text:
# Symbol

A symbol is a mark, sign or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different concepts and experiences. All communication (and data processing) is achieved through the use of symbols. Symbols take the form of words, sounds, gestures, ideas or visual images and are used to convey other ideas and beliefs. For example, a red octagon may be a symbol for "STOP". On a map, a blue line might represent a river. Numerals are symbols for numbers. Alphabetic letters may be symbols for sounds. Personal names are symbols representing individuals. A red rose may symbolize love and compassion. The variable 'x', in a mathematical equation, may symbolize the position of a particle in space.

In cartography, an organized collection of symbols forms a legend for a map.

A red octagon symbolizes "stop" even without the word.

## Etymology

The word symbol derives from the Greek σύμβολον symbolon, meaning "token, watchword" from σύν syn "together" and βάλλω bállō " "I throw, put." The sense evolution in Greek is from "throwing things together" to "contrasting" to "comparing" to "token used in comparisons to determine if something is genuine." Hence, "outward sign" of something. The meaning "something which stands for something else" was first recorded in 1590, in Edmund Spenser's Faerie Queene.[1]

## Concepts and definitions

Symbols are a means of complex communication that often can have multiple levels of meaning.[2] Symbols are the basis of all human understanding and serve as vehicles of conception for all human knowledge.[3] Symbols facilitate understanding of the world in which we live, thus serving as the grounds upon which we make judgments.[4] In this way, people use symbols not only to make sense of the world around them, but also to identify and cooperate in society through constitutive rhetoric.

Human cultures use symbols to express specific ideologies and social structures and to represent aspects of their specific culture. Thus, symbols carry meanings that depend upon one's cultural background; in other words, the meaning of a symbol is not inherent in the symbol itself but is culturally learned.[2]

In considering the effect of a symbol on the psyche, in his seminal essay The Symbol without Meaning Joseph Campbell proposes the following definition:

A symbol is an energy evoking, and directing, agent.[5]

Later, expanding on what he means by this definition Campbell says:

a symbol, like everything else, shows a double aspect. We must distinguish, therefore between the 'sense' and the 'meaning' of the symbol. It seems to me perfectly clear that all the great and little symbolical systems of the past functioned simultaneously on three levels: the corporeal of waking consciousness, the spiritual of dream, and the ineffable of the absolutely unknowable. The term 'meaning' can refer only to the first two but these, today, are in the charge of science – which is the province as we have said, not of symbols but of signs. The ineffable, the absolutely unknowable, can be only sensed. It is the province of art which is not 'expression' merely, or even primarily, but a quest for, and formulation of, experience evoking, energy-waking images: yielding what Sir Herbert Read has aptly termed a 'sensuous apprehension of being'.[6]

Heinrich Zimmer gives a concise overview of the nature, and perennial relevance, of symbols.

Concepts and words are symbols, just as visions, rituals, and images are; so too are the manners and customs of daily life. Through all of these a transcendent reality is mirrored. There are so many metaphors reflecting and implying something which, though thus variously expressed, is ineffable, though thus rendered multiform, remains inscrutable. Symbols hold the mind to truth but are not themselves the truth, hence it is delusory to borrow them. Each civilisation, every age, must bring forth its own."[7]

In the book Signs and Symbols, it is stated that

A symbol ... is a visual image or sign representing an idea -- a deeper indicator of a universal truth.[8]

## Symbols and semiotics

Semiotics is the study of signs, symbols, and signification as communicative behavior. Semiotics studies focus on the relationship of the signifier and the signified, also taking into account interpretation of visual cues, body language, sound, and other contextual clues. Semiotics is linked with both linguistics and psychology. Semioticians thus not only study what a symbol implies, but also how it got its meaning and how it functions to make meaning in society. Symbols allow the human brain continuously to create meaning using sensory input and decode symbols through both denotation and connotation.

## Psychoanalysis, rhetoric and archetypes

An alternative definition of symbol, distinguishing it from the term sign was proposed by Swiss psychoanalyst Carl Jung. In his studies on what is now called Jungian archetypes, a sign stands for something known, as a word stands for its referent. He contrasted a sign with a symbol: something that is unknown and that cannot be made clear or precise. An example of a symbol in this sense is Christ as a symbol of the archetype called self.[9]

Kenneth Burke described Homo sapiens as a "symbol-using, symbol making, and symbol misusing animal" to suggest that a person creates symbols as well as misuses them. One example he uses to indicate what he means by the misuse of symbol is the story of a man who, when told that a particular food item was whale blubber, could barely keep from throwing it up. Later, his friend discovered it was actually just a dumpling. But the man's reaction was a direct consequence of the symbol of "blubber" representing something inedible in his mind. In addition, the symbol of "blubber" was created by the man through various kinds of learning.

Burke goes on to describe symbols as also being derived from Sigmund Freud's work on condensation and displacement, further stating that symbols are not just relevant to the theory of dreams but also to "normal symbol systems". He says they are related through "substitution", where one word, phrase, or symbol is substituted for another in order to change the meaning. In other words, if one person does not understand a certain word or phrase, another person may substitute a synonym or symbol in order to get the meaning across. However, upon learning the new way of interpreting a specific symbol, the person may change his or her already-formed ideas to incorporate the new information.

Jean Dalby Clift says that people not only add their own interpretations to symbols, they also create personal symbols that represent their own understanding of their lives: what she calls "core images" of the person. She argues that symbolic work with these personal symbols or core images can be as useful as working with dream symbols in psychoanalysis or counseling.[10]

William Indick suggests that the symbols that are commonly found in myth, legend, and fantasy fulfil psychological functions and hence are why archetypes such as "the hero," "the princess" and "the witch" have remained popular for centuries.[11]

## Symbolic value

Symbols can carry symbolic value in three primary forms: Ideological, comparative, and isomorphic.[12] Ideological symbols such as religious and state symbols convey complex sets of beliefs and ideas that indicate "the right thing to do". Comparative symbols such as prestigious office addresses, fine art, and prominent awards indicate answers to questions of "better or worse" and "superior or inferior". Isomorphic symbols blend in with the surrounding cultural environment such that they enable individuals and organizations to conform to their surroundings and evade social and political scrutiny. Examples of symbols with isomorphic value include wearing professional dress during business meetings, shaking hands to greet others in the West, or bowing to greet others in the East. A single symbol can carry multiple distinct meanings such that it provides multiple types of symbolic value.[12]

## Paul Tillich

Paul Tillich argued that, while signs are invented and forgotten, symbols are born and die.[13] There are, therefore, dead and living symbols. A living symbol can reveal to an individual hidden levels of meaning and transcendent or religious realities. For Tillich a symbol always "points beyond itself" to something that is unquantifiable and mysterious; symbols open up the "depth dimension of reality itself".[14] Symbols are complex, and their meanings can evolve as the individual or culture evolves. When a symbol loses its meaning and power for an individual or culture, it becomes a dead symbol. When a symbol becomes identified with the deeper reality to which it refers, it becomes idolatrous as the "symbol is taken for reality." The symbol itself is substituted for the deeper meaning it intends to convey. The unique nature of a symbol is that it gives access to deeper layers of reality which are otherwise inaccessible.[15]

## Role of context in symbolism

A symbol's meaning may be modified by various factors including popular usage, history, and contextual intent.

### Historical meaning

The history of a symbol is one of many factors in determining a particular symbol's apparent meaning. Consequently, symbols with emotive power carry problems analogous to false etymologies.[16]

### Context

The context of a symbol may change its meaning. Similar five-pointed stars might signify a law enforcement officer or a member of the armed services, depending upon the uniform.

## Symbols in cartography

The three categories of cartographic symbol shapes

Symbols are used in cartography to communicate geographical information (generally as point, line, or area features).[17] As with other symbols, visual variables such as size, shape, orientation, texture, and pattern provide meaning to the symbol.[18] According to semiotics, map symbols are "read" by map users when they make a connection between the graphic mark on the map (the sign), a general concept (the interpretant), and a particular feature of the real world (the referent). Map symbols can thus be categorized by how they suggest this connection:[19][20]

• Pictorial Symbols (also "Image", "Iconic", or "Replicative") appear as the real-world feature, although it is often in a generalized manner; e.g. a tree icon to represent a forest, or green denoting vegetation.
• Functional Symbols (also "Representational") directly represent the activity that takes place at the represented feature; e.g. a picture of a skier to represent a ski resort or a tent to represent a campground.
• Conceptual Symbols directly represent a concept related to the represented feature; e.g. a dollar sign to represent an ATM, or a Star of David to represent a Jewish synagogue.
• Conventional Symbols (also "Associative") do not have any intuitive relationship but are so commonly used that map readers eventually learn to recognize them; e.g. a red line to represent a highway or a cross to represent a hospital.
• Abstract/Geometric Symbols (also "Ad Hoc") are arbitrary shapes chosen by the cartographer to represent a certain feature.

## Related terms

A symbolic action is an action that has no, or little, practical effect but symbolizes, or signals, what the actor wants or believes. The action conveys meaning to the viewers. Symbolic action may overlap with symbolic speech, such as the use of flag burning to express hostility or saluting the flag to express patriotism.[21] In response to intense public criticism, businesses, organizations, and governments may take symbolic actions rather than, or in addition to, directly addressing the identified problems.[22]

Wearing variously colored ribbons is a symbolic action that shows support for certain campaigns.

## References

1. ^ Online Etymological Dictionary
2. ^ a b Womack, Mari. Symbols and Meaning: A Concise Introduction. California: AltaMira Press, 2005.
3. ^ Langer, Susanne K. A Theory of Art, Developed From: Philosophy in a New Key. New York: Charles Scribner’s Sons, 1953.
4. ^ Palczewski, Catherine, and Ice, Richard, and Fritch, John. Rhetoric in Civic Life. Pennsylvania: Strata Publishing, Inc., 2012.
5. ^ Campbell, Joseph (2002). Flight of the Wild Gander:- The Symbol without Meaning. California: New World Library. p. 143. ISBN 1-57731-210-4.
6. ^ Campbell, The Symbol without Meaning p153
7. ^ Campbell, Heinrich Zimmer; edited by Joseph (1969). Philosophies of India (9. paperback print. ed.). Princeton: Princeton Univ. Press. pp. 1–2. ISBN 0-691-01758-1.
8. ^ Dorling Kindersley Limited. Signs and Symbols. p.6. ISBN 978-0-7566-3393-6. 2008
9. ^ Christ, A symbol of the self CW vol 9i Aion RKP 1958
10. ^ Jean Dalby Clift, Core Images of the Self: A Symbolic Approach to Healing and Wholeness. Crossroad, 1992.
11. ^ Indick, William. Ancient Symbology in Fantasy Literature: A Psychological Study. Jefferson: McFarland &, 2012. Print.
12. ^ a b Schnackenberg, Andrew K.; Bundy, Jonathan; Coen, Corinne; Westphal, James. "Capitalizing on Categories of Social Construction: A Review and Integration of Organizational Research on Symbolic Management Strategies". Academy of Management Annals. doi:10.5465/annals.2017.0096.
13. ^ Tillich, Paul (1964). Theology of Culture. Oxford University Press. p. 58. ISBN 0195007115.
14. ^ Tillich, Paul (1964). Theology of Culture. Oxford University Press. p. 59. ISBN 0195007115.
15. ^ Tillich, Paul (1964). Theology of Culture. Oxford University Press. p. 54. ISBN 0195007115.
16. ^ Compare: Basso, Michele (1982). Eschatological symbolism in the Vatican Necropolis. Tipografia Poliglotta Vaticana. p. 78. Retrieved 2019-01-05. In a late period the Greeks made [Pan] the incarnation of All (giving a false etymology to his name, which is really connected with the pastures), that is to say, the universe.
17. ^ Tyner, Judith A. (2010). Principles of map design. New York: Guilford Press. ISBN 9781606235447. OCLC 437300476.
18. ^ Dent, Borden D.; Torguson, Jeffrey; Hodler, T. W. Cartography : thematic map design (6th ed.). New York: McGraw-Hill Higher Education. ISBN 0072943823. OCLC 184827987.
19. ^ MacEachren, Alan (1995) How Maps Work: Representation, visualization, and design, New York: Guilford Press
20. ^ Dent, Borden D. Cartography : thematic map design (5th ed.). New York: McGraw-Hill Higher Education. ISBN 0697384950.
21. ^ Bagossy, Renate. The Difficulty of the Amendment Process of the Constitution of the United States of America and Freedom of Speech and its limits. GRIN Verlag; 2008-08-11 [cited 5 November 2012]. ISBN 9783640129546. p. 16–17.
22. ^ Bednar, Michael Kay. How Symbolic Action Affects the Media as a Governance Mechanism. ProQuest; 2008. ISBN 9780549738817. p. 17.


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# Simple PHP Router for home grown MVC framework

I don't know if you guys get tired of seeing a bunch of requests for review of similar projects, but I was really looking for advice.

My website is designed on the MVC pattern. I have a very simple router that seems to be working just fine! If there is any upgrade I would add to it would be the ability to catch a third parameter (optional ID number, for example).

Any thoughts on the design/execution would be greatly appreciated.

Here is the Router class:

namespace Framework
{
use App\Controllers;

class Router
{
private $_url = []; public function addRoute($route, $dest) {$this->_url[$route] =$dest;
}

public function redirect()
{
$url = isset($_GET["url"]) ? $_GET["url"] : ""; foreach ($this->_url as $route =>$dest)
{
if("/$url" ==$route)
{
$this->parsecommand($dest);
break;
}
}
}

private function parsecommand($dest) {$goto = explode("@", $dest);$controller = $goto[0];$action = $goto[1]; require_once("../app/controllers/$controller.php");

$class = '\\App\\Controllers\\' .$controller;
$obj = new$class;

return $obj->$action();
}
}
}

The routes are entered this way:

namespace App
{
use Framework\Router;

$routes = new Router;$routes->addRoute("/", "HomeController@index");
$routes->addRoute("/aboutus", "HomeController@aboutus");$routes->addRoute("/blog", "BlogController@index");

return $routes; }  ...which runs as a part of a bootstrap process called from index. And my controllers look like this: namespace App\Controllers { use App\Controller as Controller; use App\Models\Update as Update; class HomeController extends Controller { public function index() {$this->view('index', [
'update' => Update::orderBy('id', 'desc')->first(),
]);
}

{
$this->view('aboutus'); } } }  Rendering the views is handled by Twig in the Controller base class (not really relevant to this question). Like I said, this works perfectly (for my needs, I wouldn't market it or anything, haha), just wondering if I could get some advice. EDIT: This does not handle 404 (or any other error for that matter), I realize that would probably the first thing to upgrade. ## 1 Answer Welcome to code review! Don't worry, we don't get tired of these things (or at least I don't). In retrospect I would have loved to have something like this in my early days - and it's still useful to me now even though I'm well past my early years. I'll just start from small items and work my way up. To be fair, I'm a stickler for the little things. You'd be surprised how often the little things can make a big difference in the long run, especially when you are talking about the core part of a system (such as this). So let's start with the little stuff: 1. You don't have to use braces and indent after a namespace. This is actually the only place I suggest not indenting or including braces. The reason is because it simply pushes the indentation of your entire file up one level unnecessarily. Just end your namespace declaration with a semi-colon and leave the use lines and class definition without indentation. 2. The usage of the redirect method in your router is unclear, and as such I'm not even 100% sure if your redirect method even belongs in the router. That sounds more like something that should be part of the object that manages the HTTP response (which would also handle things like 404 errors and what not). Then again it seems like the only part that actually does routing, so maybe the issue is your name. Perhaps it should be called route()? That makes sense to me: in your index file you would call $router->route() and expect a controller to be executed.
3. In the redirect method you use a loop over the routes, which is costly (in terms of performance). A better option would simply be to do a lookup via isset. if (isset($this->_url[$url])) {}.
4. You have no handling of error conditions. What happens if someone tries to redirect to a route that doesn't exist? What happens if there is no @ in the route? It is best to explicitly check for such situations and throw an exception so that you can provide clear details to the developer.
5. Similar, enforcing some consistency in your data can be helpful. Your router obviously assumes that routes start with a slash, so you should enforce that in the addRoute method. This will take care of a whole class of subtle but hard-to-identify bugs down the road.
6. Your names are a bit inconsistent. See addRoute vs parsecommand. Camel case for one but all lowercase for the other. Pick a convention and stick to it. If in doubt use PSR.
7. Your variables names could use a bit more consistency too. Instead of using a private variable named _urls in your router, I think routes would make much more sense. Also (this could be a matter of preference), you don't really need the leading underscore in the name of private variables. IMO, that's a convention that primarily belongs in languages that don't have enforced visibility rules.
8. Writing docblocks will help a lot in the long run.
9. Your parsecommand method returns whatever the controller returns, but the redirect method ignores the return value. This makes sense because your controllers don't actually return anything. If the controllers will always print directly, then there is probably no reason for paresecommand to return anything.

Some larger suggestions:

Dependency Injection:

As I mentioned before, you don't really want to access the $_GET super global (or other super globals) directly. It is better to use a separate class to get that information out. It all boils down to separation of concerns. As a simple example of where this can break down, how would your current setup handle things if you decided to add a command line component? Perhaps that would have a completely separate router, but perhaps you would rather use the same system you already have in place. In that case your current setup simply won't work - it is hard-coded to look at $_GET, which doesn't exist in the command line environment. Instead you could have your router expect to receive a request object in the constructor, and that request would tell it the requested URL. In the case of a normal web request the request object would simply get the URL out of the $_GET super global, but for a command line request you would perhaps send in a different request object that gets the url out of the command line arguments. This all boils down to the concept of dependency injection - instead of directly creating/managing your own dependencies, you let the person in charge of you give the necessary dependencies. This makes the code much more flexible. It also allows you to create integration and unit tests, which is otherwise impossible when you are directly hooked into the request itself. For the moment of course I wouldn't suggest switching completely over to managing your system with a full dependency injection container. However, if you get in the habit of separating out your services a bit more and (in this example), expecting a request object to come in with the constructor, you'll start getting in much better habits. While you are keeping things simple, now is the time to start learning about dependency injection and test writing. Autoloading In your router you require the controller PHP file directly. This implies that you don't have autoloading setup. Setting that up in your bootstrap process will save you a lot of trouble. For instance, your current setup requires your controllers to all live in the same directory. With an autoload setup that maps namespaces to file directories, you can remove that requirement and make it easier to organize your app. Then you could do things like: $routes->addRoute('/shopping/products', '\Shopping\ProductController@index');

Presumably your files would then be located in (something like) Controllers/Shopping/ProductController.php, Controllers/Support/ContactController.php, etc... This will help you keep your app organized better if it starts growing larger than a handful of controllers.

Performance

I don't think this is either a surprise or a problem for you, but just to say out loud, this setup will start to cause (performance) trouble if you start to add dozens/hundreds of endpoints. It doesn't sound like that is your intention, but for something like this to scale to large apps you may need a different routing mechanism or some caching mechanism (or a completely different solution).

That's what I have for now! Let me know if you have any followup questions/comments.

• I appreciate the feedback. I have taken most of your suggestions. And, I am autoloading, calling the controller class was actually a vestige. It was there during a test and I never removed it! Thanks again for the comments, this gives me some inspiration. – aserwin May 9 '18 at 20:29
• I am considering rebuilding the Router class as a singleton. Would that improve performance in the case of many routes? – aserwin May 9 '18 at 20:56
• Presumably your router object is only used once, so making it a singleton wouldn't actually change anything. To be fair, I doubt you will have much of a serious problem with performance as-is, especially with exact matches. If you make your routing logic more complicated (regular expression matching for greater flexibility, etc...) and have to actually match against every record, then things can cause problems. With an isset lookup route matching is relatively constant, and you just need one function call per route - very fast. – Conor Mancone May 9 '18 at 23:18
• Yeah, I thought about that after I asked... the object is destroyed almost immediately after it is instantiated! Thanks again for the advice. – aserwin May 10 '18 at 0:21
• I have put the entire framework on github if anyone cares to contribute... github.com/erwininteractive/phpmvc – aserwin May 11 '18 at 3:45

format: plain


text:
## Cryptology ePrint Archive: Report 2015/345

Two Round Multiparty Computation via Multi-Key FHE

Pratyay Mukherjee and Daniel Wichs

Abstract: We construct a general multiparty computation (MPC) protocol with only two rounds of interaction in the common random string model, which is known to be optimal. In the honest-but-curious setting we only rely on the learning with errors (LWE) assumption, and in the fully malicious setting we additionally assume the existence of non-interactive zero knowledge arguments (NIZKs). Previously, Asharov et al. (EUROCRYPT '12) showed how to achieve three rounds based on LWE and NIZKs, while Garg et al. (TCC '14) showed how to achieve the optimal two rounds based on indistinguishability obfuscation, but it was unknown if two rounds were possible under standard assumptions without obfuscation.

Our approach relies on multi-key fully homomorphic encryption (MFHE)", introduced by Lopez-Alt et al. (STOC '12), which enables homomorphic computation over data encrypted under different keys. We present a construction of MFHE based on LWE that significantly simplifies a recent scheme of Clear and McGoldrick (CRYPTO '15). We then extend this construction to allow for a one-round distributed decryption of a multi-key ciphertext. Our entire MPC protocol consists of the following two rounds:

1. Each party individually encrypts its input under its own key and broadcasts the ciphertext. All parties can then homomorphically compute a multi-key encryption of the output.

2. Each party broadcasts a partial decryption of the output using its secret key. The partial decryptions can be combined to recover the output in plaintext.

Category / Keywords: public-key cryptography / Full Homomorphic Encryption, MPC

Date: received 16 Apr 2015, last revised 27 Feb 2016

Contact author: pratyay85 at gmail com

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2015/345

[ Cryptology ePrint archive ]


text:
# An Inequality from Marocco

### Statement

$1\le a,b,c,d\le 2.$ Prove that

$\displaystyle 4|(a-b)(b-c)(c-d)(d-a)|\le abcd.$

### Solution 1

Set $\displaystyle x=\frac{a}{b},\;y==\frac{b}{c},\;z=\frac{c}{d},\;t=\frac{d}{a}.$ From the defintion $\displaystyle\frac{1}{2}\le x,y,z,t\le 2$ and $xyzt=1.$ Under this condition we need to prove that

$\displaystyle |(1-x)(1-y)(1-z)(1-t)|\le\frac{1}{4}.$

If $1\in\{x,y,z,\},$ we are done. Otherwise, we shall consider three cases:

1. $x,y,z\lt 1\lt t:$

We have $\displaystyle 1-x\le\frac{1}{2},$ $\displaystyle 1-y\le\frac{1}{2},$ $\displaystyle 1-z\le\frac{1}{2},$ $|1-t|\le 1,$ implying

$\displaystyle |(1-x)(1-y)(1-z)(1-t)|\le\frac{1}{8}\lt\frac{1}{4}.$

2. $t\lt\ 1\lt x,y,z:$

This case reduces to the previous by inverting the four fractions that we defined.

3. $x,y\lt 1\lt z,t:$

We have $\displaystyle 1-x\le\frac{1}{2},$ $\displaystyle 1-y\le\frac{1}{2},$ $|1-z|\le 1,$ $|1-t|\le 1,$ implying

$\displaystyle |(1-x)(1-y)(1-z)(1-t)|\le\frac{1}{4}.$

The equality clearly holds when two of them are $\displaystyle\frac{1}{2}$ and the other two equal $2.$ In the original notations we have two solutions $(1,2,1,2)$ and $(2,1,2,1).$

### Solution 2

From $\displaystyle\frac{1}{2}\le x,y,z,t\le 2$ we get $\displaystyle (1-x)^{2}\le\frac{x}{2},$ $\displaystyle (1-y)^{2}\le\frac{y}{2},$ $\displaystyle (1-z)^{2}\le\frac{z}{2},$ $\displaystyle (1-t)^{2}\le\frac{t}{2},$ multiplying which we get

$\displaystyle |(1-x)(1-y)(1-z)(1-t)|\le\sqrt{\frac{xyzt}{16}}=\frac{1}{4}.$

### Acknowledgment

Leo Giugiuc has kindly posted the problem and two solutions. One of his and Dan Sitaru (Solution 1) and that by Amine Idirissi from Morocco (Solution 2), with the reamrk that the problem was offered at the the Morroco Mathematical Olympiad. There is also one invalid solution that conceals a misleading argument. You may want to locate it.

 62838333


text:
What is the general solution of the differential equation (x+y)dx-xdy = 0?

Dec 30, 2016

$y = x \ln | x | + A x$

Explanation:

We can write the equation $\left(x + y\right) \mathrm{dx} - x \mathrm{dy} = 0$ as:

$\text{ } x \mathrm{dy} = \left(x + y\right) \mathrm{dx}$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = \frac{x + y}{x}$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = 1 + \frac{y}{x}$

$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} - \frac{1}{x} y = 1$

This is a First Order DE of the form:

$y ' \left(x\right) + P \left(x\right) y = Q \left(x\right)$

Which we know how to solve using an Integrating Factor given by:

$I F = {e}^{\int P \left(x\right) \setminus \mathrm{dx}}$

And so our Integrating Factor is:

$I F = {e}^{\int - \frac{1}{x} \setminus \mathrm{dx}}$
$\setminus \setminus \setminus \setminus = {e}^{- \ln | x |}$
$\setminus \setminus \setminus \setminus = {e}^{\ln | \frac{1}{x} |}$
$\setminus \setminus \setminus \setminus = \frac{1}{x}$

If we multiply by this Integrating Factor we will (by its very design) have the perfect differential of a product:

$\text{ } \frac{\mathrm{dy}}{\mathrm{dx}} - \frac{1}{x} y = 1$

$\therefore \frac{1}{x} \frac{\mathrm{dy}}{\mathrm{dx}} - \frac{1}{x} ^ 2 y = \frac{1}{x}$
$\therefore \setminus \setminus \setminus \setminus \setminus \frac{d}{\mathrm{dx}} \left(\frac{1}{x} y\right) = \frac{1}{x}$

Which is now a separable DE, and we can separate the variables to get:

$\text{ } \frac{y}{x} = \int \setminus \frac{1}{x} \setminus \mathrm{dx}$
$\therefore \frac{y}{x} = \ln | x | + A$ (where $A$ is an arbitrary constant)
$\therefore \setminus \setminus y = x \ln | x | + A x$


text:
# Chapter 3 Association Rules

## 3.1 Item Sets

The relationship between items is the joint occurrence of items in the shopping basket.

In the jargon of market basket analysis, we speak of item sets, and of association rules.

An item set is simply a collection of one or more items. We display these collections with curly brackets {}.

An example of an item set in a customer's shopping basket in the supermarket is the combination of bread and peanut butter, shown as:

But also

and

are examples of item sets.

The number of possible item sets quickly takes on enormous proportions.

Suppose a very small store sells 10 types of products (or items). A customer may or may not buy any item, which results in:

$$2^{10} = 1024$$

possible item sets!

For a slightly larger supermarket with 100 different items, the number of options is

$$2^{10} = 1.27*10^{30}$$

(1270000000000000000 ... stops at 28 zeros)

In those situations it is not feasible to evaluate all possible combinations. We have to look for a smart and efficient algorithm to generate rules that connect item sets.

An example of such a rule is:


text:
Volume 390 - 40th International Conference on High Energy physics (ICHEP2020) - Parallel: Strong Interactions and Hadron Physics
QCD effects in lepton angular distributions of Drell-Yan/$Z$ production and jet discrimination
W.C. Chang,* R. Evan McClellan, J.C. Peng, O. Teryaev
*corresponding author
Full text: Not available
Abstract
We present a comparison of data of lepton angular distributions of Drell-Yan/$Z$ production with the fixed-order pQCD calculations by which the baseline of pQCD effects is illustrated. As for the $Z$ production, we predict that $A_0$ and $A_2$ for $Z$ plus single gluon-jet events are very different from that of $Z$ plus single quark-jet events, allowing a new experimental tool for checking various algorithms which attempt to discriminate quark jets from gluon jets. Using an intuitive geometric approach, we show that the violation of the Lam-Tung relation, appearing at large transverse-momentum region, is attributed to the presence of a non-coplanarity effect. This interpretation is consistent with the appearance of violation beyond LO-QCD effect.
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# 6.12: The Frequency of Collisions between Unlike Gas Molecules

Thus far in our theoretical development of the properties of gases, we have assumed that ideal gas molecules are point masses. While they can collide with the walls of their container, point masses cannot collide with one another. As we saw in our discussion of van der Waals equation, the deviation of real gases from ideal gas behavior is one indication that an individual gas molecule occupies a finite volume.

To develop a model for molecular collisions, we need to know the size and shape of the colliding molecules. For a general model, we want to use the simplest possible size and shape. Accordingly, we consider a model in which gas molecules are spheres with well-defined radii. We let the radii of molecules $$1$$ and $$2$$ be $$\sigma_1$$ and $$\sigma_2$$, respectively. See Figure 10. When such molecules collide, their surfaces must come into contact, and the distance between their centers must be $$\sigma_{12}=\sigma_1+\sigma_2$$. We call $$\sigma_{12}$$ the collision radius.

Let us consider a molecule of type $$1$$ in a container with a large number of molecules of type $$2$$. We suppose that there are $$N_2$$ molecules of type $$2$$ per unit volume. Every molecule of type $$2$$ has some velocity, $$v_{12}$$, relative to the molecule of type $$1$$. From our development above, we know both the probability density function for $$v_{12}$$ and the expected value $$\left\langle v_{12}\right\rangle$$. Both molecule $$1$$ and all of the molecules of type $$2$$ are moving with continuously varying speeds. However, it is reasonable to suppose that—on average—the encounters between molecule $$1$$ and molecules of type $$2$$ are the same as they would be if all of the type $$2$$ molecules were fixed at random locations in the volume, and molecule $$1$$ moved among them with a speed equal to the average relative velocity, $$\left\langle v_{12}\right\rangle$$.

Under this assumption, a molecule 1 travels a distance equal to $$\left\langle v_{12}\right\rangle$$ in unit time. As it does so, it collides with any type $$2$$ molecule whose center is within a distance $$\sigma_{12}$$ of its own center. For the moment, let us suppose that the trajectory of molecule $$1$$ is unaffected by the collisions it experiences. Then, in unit time, molecule $$1$$ sweeps out a cylinder whose length is $$\left\langle v_{12}\right\rangle$$ and whose cross-sectional area is $$\pi \sigma^2_{12}$$. The volume of this cylinder is $$\pi \sigma^2_{12}\left\langle v_{12}\right\rangle$$. (See Figure 11.)

Since there are $$N_2$$ molecules of type $$2$$ per unit volume, the number of type $$2$$ molecules in the cylinder is $$N_2\pi \sigma^2_{12}\left\langle v_{12}\right\rangle$$. Each of these molecules is a molecule of type $$2$$ that experiences a collision with molecule $$1$$ in unit time. Letting $${\widetilde{\nu }}_{12}$$ be the frequency (number of collision per unit time) with which molecule $$1$$ collides with molecules of type $$2$$, we have

${\widetilde{\nu }}_{12}=N_2\pi \sigma^2_{12}\left\langle v_{12}\right\rangle =N_2\pi \sigma^2_{12}{\left(\frac{8kT}{\pi \mu }\right)}^{1/2}$

$=N_2\sigma^2_{12}{\left(\frac{8\pi kT}{\mu }\right)}^{1/2}$

Two additional parameters that are useful for characterizing molecular collisions are $${\tau }_{12}$$, the mean time between collisions, and $${\lambda }_{12}$$, the mean distance that molecule $$1$$ travels between collisions with successive molecules of type $$2$$. $${\lambda }_{12}$$ is called the mean free path. The mean time between collisions is simply the reciprocal of the collision frequency,

${\tau }_{12}={1}/{\widetilde{\nu }_{12}}$

and the mean free path for molecule $$1$$ is the distance that molecule $$1$$ actually travels in this time, which is $$\left\langle v_1\right\rangle$$, not $$\left\langle v_{12}\right\rangle$$, so that

${\lambda }_{12}=\left\langle v_1\right\rangle {\tau }_{12}=\frac{\left({\mu }/{m}\right)^{1/2}}{N_2\pi \sigma^2_{12}}$

Now, we need to reevaluate the assumption that the trajectory of a molecule of a molecule $$1$$ is unaffected by its collisions with molecules of type $$2$$. Clearly, this is not the case. The path of molecule $$1$$ changes abruptly at each collision. The actual cylinder that molecule $$1$$ sweeps out will have numerous kinks, as indicated in Figure 12. The kinked cylinder can be produced from a straight one by making a series oblique cuts (one for each kink) across the straight cylinder and then rotating the ends of each cut into convergence. If we think of the cylinder as a solid rod, its volume is unchanged by these cuttings and rotations. The volume of the kinked cylinder is the same as that of the straight cylinder. Thus, our conclusions about the collision frequency, the mean time between collisions, and the mean free path are not affected by the fact that the trajectory of molecule $$1$$ changes at each collision.


text:
# 6.9 Integer Optimization¶

An optimization problem where one or more of the variables are constrained to integer values is called a (mixed) integer optimization problem. MOSEK supports integer variables in combination with linear, quadratic and quadratically constrtained and conic problems (except semidefinite). See the previous tutorials for an introduction to how to model these types of problems.

## 6.9.1 Example MILO1¶

We use the example

(6.20)$\begin{split}\begin{array}{lccl} \mbox{maximize} & x_0 + 0.64 x_1 & & \\ \mbox{subject to} & 50 x_0 + 31 x_1 & \leq & 250, \\ & 3 x_0 - 2 x_1 & \geq & -4, \\ & x_0, x_1 \geq 0 & & \mbox{and integer} \end{array}\end{split}$

to demonstrate how to set up and solve a problem with integer variables. It has the structure of a linear optimization problem (see Sec. 6.1 (Linear Optimization)) except for integrality constraints on the variables. Therefore, only the specification of the integer constraints requires something new compared to the linear optimization problem discussed previously.

This is easily programmed in R using the piece code shown in Listing 6.11,

Listing 6.11 R implementation of problem (6.20). Click here to download.
##
#
#  File :      milo1.R
#
#  Purpose :   To demonstrate how to solve a small mixed integer linear
#              optimization problem using the Rmosek package.
##
library("Rmosek")

milo1 <- function()
{
# Specify the continuous part of the problem.
prob <- list(sense="max")
prob$c <- c(1, 0.64) prob$A  <- Matrix(rbind(c(50, 31),
c( 3, -2)), sparse=TRUE)
prob$bc <- rbind(blc=c(-Inf, -4), buc=c( 250, Inf)) prob$bx <- rbind(blx=c(  0,   0),
bux=c(Inf, Inf))

# Specify the integer constraints
prob$intsub <- c(1 ,2) # Solve the problem r <- mosek(prob) # Return the solution stopifnot(identical(r$response$code, 0)) r$sol
}

milo1()

where $$x_1$$ and $$x_2$$ are pointed out as integer variables.

The input arguments follow those of a linear or conic program with the additional identification of the integer variables. The column vector intsub should simply contain indexes to the subset of variables for which integrality is required. For instance if $$x$$ should be a binary $$\{0,1\}$$-variable, its index in the problem formulation should be added to intsub, and its bounds $$0 \leq x \leq 1$$ should be specified explicitly.

If executed correctly you should be able to see the log of the interface and optimization process printed to the screen. The output structure will only include an integer solution int, since we are no longer in the continuous domain for which the interior-point algorithm operates. The structure also contains the problem status as well as the solution status based on certificates found by the MOSEK optimization library.

## 6.9.2 Specifying an initial solution¶

It is a common strategy to provide a starting feasible point (if one is known in advance) to the mixed-integer solver. This can in many cases reduce solution time.

It is not necessary to specify the whole solution. MOSEK will attempt to use it to speed up the computation. MOSEK will first try to construct a feasible solution by fixing integer variables to the values provided by the user (rounding if necessary) and optimizing over the continuous variables. The outcome of this process can be inspected via information items "MSK_IINF_MIO_CONSTRUCT_SOLUTION" and "MSK_DINF_MIO_CONSTRUCT_SOLUTION_OBJ", and via the Construct solution objective entry in the log. We concentrate on a simple example below.

(6.21)$\begin{split}\begin{array} {ll} \mbox{maximize} & 7 x_0 + 10 x_1 + x_2 + 5 x_3 \\ \mbox{subject to} & x_0 + x_1 + x_2 + x_3 \leq 2.5\\ & x_0,x_1,x_2 \in \integral \\ & x_0,x_1,x_2,x_3 \geq 0 \end{array}\end{split}$

Solution values can be set using the appropriate fields in the problem structure.

Listing 6.12 Implementation of problem (6.21) specifying an initial solution. Click here to download.
    # Specify start guess for the integer variables.
prob$sol$int$xx <- c(1, 1, 0, NaN)  The log output from the optimizer will in this case indicate that the inputted values were used to construct an initial feasible solution: Construct solution objective : 1.950000000000e+01  The same information can be obtained from the API: Listing 6.13 Retrieving information about usage of initial solution Click here to download.  print(r$iinfo$MIO_CONSTRUCT_SOLUTION) print(r$dinfo$MIO_CONSTRUCT_SOLUTION_OBJ)  ## 6.9.3 Example MICO1¶ Integer variables can also be used arbitrarily in conic problems (except semidefinite). We refer to the previous tutorials for how to set up a conic optimization problem. Here we present sample code that sets up a simple optimization problem: (6.22)$\begin{split}\begin{array}{ll} \mbox{minimize} & x^2+y^2 \\ \mbox{subject to} & x \geq e^y+3.8, \\ & x, y \ \mbox{integer}. \end{array}\end{split}$ The canonical conic formulation of (6.22) suitable for Rmosek package is (6.23)$\begin{split}\begin{array}{llr} \mbox{minimize} & t & \\ \mbox{subject to} & (t,x,y)\in\Q^3 & (t\geq\sqrt{x^2+y^2}) \\ & (x-3.8, 1, y) \in\EXP & (x-3.8\geq e^y) \\ & x, y \ \mbox{integer}, & \\ & t\in\real. \end{array}\end{split}$ Listing 6.14 Implementation of problem (6.23). Click here to download. library("Rmosek") mico1 <- function() { # Specify the continuous part of the problem. # Variables are [t; x; y] prob <- list(sense="min") prob$c <- c(1, 0, 0)
prob$A <- Matrix(nrow=0, ncol=3) # 0 constraints, 3 variables prob$bx <- rbind(blx=rep(-Inf,3), bux=rep(Inf,3))

# Conic part of the problem
prob$F <- rbind(diag(3), c(0,1,0), c(0,0,0), c(0,0,1)) prob$g <- c(0, 0, 0, -3.8, 1, 0)
prob$cones <- cbind(matrix(list("QUAD", 3, NULL), nrow=3, ncol=1), matrix(list("PEXP", 3, NULL), nrow=3, ncol=1)) rownames(prob$cones) <- c("type","dim","conepar")

# Specify the integer constraints
prob$intsub <- c(2 ,3) # Solve the problem r <- mosek(prob) # Return the solution stopifnot(identical(r$response$code, 0)) print(r$sol$int$xx[2:3])
}

Note that the conic constraints are described using the format $$Fx+g\in\K$$, that is as affine conic constraints. See Sec. 6.7 (Affine conic constraints (new)) for details.

Error and solution status handling were omitted for readability.


text:
# The asymptotic smile of a multiscaling stochastic volatility model

Francesco Caravenna and Jacopo Corbetta

Papers from arXiv.org

Abstract: We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear mean reversion. Using large deviations techniques, we determine the asymptotic shape of the implied volatility surface in any regime of small maturity $t \to 0$ or extreme log-strike $|\kappa| \to \infty$ (with bounded maturity). Even if the price has continuous paths, out-of-the-money implied volatility diverges for small maturity, producing a very pronounced smile.

Date: 2015-01, Revised 2017-07
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## How to find fx^-1

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text:
# Kollektion: Wristband Replacement

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text:
0
Research Papers: Materials and Fabrication

# Effect of High-Pressure Hydrogen Gas on Fracture of Austenitic Steels

[+] Author and Article Information
C. San Marchi, D. K. Balch, K. Nibur, B. P. Somerday

Sandia National Laboratories, Livermore, CA 94550

J. Pressure Vessel Technol 130(4), 041401 (Aug 20, 2008) (9 pages) doi:10.1115/1.2967833 History: Received February 28, 2006; Revised April 24, 2007; Published August 20, 2008

## Abstract

Applications requiring the containment and transportation of hydrogen gas at pressures greater than $70MPa$ are anticipated in the evolving hydrogen economy infrastructure. Since hydrogen is known to alter the mechanical properties of materials, data are needed to guide the selection of materials for structural components. The objective of this study is to characterize the role of yield strength, microstructural orientation, and small concentrations of ferrite on hydrogen-assisted fracture in two austenitic stainless steels: 21Cr–6Ni–9Mn (21-6-9) and 22Cr–13Ni–5Mn (22-13-5). The testing methodology involves exposure of tensile specimens to high-pressure hydrogen gas at elevated temperature in order to precharge the specimens with hydrogen, and subsequently testing the specimens in laboratory air to measure strength and ductility. In all cases, the alloys remain ductile despite precharging to hydrogen concentrations of $∼1at.%$, as demonstrated by reduction in area values between 30% and 60% and fracture modes dominated by microvoid processes. Low concentrations of ferrite and moderate increases in yield strength do not exacerbate hydrogen-assisted fracture in 21-6-9 and 22-13-5, respectively. Microstructural orientation has a pronounced effect on ductility in 22-13-5 due to the presence of aligned second-phase particles.

<>

## Figures

Figure 6

Scanning electron microscope images of fracture surfaces from high-strength 22-13-5 tested with precharged hydrogen: (a) L-orientation and (b) C-orientation. The arrows indicate Z-phase particles.

Figure 7

Scanning electron microscope images of fracture surfaces from 21-6-9 Heat B tested with precharged hydrogen: (a) L-orientation and (b) C-orientation

Figure 4

Scanning electron microscope images of fracture surfaces from low-strength 22-13-5 tested in C-orientation: (a) noncharged condition and (b) hydrogen-precharged condition

Figure 5

Scanning electron microscope images of fracture surfaces from 21-6-9 Heat A tested in L-orientation: (a) noncharged condition and (b) hydrogen-precharged condition. The arrows indicate elongated dimples in (b).

Figure 1

Optical micrographs of (a) 21-6-9 Heat A, (b) 21-6-9 Heat B, (c) low-strength 22-13-5, and (d) high-strength 22-13-5. The longitudinal axis of the forging is parallel to the horizontal edges of these micrographs, and taken near the middle of the length and toward the outside diameter of the forging. Note the magnification is different between the 21-6-9 and the 22-13-5 micrographs.

Figure 2

Micrographs of as-received 22-13-5 bar stock showing distribution of Z-phase; (a) backscattered scanning electron microscope image, bright phase is Z-phase; (b) transmission electron microscope image, dark precipitates are Z-phase

Figure 3

Stress-strain curves of noncharged and hydrogen-precharged (a) 21-6-9 Heat A, L-orientation and (b) high-strength 22-13-5, C-orientation

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Spend an extra 20 minutes after the GMAT and get goodies? : General GMAT Questions and Strategies
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# Spend an extra 20 minutes after the GMAT and get goodies?

Author Message
Manager
Joined: 27 Jan 2010
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Spend an extra 20 minutes after the GMAT and get goodies? [#permalink]

### Show Tags

26 May 2011, 11:37
So a few days ago I booked my GMAT retake date (25 July 2011) and while finishing up the payment I was informed that I need to consent to some sort of a survey (20-30 minutes long) and questions that I need to fill out after the exam but before the scores were shown (I think). They also specifically stated that if I take the effort to answer the questions I stand to receive some really cool goodies. I believe this is only between the months of July - Sep 2011.

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Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink]

### Show Tags

26 May 2011, 11:58
Yes, this is in preparation for the new section that will be released in 2012. They have been doing some sampling to help them with grading/preparing for the new section.

More here: gmat-test-prep-changes-on-the-way-in-99691.html

and here: when-to-take-gmat-98680.html
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Kudos [?]: 21 [0], given: 53

Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink]

### Show Tags

26 May 2011, 12:01
Awesome! Its nice to know that my inputs are going to make a (tiny tiny) contribution to how the GMAT will look in the future!

Do you have any ideas about what the goodies are? Are the goodies worth the wait?
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Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink]

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26 May 2011, 12:02
ra011y wrote:
Awesome! Its nice to know that my inputs are going to make a (tiny tiny) contribution to how the GMAT will look in the future!

Do you have any ideas about what the goodies are? Are the goodies worth the wait?

Let me check
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Kudos [?]: 22424 [0], given: 4439

Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink]

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31 May 2011, 20:42
I just heard back and the word is that they actually don't know - the goodies will be revealed in a few weeks. So.... I guess we will all just to wait. Bummer.
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### Show Tags

06 Jul 2011, 15:48
So for the sure this extra part will be at the end? I take my GMAT in a few days and I think it would suck to sit through 30 minutes of this and then 1 hour of AWA. Somebody please confirm. I remember reading about this but I'm not sure if its at beginning or end. Also, the goodies are you get $20 refund or, if you're real lucky, get full refund. Senior Manager Joined: 05 Jul 2010 Posts: 359 Followers: 15 Kudos [?]: 51 [0], given: 17 Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink] ### Show Tags 07 Jul 2011, 04:30 They sent me the same thing. I hope these extra set of questions are going to appear at the end? In which case, do you guys really think you will have any motivation left to complete that set? Intern Joined: 21 Dec 2010 Posts: 25 Followers: 1 Kudos [?]: 1 [0], given: 0 Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink] ### Show Tags 07 Jul 2011, 12:01 Just received confirmation from the GMAC, the extra portion will begin AFTER THE EXAM. Senior Manager Joined: 21 Jul 2010 Posts: 272 Followers: 8 Kudos [?]: 29 [0], given: 17 Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink] ### Show Tags 11 Jul 2011, 17:33 got an email recently - reward is$20 for completing the section and a "chance" at a full GMAT test refund.

see here:
july-to-aug-extra-integrated-section-reward-116250.html
Status: How can I crack Verbal
Joined: 12 May 2011
Posts: 209
Location: India
Concentration: General Management, Finance
GMAT 1: 700 Q51 V32
GPA: 3
Followers: 2

Kudos [?]: 19 [0], given: 33

Re: Spend an extra 20 minutes after the GMAT and get goodies? [#permalink]

### Show Tags

18 Jul 2011, 12:47
great offer..i wish i had known about this offer before i registered for the exam..i did not want to sit thru the survey,hence opted out of the survey..
Re: Spend an extra 20 minutes after the GMAT and get goodies?   [#permalink] 18 Jul 2011, 12:47
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# Spend an extra 20 minutes after the GMAT and get goodies?

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# Do we not need [knot-theory]?

A recent challenge (A Rather Knotty Conundrum) added the tag. No previous knot theory challenges use this tag yet. Before I consider using the tag, I want to see if the tag is really necessary. This tag might make sense on Math.SE, but it seems pretty specific for our use on PPCG, and there are only three or four existing challenges that could deserve the tag:

Should we remove this tag, or keep it (and tag the existing challenges)?

• New title: I have a theory: we do 'knot' need this tag – DJMcMayhem Dec 19 '16 at 20:20

## Keep it

It's not doing any harm. The difficulty of the tagged challenges, or the number of answers they receive is irrelevant for whether the tag is useful. If someone does answer one of those tough challenges, there's a good chance they're interested in the general topic and would like to find more of knot theory challenges. The tag helps them do exactly that, regardless of whether there's only 4 or 40 applicable challenges.

• As a side note I'm not entirely convinced that this entire question isn't just a setup for a really bad pun... – Martin Ender Dec 19 '16 at 19:50
• It's not a setup. I found all the questions that were related simply by searching for the word "knot", and so I think we don't need the tag. – mbomb007 Dec 19 '16 at 19:57
• In fact, I was primarily asking because I was going to ask a knot-theory question, and I wanted to know how to tag it. codegolf.stackexchange.com/q/103743/34718 – mbomb007 Dec 19 '16 at 20:09

# It's not necessary. Remove it.

There are only a few related questions, and the existing questions receive few answers due to the complexity of the field and the programming required (each of the likely candidates has only a single answer.)

Because of this, the tag is not necessary, and can be used instead.

• Knot theory is topology, not geometry. – Peter Taylor Dec 20 '16 at 8:22
• @PeterTaylor Well, the questions using knot theory were tagged geometry. – mbomb007 Dec 20 '16 at 14:49


text:
# Kernel of Ring Epimorphism is Ideal

## Theorem

Let $\phi: \struct {R_1, +_1, \circ_1} \to \struct {R_2, +_2, \circ_2}$ be a ring epimorphism.

Then:

### Kernel of Ring Homomorphism is Ideal

The kernel of $\phi$ is an ideal of $R_1$.

### Quotient Ring of Kernel of Ring Epimorphism

There exists a unique ring isomorphism $g: R_1 / K \to R_2$ such that:

$g \circ q_K = \phi$

### Ring Epimorphism with Trivial Kernel is Isomorphism

$\phi$ is an isomorphism if and only if $K = \set {0_{R_1} }$.


text:
# SMILE

## Ranked Tree Shapes, Nonrandom Extinctions, and the Loss of Phylogenetic Diversity

### 2018

Phylogenetic diversity (PD) is a measure of the evolutionary legacy of a group of species, which can be used to define conservation priorities. It has been shown that an important loss of species diversity can sometimes lead to a much less important loss of PD, depending on the topology of the species tree and on the distribution of its branch lengths. However, the rate of decrease of PD strongly depends on the relative depths of the nodes in the tree and on the order in which species become extinct. We introduce a new, sampling-consistent, three-parameter model generating random trees with covarying topology, clade relative depths and clade relative extinction risks. This model can be seen as an extension to Aldous' one parameter splitting model ($\beta$, which controls for tree balance) with two additional parameters: a new parameter $\alpha$ quantifying the correlation between the richness of a clade and its relative depth, and a parameter $\eta$ quantifying the correlation between the richness of a clade and its frequency (relative abundance or range), taken herein as a proxy for its overall extinction risk. We show on simulated phylogenies that loss of PD depends on the combined effect of all three parameters, $\beta$, $\alpha$ and $\eta$. In particular, PD may decrease as fast as species diversity when high extinction risks are clustered within small, old clades, corresponding to a parameter range that we term the `thin ice zone' ($\beta<-1$ or $\alpha<0$; $\eta>1$). Besides, when high extinction risks are clustered within large clades, the loss of PD can be higher in trees that are more balanced ($\beta>0$), in contrast to the predictions of earlier studies based on simpler models. We propose a Monte-Carlo algorithm, tested on simulated data, to infer all three parameters. Applying it to a real dataset comprising 120 bird clades (class Aves) with known range sizes , we show that parameter estimates precisely fall close to close to a 'thin ice zone': the combination of their ranking tree shape and non-random extinctions risks makes them prone to a sudden collapse of PD.

# Bibtex

@article{maliet2018ranked,
title={Ranked Tree Shapes, Nonrandom Extinctions, and the Loss of Phylogenetic Diversity},
author={Maliet, Odile and Gascuel, Fanny and Lambert, Amaury},
journal={Systematic biology},
volume={67},
number={6},
pages={1025--1040},
year={2018},
doi={10.1093/sysbio/syy030},
publisher={Oxford University Press}
}


text:
# Which of the following statement regarding cyclins IS NOT CORRECT? When a cell moves through a...

###### Question:

Which of the following statement regarding cyclins IS NOT CORRECT?

When a cell moves through a predetermined cell cycle genetic circuit, cyclins (e.g., G1/S-cyclin, S-cyclin, M-cyclin and G1-cyclin) appear and disappear in a cyclical fashion. Which of the following statement regarding cyclins IS NOT CORRECT? cyclins are part of a complex (cyclin-dependent protein kinase complexes, CDKCs) that catalyze the phosphorylation of target proteins. O A O Bcyclins are activated by cell-cycle kinases and deactivated by a phosphatase. cyclins are synthesized at the beginning of a specific cell-phase (e.g., at the onset of S-phase) and degraded by proteolysis at the end and or beginning of the next phase (e.g., M-phase). O C O D cyclins contain specific amino acid sequence motifs that target them for proteolysis (degradation)

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text:
# Thread: structural mehanics help needed!! - centre of gravity

1. ## structural mehanics help needed!! - centre of gravity

please could i have help with the question attatched
it is about centre of gravity.
thanks

2. Cut your figure into two pieces. (a square and a triangle)
You can easily find the coordinates of the center of mass of the square using symmetry arguments.
You can find the coordinates of the center of mass of the triangle using the definition of the mean
$c_x=\frac{\int x f(x) dx}{\int f(x) dx}$
$c_y=\frac{\int y f(y) dy}{\int f(y) dy}$
Then you can find the center of mass of the whole thing with
$*MR = m_1r_1+m_2r_2$*r being the vectors of position.

3. ## thanks

thanks alot thats a big help.


text:
1. ## Taking The Derivative

What is the derivative of this equation:

2. The chain rule is

$\frac{dy}{dt} = \frac{dy}{du}\times \frac{du}{dt}$

For your function $y = \arcsin(\sqrt{2t})$ make $u = \sqrt{2t}$ so $y = \arcsin(u)$

Now find $\frac{dy}{du}$ and $\frac{du}{dt}$

3. hi
just to add, $\forall x\in (-1,1),\arcsin'(x)=\frac{1}{\sqrt{1-x^2}}$

4. Then what is the derivative of (2t^.5)

5. When i took the derivative of (2t^.5) i got 1/(2t^.5)
does that even make sense?

6. Originally Posted by emilyroy10
Then what is the derivative of (2t^.5)
$\frac{d}{dt}(2 \sqrt{t}) = \frac{1}{\sqrt{t}}$

7. what is the derivative of ((2t)^.5)

8. $(\sqrt{2t})'=\frac{1}{2}(2t)^{-\frac{1}{2}}\times2=\frac{1}{\sqrt{2t}}$

9. okay thats what i got when i took the derivative of ((2t)^.5), which was 1/((2t)^.5).
but what do you get when you multiply it by the derivative of arcsin, which is 1/((1-((2t)^2))^.5)

10. you should get, $\frac{1}{\sqrt{2}\sqrt{1-2t}\sqrt{t}}$


text:
# Is this skew symmetry?

In this challenge, your task is to detect (vertical) Skewer Symmetry. This means that one half of the pattern can be produced by mirroring the other half along a vertical axis, and then moving it vertically.

For example, the following pattern has skewer symmetry:

asdf
jkl;fdsa
;lkj

Because if you start from the left half...

asdf
jkl;

...then mirror it along a vertical axis...

    fdsa
;lkj

...then move it down by a character (filling the empty rows with spaces)...

fdsa
;lkj

...you get the second half.

## Rules:

• You may assume the input is rectangle and has an even number of columns.
• If the pattern itself exhibits reflection symmetry, it is considered skewer symmetry.
• This is strict character by character symmetry, so [[ is considered symmetrical, but not [].
• You should output truthy if the input has skewer symmetry, falsy otherwise.
• Default I/O rules apply, standard loopholes are banned.

## Test Cases

Truthy cases:

asdf
jkl;fdsa
;lkj

asdffdsa

[

[

  ba
abdc
cd

Falsy cases:

[
]

ab
ba

aa
a
a

a  a
b b

ab
b
a

• suggested test case: ["abfe","cdhg","efba","ghdc"]. i don't know what the result should be. – ngn Oct 4 '19 at 13:49
• Suggested test case: ["ab ", " b ", " a"] (where the columns are symmetric with the spaces stripped, but not with spaces present) – user48543 Oct 4 '19 at 15:16
• @ngn This is similar to the ["ab", "ba"] test case, result should be falsy (it’s a symmetry+rotation, while skew symmetry is only symmetry+translation). – Grimmy Oct 4 '19 at 18:12
• @Grimy Formatting ate the array. It's supposed to be four columns, with 'a' in the first and last and 'b' in the second and third. So ["ab..", "..b.", "...a"], with the dots replaced with spaces. – user48543 Oct 4 '19 at 18:19
• Suggested test case: [" ba","abdc","cd "] -> truthy (left part is moved downwards). May we assume, that the input contains only printable ASCII (' ' (space) to '~')? – nimi Oct 5 '19 at 8:29

f s=uncurry(#)$unzip$splitAt(div(length$s!!0)2)<$>s
a#b@(x:y)|e$last a++x=init a#y|e$last b++a!!0=b#a|r<-reverse<\$>b=a==r
e=all(<'!')

Try it online!

# J, 3423 38 bytes

1 e.[:(e.&:((-:@#{.])"1)|."1\.)"2],:|.

Try it online!

thanks to nimi for catching a bug

Will attempt to regolf the fixed version later.


text:
Browse Questions

# A thin string is wrapped several times around a cylinder kept on a rough horizontal surface. A boy standing at a distance l from the cylinder draws the string towards him as shown. The cylinder rolls without slipping . The length of the string passed through the hand of the boy while the cylinder reaches his hand is

$\begin {array} {1 1} (a)\;l & \quad (b)\;2l \\ (c)\;3l & \quad (d)\;4l \end {array}$

Speed of $A= 2 V_{cm}$
So $2l$ is the correct answer
edited Jun 22, 2014


text:
Question

# The length, the breadth and the height of a cuboid are in the ratio of 5:3:2. If it’s volume is $240c{{m}^{3}}$, then find the total surface area of the cuboid in $c{{m}^{3}}$.

Verified
146.7k+ views
Hint: We will use the formula for the volume of the cuboid to solve this question. If l is the length of a cuboid, b is the breadth of a cuboid and h is the height of a cuboid, then the volume of a cuboid is given by $lbh$ and the total surface area is given by $2\left( lb+bh+hl \right).$

It is given in the question that the length, breadth and height of a cuboid are in the ratio of 5:3:2. Let us consider a variable $x$ such that we can write the given ratios in proportions. The length of a cuboid can be written as $5x$, the breadth of cuboid as $3x$ and height of the cuboid as $2x$.
Now, we use the formula for the volume of the cuboid, as the volume of the cuboid is already given in the question. Using this, we can find the value of x and then we can find the length, breadth and height. Then, we can find the total surface area of the cuboid.
All units are in $c{{m}^{3}}$, so we don’t have to do unit conversions.
The volume of the cuboid is given by $lbh$ where $l=5x$, $b=3x$and $h=2x$. Therefore, substituting the values, we get
Volume = $(5x)(3x)(2x)=30{{x}^{3}}$
Now, according to the question, the volume of a cuboid = $240c{{m}^{3}}$. So, we can equate obtained volume to given volume as,
$30{{x}^{3}}=240c{{m}^{3}}$
\begin{align} & \Rightarrow {{x}^{3}}=8c{{m}^{3}} \\ & \Rightarrow x=2cm \\ \end{align}
So, now we can obtain the length of cuboid as $=5\times 2=10cm$, breadth of cuboid $=3\times 2=6cm$ and height of the cuboid $=2\times 2=4cm$.
Now we will find the total surface area of cuboid give by the formula,
\begin{align} & \Rightarrow 2(lb+bh+hl) \\ & \Rightarrow 2(10\times 6+6\times 4+4\times 10) \\ & \Rightarrow 2(60+24+40) \\ & \Rightarrow 2(124) \\ & =248c{{m}^{3}} \\ \end{align}
So, the total surface area of a cuboid is $=248c{{m}^{3}}$.

Note: All units are in $c{{m}^{3}}$, so there is no need of doing unit conversions. The student must remember the important formula of volume and total surface area of the cuboid. When ratios are given, we need to consider a variable $x$ and then we can write ratios in terms of that variable.


text:
# Tapatalk - XenForo support (iPhone, iPad, Android, BlackBerry, Windows Phone 7, webOS, Nokia app)

Status
Not open for further replies.

#### tapatalk

##### Well-known member
Thanks. It may have the same issue on iPhone as I have not tested on that version.

Andy,

Originally we omitted the image in quoted was to hope to save user bandwidth but it appears not a good experience. The iPhone side has a switch allowing user to turn on / off the downloading quoted images and by default it is off. We may just simply set it to on by default and do the same for Android.

#### tapatalk

##### Well-known member
Hello all,

We have just released a 1.0.1. Changelog can be found at the first post.

#### Andy.N

##### Well-known member
Hello all,

We have just released a 1.0.1. Changelog can be found at the first post.
Is the latex problem fixed yet?

#### tapatalk

##### Well-known member
I just double checked the posted version is indeed 1.0.1.

#### Andy.N

##### Well-known member
I just double checked the posted version is indeed 1.0.1.
No. I downloaded it again, the zip file is 1.0.1 but the xml file inside shows last updated 3/20/2011

And here is the header of that xml file
Code:
<?xml version="1.0" encoding="utf-8"?>
<addon addon_id="tapatalk" title="Tapatalk" version_string="1.0.0" version_id="1" url="" install_callback_class="" install_callback_method="" uninstall_callback_class="" uninstall_callback_method="">

#### tapatalk

##### Well-known member
version string in XML file now corrected - Looks like our build script need to retool for XenForo

#### Andy.N

##### Well-known member
Andy,

Originally we omitted the image in quoted was to hope to save user bandwidth but it appears not a good experience. The iPhone side has a switch allowing user to turn on / off the downloading quoted images and by default it is off. We may just simply set it to on by default and do the same for Android.
My Android tester reports the problem with latex is till the same.

#### tapatalk

##### Well-known member
We will get DarkImmortal to chime it. Our standard plugin does not support special tag but we can always incorporate if Dark can push the change into our repo.

#### Luke F

##### Well-known member
We will get DarkImmortal to chime it. Our standard plugin does not support special tag but we can always incorporate if Dark can push the change into our repo.

The Android app just needs to display a white background on transparent gifs/pngs when viewing them fullscreen - currently it is black resulting in black-on-black text.

#### Andy.N

##### Well-known member
The url for the mathtex script is still not correct.

#### Luke F

##### Well-known member
My user said it's already on white background.

Oh sorry I thought that was still the issue at hand.

I've added a rewrite on your site so the URL including /forum should work

#### Andy.N

##### Well-known member
Oh sorry I thought that was still the issue at hand.

I've added a rewrite on your site so the URL including /forum should work

Here is what it looks like. I'm afraid we will eventually have a spaghetti mess of all the redirect you put in there, DI

The image looks like the mathtex.cgi was not decode everything after \frac properly

#### tapatalk

##### Well-known member
Here is what it looks like. I'm afraid we will eventually have a spaghetti mess of all the redirect you put in there, DI

The image looks like the mathtex.cgi was not decode everything after \frac properly

View attachment 13377
Would it help if we put a white background behind the image thumbnail? So it works with different skins/color-themes.

#### trilogy33

##### Well-known member
Can someone please confirm that these things aren't happening in the Public non-Beta release?

First picture:
When someone is quoted, an smiley is parsed where there wasn't one.

Second picture:
And again...

Third picture:
This smiley is presented as an attachment and not inline with the text flow.

EDIT: Pictures changed to show correct product

#### tapatalk

##### Well-known member
Can someone please confirm that these things aren't happening in the Public non-Beta release?

View attachment 13400View attachment 13401

In the first picture it's not parsing smilies correctly, it's picking up the :o in :oops and not fulfilling the entire smiley :oops
Second picture: Again, not parsing :coffee:
Hello,

The product shown in the pictures are not from us

#### ddmmh

##### Well-known member
Hi Tapatalk,

Ive been playing around with the photo upload feature.

If i upload the photo in the 40kb size its fine, if I try the full size which in this case was 4 MB I get the following error;

I thought it may be my php upload limit even though I know its set to 10mb. So i zipped up an mp3 and it came to just over 7mb in size. It uploaded fine via the website. Also I checked my php settings in cpanel and it is infact set to 10mb so I believe this may be a bug?

Also when images are uploaded, if tapatalk is used for hosting the image they are inserted as images which looks nice, whereas if the option to host it on the 'forum' is chosen then the file is an attachment... doesnt look quite as good, is this going to change in a future update?

On a lighter note, I am really really starting to like tapatalk and appreciate its potential, the GUI is gorgeous, I cant wait for all the bugs to be ironed out, will be a very solid product I believe.

Cheers.

#### Crazyfruitbat

##### Well-known member
Hey Tapatalk, just installed and its all working fine!

Is there any way that we can choose the way to insert the images? For example, here on xenforo after uploading the image we have the choice of having it an attachment or to put it full width. Is there any way we can have a similar function on Tapatalk?

#### Crazyfruitbat

##### Well-known member
damn I really should have read the post before mine!

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