it is instead a consequence of the fact that inertial mass and gravitational mass are (so far) equivalent. This undergoes the name of, in fact, equivalence principle and there is a lot of literature explaining why it is so: see for example here or any other similar question asked in the database.
• You can describe accelerated systems perfectly well from within special relativity. You just have a global notion of an unaccelerated frame. Also, there are many theories that are not general relativity that admit the equivalence principle. Namely, any metric theory will. – Jerry Schirmer Jul 8 '15 at 23:46
• How do you describe accelerated systems in special relativity? – gented Jul 8 '15 at 23:54
• You do the coordinate transformations to the accelerated frames. There will be effects analogous to Coriolis forces, and it will be clear that you are not in an inertial frame, but you can still make predictions and know things like how much proper time has been elapsed in the accelerated frame. – Jerry Schirmer Jul 8 '15 at 23:56
• Yes, and that's exactly how you pass to general relativity once you realise that the same additional non-inertial forces can be described by having a non-Euclidean metric. This is exactly the step taking you from SR to GR, isn't it? – gented Jul 9 '15 at 0:00
• In principle, yes. You still need an equation of motion for the metric. – Jerry Schirmer Jul 9 '15 at 0:14
## protected by Qmechanic♦Jul 12 '15 at 13:10
Thank you for your interest in this question. Because it has attracted low-quality or spam answers that had to be removed, posting an answer now requires 10 reputation on this site (the association bonus does not count).
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2019-08-24 16:44:33
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http://www.tug.org/pipermail/texhax/2010-April/014572.html
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# [texhax] how to copy a file within eTeX?
Ulrike Fischer news3 at nililand.de
Tue Apr 6 09:52:05 CEST 2010
Am Mon, 05 Apr 2010 16:58:16 -0600 schrieb D. R. Evans:
> My problem:
>
> I need to process a single ToC file multiple times within the course of
> compiling a single TeX file. However, since I'm also regenerating the ToC,
> I can't simply put the usual \readtoc at the points where I want the ToC
> processing to occur.
Well actually the contents of .toc aren't written directly when
e.g. a \section command is encountered. This wouldn't work if the
\tableofcontents command isn't the first thing in a document like
here:
\documentclass{article}
\begin{document}
\section{A}
\tableofcontents
\section{B}
\end{document}
What really happens is that a \addtocontents command first writes a
\@writefile command in the aux-file, and at \end{document} the
aux-file is input and then all entries are written in one go to the
toc.
The reason that you can't normally use two \tableofcontents command
is that \jobename.toc is already opened for writing by the first
\tableofcontents command. The memoir class moves the opening of
\jobname.toc to the end of document and so allows two (or more)
\tableofcontents commands. You could copy this method:
\documentclass{article}
\makeatletter
\renewcommand{\@starttoc}[1]{%
\begingroup\makeatletter
\@input{\jobname.#1}%
\if at filesw
\AtEndDocument{%
\expandafter\newwrite\csname tf@#1\endcsname
\immediate\openout \csname tf@#1\endcsname \jobname.#1\relax
}%
\fi
\@nobreakfalse
\endgroup}
\makeatother
\begin{document}
\tableofcontents
\setcounter{tocdepth}{2}
\tableofcontents
\setcounter{tocdepth}{1}
\tableofcontents
\section{A}
\subsection{b}
\subsubsection{c}
\section{B}
\end{document}
--
Ulrike Fischer
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2018-02-23 10:23:36
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https://cms.math.ca/10.4153/CJM-2017-039-6
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location: Publications → journals → CJM
Abstract view
Author's Draft
# Order $3$ elements in $G_2$ and idempotents in symmetric composition algebras
Order three elements in the exceptional groups of type $G_2$ are classified up to conjugation over arbitrary fields. Their centralizers are computed, and the associated classification of idempotents in symmetric composition algebras is obtained. Idempotents have played a key role in the study and classification of these algebras. Over an algebraically closed field, there are two conjugacy classes of order three elements in $G_2$ in characteristic not $3$ and four of them in characteristic $3$. The centralizers in characteristic $3$ fail to be smooth for one of these classes.
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2017-12-11 02:19:16
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https://forums.obsidian.net/topic/99613-changing-multiclass-names/?tab=comments#comment-2025246
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# Changing Multiclass names
## Recommended Posts
I'm looking to switch some multiclass names around, wanna call my Wizard/FIghter a Warlock, and make barb/wiz the battlemage.
Any tips anyone on doing this and what program to use?
If anyone wants to do this for me also I wouldn't complain and would be grateful, incase it's an easy knock-out for someone.
##### Share on other sites
In the global.gamedatabundle there is an entry called:
"HybridClassTitles": [
{
"Class1": "Fighter",
"Class2": "Barbarian",
"Title": 2592
}...
If you switch those "Title" numbers for the classes you want, that might do it. I haven't tried this myself though, so it only a theory at this point
##### Share on other sites
MA MAAAAAN!
I only see globalprefabs personally, hopefully thats the one when this other guy releases his modding tools.
Edited by alexis13
##### Share on other sites
MA MAAAAAN!
I only see globalprefabs personally, hopefully thats the one when this other guy releases his modding tools.
I have the steam version of the game. On my computer the file is found at: C:\Program Files (x86)\Steam\steamapps\common\Pillars of Eternity II\PillarsOfEternityII_Data\exported\design\gamedata\global.gamedatabundle. Try this:
1. Open that file in notepad and copy all.
2. Paste it here: http://jsonviewer.stack.hu/
3. Press the format button in jsonviewer.
4. Copy all
5. Create a new blank text file called something.gamebundle. "Something" can be whatever you want. Make sure it's called something.gamebundle NOT something.gamebundle.txt. You might have to make you OS display file endings.
6. Paste the formatted output from jsonviewer into the textfile.
7. Find the entry I listed in my previous post and switch the two values.
8. Save the file.
9. Create the folder: Pillars of Eternity II\PillarsOfEternityII_Data\override
10. Drop your custom gamebundle file in there.
11. Profit!
Edited by OlleDenStore
##### Share on other sites
What if I want to change a multiclass name, not switch two of them?
Aloth massages his temples, shaking his head.
##### Share on other sites
In the global.gamedatabundle there is an entry called:
"HybridClassTitles": [
{
"Class1": "Fighter",
"Class2": "Barbarian",
"Title": 2592
}...
If you switch those "Title" numbers for the classes you want, that might do it. I haven't tried this myself though, so it only a theory at this point
If you want to change the class name, take the title number and go to the string file in "PillarsOfEternityII_Data\exported\localized\en\text\game" and find the gui.gamedatabundle. Open it and search the number to find the name. Change it to whatever you want and either save it or copy the file to the override folder using the method found in the sticky here. I've renamed a few classes myself this way.
##### Share on other sites
I don't get an option to "Open with" when I right-click a gamebundle file, is there something I need to do first?
EDIT: Nevermind, when I chose "Open" I was able to pick a program to open it with. Thanks for the instructions!
Edited by CENIC
Aloth massages his temples, shaking his head.
##### Share on other sites
MA MAAAAAN!
I only see globalprefabs personally, hopefully thats the one when this other guy releases his modding tools.
I have the steam version of the game. On my computer the file is found at: C:\Program Files (x86)\Steam\steamapps\common\Pillars of Eternity II\PillarsOfEternityII_Data\exported\design\gamedata\global.gamedatabundle. Try this:
1. Open that file in notepad and copy all.
2. Paste it here: http://jsonviewer.stack.hu/
3. Press the format button in jsonviewer.
4. Copy all
5. Create a new blank text file called something.gamebundle. "Something" can be whatever you want. Make sure it's called something.gamebundle NOT something.gamebundle.txt. You might have to make you OS display file endings.
6. Paste the formatted output from jsonviewer into the textfile.
7. Find the entry I listed in my previous post and switch the two values.
8. Save the file.
9. Create the folder: Pillars of Eternity II\PillarsOfEternityII_Data\override
10. Drop your custom gamebundle file in there.
11. Profit!
aaaaayyy it worked.
EDIT: Thanks, also tried to edit fire godlike racial "Battle-Forged" but can't seem to get it to be active all the time instead of 50%.
Edited by alexis13
##### Share on other sites
• 7 months later...
The way to change multiclass names is in C:\Program Files (x86)\Steam\steamapps\common\Pillars of Eternity II\PillarsOfEternityII_Data\localized\en\text\game\gui.stringtable
Not the global prefabs mentioned above, just cntrl+F in notepad the name you are looking to switch and type in what you want.
##### Share on other sites
• 2 weeks later...
Yep, it was moved to CharacterClassGameData a while back for better compatibility with multiple class mods.
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2021-10-27 11:11:45
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http://pldml.icm.edu.pl/pldml/element/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1602
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## Discussiones Mathematicae Graph Theory
2012 | 32 | 2 | 321-330
Tytuł artykułu
### The vertex detour hull number of a graph
Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For vertices x and y in a connected graph G, the detour distance D(x,y) is the length of a longest x - y path in G. An x - y path of length D(x,y) is an x - y detour. The closed detour interval I_D[x,y] consists of x,y, and all vertices lying on some x -y detour of G; while for S ⊆ V(G), $I_D[S] = ⋃_{x,y ∈ S} I_D[x,y]$. A set S of vertices is a detour convex set if $I_D[S] = S$. The detour convex hull $[S]_D$ is the smallest detour convex set containing S. The detour hull number dh(G) is the minimum cardinality among subsets S of V(G) with $[S]_D = V(G)$. Let x be any vertex in a connected graph G. For a vertex y in G, denoted by $I_D[y]^x$, the set of all vertices distinct from x that lie on some x - y detour of G; while for S ⊆ V(G), $I_D[S]^x = ⋃_{y ∈ S} I_D[y]^x$. For x ∉ S, S is an x-detour convex set if $I_D[S]^x = S$. The x-detour convex hull of S, $[S]^x_D$ is the smallest x-detour convex set containing S. A set S is an x-detour hull set if $[S]^x_D = V(G) -{x}$ and the minimum cardinality of x-detour hull sets is the x-detour hull number dhₓ(G) of G. For x ∉ S, S is an x-detour set of G if $I_D[S]^x = V(G) - {x}$ and the minimum cardinality of x-detour sets is the x-detour number dₓ(G) of G. Certain general properties of the x-detour hull number of a graph are studied. It is shown that for each pair of positive integers a,b with 2 ≤ a ≤ b+1, there exist a connected graph G and a vertex x such that dh(G) = a and dhₓ(G) = b. It is proved that every two integers a and b with 1 ≤ a ≤ b, are realizable as the x-detour hull number and the x-detour number respectively. Also, it is shown that for integers a,b and n with 1 ≤ a ≤ n -b and b ≥ 3, there exist a connected graph G of order n and a vertex x such that dhₓ(G) = a and the detour eccentricity of x, $e_D(x) = b$. We determine bounds for dhₓ(G) and characterize graphs G which realize these bounds.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
321-330
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-08-31
poprawiono
2011-05-26
zaakceptowano
2011-06-06
Twórcy
autor
• Department of Mathematics, St. Xavier's College (Autonomous), Palayamkottai - 627 002, India
autor
• Department of Mathematics, Amrita Vishwa Vidyapeetham University, Amritapuri Campus, Clappana, Kollam - 690 525, India
Bibliografia
• [1] F. Buckley and F. Harary, Distance in Graphs (Addison-Wesley, Reading MA, 1990).
• [2] G. Chartrand, H. Escuadro and P. Zhang, Detour distance in graphs, J. Combin. Math. Combin. Comput. 53 (2005) 75-94.
• [3] G. Chartrand, G.L. Johns and P. Zhang, Detour number of a graph, Util. Math. 64 (2003) 97-113.
• [4] G. Chartrand, G.L. Johns and P. Zhang, On the detour number and geodetic number of a graph, Ars Combin. 72 (2004) 3-15.
• [5] G. Chartrand, L. Nebesky and P. Zhang, A survey of Hamilton colorings of graphs, preprint.
• [6] G. Chartrand and P. Zhang, Introduction to Graph Theory (Tata McGraw- Hill Edition, New Delhi, 2006).
• [7] W. Hale, Frequency Assignment, in: Theory and Applications, Proc. IEEE 68 (1980) 1497-1514, doi: 10.1109/PROC.1980.11899.
• [8] A.P. Santhakumaran and S. Athisayanathan, Connected detour number of a graph, J. Combin. Math. Combin. Comput. 69 (2009) 205-218.
• [9] A.P. Santhakumaran and P. Titus, The vertex detour number of a graph, AKCE J. Graphs. Combin. 4 (2007) 99-112.
• [10] A.P. Santhakumaran and S.V. Ullas Chandran, The detour hull number of a graph, communicated.
Typ dokumentu
Bibliografia
Identyfikatory
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2021-06-22 10:36:10
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https://mathspace.co/textbooks/syllabuses/Syllabus-453/topics/Topic-8419/subtopics/Subtopic-111605/?activeTab=theory
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# Solve quadratics by algebraic manipulation
Lesson
Solving basic or simple quadratics involves using algebraic manipulation. Let's look at a few examples of this process.
#### Examples
##### Question 1
Solve the quadratic equation $x^2-9=0$x29=0.
Think: We want to end up with an expression like $x=\dots$x=, and to get there we will need to isolate $x$x
Do: Considering the order of operations, we will first move the constant term to the other side, then undo the square:
$x^2-9$x2−9 $=$= $0$0 $x^2$x2 $=$= $9$9 $x$x $=$= $\pm3$±3
Since there are two numbers that, when squared, give $9$9, the solutions to this equation are $x=3$x=3 or $x=-3$x=3.
##### Question 2
Find solutions to $\left(2x+7\right)^2=64$(2x+7)2=64.
Think: Identify the order of operations necessary to isolate the $x$x variable. In this case we will deal with the square root first, then the addition and finally the multiplication by $2$2.
Do:
$\left(2x+7\right)^2$(2x+7)2 $=$= $64$64 $2x+7$2x+7 $=$= $\pm\sqrt{64}$±√64
We use inverse operations to remove the square from the $LHS$LHS, the opposite of a square is a square root. Next we have
$2x+7$2x+7 $=$= $\pm8$±8 (from here on, this is just like solving linear equations)
Where we have evaluate the square root. There are two solutions now, let's continue to solve both for $x$x:
$2x$2x $=$= $8-7$8−7 or $2x$2x $=$= $-8-7$−8−7 $2x$2x $=$= $1$1 or $2x$2x $=$= $-15$−15 $x$x $=$= $\frac{1}{2}$12 or $x$x $=$= $\frac{-15}{2}$−152
##### Question 3
Find the solutions to $x^2-17=0$x217=0.
Think: Identify the order of operations necessary to isolate the $x$x variable. In this case we will deal with the subtraction first, then the square.
Do:
$x^2-17$x2−17 $=$= $0$0 $x^2$x2 $=$= $17$17
Here we use inverse operations to remove the $-17$17 from the $LHS$LHS, the opposite of a $-17$17 is a $+$+ $17$17. Then we have
$x$x $=$= $\sqrt{17}$√17 OR $x$x $=$= $-\sqrt{17}$−√17
Where we use inverse operations to remove the square from the $LHS$LHS, the opposite of a square is a square root.
Remember that all square roots can have a positive or negative answer. This is normally written $\pm$±.
For example, what is $4^2$42 and what is $\left(-4\right)^2$(4)2? They are both equal to $16$16! Hence $\sqrt{16}=\pm4$16=±4.
A special note about exact solutions
For nearly all of our work with solutions to functions and equations it is standard practice to leave our final expression in exact form. In this case, $\sqrt{17}$17 is as far as we will go, we cannot simplify the root any further.
In questions involving applications of quadratics we may be asked to evaluate the square root at the very end and then approximate to a specific number of decimal places. For example, perhaps we want the time taken to travel a certain distance, or an estimate of the area of a block of land.
##### Question 5
Solve for $p$p:
$5\left(p^2-3\right)=705$5(p23)=705
##### Question 6
Solve $\left(x-4\right)^2=10$(x4)2=10 for $x$x.
1. Write all solutions on the same line, separated by commas.
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2022-01-17 07:09:14
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https://www.physicsforums.com/threads/interaction-representation.183656/
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# Interaction representation
1. Sep 9, 2007
### DonnerJack
Hi,
Can someone explain to me why do we actually need the Interaction/Intermediate representation?
In my past, each course in QM touched it only for a few minutes and then it got... forgotten.
Can someone please give me an example as to how (and when) it is used (and a good reason why)?
Thanks!
2. Sep 10, 2007
### quetzalcoatl9
the interaction picture is useful because it's decomposition of the hamiltonian allows for time-dependent perturbation methods
3. Sep 10, 2007
### f95toli
We don't really "need" the interaction picture, but it is very convenient sometimes.
The interaction picture is a representation which is somewhere in-between the Schrödinger and the Heisenberg picture. Note, however, that you can easily move between all of these representations using unitary transformations.
I think the word "picture" is somewhat missleading. Today there is no "philosophical" reason why you choose one over the other, you use whichever one s the most convenient for the problem you are trying to do. Moving between pictures is therefore somewhat akin to e.g. moving between coordinate-systems in classical mechanics.
A good example would be a driven Jaynes-Cummings Hamiltonian on resonance (being driven at some frequency $$\omega_l=\omega_0=\omega_r, where \omega_0, \omega_r$$ are the splitting of the 2-level system and the resonance frequency of the resonator, respectively).
Moving to the interaction picture here essentially means that you are solving your problem in a 'rotating coordinate system' which simplifies the problem A LOT since all but two terms become zero and the time dependence dissapears.
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2016-10-22 07:33:50
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https://math.stackexchange.com/questions/3690791/non-elementary-integral/3690797
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# Non elementary integral
Okay, so one of the places I looked up, there was a result that integration of cosx/x is from 0 to ∞ is 0.5π. I'm not sure if the result is correct or not. How can I solve the integral? It was given as a result to be used in some other problem. Now how does one calculate it? I know it's non elementary, but I have seen that some non elementary integrals can be evaluated provided the limits are specified. Like erf(x). So can someone provide the derivation or a reference link maybe?
You can use the following formula:
$$\int_0^\infty \frac{f(x)}{x}dx=\int_0^\infty \mathcal{L}\{f(x)\}(s)ds$$
where $$\mathcal{L}\{f(x)\}(s)$$ is the laplace transform of your function $$f$$. The laplace transform is defined as: $$\mathcal{L}\{f(x)\}(s)=\int_0^\infty f(x)e^{-sx} dx$$
so the final result will be a function of $$s$$.
$$\int_0^\infty \frac{\cos(x)}{x}dx=\int_0^\infty \mathcal{L}\{\cos(x)\}(s)ds$$
and the laplace transform of $$\cos(x)$$ is $$\frac{s}{s^2+1}$$
So
$$\int_0^\infty \frac{\cos(x)}{x}dx=\int_0^\infty \frac{s}{s^2+1} ds$$
and the second integral it's easy to evaluate and you can see that it diverges. So $$\int_0^\infty \frac{\cos(x)}{x}dx$$ diverges as well.
I think you mixed up this integrals: $$\int_0^\infty \frac{\cos(x)}{x}dx$$, that diverges, and $$\int_0^\infty \frac{\sin(x)}{x}dx$$ that actually converges do $$\pi/2$$. To evaluate $$\int_0^\infty \frac{\sin(x)}{x}dx$$ you can use the same process. The laplace transform of $$\sin(x)$$ is $$\frac{1}{s^2+1}$$, so:
$$\int_0^\infty \frac{\sin(x)}{x}dx=\int_0^\infty \frac{1}{s^2+1}ds$$
The primitive of $$\frac{1}{s^2+1}$$ is $$\arctan(s)$$ so you have that:
$$\int_0^\infty \frac{1}{s^2+1}ds=\lim_{s\rightarrow \infty} \arctan(s) - \arctan(0)$$
$$\arctan(0)=0$$ and $$\lim_{s\rightarrow \infty} \arctan(s)=\pi/2$$, so we end up with:
$$\int_0^\infty \frac{\sin(x)}{x}dx = \frac{\pi}{2}$$
• That was nice to know. – Tesla's Coil May 25 at 14:49
$$\displaystyle \int \frac {\cos a x \ \mathrm d x} x = \ln |x| + \sum_{k \ge 1} \frac {(-1)^k (a x)^{2 k} } {(2 k) (2 k)!} + C = \ln |x| - \frac {(a x)^2} {2 \times 2!} + \frac {(a x)^4} {4 \times 4!} - \frac {(a x)^6} {6 \times 6!} - \cdots + C$$
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2020-08-07 23:33:33
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https://latticeplusmotif.wordpress.com/conceptroll/
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Concept Roll
Announcements
Hello There!
Hello Internet!
In this data driven world, there is no shortage of databases in the internet that try to give a holistic picture of everything (take Wikipedia, for instance). But, if you have read my home page, you’ll know that this blog is by no means an attempt to replace any such collection. The aim here is only to solidify the concepts in both my head and hopefully, by doing so, I’ve helped you do it too.
There are multiple ways to get to posts :
1. Concept Roll : Where all posts are lined latest to oldest.
2. Concept Trees : Where posts are clustered based on the principles involved.
3. Search : This is just a good old “Search” where you can quickly find out if what you’re looking for is here.
4. Categories : This is also a way of clustering, but the only difference is that you don’t immediately see what else is inside.
5. Tags : Sometimes, some basic principles may be involved in concepts from many different catergories. Tags solve this problem.
Do write back/comment if you agree with something or if you feel something should change. I’m listening to what you’ve got to say!
Have a good time here, and may the force be with you.
Sincerely,
Mythreyi
Dislocations – Why even care?
To start off on an exploration of dislocations, it’s important that we first understand why is it that we need to know about dislocations.
It all started with a rather simple question : What is the minimum shear force that’s required to start plastic deformation1 of a single crystal2?
Ideal Shear Strength
When a material is subjected to a shearing force, it can deform like in Figure 1. It’s important to quantify the ability of the material to withstand shearing force and this quantity is the shear strength of the material. The shear strength is defined as the The applied shear stress needed to plastically deform a single crystal. There were attempts made by scientists to estimate the shear strength of materials theoretically. This value (obtained theoretically) is the ideal shear strength.
Obtaining this theoretical value is simple enough. Suppose there is an atom isolated in space. When another atom is brought into its vicinity, the new atom is initially attracted by the first atom (gravitation), however, when the new atom comes very close the first atom, it gets repelled (electrostatic interactions between both the atoms) and there is a spot in between where the atoms are ’at equilibrium’ (the same thing also known as a ’chemical bond’). If there are a lot of atoms lined up as a bunch of rows (assume, for now, infinitely), they arrange themselves such that they are all at equilibrium. If one of these lines of atoms are perturbed, they are initially repelled, but soon, they sit in the next available equilibrium spot (previously occupied by their neighbour). If we look at the energy of the atoms, it’ll first increase and then decrease. This can be approximated to a sinusoidal function like in Figure 2.
We can now model the ideal shear strength using this input. The notation for the problem is defined in Figure 3. The assumption made is that: All the bonds break simultaneously. This can be visualised like in Figure 3. Thus, the energy (and therefore stress) of an atom can be represented by $S = S' sin(\frac{2 \pi x} {a})$. For small values of $sin(\theta)$, $sin(\theta) \approx \theta$. Therefore, $S = S' ( \frac{2 \pi x} {a})$. We know from Hooke’s Law that for small strains, the stress is directly proportional to the strain and the constant of proportionality is the Shear Modulus ($G$) (if the stress and strain are shear stress and shear strain respectively). The strain is $\frac{x}{d}$. Thus, stress is given as $S = G(\frac{x}{d})$. Equating both stresses, we get $S' = \frac{G}{2 \pi}$, if $a \approx d$. This is, by definition, the ideal shear strength because the material “deforms” beyond the maximum of the stress sinusoidal curve.
Though the derivation doesn’t have flaws, the resultant shear strength differs by orders of magnitude compared to the observed experimental shear stress. This difference says that the assumption that all bonds break at once is incorrect. Thus the search was on to find a better explanation for plastic deformation.
A Novel Plan – Introducing Missing Half-planes
In 1934, three scientists – Orowan, Polanyi and Taylor, independently came up with a new solution. They envisioned missing half-planes of atoms. Imagine that in the line up of rows of atoms, there is a missing half plane of atoms or an additional half plane of atoms. This is depicted in Figure 5. The assumption that all the bonds must break simultaneously is not necessary once half planes are introduced.
In fact, these half-planes can ‘move’ and the end result is the same deformation of the material, as can be seen in Figure 6. The reason for the ideal shear strength to be much larger than experimental values was the assumption that all the bonds break at once, and breaking bonds is not easily achieved. By introducing half planes, with only one bond breaking while another being formed immediately, the values of shear strengths calculated began to match the experimental values. These half-planes were therefore a very successful explanation for the problem.
Connection with Dislocations
The missing (or extra) half-planes have an edge (a line of atoms that don’t have neighbouring atoms below (or above) them). This edge came to be known as the Edge Dislocation3. Soon, all the mathematics of dislocations was established. The mathematics was so convincing that despite the fact that no one had ever ‘seen’ a dislocation before (microscopy techniques needed more development), the scientist community was next to certain on the existence of dislocations. When dislocations were finally ‘seen’ in the 1950’s, it only provided the final formality of a confirmation. From then on, there have been more additions to the theory and now, to learn about dislocations in detail, you might have to read thick books running for more than 1000 pages!
So, we care.
And hence, there’ll be more on dislocations to follow.
1Plastic deformation is the permanent deformation beyond the elastic limit of a material.
2More on single crystals later.
3There’s another kind of dislocations called Screw Dislocations. Dislocations which exhibit traits of both are called Mixed Dislocations. More on these types and the definition of dislocations later.
Announcements
[Temp] Action Plan for June 2017
Hello World!
Before you run away thinking this is yet another blog that gets a domain, a page to declare the plan (see : May 2017 Plan), but never kicks off, let me tell you why it’s been dormant for a while, again, and what I plan to do to start the volcanic activity.
I started this blog to make sure that what learn, I learn right. I must say this thought has in a way transformed me and I want to sustain it. I understand this needs to start somewhere, hence, inspite of the initial plan not kicking off, I decided I might as well start off from where I left.
Briefly, my action plan stays as follows :
1. Get the first post up and measure how long it takes to produce a good post.
2. Get three more posts up and keep measuring to get an average time estimate.
3. Based on estimate and free hours per day, make a detailed list of post topics to cover.
4. Work to achieve at least 85% of the target by the month end.
Which topics? I’ll try to stick to what I’ve mentioned in the Seeds page.
So that’s that, hope things start shaping up. May the force be with you.
Sincerely,
Mythreyi
Announcements
[Temp] Action Plan for May 2017
Hello World!
Before you run away thinking this is yet another blog that gets a domain but never kicks off, let me tell you why it’s been dormant for a while, and what I plan to do to start the volcanic activity.
I started this blog to make sure that what learn, I learn right. Just the thought of writing about it led me to think deeper about whatever I was learning (I even got a perfect score in one of the exams as soon as I implemented this idea). But however, like many other things, only when someone actually takes the plunge, they’ll know whether they’ve really learnt swimming, it’s difficult to gauge watching from the shoreline. I understand this, hence, now that my official commitments are not going to be contiguous, I decided I might as well start off from where I left.
Briefly, my action plan is as follows :
1. Get the first post up and measure how long it takes to produce a good post.
2. Get three more posts up and keep measuring to get an average time estimate.
3. Based on estimate and free hours per day, make a detailed list of post topics to cover.
4. Work to achieve at least 85% of the target by the month end.
Which topics? I’ll try to stick to what I’ve mentioned in the Seeds page.
So that’s that, hope things start shaping up. May the force be with you.
Sincerely,
Mythreyi
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2017-12-17 11:38:51
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https://www.cheenta.com/lhospitals-rule-tifr-gs-2017-part-a-problem-5/
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Select Page
# Understand the problem
True or False? Suppose $$f(x)$$ is a continuosy differentiable function on $$\Bbb R$$ such that $$\lim_{x \to \infty} f(x)= 1$$ and $$\lim_{x \to \infty} f'(x)=b$$. Then $$b=1$$.
##### Source of the problem
TIFR GS 2017 Entrance Examination Paper
##### Topic
L’Hospital’s principle
easy
##### Suggested Book
Mathematical Analysis, Second Edition 520pp/PB 2nd Edition (English, Paperback, T. M. Apostol)
Do you really need a hint? Try it first!
Can you calculate the value of $$\lim_{x \to \infty} f'(x)$$ using the value of $$\lim_{x \to \infty} f(x)$$.
See you can write $$f(x)$$ as $$\frac{e^x f(x)}{e^x}$$. Then taking limit on both sides as $$x \to \infty$$, we get
$$lim_{x \to \infty} f(x) = lim_{x \to \infty} \frac{e^x f(x)}{e^x} = lim_{x \to \infty} \frac{e^x f(x)+ e^x f'(x)}{e^x}$$, using L’Hospital’s rule.
Put the values of $$lim_{x \to \infty}f(x)=1$$ in the above equation. What do you get?
You will get that $$\lim_{x \to \infty}f'(x)=0$$. Hence the value of $$b=0$$. Therefore, the statement is false.
# Connected Program at Cheenta
#### College Mathematics Program
The higher mathematics program caters to advanced college and university students. It is useful for I.S.I. M.Math Entrance, GRE Math Subject Test, TIFR Ph.D. Entrance, I.I.T. JAM. The program is problem driven. We work with candidates who have a deep love for mathematics. This program is also useful for adults continuing who wish to rediscover the world of mathematics.
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2019-07-19 03:53:18
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https://www.zbmath.org/?q=an%3A0915.65042
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# zbMATH — the first resource for mathematics
A general view of minimally extended systems for simple bifurcation points. (English) Zbl 0915.65042
The development of the minimally extended systems method [cf. A. Griewank and G. W. Reddien, SIAM J. Numer. Anal. 21, 176-185 (1984; Zbl 0536.65031); V. Janovskij, Computing 43, No. 1, 27-36 (1989; Zbl 0695.65033)] for calculation of simple bifurcation points is suggested. In this method the simple bifurcation point $$(x^{*},\lambda^{*})$$ of the equation $$F(x,\lambda)=0,\quad (x\in \mathbb{R}^{n};\lambda\in \mathbb{R}$$ is bifurcation parameter) becomes as regular point $$z^{*}=(x^{*},\lambda^{*},0)$$ of the extended system $G(x,\lambda,\mu):=[ {F(x,\lambda)+\mu d \atop f(x,\lambda)}]=0$ $$(d\in \mathbb{R}^{n}, f:\mathbb{R}^{n}\times \mathbb{R}\rightarrow \mathbb{R}^{2},$$ the Jacobian $$\partial G(x^{*},\lambda^{*},0)\in \mathbb{R}^{(n+2)\times(n+2)}$$ is nonsingular) and for its calculation superlinearly convergent Newton type methods can be applied.
##### MSC:
65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
Full Text:
##### References:
[1] ; : Numerical continuation methods: An introduction. Springer, Berlin 1990. · Zbl 0717.65030 · doi:10.1007/978-3-642-61257-2 [2] ; : Stable computation of simple bifurcation points and emanating branches. Lecture, held at the Conference ”Computational methods for nonlinear phenomena”, January 1993, Oberwolfach, Germany 1993. [3] ; : Matrix computations. 2nd ed. Johns Hopkins University Press, Baltimore-London 1989. [4] ; (eds.): Automatic differentiation of algorithms: Theory, implementation, and application. SIAM, Philadelphia 1991. [5] Griewank, SIAM J. Numer. Anal. 21 pp 176– (1984) [6] Griewank, J. Computat. Appl. Math. 26 pp 133– (1989) [7] Janovský, Computing 43 pp 27– (1989) · Zbl 0695.65033 [8] Moore, SIAM J. Numer. Anal. 17 pp 567– (1980) [9] Pönisch, Computing 35 pp 277– (1985) [10] Pönisch, Computing 26 pp 107– (1981) [11] : Personal communication to A. Griewank 1995. [12] : Numerical analysis of parametrized nonlinear equations. J. Wiley, New York 1986. · Zbl 0582.65042 [13] Seydel, Numer. Math. 33 pp 339– (1979) [14] Weber, Numer. Funct. Anal. Optim. 3 pp 341– (1981)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.
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2021-04-13 20:24:13
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https://www.physicsforums.com/threads/charge-density.254464/
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# Charge density
1. Sep 7, 2008
### kjintonic
A semicircular loop of radius a carries positive charge Q distributed uniformly over its length.?
Find the electric field at the center of the loop (point P in the figure). Hint: Divide the loop into charge elements dq as shown in the figure, and write dq in terms of the angle d\theta. Then integrate over \theta to get the net field at P.
http://i533.photobucket.com/albums/ee336/shaneji_kotoba/RW-20-72.jpg
I dunno how to start this question....
2. Sep 7, 2008
### Hootenanny
Staff Emeritus
You must have some idea how to start, have you tried using the hint?
3. Sep 7, 2008
### kjintonic
Probably I can use E= (S)dE= (S)kdq/r^2 inwhich r=a
(S) is integral sign
4. Sep 7, 2008
### Hootenanny
Staff Emeritus
You're on the right lines, how about writing dq in terms of $d\theta$?
HINT: Notice that the horizontal components will cancel so you need only consider the vertical components of the electric field.
5. Sep 7, 2008
### kjintonic
hmmm... Sorry I kinda don't understant how to write dq in terms of d[itex]d\theta[itex] :(
6. Sep 7, 2008
bump?
7. Sep 7, 2008
### Defennder
First step you should note that by symmetry, one of field components in an axial direction is 0. Now you only have to find the other component. Set this problem up in the coordinate plane with point P at the origin. Draw a triangle for E in terms of E_x and E_y and theta. What can you say about how E_x is related to x? Write down the expression for dE, the differential electric field magnitude due to dq, then try to write dq in terms of $$\lambda dr$$, where lambda is Q/length.
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2017-12-11 23:52:25
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https://codegolf.stackexchange.com/questions/33033/has-my-milk-expired
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# Has my milk expired?
Aww, man, this expiry date doesn't write the months with letters! I can't tell if it's expiring on March 10th or October 3rd... Wait, no, never mind, the year says 2012. (alley-oops half-used brick of cheese into the trash can like a pro)
So let's suppose for a moment that you're too busy to try to reason out when this jar of marinara is supposed to expire. You just want the Cliff Notes version: how likely is it that it's past due? Let's write some code!
You know that the manufacturers print the date as an ordered triple of integers, in one of three formats:
YEAR MONTH DAY
MONTH DAY YEAR
DAY MONTH YEAR
And you know that some dates can only be interpreted in one or two ways, not all three: the 55 in 55-11-5 has to be a year, meaning this particular box of Twinkies expired November 5th, 1955. The year is sometimes given in four digits and not two, which can rule out some options. When it's two digits, though, 50..99 means 1950..1999 and 0..49 means 2000..2049.
Your job is to write a program or function that takes an array of integers which is a valid date in at least one of the interpretations above, and outputs a percent chance it is still good. The percent chance is simply the percentage of valid interpretations of the date that are on or later than today's date.
The array of integers will be your language's [Int] type of length three if it is an argument to a function, and given as either dash-, slash-, or space-separated (you get to pick) integers if used as input on STDIN to a full program.*
"Today's date" can be today's actual date, as obtained through a date function, or the date given in an extra argument to function or extra paramater in STDIN. It may be in Unix epoch seconds, another year-month-day triple entered in one of the three ways above, or another more convenient fashion.
Let's have some examples! The expiry date input will be in the dash-separated style, and assume for the examples below that today's date is July 5th, 2006.
• 14-12-14 - Both valid interpretations for this (DMY and YMD) are equivalent, December 14, 2014. The output is 100 because this product is definitely still good.
• 8-2-2006 - The last number is a year, for sure, since it has four digits. This could be either February 8th (expired) or August 2nd (still good). The output is 50.
• 6-7-5 - This could be anything! The "July 5th, 2006" interpretation is still good (for one day only), but the remaining two are both in 2005 and should be tossed as quickly as possible. The output is 33.
• 6-5-7 - Here, two out of three interpretations are safe. You can round your decimal up or down, so 66 or 67 are both okay.
• 12-31-99 - Okay, this one is unambiguously from the turn of the century (years from 50 to 99 are 19XX, and 31 can't possibly be a month). A big fat 0, and you really should clean out your fridge more often.
You can safely assume that any input which does not meet the standards above is not privy to the output rules above.
No web requests or standard loopholes. Date handling libraries are allowed. This is code golf: may the shortest program win.
* If you are using brainfuck or some similarly datatype-handicapped language, you can assume the ASCII values of the first three characters in input are the integers for the date. This excludes the four-digit year logic, sure, but I think we would be too astounded by seeing a solution to this in Brainfuck to slight you for it.
• Umm... the current year is 2014, not 2006. Your milk is eight years past its expiry at best. Jul 6, 2014 at 1:32
• @JanDvorak I just didn't want to try very hard to construct meaningful examples, so I tweaked today's date to make it easier. Jul 6, 2014 at 2:08
• @Dgrin91 don't care, I'll still eat them :D Jul 6, 2014 at 15:35
• In Australia, the milk expires about a week before the use by date Jul 7, 2014 at 5:24
• You should add a test with a 00 in it, since that can't be a legal day or month. Jul 8, 2014 at 5:59
## Ruby, 115 characters
f=->a,t{[a,a.rotate(~s=r=0),a.reverse].map{|x,*y|(t>Time.gm(x<100?x+2e3-100*x/=50:x,*y)||r+=100
s+=1)rescue p}
r/s}
This defines a function f that takes two arguments: an array containing the input, and "today's" date.
Examples:
f[[14,12,14], Time.new]
100
f[[8,2,2006], Time.new]
0
f[[8,2,2006], Time.new(2006, 7, 5)]
50
f[[6,7,5], Time.new(2006, 7, 5)]
33
# Python 2.7 - 172
I use the datetime module for validity and comparison of dates. If date can't make a valid datetime out of the input, it raises ValueError. This way s is the sum of the non-expired dates and t is the total number of valid dates. I'm taking advantage of the fact that True == 1 for the purposes of addition and indexing in Python. I also save a character by using 25*(76,80) instead of (1900,2000).
Note the lines in the second level of indentation use a tab character, not 2 spaces.
def f(e,c,s=0,t=3):
for Y,M,D in(0,1,2),(2,0,1),(2,1,0):
y=e[Y]
try:s+=date(y+25*[[76,80][y<50],0][y>99],e[M],e[D])>=c
except:t-=1
return 100*s/t
Add this to the end to test:
examples = [[14,12,14],[8,2,2006],[6,7,5],[6,5,7],[12,31,99]]
for e in examples:
print f(e, date(2006,7,5))
## PowerShell, 183173 168
[int](100*(($d=@(($a,$b,$c=$args[0]),($c,$a,$b),($c,$b,$a)|%{$_[0]+=1900*($_[0]-le99)+100*($_[0]-le49)
.{date($_-join'-')}2>$x}|sort -u))-ge(date)+'-1').Count/$d.Count) • Input as int[] via parameter, e.g. PS> ./milk.ps1 5,6,7 • Error messages are silenced via try/catch, as long as I don't know whether output on stderr is allowed or not. • Using +"-1" on the date, which gets interpreted as .AddDays(-1) to shift the current date by one day, so that we can compare to yesterday (instead of just today). This solves the problem that we get a date with 0:00 as time but need to compare with a date with time from today. • Heavily inlined by now • Using a new trick for silencing errors that's quite a bit shorter ## R, 269 I was expecting this to be easy in R, but the single-digit years were a pretty big curveball. I feel like this could be much better than it is. lubridate is a package from CRAN, you might need to install it with install.packages("lubridate"). require(lubridate) f = function(d){ d=sapply(d,function(l)if(nchar(l)==1)sprintf("%02d",l)else l) d=paste0(d,collapse="-") t=ymd(Sys.Date()) s=na.omit(c(ymd(d),mdy(d),dmy(d))) s=lapply(s,function(d){ if(year(d)>2049){year(d)=year(d)-100;d} else d}) sum(s>t)/length(s)} Usage: f(c(d1,d2,d3)) where c(d1,d2,d3) is a vector of integers. e.g. f(c(6,10,14)) returns 0.3333333. The lubridate package has a series of wrapper functions for parsing dates in different orders. I use these to see which formats produce valid dates, throw out the invalid ones, and then see which ones haven't occurred yet. ## Mathematica, 163153 164 bytes (edit: fixed dates outside the 1950 - 2049 range) f=100.Count[#,x_/;x<1]/Length@#&[DateDifference[#,Date[]]&/@Cases[{If[#<100,Mod[#+50,100]+1950,#],##2}&@@@{{##},{#3,#2,#},{#3,#,#2}}&@@#,d_/;DateList@d~Take~3==d]]& This defines a function which you can call like f[{6,7,5}] Currently, the percentage isn't rounded (waiting for the OP to clarify). Here is a slightly lengthy explanation that should be understandable without any Mathematica knowledge (note that & makes everything left of it an anonymous function whose parameters are referred to as #, #2, #3...): {{##},{#3,#2,#},{#3,#,#2}}& This defines a function, which turns 3 parameters a,b,c into 3 lists {{a,b,c},{c,b,a},{c,a,b}. Note that ## is just a sequence of all parameters. {{##},{#3,#2,#},{#3,#,#2}}&@@# Applied to the expiry date, this gives a list of {y,m,d} for each of the three possible permutations. {If[#<100,Mod[#+50,100]+1950,#],##2}& This is an anonymous function that takes three parameters a,b,c and returns a list of the three, where the first has been converted to a year as per the given rules: numbers between 50 and 99 (modulo 100) are turned into a 20th century year, numbers between 0 and 49 (modulo 100) are turned into a 21st century year, all others are left along. Here, ##2 is a sequence of parameters starting with the second one, i.e. b,c. {If[#<100,Mod[#+50,100]+1950,#],##2}&@@@{{##},{#3,#2,#},{#3,#,#2}}&@@# Applied to each of the three previous results, this just canonicalises the year formats. Let's call this canonicalDates to shorten the following expression: Cases[canonicalDates,d_/;DateList@d~Take~3==d] This filters out invalid interpretations. DateList@d makes a full {y,m,d,h,m,s} representation out of various date formats. It will interpret lists in the same order, but the catch is that you can pass it things like {8,2,2006} in which case it will calculate 8 years + 2 months + 2006 days. So we check that the first three elements of the returned list are identical to the input (which can only happen if the month and day in the appropriate ranges). To shorten the following lines, I'll refer to the result of that expression as validDates from now on: DateDifference[#,Date[]]& Another anonymous function which takes a date and returns the difference in days to today (obtained from Date[]). DateDifference[#,Date[]]&/@validDates Map that onto the valid date interpretations. 100.Count[#,x_/;x<1]/Length@#& Yet another anonymous function which, given a list (#), returns the percentage of non-positive numbers in that list. The . is not a multiplication but just the decimal digit, to avoid rational numbers as the result (you'd get things like 100/3 instead of 33.333 - I don't actually know if that's a problem). 100.Count[#,x_/;x<1]/Length@#&[DateDifference[#,Date[]]&/@validDates] Applied to the list of date differences, this gives us the fraction of interpretations which are not yet expired. • I think you incorrectly convert years like 2999 or 2099 to 1999. Jul 6, 2014 at 18:42 • @Ventero that's true. I kinda assumed we were only dealing with years 1950 - 2049 (and their 1 or 2 digit versions), but re-reading the challenge there's no mention of that. Jul 6, 2014 at 18:59 • @Ventero fixed (but you had already beaten me significantly anyway ;)) Jul 7, 2014 at 1:23 • I am surprised to see that you have an account on Mathematica but haven't posted any Questions or Answers. Is something holding you back? Jul 9, 2014 at 6:54 • @Mr.Wizard sorry, totally forgot to respond to you. Questions: so far every problem I had could be solved with googling/other SE questions. Answers: I don't know... I guess I don't view myself as that proficient when it comes to using Mathematica productively... I only use it for quick snippets here and there (and code golf). Also, I guess to answer questions I'd have to actively watch new ones to see what I can answer, and currently all my SE time is allocated for PPCG. ;) If you want to me convince me otherwise, feel free to do so in chat! :) Jul 16, 2014 at 17:52 # k4 (90)(88)(87) (82) {100*(+/~d<x)%3-+/^d:{"D"$"."/:$|z,y,x+(x<100)*100*19+x<50}.'y@/:3 3#.:'$21020101}
Invoke with x of .z.D (a builtin) for comparison to today, or a date literal of your choice otherwise:
f:{100*(+/~d<x)%3-+/^d:{"D"$"."/:$|z,y,x+(x<100)*100*19+x<50}.'y@/:3 3#.:'$21020101} .z.D f'(14 12 14;8 2 2006;6 7 5;6 5 7;12 31 99) 100 0 0 0 0f 2006.07.05 f'(14 12 14;8 2 2006;6 7 5;6 5 7;12 31 99) 100 50 33.33333 66.66667 0 This is basically a port of @Alex-l's Python solution, with a few miscellaneous golfing tricks added: • The rearrangement instructions are encoded in a string to save a couple characters. • The conditional logic (ab)uses truth-as-integer (but in a different way from the Python solution). • The validity test is slightly different--k4/q will happily parse any string into any datatype; it simply returns a null if it can't make sense of it. Thus, I return a list of dates from the inner function, which may or may not be null. • The final result comes from checking how many of the possible date interpretations are null vs. how many are less than the comparison date; it's important here that the null date is considered less than any other date. • You can save a char by removing the last 0 from "012201210", since # takes its items cyclically. In fact, you can save a second char this way by swapping the last two cases: 3 3#.:'"0122102". Jul 8, 2014 at 17:23 • Shaved one more char by reversing args of inner func, saving the parens (but adding a reverse). Can anyone help me save another two chars? APL is beating me! Jul 10, 2014 at 23:31 • Shaved another five by rewriting the math at the end. Back in the lead! Jul 10, 2014 at 23:50 • And if I stoop to writing seriously non-functional code, I can shave another byte by polluting the global namespace: {c*(+/~d<x)%3-+/^d:{"D"$"."/:$|z,y,x+(c*19+x<50)*x<c::100}.'y@/:3 3#.:'$21020101}. Jul 17, 2014 at 22:59
# JavaScript (E6) 159 164 172
Edit Thanks to nderscore for the hints and for pushing me to think again. Reorganized D avoiding parameters and cutting some chars.
Edit 2 Another trick by nderscore, 2 functions merged into 1. Then two parenthesis removed merging comma separated expressions into one. Readability near 0. Sidenote: Not rounding could save another 2 chars (|0).
F=(a,t)=>t?100*(3-((i=F([y,m,d]=a))<t)-((j=F([m,d,y]=a))<t)-((k=F([d,m]=a))<t))/(3-!i-!j-!k)|0:(q=new Date(y<50?y+2e3:y,--m,d)).getMonth()==m&q.getDate()==d&&q
Test In FireFox console
;[[14,12,14],[8,2,2006],[6,7,5],[6,5,7],[12,31,99]]
.map(x=>x + ' ' + F(x, new Date(2006,6,5)))
Output:
["14,12,14 100", "8,2,2006 50", "6,7,5 33", "6,5,7 66", "12,31,99 0"]
Ungolfed
NB D function tries to create a Date with given year, month, day but returns false if the created date is not what was intented (!= day or month)
F=(d,t)=>
(
D=(y,m,d)=>(
q=new Date(y<50?y+2000:y, --m, d), // decr m as javascript (like java) counts months starting at 0
q.getMonth() == m & q.getDate() == d && q
),
[a,b,c] = d,
x=D(...d), // three ways of express the date ...
y=D(c,a,b),
z=D(c,b,a),
100 * (3-(x<t)-(y<t)-(z<t)) / (3-!x-!y-!z) | 0
)
• @nderscore OK for changes in D, sintax error for the other. But saved even more anyway Jul 7, 2014 at 20:18
• Weird. Something must've happened when I pasted it into the comment. Your latest optimizations make it irrelevant though :) Jul 7, 2014 at 20:42
• Putting this in a paste, as I don't trust SE's comments anymore: (-3) pastie.org/private/6bemdweyndcaiseay70kia Jul 7, 2014 at 20:59
# C# in LINQPad - 446408 272 Bytes
Third Edit: Thanks to Le Canard fou for pointing out that DateTime.Today is correct, not DateTime.Now. Second Edit: Thanks VisualMelon for this clever solution!
void g(int[]d){var p=".";int a=d[2],b=d[1],e=d[0],y=a+(a<100?a>49?1900:2000:0),q=0,s=0;DateTime c;Action<string>z=x=>{if(DateTime.TryParse(x,out c)){s++;if(c>=DateTime.Today)q+=100;}};z(e+p+b+p+y);z(b+p+e+p+y);z(a+p+b+p+(e<100?e>49?1900+e:2000+e:e));(q/(s>0?s:1)).Dump();}
Edit: Thanks to podiluska and edc65 for helping me shorting the code! I also noticed that my solution wasn't correct if the year input was 4 bytes long, therefore I included the fix for that problem. The score for this solution is 408 Bytes.
Even though I'm not beating any of the previous answers, I still wanted to share my C# solution. Any help/suggestions are appreciated! ;)
void g(int[]d){var q=new List<DateTime>();var p=".";int s=0,a=d[2],b=d[1],e=d[0],y=0;var c=new DateTime();y=(a<100)?(a>49)?1900+a:2000+a:a;if(DateTime.TryParse(e+p+b+p+y,out c)){q.Add(c);s++;}if(DateTime.TryParse(b+p+e+p+y,out c)){q.Add(c);s++;}y=(e<100)?(e>49)?1900+e:2000+e:e;if(DateTime.TryParse(a+p+b+p+y,out c)){q.Add(c);s++;}q=q.Where(i=>i>=DateTime.Now).ToList();if(s==0){s=1;}(q.Count*100/s).Dump();}
Formatted and ungolfed version:
void g(int[] d)
{
var q = new List<DateTime>();
var p = ".";
int s = 0, a = d[2],b = d[1],e = d[0], y=0;
var c = new DateTime();
y = (a < 100) ?((a > 49) ? 1900 + a : 2000 + a) : a;
if (DateTime.TryParse(e + p + b + p + y, out c))
{
s++;
}
if (DateTime.TryParse(b + p + e + p + y, out c))
{
s++;
}
y = (e < 100) ? ((e > 49) ? 1900 + e : 2000 + e) : e;
if (DateTime.TryParse(a + p + b + p + y, out c))
{
s++;
}
q = q.Where(i => i >= DateTime.Now).ToList();
if (s == 0)
{
s = 1;
}
(q.Count*100/s).Dump();
}
I tried to make a solution where the "DateTime.TryParse"-Part isn't repeated as in this solution, but it was 21 bytes longer.
Solution without repeating "DateTime.TryParse" : 467 Bytes
void g(int[]d){var q=new List<DateTime>();int s=0;int a=d[2];int b=d[1];int e=d[0];int y=0;if(a<100){if(a>49){y=1900+a;}else{y=2000+a;}}if(z(e,b,y,q)){s++;}if(z(b,e,y,q)){s++;}if(e<100){if(e>49){y=1900+e;}else{y=2000+e;}}if(z(a,b,y,q)){s++;}q=q.Where(i=>i>=DateTime.Now).ToList();if(s==0){s=1;}(q.Count*100/s).Dump();}bool z(int a,int b,int d,List<DateTime> q){var c=new DateTime();var p=".";if(DateTime.TryParse(a+p+b+p+d,out c)){q.Add(c);return true;}return false;}
Ungolfed version:
private void g(int[] d)
{
var q = new List<DateTime>();
int s = 0;
int a = d[2];
int b = d[1];
int e = d[0];
int y = 0;
if (a < 100)
{
if (a > 49)
{
y = 1900 + a;
}
else
{
y = 2000 + a;
}
}
if (z(e, b, y, q))
{
s++;
}
if (z(b, e, y, q))
{
s++;
}
if (e < 100)
{
if (e > 49)
{
y = 1900 + e;
}
else
{
y = 2000 + e;
}
}
if (z(a, b, y, q))
{
s++;
}
q = q.Where(i => i >= DateTime.Now).ToList();
if (s == 0)
{
s = 1;
}
(q.Count*100/s).Dump();
}
private bool z(int a, int b, int d, List<DateTime> q)
{
var c = new DateTime();
string p = ".";
if (DateTime.TryParse(a + p + b + p + d, out c))
{
return true;
}
return false;
}
• int s=0;int a=d[2];int b=d[1];int e=d[0]; -> int s=0,a=d[2],b=d[1],e=d[0]; Jul 7, 2014 at 13:43
• suggestion: use ternary (?:) when possible instead of if/else Jul 7, 2014 at 20:29
• @ThomasW. I don't think since y has 2 different values, one time it is depending on a, the other time it is depending on e. Thanks anyway! Jul 8, 2014 at 8:47
• Removing the DateTime.TryParse calls was my first instinct, replaced it with a lambda that also put the value back into q. Also performed some other steps (pastebin) to get 328chars: void g(int[]d){var q=new List<DateTime>();var p=".";int a=d[2],b=d[1],e=d[0],y;DateTime c;y=(a<100)?(a>49)?1900+a:2000+a:a;Action<string>z=(x)=>{if(DateTime.TryParse(x,out c))q.Add(c);};z(e+p+b+p+y);z(b+p+e+p+y);y=(e<100)?(e>49)?1900+e:2000+e:e;z(a+p+b+p+y);(q.Where(i=>i>=DateTime.Now).Count()*100/(q.Any()?q.Count:1)).Dump();} Jul 8, 2014 at 12:42
• @VisualMelon Wow, you're really good at code-golfing! I never saw Action<string> before, so I could learn something from you ;) I was able to get your answer down to 318 chars by replacing q.Where(i=>i>=DateTime.Now).Count with q.Count(i=>i>=DateTime.Now. I also removed the brackets around x so I could save 2 more characters! Jul 8, 2014 at 14:09
l=length
r y|y<100=(y+50)mod100+1950|y>0=y
q d m y z|d<32&&m<13&&d*m>0=(r y,m,d):z|1<3=z
v(a,b,c)=q c b a$q b a c$q a b c[]
t%d=(l\$filter(>t)(v d))*100divl(v d)
The function's name is %. Run with the test date as an tuple in canonical (y,m,d) order with actual year, and the carton stamp as a tuple of three numbers:
λ: (2006,6,5)%(14,12,14)
100
λ: (2006,6,5)%(8,2,2006)
50
λ: (2006,6,5)%(6,7,5)
33
λ: (2006,6,5)%(6,5,7)
66
λ: (2006,6,5)%(12,31,99)
0
λ: (2006,6,5)%(0,1,7)
0
# Erlang, 146
f([A,B,C]=U,N)->F=[T||T<-[{(Y+50)rem 100+1950,M,D}||[Y,M,D]<-[U,[C,A,B],[C,B,A]]],calendar:valid_date(T)],100*length([1||T<-F,T>=N])div length(F).
Test function would be:
t() ->
0 = f([12,31,99],{2006,6,5}),
66 = f([6,5,7],{2006,6,5}),
33 = f([6,7,5],{2006,6,5}),
100 = f([14,12,14],{2006,6,5}),
50 = f([8,2,2006],{2006,6,5}),
100 = f([29,2,2],{2006,6,5}).
Ungolfed
f([A,B,C]=U,Today)->
Perms = [U,[C,A,B],[C,B,A]],
WithYears = [{(Y+50) rem 100+1950,M,D} || [Y,M,D] <- Perms],
ValidDates = [T || T <- WithYears, calendar:valid_date(T)],
100*length([1 || T <- ValidDates, T >= Today]) div length(ValidDates).
This solution relies on list comprehensions. It borrows the modulo trick for the year from the Haskell solution. It also uses calendar:valid_date/1 to handle impossible dates because of the number of days in a given month (e.g. "29-2-2" can only be in YMD format). Also, Today is in Erlang's date() format (a YMD tuple).
## APL (85)
This uses some of Dyalog APL 14's new functions, but no external libraries. For a change, it works on TryAPL.
{100×(+/÷⍴)⍺≤{(3/100)⊥⍵+(99≥⊃⍵)×3↑1900+100×50>⊃⍵}¨Z/⍨{∧/12 31≥1↓⍵}¨Z←(⊂⌽⍵),(⊂2⌽⍵),⊂⍵}
This is a function that takes the 3-element array as its right side (⍵) argument, and the date to check against as its left side (⍺) argument, as an integer of YYYYMMDD format. I.e., the date 2014-07-09 is represented as the number 20140709.
Test:
20060705 {100×(+/÷⍴)⍺≤{(3/100)⊥⍵+(99≥⊃⍵)×3↑1900+100×50>⊃⍵}¨Z/⍨{∧/12 31≥1↓⍵}¨Z←(⊂⌽⍵),(⊂2⌽⍵),⊂⍵} 14 12 14
100
20060705 {100×(+/÷⍴)⍺≤{(3/100)⊥⍵+(99≥⊃⍵)×3↑1900+100×50>⊃⍵}¨Z/⍨{∧/12 31≥1↓⍵}¨Z←(⊂⌽⍵),(⊂2⌽⍵),⊂⍵} 8 2 2006
50
20060705 {100×(+/÷⍴)⍺≤{(3/100)⊥⍵+(99≥⊃⍵)×3↑1900+100×50>⊃⍵}¨Z/⍨{∧/12 31≥1↓⍵}¨Z←(⊂⌽⍵),(⊂2⌽⍵),⊂⍵} 6 7 5
33.3333
20060705 {100×(+/÷⍴)⍺≤{(3/100)⊥⍵+(99≥⊃⍵)×3↑1900+100×50>⊃⍵}¨Z/⍨{∧/12 31≥1↓⍵}¨Z←(⊂⌽⍵),(⊂2⌽⍵),⊂⍵} 12 31 99
0
Explanation:
• Z←(⊂⌽⍵),(⊂2⌽⍵),⊂⍵: turn the given date into Y-M-D format by flipping (⊂⌽⍵), rotating it to the left by 2 (⊂2⌽⍵), or just doing nothing ⊂⍵. At least one of these is now a proper date in Y-M-D format, maybe more than one if the date is ambiguous.
• {∧/12 31≥1↓⍵}¨Z: test if each date is valid: the year (first element) is dropped, and then the month must be no higher than 12 and the day must be no higher than 31.
• Z/⍨: filter the valid dates from Z.
• {...}¨: for each valid date:
• ⍵+(99≥⊃⍵)×3↑1900+100×50>⊃⍵: if the year is not higher than 99, add 1900, then 100 if the year is lower than 50.
• (3/100)⊥: decode it as if it were a set of base-100 numbers. (The year is higher than 100, but this doesn't matter as it's the first element.) This gives a number for each valid date in the same format as the left argument.
• ⍺≤: for each date, see if it is not smaller than ⍺. This will give a binary vector where 1 means OK and 0 means spoiled.
• 100×(+/÷⍴): divide the sum of the binary vector by its length and multiply by 100.
• Save 7 bytes (and beat K by a nice margin) with stranding and making an inner function tacit: {100×(+/÷⍴)⍺≤((3/100)⊥⊢+(99≥⊃)×3↑1900+100×50>⊃)¨Z/⍨{∧/12 31≥1↓⍵}¨Z←(⌽⍵)(2⌽⍵)⍵}
May 29, 2017 at 12:05
## Java: 349 Characters (3 w/o spaces)
int e(int[]n,Date t){int a=n[0],b=n[1],c=n[2];Date[]d=new Date[3];if(b<13&&c<32)d[0]=new Date((a<50?100:(a>100?-1900:0))+a,b-1,c);if(b<13&&a<32)d[1]=new Date((c<50?100:(c>100?-1900:0))+c,b-1,a);if(a<13&&b<32)d[2]=new Date((c<50?100:(c>100?-1900:0))+c,a-1,b);int v=0,g=0;for(int i=0;i<3;i++)if(d[i]!=null){if(!d[i].before(t))g++;v++;}return 100*g/v;}
Here is a containing class that can be used to test it, including a (slightly) degolfed version of the method:
import java.util.*;
class i{
int e(int[]n,Date t){
int a=n[0],b=n[1],c=n[2];
Date[]d=new Date[3];
if(b<13&&c<32)d[0]=new Date((a<50?100:(a>100?-1900:0))+a,b-1,c);
if(b<13&&a<32)d[1]=new Date((c<50?100:(c>100?-1900:0))+c,b-1,a);
if(a<13&&b<32)d[2]=new Date((c<50?100:(c>100?-1900:0))+c,a-1,b);
int v=0,g=0;
for(int i=0;i<3;i++)
if(d[i]!=null){
if(!d[i].before(t))
g++;
v++;
}
return 100*g/v;}
public static void main(String[] args){
int[]i=new int[3];
for(int k=0;k<3;k++)
i[k] = Integer.parseInt(args[k]);
int j = new i().e(i,new Date());
System.out.println(j+"%");
}
}
This is my first round of code golf, and I think I figured out why I don't usually see very many Java golfers.
• You need to accept an int[] as argument, not three ints.
– Joey
Jul 8, 2014 at 5:52
• ok, i fixed it. Jul 8, 2014 at 16:18
# C# 287 bytes
namespace System{class E{static float a,o,l;void M(int[]i){int d=i[0],m=i[1],y=i[2],t;if(l<3)try{if(l==1){t=y;y=d;d=t;}if(l++==0){t=d;d=m;m=t;}if(y<100&&(y+=1900)<1950)y+=100;o+=new DateTime(y,m,d)>=DateTime.Today?1:0;a++;if(l<3)i[9]=9;}catch{M(i);throw;}Console.Write(o/a);}}}
First time golfing, looking for advices. Notably, removing bytes due to namespace.
Abusing the fact that only a function is required, not an actual program. Also, the function always results in an uncaught exception.
Ungolfed
namespace System {
class E {
static float a, o, l;
void M(int[] i) {
int d = i[0], m = i[1], y = i[2], t;
if (l < 3)
try {
if (l == 1) {
t = y; y = d; d = t;
}
if (l++ == 0) {
t = d; d = m; m = t;
}
if (y < 100 && (y += 1900) < 1950)
y += 100;
o += new DateTime(y, m, d) >= DateTime.Today ? 1 : 0; // # not expired
a++; // # valid dates
if (l < 3)
i[9] = 9; // throw new Exception()
}
catch {
M(i);
throw; // fail after the first Console.Write()
}
Console.Write(o / a);
}
}
}
## Mathematica, 118
Using m.buettner's code as a starting point I have a few improvements:
⌊100Mean@UnitStep@Cases[DateDifference@{If[#<100,Mod[#+50,100]+1950,#],##2}&@@@{#,RotateRight@#,Reverse@#},_Integer]⌋&
• The golf may be a function taking a three-Int list as argument. Jul 9, 2014 at 15:45
• @algorithmshark Thanks. I don't know how I missed that. Updating... Jul 9, 2014 at 18:54
|
2022-12-09 21:46:16
|
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|
https://aimsciences.org/article/doi/10.3934/dcdss.2018038
|
American Institute of Mathematical Sciences
• Previous Article
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August 2018, 11(4): 631-641. doi: 10.3934/dcdss.2018038
Symmetries and conservation laws of a KdV6 equation
Department of Mathematics, University of Cádiz, PO.BOX 40, 11510 Puerto Real, Cádiz, Spain
* Corresponding author: M.S. Bruzón.
Received December 2016 Revised May 2017 Published November 2017
In the present work we make an analysis of the Korteweg-de Vries of sixth order. We apply the classical Lie method of infinitesimals and the nonclassical method, due to Bluman and Cole, to deduce new symmetries of the equation which cannot be obtained by Lie classical method. Moreover, we obtain ten different conservation laws depending on the parameters and we conclude that potential symmetries project on the infinitesimals corresponding to the classical symmetries.
Citation: María Santos Bruzón, Tamara María Garrido. Symmetries and conservation laws of a KdV6 equation. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 631-641. doi: 10.3934/dcdss.2018038
References:
show all references
References:
[1] Wen-Xiu Ma. Conservation laws by symmetries and adjoint symmetries. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 707-721. doi: 10.3934/dcdss.2018044 [2] M. S. Bruzón, M. L. Gandarias, J. C. Camacho. Classical and nonclassical symmetries and exact solutions for a generalized Benjamin equation. Conference Publications, 2015, 2015 (special) : 151-158. doi: 10.3934/proc.2015.0151 [3] Stephen Anco, Maria Rosa, Maria Luz Gandarias. Conservation laws and symmetries of time-dependent generalized KdV equations. Discrete & Continuous Dynamical Systems - S, 2018, 11 (4) : 607-615. doi: 10.3934/dcdss.2018035 [4] María Rosa, María de los Santos Bruzón, María de la Luz Gandarias. Lie symmetries and conservation laws of a Fisher equation with nonlinear convection term. Discrete & Continuous Dynamical Systems - S, 2015, 8 (6) : 1331-1339. doi: 10.3934/dcdss.2015.8.1331 [5] Juan Belmonte-Beitia, Víctor M. Pérez-García, Vadym Vekslerchik, Pedro J. Torres. Lie symmetries, qualitative analysis and exact solutions of nonlinear Schrödinger equations with inhomogeneous nonlinearities. Discrete & Continuous Dynamical Systems - B, 2008, 9 (2) : 221-233. doi: 10.3934/dcdsb.2008.9.221 [6] Carsten Collon, Joachim Rudolph, Frank Woittennek. Invariant feedback design for control systems with lie symmetries - A kinematic car example. Conference Publications, 2011, 2011 (Special) : 312-321. doi: 10.3934/proc.2011.2011.312 [7] José F. Cariñena, Fernando Falceto, Manuel F. Rañada. Canonoid transformations and master symmetries. Journal of Geometric Mechanics, 2013, 5 (2) : 151-166. doi: 10.3934/jgm.2013.5.151 [8] Miriam Manoel, Patrícia Tempesta. Binary differential equations with symmetries. Discrete & Continuous Dynamical Systems - A, 2019, 39 (4) : 1957-1974. doi: 10.3934/dcds.2019082 [9] Olivier Brahic. Infinitesimal gauge symmetries of closed forms. Journal of Geometric Mechanics, 2011, 3 (3) : 277-312. doi: 10.3934/jgm.2011.3.277 [10] L. Bakker, G. Conner. A class of generalized symmetries of smooth flows. Communications on Pure & Applied Analysis, 2004, 3 (2) : 183-195. doi: 10.3934/cpaa.2004.3.183 [11] Michael Baake, John A. G. Roberts, Reem Yassawi. Reversing and extended symmetries of shift spaces. Discrete & Continuous Dynamical Systems - A, 2018, 38 (2) : 835-866. doi: 10.3934/dcds.2018036 [12] Marin Kobilarov, Jerrold E. Marsden, Gaurav S. Sukhatme. Geometric discretization of nonholonomic systems with symmetries. Discrete & Continuous Dynamical Systems - S, 2010, 3 (1) : 61-84. doi: 10.3934/dcdss.2010.3.61 [13] Júlio Cesar Santos Sampaio, Igor Leite Freire. Symmetries and solutions of a third order equation. Conference Publications, 2015, 2015 (special) : 981-989. doi: 10.3934/proc.2015.0981 [14] Michael Hochman. Smooth symmetries of $\times a$-invariant sets. Journal of Modern Dynamics, 2018, 13: 187-197. doi: 10.3934/jmd.2018017 [15] Martin Oberlack, Andreas Rosteck. New statistical symmetries of the multi-point equations and its importance for turbulent scaling laws. Discrete & Continuous Dynamical Systems - S, 2010, 3 (3) : 451-471. doi: 10.3934/dcdss.2010.3.451 [16] Giovanni Rastelli, Manuele Santoprete. Canonoid and Poissonoid transformations, symmetries and biHamiltonian structures. Journal of Geometric Mechanics, 2015, 7 (4) : 483-515. doi: 10.3934/jgm.2015.7.483 [17] Leonardo Colombo, David Martín de Diego. Optimal control of underactuated mechanical systems with symmetries. Conference Publications, 2013, 2013 (special) : 149-158. doi: 10.3934/proc.2013.2013.149 [18] Dario Bambusi, D. Vella. Quasi periodic breathers in Hamiltonian lattices with symmetries. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 389-399. doi: 10.3934/dcdsb.2002.2.389 [19] Henrique Bursztyn, Alejandro Cabrera. Symmetries and reduction of multiplicative 2-forms. Journal of Geometric Mechanics, 2012, 4 (2) : 111-127. doi: 10.3934/jgm.2012.4.111 [20] Virginia Agostiniani, Rolando Magnanini. Symmetries in an overdetermined problem for the Green's function. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 791-800. doi: 10.3934/dcdss.2011.4.791
2018 Impact Factor: 0.545
|
2019-09-22 06:26:44
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https://socratic.org/questions/573b67f97c01497c71c3da40
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# What complex numbers have the same absolute value as sqrt(3)+i but subtend a right angle with it at O in the complex plane?
Oct 31, 2016
(2) $\text{ "-1+isqrt(3)" }$ or $\text{ } 1 - i \sqrt{3}$
#### Explanation:
Assuming 'O' is $0$, i.e. the origin, we are basically asking what Complex numbers do you get from $\sqrt{3} + i$ by rotating by a right angle - clockwise or anticlockwise - about $0$.
Rotating anticlockwise about $0$ by a right angle is the same as multiplying by $i = \cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)$:
$i \left(\sqrt{3} + i\right) = i \sqrt{3} + {i}^{2} = i \sqrt{3} - 1 = - 1 + i \sqrt{3}$
Rotating clockwise about $0$ by a right angle is the same as multiplying by $- i = \cos \left(- \frac{\pi}{2}\right) + i \sin \left(- \frac{\pi}{2}\right)$:
$- i \left(\sqrt{3} + i\right) = - i \sqrt{3} - {i}^{2} = - i \sqrt{3} + 1 = 1 - i \sqrt{3}$
(2) $\text{ "-1+isqrt(3)" }$ or $\text{ } 1 - i \sqrt{3}$
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2020-04-03 03:33:00
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