text:
Talk:Folk rock

Bad content forking
To clarify on the tags I placed, there is a huge amount of WP:COATRACK regarding 1960s folk and rock music. Demonstrating my point is the fact that there is actually more info about the British Invasion here than at the actual British Invasion article. More examples:

Great info, only problem is that it has nothing to do with folk rock. Per WP:DETAIL, a lot of this material needs to be moved somewhere else, like 1960s in music, Folk revival, British Invasion, Bob Dylan, the Byrds, Cultural impact of the Beatles, and Contemporary folk. --Ilovetopaint (talk) 23:43, 27 February 2017 (UTC)

 * I agree. Most of it was added by  in a major expansion in 2010 (see thread up above), so it would be worth getting their opinion.   Ghmyrtle (talk) 07:31, 28 February 2017 (UTC)
 * I don't mind if some of the text/information that I added is relocated, as long as attribution is maintained. However, I think we also need to be careful not to eliminate material that provides context within this article. For instance, the Beatles' adoption of folk/protest elements and how the band first encountered them in Bob Dylan's music, along with George Harrison's distinctive 12-string Rickenbacker sound and its influence on the Byrds and folk rock in general, are all just as relevant to this article as they might be to the Cultural impact of the Beatles one. Likewise, the fact that this article may contain more information about the British Invasion than the British Invasion article does, is not, in and of itself, a good enough justification to delete content from this article and relocate it.

 * That said, if others do legitimately feel that some text here should be relocated, I guess I'm fine with that, with the caveat being my point about maintaining context in this article. I happen to think that an awful lot of what is written in the Folk revival section, for instance, is pretty relevant to any reader attempting to understand how the sub-genre of folk rock came to be.

 * Also, regarding where to move stuff to, as someone who has worked very closely on the Byrds article, I can say with 100% certainty that there is nothing in this article that isn't already in the Byrds one. So, I would definitely advise against moving anything from this page over there. Kohoutek1138 (talk) 13:22, 28 February 2017 (UTC)

 * OK, having just had a look at Ilovetopaint's recent edits, I think he/she needs to tread very carefully here. The fact that this user mistakenly believes that jangle pop predates folk rock (when the very term "jangle pop" was coined in the mid-80s to describe a guitar-based sub-genre from that decade), that he's removing information that is clearly supported by inline refs, and the addition of "according to whom" type tags, when "who" it is that has made these points is obvious from the cited refs is worrisome. They've done much good work to this article, to be sure, but we need to be careful not to throw the baby out with the bathwater. I am going to reinstate some of the deleted material and also reword parts, citing the critics in question, to try and remove the "according to whom" tags. Kohoutek1138 (talk) 13:40, 28 February 2017 (UTC)

After looking at this article for a while and trying to work though it, I agree that the large Antecedents section is unhelpful. There is too much of it for this general encyclopedia article on folk rock. Because of the importance and complexity of the subject it is appropriate and helpful to have some introduction to the origins of the genre, though the current 20 kB of text (3,301 words) is too long - that amounts to 1/3 of the entire article. I also wonder how much is strictly relevant to the subject matter of folk rock - the first paragraph of the Folk revival sub-section, with material such as "By 1951, however, the [Weavers] had fallen afoul of the U.S. Red Scare of the McCarthy era, and as a result they disbanded in 1952.", may be relevant to the American folk music revival, but is too detailed and too distant to be relevant here. I'm not sure how helpful it would be to work though the three thousand words to trim them. I suspect it would be easier to remove them entirely and replace them with a freshly written paragraph.  SilkTork  ✔Tea time  21:03, 13 June 2017 (UTC)

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Wiki Education Foundation-supported course assignment
Howdy, Wiki editors! I will be working on this article as part of a class assignment for the next few weeks. I hope to contribute to this article and collaborate with all of you, and any input you have and any changes you can make that will make the article better will be greatly appreciated.

Aside from this article, I will be editing the British Invasion article, so I will hopefully be able to help with edit this section and make it appear more as a summary as Wiki guidelines have suggested. I think that the lead introduction has parallels and repeated information within “Definition and Etymology” section that can be edited. Also, there are a lot of long sections and subsections. Like some of you mentioned, the Antecedents and 1960s sections are very long and very detailed. Perhaps we could summarize and link the Byrds and Dylan subsections to their main articles so it could read more like a general encyclopedia article?

Thanks! Luridshadow (talk) 18:20, 26 February 2018 (UTC)
 * Welcome Luridshadow! I added a lot of the content present in this article and, as noted in the discussion above, I don't mind if some of the text/information I added is relocated, as long as attribution is maintained. However, I think we also need to be careful not to throw the baby out with the bath water and eliminate material that provides context within this article. For instance, the Beatles' adoption of folk/protest elements and how the band first encountered them in Bob Dylan's music, along with George Harrison's distinctive 12-string Rickenbacker sound and its influence on the Byrds and folk rock in general, are all just as relevant to this article as they might be to the Cultural impact of the Beatles one.

 * As an aside, I've worked very closely on the Byrds article and added a lot of material, bringing it up to Good Article status, and I can say with 100% certainty that there is nothing in this article that isn't already in the Byrds one. So, I would advise against relocating anything there. --Kohoutek1138 (talk) 12:04, 27 February 2018 (UTC)

 * Kohoutek1138, I'm considering separating/bringing out to focus the 12-string guitar section under the British Invasion section because I think that it is a pretty important instrument within Folk music. Any thoughts or suggestions for or against?
 * Thanks! Luridshadow (talk) 20:11, 9 March 2018 (UTC)
 * Go for it. Be bold! It's not my place to say "yay" or "nay", since it's the community's article. If I or another editor have a problem with your edits, they'll revert them and explain why in the edit summary. --Kohoutek1138 (talk) 21:04, 12 March 2018 (UTC)
 * Howdy again! I tried to summarize the American Folk Music Revival Section, Bob Dylan, and the Byrds. It is currently in my Sandbox and I was wondering if you wouldn't mind taking a look at it before I try to make the changes to the main page. User:Luridshadow/sandbox
 * Thanks again! Luridshadow (talk) 20:53, 21 March 2018 (UTC)

Wiki Education Foundation-supported course assignment
This article is or was the subject of a Wiki Education Foundation-supported course assignment. Further details are available on the course page. Student editor(s): Luridshadow.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 21:34, 16 January 2022 (UTC)

How could Dylan have been influenced by a song that wasn't recorded yet?
"Dylan's decision to record with an electric backing band had been influenced by a number of factors, including the Beatles' coupling of folk derived chord progressions and beat music, the Byrds' rock adaptation of "Mr. Tambourine Man." This makes little sense. As it is stated just above that the recording of Bringing it all Back Home was wrapped up before the Byrds recorded Mr. Tambourine Man. 80.216.164.75 (talk) 20:20, 10 November 2023 (UTC)
 * The Byrds' version of "Mr. Tambourine Man" influenced Dylan to record with an electric band because he had come to one of the Byrds' rehearsals in late 1964 and listened to them play it. He liked what the band had done with his song and enthusiasticly exclaimed, "Wow, man! You can dance to that!" This was some months before the start of recording sessions for Bringing It All Back Home. The "Mr. Tambourine Man" article and the main Byrds article have more details on this. I have now added a brief comment with supporting reference explaining this in the relevant "Bob Dylan" section of the article. --Kohoutek1138 (talk) 16:19, 13 November 2023 (UTC)
 * @Kohoutek1138 Thanks for the clarification! 37.205.120.73 (talk) 08:47, 17 November 2023 (UTC)

title: Talk:Folk rock


text:
Talk:Industrial espionage

Requested move

 * The following discussion is an archived discussion of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

No consensus to move. Note that there was a lot of discussion on how to move an article and other discussions about the process. In my opinion it is better to close this and start fresh with a clean nomination. I'll add that WP:COMMONNAME should probably be considered and addressed in any follow on nomination. Also everyone needs to sign their comments! Vegaswikian (talk) 22:13, 18 December 2010 (UTC)

Industrial espionage → Economic and industrial espionage — User:Paddingtonbaer keeps trying to cut/paste move this page. His methods aside, is there anybody who wants to comment on this move request? Yoenit (talk) 20:57, 11 December 2010 (UTC)

Proposed move to new title page entitled 'Economic and industrial espionage'
This would better reflect the scope of the article because it deals with 'economic' and 'industrial' espionage. Though the two are distinct, they are also closely entwined, not justifying separate articles but meriting continuing to recognise the distinction, from the title onwards. Including economic espionage under the title industrial espionage may be inappropriate as it does not fully convey the economic incentive of espionage of this kind which is conducted for the purpose of gaining particular economic advantage, going beyond the mere inveigling of industrial secrets.

No changes will be made to the overall content of the article associated with this move.

I appreciate your questioning of the method - good call! Hope the above explains that there is a very clear rationale for this move which takes account of the article content. PaddingtonBaer 0950hrs GMT 10.12.12 — Preceding unsigned comment added by Paddingtonbaer (talk • contribs) 10:00, 12 December 2010 (UTC)
 * The above discussion is preserved as an archive of the proposal. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

Restored discussion from history
Restored previous discussion - inadvertently deleted - from history for 11th December 2010 - PaddingtonBaer 19:18 GMT 10.12.14
 * I removed it again. The previous discussion was not removed, merely archived. This was done because nearly all of it was several years old and no longer relevant. Yoenit (talk) 19:31, 14 December 2010 (UTC)

Proposed move to new title
Please provide a convincing argument based on the subject content as to why this page should stay named 'industiral espionage' rather than 'economic and industrial espionage' - as proposed - or I will rename the page in a few weeks.

Note to future editors If no argument based on knowledge of the content of the article is provided then please do not try to delete renamed page - thanks!
 * The page was deleted because you did a cut/paste move, not because anybody disagreed with the new title. We have a special tool called Move and you should use that if you want to change the name of a page. You should have wp:autoconfirmed status by now, and be able to move the page with Move (little downward pointing arrow next to the searchbox). Feel free to test it out, as I don't think anybody will object to this move. Yoenit (talk) 19:31, 14 December 2010 (UTC)

Perhaps because the discussion to rename the article "corporate espionage" has not yet even begun.

Mydogtrouble (talk) 18:28, 2 March 2011 (UTC) Great article! Thanks. Another example of industrial espionage was when Global Crossing sued Tyco Submarine for stealing their business plan. I think the suit was more than $1billion.Jksgvb (talk) 06:15, 16 February 2012 (UTC)

No pressure for such or anyx. Do things not pressured about things. — Preceding unsigned comment added by Lyhendq (talk • contribs) 23:53, 20 September 2018 (UTC)

Can this be added to this article?
http://www.reuters.com/article/2014/03/05/us-dupont-china-verdict-idUSBREA241WC20140305 XOttawahitech (talk) 05:05, 7 March 2014 (UTC)

Tiananmen square shooting and the art of Oriental espionage
Much of modern Chinese industrial advances can be traced back to two incidences. One the much planned governmental action that led to the Tiananmen square shooting. Any person with some intelligence and information on how individuals and institutions use very powerful cunning to subdue the wariness of prospective preys will know that this shooting was a very planned action. And very much part of a grand espionage endeavour.

The US swallowed the false incident as true and many of the participants, willing or unwilling, reached the very vitals of US industrial and scientific might.

The second item was not espionage and cannot be discussed here. It was the grandiose idiot-ism of England in giving Hong Kong to China. Literally giving them a platform to stand on a level of equality, which is not there in most Asian language systems. — Preceding unsigned comment added by 117.201.241.8 (talk) 07:57, 22 April 2016 (UTC)

If you are talking about the Transfer of sovereignty over Hong Kong (1997), it was partly based on the terms of the Convention for the Extension of Hong Kong Territory (1898). Instead of the Qing dynasty simply passing the areas to the British Empire, the agreement leased them to the British "for 99 years rent-free". The agreement for the return of Hong Kong to China came with the Sino-British Joint Declaration (1984).

An underlying cause of the agreement was that the United Kingdom in the 1980s was in no condition to military defend Hong Kong in a potential conflict with China. Another was that the water and food supply Hong Kong was largely imported from China. China could easily severe the supply and starve the territory. What would you expect Margaret Thatcher to do, declare a war that she could not win? Dimadick (talk) 09:05, 23 April 2016 (UTC)

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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Industrial espionage


text:
Thomas Waller

Thomas Waller may refer to:

Politics

 * Thomas M. Waller (1840–1924), American politician, Democrat from Connecticut
 * Thomas Waller (fl. 1421–1435), English politician, MP for Guildford
 * Thomas Waller (died 1613) (c. 1569–1613), MP for Dover
 * Thomas Wathen Waller, United Kingdom ambassador to Belgium (1845–1846)

Media

 * Fats Waller (Thomas Waller, 1904–1943), American jazz pianist, organist, composer and comedic entertainer
 * Tom Waller (born 1974), film producer and director

title: Thomas Waller


text:
Business intelligence

Business intelligence (BI) consists of strategies and technologies used by enterprises for the data analysis and management of business information. Common functions of BI technologies include reporting, online analytical processing, analytics, dashboard development, data mining, process mining, complex event processing, business performance management, benchmarking, text mining, predictive analytics, and prescriptive analytics.

BI tools can handle large amounts of structured and sometimes unstructured data to help organisations to identify, develop, and otherwise create new strategic business opportunities. They aim to allow for the easy interpretation of these big data. Identifying new opportunities and implementing an effective strategy based on insights can provide businesses with a competitive market advantage and long-term stability, and help them take strategic decisions.

Business intelligence can be used by enterprises to support a wide range of business decisions ranging from operational to strategic. Basic operating decisions include product positioning or pricing. Strategic business decisions involve priorities, goals, and directions at the broadest level. In all cases, BI is most effective when it combines data derived from the market in which a company operates (external data) with data from company sources internal to the business such as financial and operations data (internal data). When combined, external and internal data can provide a complete picture which, in effect, creates an "intelligence" that cannot be derived from any singular set of data.

Among myriad uses, business intelligence tools empower organizations to gain insight into new markets, to assess demand and suitability of products and services for different market segments, and to gauge the impact of marketing efforts.

BI applications use data gathered from a data warehouse (DW) or from a data mart, and the concepts of BI and DW combine as "BI/DW" or as "BIDW". A data warehouse contains a copy of analytical data that facilitates decision support.

History
The earliest known use of the term business intelligence is in Richard Millar Devens' Cyclopædia of Commercial and Business Anecdotes (1865). Devens used the term to describe how the banker Sir Henry Furnese gained profit by receiving and acting upon information about his environment, prior to his competitors: "Throughout Holland, Flanders, France, and Germany, he maintained a complete and perfect train of business intelligence. The news of the many battles fought was thus received first by him, and the fall of Namur added to his profits, owing to his early receipt of the news."

- Devens

The ability to collect and react accordingly based on the information retrieved, Devens says, is central to business intelligence.

When Hans Peter Luhn, a researcher at IBM, used the term business intelligence in an article published in 1958, he employed the Webster's Dictionary definition of intelligence: "the ability to apprehend the interrelationships of presented facts in such a way as to guide action towards a desired goal."

In 1989, Howard Dresner (later a Gartner analyst) proposed business intelligence as an umbrella term to describe "concepts and methods to improve business decision making by using fact-based support systems." It was not until the late 1990s that this usage was widespread.

Definition
According to Solomon Negash and Paul Gray, business intelligence (BI) can be defined as systems that combine:
 * Data gathering
 * Data storage
 * Knowledge management

with analysis to evaluate complex corporate and competitive information for presentation to planners and decision makers, with the objective of improving the timeliness and the quality of the input to the decision process."

According to Forrester Research, business intelligence is "a set of methodologies, processes, architectures, and technologies that transform raw data into meaningful and useful information used to enable more effective strategic, tactical, and operational insights and decision-making." Under this definition, business intelligence encompasses information management (data integration, data quality, data warehousing, master-data management, text- and content-analytics, et al.). Therefore, Forrester refers to data preparation and data usage as two separate but closely linked segments of the business-intelligence architectural stack.

Some elements of business intelligence are:

 * Multidimensional aggregation and allocation
 * Denormalization, tagging, and standardization
 * Realtime reporting with analytical alert
 * A method of interfacing with unstructured data sources
 * Group consolidation, budgeting, and rolling forecasts
 * Statistical inference and probabilistic simulation
 * Key performance indicators optimization
 * Version control and process management
 * Open item management

Forrester distinguishes this from the business-intelligence market, which is "just the top layers of the BI architectural stack, such as reporting, analytics, and dashboards."

Compared with competitive intelligence
Though the term business intelligence is sometimes a synonym for competitive intelligence (because they both support decision making), BI uses technologies, processes, and applications to analyze mostly internal, structured data and business processes while competitive intelligence gathers, analyzes, and disseminates information with a topical focus on company competitors. If understood broadly, competitive intelligence can be considered as a subset of business intelligence.

Compared with business analytics
Business intelligence and business analytics are sometimes used interchangeably, but there are alternate definitions. Thomas Davenport, professor of information technology and management at Babson College argues that business intelligence should be divided into querying, reporting, Online analytical processing (OLAP), an "alerts" tool, and business analytics. In this definition, business analytics is the subset of BI focusing on statistics, prediction, and optimization, rather than the reporting functionality.

Unstructured data
Business operations can generate a very large amount of data in the form of e-mails, memos, notes from call-centers, news, user groups, chats, reports, web-pages, presentations, image-files, video-files, and marketing material. According to Merrill Lynch, more than 85% of all business information exists in these forms; a company might only use such a document a single time. Because of the way it is produced and stored, this information is either unstructured or semi-structured.

The management of semi-structured data is an unsolved problem in the information technology industry. According to projections from Gartner (2003), white-collar workers spend 30–40% of their time searching, finding, and assessing unstructured data. BI uses both structured and unstructured data. The former is easy to search, and the latter contains a large quantity of the information needed for analysis and decision-making. Because of the difficulty of properly searching, finding, and assessing unstructured or semi-structured data, organizations may not draw upon these vast reservoirs of information, which could influence a particular decision, task, or project. This can ultimately lead to poorly informed decision-making.

Therefore, when designing a business intelligence/DW-solution, the specific problems associated with semi-structured and unstructured data must be accommodated for as well as those for the structured data.

Limitations of semi-structured and unstructured data
There are several challenges to developing BI with semi-structured data. According to Inmon & Nesavich, some of those are:

 * Physically accessing unstructured textual data – unstructured data is stored in a huge variety of formats.
 * Terminology – Among researchers and analysts, there is a need to develop standardized terminology.
 * Volume of data – As stated earlier, up to 85% of all data exists as semi-structured data. Couple that with the need for word-to-word and semantic analysis.
 * Searchability of unstructured textual data – A simple search on some data, e.g. apple, results in links where there is a reference to that precise search term. (Inmon & Nesavich, 2008) gives an example: "a search is made on the term felony. In a simple search, the term felony is used, and everywhere there is a reference to felony, a hit to an unstructured document is made. But a simple search is crude. It does not find references to crime, arson, murder, embezzlement, vehicular homicide, and such, even though these crimes are types of felonies".

Metadata
To solve problems with searchability and assessment of data, it is necessary to know something about the content. This can be done by adding context through the use of metadata. Many systems already capture some metadata (e.g. filename, author, size, etc.), but more useful would be metadata about the actual content – e.g. summaries, topics, people, or companies mentioned. Two technologies designed for generating metadata about content are automatic categorization and information extraction.

Applications
Business intelligence can be applied to the following business purposes:

 * Performance metrics and benchmarking inform business leaders of progress towards business goals. (Business process management).
 * Analytics quantify processes for a business to arrive at optimal decisions, and to perform business knowledge discovery. Analytics may variously involve data mining, process mining, statistical analysis, predictive analytics, predictive modeling, business process modeling, data lineage, complex event processing, and prescriptive analytics. For example within banking industry, academic research has explored potential for BI based analytics in credit evaluation, customer churn management for managerial adoption
 * Reporting, dashboards and data visualization, executive information system, and/or OLAP
 * BI can facilitate collaboration both inside and outside the business by enabling data sharing and electronic data interchange
 * Knowledge management is concerned with the creation, distribution, use, and management of business intelligence, and of business knowledge in general. Knowledge management leads to learning management and regulatory compliance.

Roles
Some common technical roles for business intelligence developers are:

 * Business analyst
 * Data analyst
 * Data engineer
 * Data scientist
 * Database administrator

Risk
In a 2013 report, Gartner categorized business intelligence vendors as either an independent "pure-play" vendor or a consolidated "mega-vendor". In 2019, the BI market was shaken within Europe for the new legislation of GDPR (General Data Protection Regulation) which puts the responsibility of data collection and storage onto the data user with strict laws in place to make sure the data is compliant. Growth within Europe has steadily increased since May 2019 when GDPR was brought. The legislation refocused companies to look at their own data from a compliance perspective but also revealed future opportunities using personalization and external BI providers to increase market share.

title: Business intelligence


text:
Arithmetic progression

An arithmetic progression or arithmetic sequence (AP) is a sequence of numbers such that the difference from any succeeding term to its preceding term remains constant throughout the sequence. The constant difference is called common difference of that arithmetic progression. For instance, the sequence 5, 7, 9, 11, 13, 15,. . . is an arithmetic progression with a common difference of 2.

If the initial term of an arithmetic progression is $$a_1$$ and the common difference of successive members is $$d$$, then the $$n$$-th term of the sequence ($$a_n$$) is given by:
 * $$a_n = a_1 + (n - 1)d$$

A finite portion of an arithmetic progression is called a finite arithmetic progression and sometimes just called an arithmetic progression. The sum of a finite arithmetic progression is called an arithmetic series.

History
According to an anecdote of uncertain reliability, young Carl Friedrich Gauss, who was in primary school, reinvented the formula $$\tfrac{n(n+1)}{2}$$ for summing the integers from 1 through $$n$$, for the case $$n=100$$, by grouping the numbers from both ends of the sequence into pairs summing to 101 and multiplying by the number of pairs. However, regardless of the truth of this story, Gauss was not the first to discover this formula, and some find it likely that its origin goes back to the Pythagoreans in the 5th century BC. Similar rules were known in antiquity to Archimedes, Hypsicles and Diophantus; in China to Zhang Qiujian; in India to Aryabhata, Brahmagupta and Bhaskara II; and in medieval Europe to Alcuin, Dicuil, Fibonacci, Sacrobosco and to anonymous commentators of Talmud known as Tosafists.

Sum
Computation of the sum 2 + 5 + 8 + 11 + 14. When the sequence is reversed and added to itself term by term, the resulting sequence has a single repeated value in it, equal to the sum of the first and last numbers (2 + 14 = 16). Thus 16 × 5 = 80 is twice the sum. The sum of the members of a finite arithmetic progression is called an arithmetic series. For example, consider the sum:

 * $$2 + 5 + 8 + 11 + 14 = 40 $$

This sum can be found quickly by taking the number n of terms being added (here 5), multiplying by the sum of the first and last number in the progression (here 2 + 14 = 16), and dividing by 2:

 * $$\frac{n(a_1 + a_n)}{2}$$

In the case above, this gives the equation:

 * $$2 + 5 + 8 + 11 + 14 = \frac{5(2 + 14)}{2} = \frac{5 \times 16}{2} = 40.$$

This formula works for any real numbers $$a_1$$ and $$a_n$$. For example: this

 * $$\left(-\frac{3}{2}\right) + \left(-\frac{1}{2}\right) + \frac{1}{2} = \frac{3\left(-\frac{3}{2} + \frac{1}{2}\right)}{2} = -\frac{3}{2}.$$

Derivation
To derive the above formula, begin by expressing the arithmetic series in two different ways:
 * $$ S_n=a+a_2+a_3+\dots+a_{(n-1)} +a_n$$
 * $$ S_n=a+(a+d)+(a+2d)+\dots+(a+(n-2)d)+(a+(n-1)d). $$

Rewriting the terms in reverse order:
 * $$ S_n=(a+(n-1)d)+(a+(n-2)d)+\dots+(a+2d)+(a+d)+a.$$

Adding the corresponding terms of both sides of the two equations and halving both sides:
 * $$ S_n=\frac{n}{2}[2a + (n-1)d].$$

This formula can be simplified as:
 * $$\begin{align}

S_n &=\frac{n}{2}[a + a + (n-1)d].\\ &=\frac{n}{2}(a+a_n).\\ &=\frac{n}{2}(\text{initial term}+\text{last term}). \end{align}$$ Furthermore, the mean value of the series can be calculated via: $$S_n / n$$:
 * $$ \overline{a} =\frac{a_1 + a_n}{2}.$$

The formula is very similar to the mean of a discrete uniform distribution.

Product
The product of the members of a finite arithmetic progression with an initial element a1, common differences d, and n elements in total is determined in a closed expression

 * $$a_1a_2a_3\cdots a_n = a_1(a_1+d)(a_1+2d)...(a_1+(n-1)d)= \prod_{k=0}^{n-1} (a_1+kd) = d^n \frac{\Gamma \left(\frac{a_1}{d} + n\right) }{\Gamma \left( \frac{a_1}{d} \right)}$$

where $$\Gamma$$ denotes the Gamma function. The formula is not valid when $$a_1/d$$ is negative or zero.

This is a generalization from the fact that the product of the progression $$1 \times 2 \times \cdots \times n$$ is given by the factorial $$n!$$ and that the product

 * $$m \times (m+1) \times (m+2) \times \cdots \times (n-2) \times (n-1) \times n $$

for positive integers $$m$$ and $$n$$ is given by

 * $$\frac{n!}{(m-1)!}.$$

Derivation

 * $$\begin{align}

a_1a_2a_3\cdots a_n &=\prod_{k=0}^{n-1} (a_1+kd) \\ &= \prod_{k=0}^{n-1} d\left(\frac{a_1}{d}+k\right) = d \left (\frac{a_1}{d}\right) d \left (\frac{a_1}{d}+1 \right )d \left ( \frac{a_1}{d}+2 \right )\cdots d \left ( \frac{a_1}{d}+(n-1) \right ) \\ &= d^n\prod_{k=0}^{n-1} \left(\frac{a_1}{d}+k\right)=d^n {\left(\frac{a_1}{d}\right)}^{\overline{n}} \end{align}$$ where $$x^{\overline{n}}$$ denotes the rising factorial.

By the recurrence formula $$\Gamma(z+1)=z\Gamma(z)$$, valid for a complex number $$z>0$$,

 * $$\Gamma(z+2)=(z+1)\Gamma(z+1)=(z+1)z\Gamma(z)$$,

 * $$\Gamma(z+3)=(z+2)\Gamma(z+2)=(z+2)(z+1)z\Gamma(z)$$,

so that

 * $$ \frac{\Gamma(z+m)}{\Gamma(z)} = \prod_{k=0}^{m-1}(z+k)$$

for $$m$$ a positive integer and $$z$$ a positive complex number.

Thus, if $$a_1/d > 0 $$,

 * $$\prod_{k=0}^{n-1} \left(\frac{a_1}{d}+k\right)= \frac{\Gamma \left(\frac{a_1}{d} + n\right) }{\Gamma \left( \frac{a_1}{d} \right)}$$,

and, finally,

 * $$a_1a_2a_3\cdots a_n = d^n\prod_{k=0}^{n-1} \left(\frac{a_1}{d}+k\right) = d^n \frac{\Gamma \left(\frac{a_1}{d} + n\right) }{\Gamma \left( \frac{a_1}{d} \right)} $$

Examples
Taking the example $$ 3, 8, 13, 18, 23, 28, \ldots $$, the product of the terms of the arithmetic progression given by $$a_n = 3 + 5(n-1) $$ up to the 50th term is
 * Example 1
 * $$P_{50} = 5^{50} \cdot \frac{\Gamma \left(3/5 + 50\right) }{\Gamma \left( 3 / 5 \right) } \approx 3.78438 \times 10^{98}. $$

The product of the first 10 odd numbers $$(1,3,5,7,9,11,13,15,17,19)$$ is given by
 * Example 2
 * $$ 1\cdot 3\cdot 5\cdots 19 =\prod_{k=0}^{9} (1+2k) = 2^{10} \cdot \frac{\Gamma \left(\frac{1}{2} + 10\right) }{\Gamma \left( \frac{1}{2} \right) } $$ = 654,729,075

Standard deviation
The standard deviation of any arithmetic progression can be calculated as

 * $$ \sigma = |d|\sqrt{\frac{(n-1)(n+1)}{12}}$$

where $$ n$$ is the number of terms in the progression and $$ d$$ is the common difference between terms. The formula is very similar to the standard deviation of a discrete uniform distribution.

Intersections
The intersection of any two doubly infinite arithmetic progressions is either empty or another arithmetic progression, which can be found using the Chinese remainder theorem. If each pair of progressions in a family of doubly infinite arithmetic progressions have a non-empty intersection, then there exists a number common to all of them; that is, infinite arithmetic progressions form a Helly family. However, the intersection of infinitely many infinite arithmetic progressions might be a single number rather than itself being an infinite progression.

title: Arithmetic progression


text:
Polystyrene

Polystyrene (PS) is a synthetic polymer made from monomers of the aromatic hydrocarbon styrene. Polystyrene can be solid or foamed. General-purpose polystyrene is clear, hard, and brittle. It is an inexpensive resin per unit weight. It is a poor barrier to air and water vapor and has a relatively low melting point. Polystyrene is one of the most widely used plastics, with the scale of its production being several million tonnes per year. Polystyrene is naturally transparent, but can be colored with colorants. Uses include protective packaging (such as packing peanuts and in the jewel cases used for storage of optical discs such as CDs and occasionally DVDs), containers, lids, bottles, trays, tumblers, disposable cutlery, in the making of models, and as an alternative material for phonograph records.

As a thermoplastic polymer, polystyrene is in a solid (glassy) state at room temperature but flows if heated above about 100 °C, its glass transition temperature. It becomes rigid again when cooled. This temperature behaviour is exploited for extrusion (as in Styrofoam) and also for molding and vacuum forming, since it can be cast into molds with fine detail. The temperatures behavior can be controlled by photocrosslinking.

Under ASTM standards, polystyrene is regarded as not biodegradable. It is accumulating as a form of litter in the outside environment, particularly along shores and waterways, especially in its foam form, and in the Pacific Ocean.

History
Polystyrene was discovered in 1839 by Eduard Simon, an apothecary from Berlin. From storax, the resin of the Oriental sweetgum tree Liquidambar orientalis, he distilled an oily substance, that he named styrol, now called styrene. Several days later, Simon found that it had thickened into a jelly, now known to have been a polymer, that he dubbed styrol oxide ("Styroloxyd") because he presumed that it had resulted from oxidation (styrene oxide is a distinct compound). By 1845 Jamaican-born chemist John Buddle Blyth and German chemist August Wilhelm von Hofmann showed that the same transformation of styrol took place in the absence of oxygen. They called the product "meta styrol"; analysis showed that it was chemically identical to Simon's Styroloxyd. In 1866 Marcellin Berthelot correctly identified the formation of meta styrol/Styroloxyd from styrol as a polymerisation process. About 80 years later it was realized that heating of styrol starts a chain reaction that produces macromolecules, following the thesis of German organic chemist Hermann Staudinger (1881–1965). This eventually led to the substance receiving its present name, polystyrene.

The company I. G. Farben began manufacturing polystyrene in Ludwigshafen, about 1931, hoping it would be a suitable replacement for die-cast zinc in many applications. Success was achieved when they developed a reactor vessel that extruded polystyrene through a heated tube and cutter, producing polystyrene in pellet form.

Ray McIntire (1918–1996), a chemical engineer of Dow Chemical, rediscovered a process first patented in early 1930s by Swedish inventor Carl Munters. According to the Science History Institute, "Dow bought the rights to Munters's method and began producing a lightweight, water-resistant, and buoyant material that seemed perfectly suited for building docks and watercraft and for insulating homes, offices, and chicken sheds." In 1944, Styrofoam was patented.

Before 1949, chemical engineer Fritz Stastny (1908–1985) developed pre-expanded PS beads by incorporating aliphatic hydrocarbons, such as pentane. These beads are the raw material for molding parts or extruding sheets. BASF and Stastny applied for a patent that was issued in 1949. The molding process was demonstrated at the Kunststoff Messe 1952 in Düsseldorf. Products were named Styropor.

The crystal structure of isotactic polystyrene was reported by Giulio Natta.

In 1954, the Koppers Company in Pittsburgh, Pennsylvania, developed expanded polystyrene (EPS) foam under the trade name Dylite. In 1960, Dart Container, the largest manufacturer of foam cups, shipped their first order.

Structure
In chemical terms, polystyrene is a long chain hydrocarbon wherein alternating carbon centers are attached to phenyl groups (a derivative of benzene). Polystyrene's chemical formula is ; it contains the chemical elements carbon and hydrogen.

The material's properties are determined by short-range van der Waals attractions between polymer chains. Since the molecules consist of thousands of atoms, the cumulative attractive force between the molecules is large. When heated (or deformed at a rapid rate, due to a combination of viscoelastic and thermal insulation properties), the chains can take on a higher degree of confirmation and slide past each other. This intermolecular weakness (versus the high intramolecular strength due to the hydrocarbon backbone) confers flexibility and elasticity. The ability of the system to be readily deformed above its glass transition temperature allows polystyrene (and thermoplastic polymers in general) to be readily softened and molded upon heating. Extruded polystyrene is about as strong as an unalloyed aluminium but much more flexible and much less dense (1.05 g/cm3 for polystyrene vs. 2.70 g/cm3 for aluminium).

Production
Polystyrene is an addition polymer that results when styrene monomers polymerize (interconnect). In the polymerization, the carbon-carbon π bond of the vinyl group is broken and a new carbon-carbon σ bond is formed, attaching to the carbon of another styrene monomer to the chain. Since only one kind of monomer is used in its preparation, it is a homopolymer. The newly formed σ bond is stronger than the π bond that was broken, thus it is difficult to depolymerize polystyrene. About a few thousand monomers typically comprise a chain of polystyrene, giving a molar mass of 100,000–400,000 g/mol.

Each carbon of the backbone has tetrahedral geometry, and those carbons that have a phenyl group (benzene ring) attached are stereogenic. If the backbone were to be laid as a flat elongated zig-zag chain, each phenyl group would be tilted forward or backward compared to the plane of the chain.

The relative stereochemical relationship of consecutive phenyl groups determines the tacticity, which affects various physical properties of the material.

Tacticity
In polystyrene, tacticity describes the extent to which the phenyl group is uniformly aligned (arranged at one side) in the polymer chain. Tacticity has a strong effect on the properties of the plastic. Standard polystyrene is atactic. The diastereomer where all of the phenyl groups are on the same side is called isotactic polystyrene, which is not produced commercially.

Atactic polystyrene
The only commercially important form of polystyrene is atactic, in which the phenyl groups are randomly distributed on both sides of the polymer chain. This random positioning prevents the chains from aligning with sufficient regularity to achieve any crystallinity. The plastic has a glass transition temperature Tg of ~90 °C. Polymerization is initiated with free radicals.

Syndiotactic polystyrene
Ziegler–Natta polymerization can produce an ordered syndiotactic polystyrene with the phenyl groups positioned on alternating sides of the hydrocarbon backbone. This form is highly crystalline with a Tm (melting point) of 270 C. Syndiotactic polystyrene resin is currently produced under the trade name XAREC by Idemitsu corporation, who use a metallocene catalyst for the polymerisation reaction.

Degradation
Polystyrene is relatively chemically inert. While it is waterproof and resistant to breakdown by many acids and bases, it is easily attacked by many organic solvents (e.g. it dissolves quickly when exposed to acetone), chlorinated solvents, and aromatic hydrocarbon solvents. Because of its resilience and inertness, it is used for fabricating many objects of commerce. Like other organic compounds, polystyrene burns to give carbon dioxide and water vapor, in addition to other thermal degradation by-products. Polystyrene, being an aromatic hydrocarbon, typically combusts incompletely as indicated by the sooty flame.

The process of depolymerizing polystyrene into its monomer, styrene, is called pyrolysis. This involves using high heat and pressure to break down the chemical bonds between each styrene compound. Pyrolysis usually goes up to 430 °C. The high energy cost of doing this has made commercial recycling of polystyrene back into styrene monomer difficult.

Organisms
Polystyrene is generally considered to be non-biodegradable. However, certain organisms are able to degrade it, albeit very slowly.

In 2015, researchers discovered that mealworms, the larvae form of the darkling beetle Tenebrio molitor, could digest and subsist healthily on a diet of EPS. About 100 mealworms could consume between 34 and 39 milligrams of this white foam in a day. The droppings of mealworm were found to be safe for use as soil for crops.

In 2016, it was also reported that superworms (Zophobas morio) may eat expanded polystyrene (EPS). A group of high school students in Ateneo de Manila University found that compared to Tenebrio molitor larvae, Zophobas morio larvae may consume greater amounts of EPS over longer periods of time.

In 2022 scientists identified several bacterial genera, including Pseudomonas, Rhodococcus and Corynebacterium, in the gut of superworms that contain encoded enzymes associated with the degradation of polystyrene and the breakdown product styrene.

The bacterium Pseudomonas putida is capable of converting styrene oil into the biodegradable plastic PHA. This may someday be of use in the effective disposing of polystyrene foam. It is worthy to note the polystyrene must undergo pyrolysis to turn into styrene oil.

Forms produced
Polystyrene is commonly injection molded, vacuum formed, or extruded, while expanded polystyrene is either extruded or molded in a special process. Polystyrene copolymers are also produced; these contain one or more other monomers in addition to styrene. In recent years the expanded polystyrene composites with cellulose and starch have also been produced. Polystyrene is used in some polymer-bonded explosives (PBX).

Sheet or molded polystyrene
Polystyrene (PS) is used for producing disposable plastic cutlery and dinnerware, CD "jewel" cases, smoke detector housings, license plate frames, plastic model assembly kits, and many other objects where a rigid, economical plastic is desired. Production methods include thermoforming (vacuum forming) and injection molding.

Polystyrene Petri dishes and other laboratory containers such as test tubes and microplates play an important role in biomedical research and science. For these uses, articles are almost always made by injection molding, and often sterilized post-molding, either by irradiation or by treatment with ethylene oxide. Post-mold surface modification, usually with oxygen-rich plasmas, is often done to introduce polar groups. Much of modern biomedical research relies on the use of such products; they, therefore, play a critical role in pharmaceutical research.

Thin sheets of polystyrene are used in polystyrene film capacitors as it forms a very stable dielectric, but has largely fallen out of use in favor of polyester.

Foams
Polystyrene foams are 95–98% air. Polystyrene foams are good thermal insulators and are therefore often used as building insulation materials, such as in insulating concrete forms and structural insulated panel building systems. Grey polystyrene foam, incorporating graphite, has superior insulation properties.

Carl Munters and John Gudbrand Tandberg of Sweden received a US patent for polystyrene foam as an insulation product in 1935 (USA patent number 2,023,204).

PS foams also exhibit good damping properties, therefore it is used widely in packaging. The trademark Styrofoam by Dow Chemical Company is informally used (mainly US & Canada) for all foamed polystyrene products, although strictly it should only be used for "extruded closed-cell" polystyrene foams made by Dow Chemicals.

Foams are also used for non-weight-bearing architectural structures (such as ornamental pillars).

Expanded polystyrene (EPS)

Expanded polystyrene (EPS) is a rigid and tough, closed-cell foam with a normal density range of 11 to 32 kg/m3. It is usually white and made of pre-expanded polystyrene beads. The manufacturing process for EPS conventionally begins with the creation of small polystyrene beads. Styrene monomers (and potentially other additives) are suspended in water, where they undergo free-radical addition polymerization. The polystyrene beads formed by this mechanism may have an average diameter of around 200 μm. The beads are then permeated with a "blowing agent", a material that enables the beads to be expanded. Pentane is commonly used as the blowing agent. The beads are added to a continuously agitated reactor with the blowing agent, among other additives, and the blowing agent seeps into pores within each bead. The beads are then expanded using steam.

EPS is used for food containers, molded sheets for building insulation, and packing material either as solid blocks formed to accommodate the item being protected or as loose-fill "peanuts" cushioning fragile items inside boxes. EPS also has been widely used in automotive and road safety applications such as motorcycle helmets and road barriers on automobile race tracks.

A significant portion of all EPS products are manufactured through injection molding. Mold tools tend to be manufactured from steels (which can be hardened and plated), and aluminum alloys. The molds are controlled through a split via a channel system of gates and runners. EPS is colloquially called "styrofoam" in the United States and Canada, an incorrectly applied genericization of Dow Chemical's brand of extruded polystyrene.

EPS in building construction
Sheets of EPS are commonly packaged as rigid panels (common in Europe is a size of 100 cm x 50 cm, usually depending on an intended type of connection and glue techniques, it is, in fact, 99.5 cm x 49.5 cm or 98 cm x 48 cm; less common is 120 x 60 cm; size 4 by or 2 by in the United States). Common thicknesses are from 10 mm to 500 mm. Many customizations, additives, and thin additional external layers on one or both sides are often added to help with various properties. An example of this is lamination with cement board to form a structural insulated panel.

Thermal conductivity is measured according to EN 12667. Typical values range from 0.032 to 0.038 W/(m⋅K) depending on the density of the EPS board. The value of 0.038 W/(m⋅K) was obtained at 15 kg/m3 while the value of 0.032 W/(m⋅K) was obtained at 40 kg/m3 according to the datasheet of K-710 from StyroChem Finland. Adding fillers (graphites, aluminum, or carbons) has recently allowed the thermal conductivity of EPS to reach around 0.030–0.034 W/(m⋅K) (as low as 0.029 W/(m⋅K)) and as such has a grey/black color which distinguishes it from standard EPS. Several EPS producers have produced a variety of these increased thermal resistance EPS usage for this product in the UK and EU.

Water vapor diffusion resistance (μ) of EPS is around 30–70.

ICC-ES (International Code Council Evaluation Service) requires EPS boards used in building construction meet ASTM C578 requirements. One of these requirements is that the limiting oxygen index of EPS as measured by ASTM D2863 be greater than 24 volume %. Typical EPS has an oxygen index of around 18 volume %; thus, a flame retardant is added to styrene or polystyrene during the formation of EPS.

The boards containing a flame retardant when tested in a tunnel using test method UL 723 or ASTM E84 will have a flame spread index of less than 25 and a smoke-developed index of less than 450. ICC-ES requires the use of a 15-minute thermal barrier when EPS boards are used inside of a building.

According to the EPS-IA ICF organization, the typical density of EPS used for insulated concrete forms (expanded polystyrene concrete) is 1.35 to 1.80 lb/ft3. This is either Type II or Type IX EPS according to ASTM C578. EPS blocks or boards used in building construction are commonly cut using hot wires.

Extruded polystyrene (XPS)

Extruded polystyrene foam (XPS) consists of closed cells. It offers improved surface roughness, higher stiffness and reduced thermal conductivity. The density range is about 28–34 kg/m3.

Extruded polystyrene material is also used in crafts and model building, in particular architectural models. Because of the extrusion manufacturing process, XPS does not require facers to maintain its thermal or physical property performance. Thus, it makes a more uniform substitute for corrugated cardboard. Thermal conductivity varies between 0.029 and 0.039 W/(m·K) depending on bearing strength/density and the average value is ~0.035 W/(m·K).

Water vapor diffusion resistance (μ) of XPS is around 80–250.

Commonly extruded polystyrene foam materials include:
 * Styrofoam, also known as Blue Board, produced by DuPont
 * Depron, a thin insulation sheet also used for model building

Water absorption of polystyrene foams
Although it is a closed-cell foam, both expanded and extruded polystyrene are not entirely waterproof or vapor proof. In expanded polystyrene there are interstitial gaps between the expanded closed-cell pellets that form an open network of channels between the bonded pellets, and this network of gaps can become filled with liquid water. If the water freezes into ice, it expands and can cause polystyrene pellets to break off from the foam. Extruded polystyrene is also permeable by water molecules and can not be considered a vapor barrier.

Water-logging commonly occurs over a long period in polystyrene foams that are constantly exposed to high humidity or are continuously immersed in water, such as in hot tub covers, in floating docks, as supplemental flotation under boat seats, and for below-grade exterior building insulation constantly exposed to groundwater. Typically an exterior vapor barrier such as impermeable plastic sheeting or a sprayed-on coating is necessary to prevent saturation.

Oriented polystyrene
Oriented polystyrene (OPS) is produced by stretching extruded PS film, improving visibility through the material by reducing haziness and increasing stiffness. This is often used in packaging where the manufacturer would like the consumer to see the enclosed product. Some benefits to OPS are that it is less expensive to produce than other clear plastics such as polypropylene (PP), (PET), and high-impact polystyrene (HIPS), and it is less hazy than HIPS or PP. The main disadvantage of OPS is that it is brittle, and will crack or tear easily.

Co-polymers
Ordinary (homopolymeric) polystyrene has an excellent property profile about transparency, surface quality and stiffness. Its range of applications is further extended by copolymerization and other modifications (blends e.g. with PC and syndiotactic polystyrene). Several copolymers are used based on styrene: The brittleness of homopolymeric polystyrene is overcome by elastomer-modified styrene-butadiene copolymers. Copolymers of styrene and acrylonitrile (SAN) are more resistant to thermal stress, heat and chemicals than homopolymers and are also transparent. Copolymers called ABS have similar properties and can be used at low temperatures, but they are opaque.

Styrene-butane co-polymers
Styrene-butane co-polymers can be produced with a low butene content. Styrene-butane co-polymers include PS-I and SBC (see below), both co-polymers are impact resistant. PS-I is prepared by graft co-polymerization, SBC by anionic block co-polymerization, which makes it transparent in case of appropriate block size.

If styrene-butane co-polymer has a high butylene content, styrene-butadiene rubber (SBR) is formed.

The impact strength of styrene-butadiene co-polymers is based on phase separation, polystyrene and poly-butane are not soluble in each other (see Flory–Huggins solution theory). Co-polymerization creates a boundary layer without complete mixing. The butadiene fractions (the "rubber phase") assemble to form particles embedded in a polystyrene matrix. A decisive factor for the improved impact strength of styrene-butadiene copolymers is their higher absorption capacity for deformation work. Without applied force, the rubber phase initially behaves like a filler. Under tensile stress, crazes (microcracks) are formed, which spread to the rubber particles. The energy of the propagating crack is then transferred to the rubber particles along its path. A large number of cracks give the originally rigid material a laminated structure. The formation of each lamella contributes to the consumption of energy and thus to an increase in elongation at break. Polystyrene homo-polymers deform when a force is applied until they break. Styrene-butane co-polymers do not break at this point, but begin to flow, solidify to tensile strength and only break at much higher elongation.

With a high proportion of polybutadiene, the effect of the two phases is reversed. Styrene-butadiene rubber behaves like an elastomer but can be processed like a thermoplastic.

Impact-resistant polystyrene (PS-I)
PS-I ( i mpact resistant  p oly s tyrene) consists of a continuous polystyrene matrix and a rubber phase dispersed therein. It is produced by polymerization of styrene in the presence of polybutadiene dissolved (in styrene). Polymerization takes place simultaneously in two ways:

 * Graft copolymerization: The growing polystyrene chain reacts with a double bond of the polybutadiene. As a result, several polystyrene chains are attached to one polybutadiene.
 * S represents in the figure the styrene repeat unit
 * B the butadiene repeat unit. However, the middle block often does not consist of such depicted butane homo-polymer but of a styrene-butadiene co-polymer:

 * SSSSSSSSSSSSSSSSSSS BB S BB S B  S BBBB S B  SS BBB S B SSSSSSSSSSSSSSSSSSSSSSSSSSSSS S

By using a statistical copolymer at this position, the polymer becomes less susceptible to cross-linking and flows better in the melt. For the production of SBS, the first styrene is homopolymerized via anionic copolymerization. Typically, an organometallic compound such as butyllithium is used as a catalyst. Butadiene is then added and after styrene again its polymerization. The catalyst remains active during the whole process (for which the used chemicals must be of high purity). The molecular weight distribution of the polymers is very low (polydispersity in the range of 1.05, the individual chains have thus very similar lengths). The length of the individual blocks can be adjusted by the ratio of catalyst to monomer. The size of the rubber sections, in turn, depends on the block length. The production of small structures (smaller than the wavelength of the light) ensure transparency. In contrast to PS-I, however, the block copolymer does not form any particles but has a lamellar structure.

Styrene-butadiene rubber
Styrene-butadiene rubber (SBR) is produced like PS-I by graft copolymerization, but with a lower styrene content. Styrene-butadiene rubber thus consists of a rubber matrix with a polystyrene phase dispersed therein. Unlike PS-I and SBC, it is not a thermoplastic, but an elastomer. Within the rubber phase, the polystyrene phase is assembled into domains. This causes physical cross-linking on a microscopic level. When the material is heated above the glass transition point, the domains disintegrate, the cross-linking is temporarily suspended and the material can be processed like a thermoplastic.

Acrylonitrile butadiene styrene
Acrylonitrile butadiene styrene (ABS) is a material that is stronger than pure polystyrene.

Others
SMA is a copolymer with maleic anhydride. Styrene can be copolymerized with other monomers; for example, divinylbenzene can be used for cross-linking the polystyrene chains to give the polymer used in solid phase peptide synthesis. Styrene-acrylonitrile resin (SAN) has a greater thermal resistance than pure styrene.

Production
Polystyrene foams are produced using blowing agents that form bubbles and expand the foam. In expanded polystyrene, these are usually hydrocarbons such as pentane, which may pose a flammability hazard in manufacturing or storage of newly manufactured material, but have relatively mild environmental impact. Extruded polystyrene is usually made with hydrofluorocarbons (HFC-134a), which have global warming potentials of approximately 1000–1300 times that of carbon dioxide. Packaging, particularly expanded polystyrene, is a contributor of microplastics from both land and maritime activities.

Environmental degradation
Polystyrene is not biodegradeable but it is susceptible to photo-oxidation. For this reason commercial products contain light stabilizers.

Litter
Animals do not recognize polystyrene foam as an artificial material and may even mistake it for food. Polystyrene foam blows in the wind and floats on water due to its low specific gravity. It can have serious effects on the health of birds and marine animals that swallow significant quantities. Juvenile rainbow trout exposed to polystyrene fragments show toxic effects in the form of substantial histomorphometrical changes.

Reducing
Restricting the use of foamed polystyrene takeout food packaging is a priority of many solid waste environmental organisations. Efforts have been made to find alternatives to polystyrene, especially foam in restaurant settings. The original impetus was to eliminate chlorofluorocarbons (CFC), which was a former component of foam.

United States
In 1987, Berkeley, California, banned CFC food containers. The following year, Suffolk County, New York, became the first U.S. jurisdiction to ban polystyrene in general. However, legal challenges by the Society of the Plastics Industry kept the ban from going into effect until at last it was delayed when the Republican and Conservative parties gained the majority of the county legislature. In the meantime, Berkeley became the first city to ban all foam food containers. As of 2006, about one hundred localities in the United States, including Portland, Oregon, and San Francisco had some sort of ban on polystyrene foam in restaurants. For instance, in 2007 Oakland, California, required restaurants to switch to disposable food containers that would biodegrade if added to food compost. In 2013, San Jose became reportedly the largest city in the country to ban polystyrene foam food containers. Some communities have implemented wide polystyrene bans, such as Freeport, Maine, which did so in 1990. In 1988, the first U.S. ban of general polystyrene foam was enacted in Berkeley, California.

On 1 July 2015, New York City became the largest city in the United States to attempt to prohibit the sale, possession, and distribution of single-use polystyrene foam (the initial decision was overturned on appeal). In San Francisco, supervisors approved the toughest ban on "Styrofoam" (EPS) in the US which went into effect 1 January 2017. The city's Department of the Environment can make exceptions for certain uses like shipping medicines at prescribed temperatures.

The U.S. Green Restaurant Association does not allow polystyrene foam to be used as part of its certification standard. Several green leaders, including the Dutch Ministry of the Environment, advise people to reduce their environmental harm by using reusable coffee cups.

In March 2019, Maryland banned polystyrene foam food containers and became the first state in the country to pass a food container foam ban through the state legislature. Maine was the first state to officially get a foam food container ban onto the books. In May 2019, Maryland Governor Hogan allowed the foam ban (House Bill 109) to become law without a signature making Maryland the second state to have a food container foam ban on the books, but is the first one to take effect on 1 July 2020.

In September 2020, the New Jersey state legislature voted to ban disposable foam food containers and cups made of polystyrene foam.

Outside the United States
China banned expanded polystyrene takeout/takeaway containers and tableware around 1999. However, compliance has been a problem and, in 2013, the Chinese plastics industry was lobbying for the ban's repeal.

India and Taiwan also banned polystyrene-foam food-service ware before 2007.

The government of Zimbabwe, through its Environmental Management Agency (EMA), banned polystyrene containers (popularly called 'kaylite' in the country), under Statutory Instrument 84 of 2012 (Plastic Packaging and Plastic Bottles) (Amendment) Regulations, 2012 (No 1.)

The city of Vancouver, Canada, has announced its Zero Waste 2040 plan in 2018. The city will introduce bylaw amendments to prohibit business license holders from serving prepared food in polystyrene foam cups and take-out containers, beginning 1 June 2019.

In 2019, the European union voted to ban expanded polystyrene food packaging and cups, with the law officially going into effect in 2021.

Fiji passed the Environmental Management Bill in December 2020. Imports of polystyrene products were banned in January 2021.

Recycling

In general, polystyrene is not accepted in curbside collection recycling programs and is not separated and recycled where it is accepted. In Germany, polystyrene is collected as a consequence of the packaging law (Verpackungsverordnung) that requires manufacturers to take responsibility for recycling or disposing of any packaging material they sell.

Most polystyrene products are currently not recycled due to the lack of incentive to invest in the compactors and logistical systems required. Due to the low density of polystyrene foam, it is not economical to collect. However, if the waste material goes through an initial compaction process, the material changes density from typically 30 kg/m3 to 330 kg/m3 and becomes a recyclable commodity of high value for producers of recycled plastic pellets. Expanded polystyrene scrap can be easily added to products such as EPS insulation sheets and other EPS materials for construction applications; many manufacturers cannot obtain sufficient scrap because of collection issues. When it is not used to make more EPS, foam scrap can be turned into products such as clothes hangers, park benches, flower pots, toys, rulers, stapler bodies, seedling containers, picture frames, and architectural molding from recycled PS. As of 2016, around 100 tonnes of EPS are recycled every month in the UK.

Recycled EPS is also used in many metal casting operations. Rastra is made from EPS that is combined with cement to be used as an insulating amendment in the making of concrete foundations and walls. American manufacturers have produced insulating concrete forms made with approximately 80% recycled EPS since 1993.

Upcycling
A March 2022 joint study by scientists Sewon Oh and Erin Stache at Cornell University in Ithaca, New York found a new processing method of upcycling polystyrene to benzoic acid. The process involved irradiation of polystyrene with iron chloride and acetone under white light and oxygen for 20 hours. The scientists also demonstrated a similar scalable commercial process of upcycling polystyrene into valulable small-molecules (like benzoic acid) taking just a few hours.

Incineration
If polystyrene is properly incinerated at high temperatures (up to 1000 °C ) and with plenty of air (14 m3/kg), the chemicals generated are water, carbon dioxide, and possibly small amounts of residual halogen-compounds from flame-retardants. If only incomplete incineration is done, there will also be leftover carbon soot and a complex mixture of volatile compounds. According to the American Chemistry Council, when polystyrene is incinerated in modern facilities, the final volume is 1% of the starting volume; most of the polystyrene is converted into carbon dioxide, water vapor, and heat. Because of the amount of heat released, it is sometimes used as a power source for steam or electricity generation.

When polystyrene was burned at temperatures of 800–900 °C (the typical range of a modern incinerator), the products of combustion consisted of "a complex mixture of polycyclic aromatic hydrocarbons (PAHs) from alkyl benzenes to benzoperylene. Over 90 different compounds were identified in combustion effluents from polystyrene." The American National Bureau of Standards Center for Fire Research found 57 chemical by-products released during the combustion of expanded polystyrene (EPS) foam.

Health
The American Chemistry Council, formerly known as the Chemical Manufacturers' Association, writes: "Based on scientific tests over five decades, government safety agencies have determined that polystyrene is safe for use in foodservice products. For example, polystyrene meets the stringent standards of the U.S. Food and Drug Administration and the European Commission/European Food Safety Authority for use in packaging to store and serve food. The Hong Kong Food and Environmental Hygiene Department recently reviewed the safety of serving various foods in polystyrene foodservice products and reached the same conclusion as the U.S. FDA."

From 1999 to 2002, a comprehensive review of the potential health risks associated with exposure to styrene was conducted by a 12-member international expert panel selected by the Harvard Center for Risk Assessment. The scientists had expertise in toxicology, epidemiology, medicine, risk analysis, pharmacokinetics, and exposure assessment. The Harvard study reported that styrene is naturally present in trace quantities in foods such as strawberries, beef, and spices, and is naturally produced in the processing of foods such as wine and cheese. The study also reviewed all the published data on the quantity of styrene contributing to the diet due to migration of food packaging and disposable food contact articles, and concluded that risk to the general public from exposure to styrene from foods or food-contact applications (such as polystyrene packaging and foodservice containers) was at levels too low to produce adverse effects.

Polystyrene is commonly used in containers for food and drinks. The styrene monomer (from which polystyrene is made) is a cancer suspect agent. Styrene is "generally found in such low levels in consumer products that risks aren't substantial". Polystyrene which is used for food contact may not contain more than 1% (0.5% for fatty foods) of styrene by weight. Styrene oligomers in polystyrene containers used for food packaging have been found to migrate into the food. Another Japanese study conducted on wild-type and AhR-null mice found that the styrene trimer, which the authors detected in cooked polystyrene container-packed instant foods, may increase thyroid hormone levels.

Whether polystyrene can be microwaved with food is controversial. Some containers may be safely used in a microwave, but only if labeled as such. Some sources suggest that foods containing carotene (vitamin A) or cooking oils must be avoided.

Because of the pervasive use of polystyrene, these serious health related issues remain topical.

Fire hazards
Like other organic compounds, polystyrene is flammable. Polystyrene is classified according to DIN4102 as a "B3" product, meaning highly flammable or "Easily Ignited". As a consequence, although it is an efficient insulator at low temperatures, its use is prohibited in any exposed installations in building construction if the material is not flame-retardant. It must be concealed behind drywall, sheet metal, or concrete. Foamed polystyrene plastic materials have been accidentally ignited and caused huge fires and losses of life, for example at the Düsseldorf International Airport and in the Channel Tunnel (where polystyrene was inside a railway carriage that caught fire).

title: Polystyrene


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Styrene

Styrene is an organic compound with the chemical formula C6H5CH=CH2. Its structure consists of a vinyl group as substituent on benzene. Styrene is a colorless, oily liquid, although aged samples can appear yellowish. The compound evaporates easily and has a sweet smell, although high concentrations have a less pleasant odor. Styrene is the precursor to polystyrene and several copolymers, and is typically made from benzene for this purpose. Approximately 25 million tonnes of styrene were produced in 2010, increasing to around 35 million tonnes by 2018.

Natural occurrence
Styrene is named after storax balsam (often commercially sold as styrax), the resin of Liquidambar trees of the Altingiaceae plant family. Styrene occurs naturally in small quantities in some plants and foods (cinnamon, coffee beans, balsam trees and peanuts) and is also found in coal tar.

History
In 1839, the German apothecary Eduard Simon isolated a volatile liquid from the resin (called storax or styrax (Latin)) of the American sweetgum tree (Liquidambar styraciflua). He called the liquid "styrol" (now called styrene). He also noticed that when styrol was exposed to air, light, or heat, it gradually transformed into a hard, rubber-like substance, which he called "styrol oxide".

By 1845, the German chemist August Wilhelm von Hofmann and his student John Buddle Blyth had determined styrene's empirical formula: C8H8. They had also determined that Simon's "styrol oxide" – which they renamed "metastyrol" – had the same empirical formula as styrene. Furthermore, they could obtain styrene by dry-distilling "metastyrol".

In 1865, the German chemist Emil Erlenmeyer found that styrene could form a dimer, and in 1866 the French chemist Marcelin Berthelot stated that "metastyrol" was a polymer of styrene (i.e. polystyrene). Meanwhile, other chemists had been investigating another component of storax, namely, cinnamic acid. They had found that cinnamic acid could be decarboxylated to form "cinnamene" (or "cinnamol"), which appeared to be styrene.

In 1845, French chemist Emil Kopp suggested that the two compounds were identical, and in 1866, Erlenmeyer suggested that both "cinnamol" and styrene might be vinylbenzene. However, the styrene that was obtained from cinnamic acid seemed different from the styrene that was obtained by distilling storax resin: the latter was optically active. Eventually, in 1876, the Dutch chemist van 't Hoff resolved the ambiguity: the optical activity of the styrene that was obtained by distilling storax resin was due to a contaminant.

From ethylbenzene
The vast majority of styrene is produced from ethylbenzene, and almost all ethylbenzene produced worldwide is intended for styrene production. As such, the two production processes are often highly integrated. Ethylbenzene is produced via a Friedel–Crafts reaction between benzene and ethene; originally this used aluminum chloride as a catalyst, but in modern production this has been replaced by zeolites.

By dehydrogenation
Around 80% of styrene is produced by the dehydrogenation of ethylbenzene. This is achieved using superheated steam (up to 600 °C) over an iron(III) oxide catalyst. The reaction is highly endothermic and reversible, with a typical yield of 88–94%.

 * StyreneProduction.svg

The crude ethylbenzene/styrene product is then purified by distillation. As the difference in boiling points between the two compounds is only 9 °C at ambient pressure this necessitates the use of a series of distillation columns. This is energy intensive and is further complicated by the tendency of styrene to undergo thermally induced polymerisation into polystyrene, requiring the continuous addition of polymerization inhibitor to the system.

Via ethylbenzene hydroperoxide
Styrene is also co-produced commercially in a process known as POSM (Lyondell Chemical Company) or SM/PO (Shell) for styrene monomer / propylene oxide. In this process, ethylbenzene is treated with oxygen to form the ethylbenzene hydroperoxide. This hydroperoxide is then used to oxidize propylene to propylene oxide, which is also recovered as a co-product. The remaining 1-phenylethanol is dehydrated to give styrene:

 * Styrol synthesis.svg

Pyrolysis gasoline extraction
Extraction from pyrolysis gasoline is performed on a limited scale.

From toluene and methanol
Styrene can be produced from toluene and methanol, which are cheaper raw materials than those in the conventional process. This process has suffered from low selectivity associated with the competing decomposition of methanol. Exelus Inc. claims to have developed this process with commercially viable selectivities, at 400–425 °C and atmospheric pressure, by forcing these components through a proprietary zeolitic catalyst. It is reported that an approximately 9:1 mixture of styrene and ethylbenzene is obtained, with a total styrene yield of over 60%.

From benzene and ethane
Another route to styrene involves the reaction of benzene and ethane. This process is being developed by Snamprogetti and Dow. Ethane, along with ethylbenzene, is fed to a dehydrogenation reactor with a catalyst capable of simultaneously producing styrene and ethylene. The dehydrogenation effluent is cooled and separated and the ethylene stream is recycled to the alkylation unit. The process attempts to overcome previous shortcomings in earlier attempts to develop production of styrene from ethane and benzene, such as inefficient recovery of aromatics, production of high levels of heavies and tars, and inefficient separation of hydrogen and ethane. Development of the process is ongoing.

Laboratory synthesis
A laboratory synthesis of styrene entails the decarboxylation of cinnamic acid:
 * C6H5CH=CHCO2H → C6H5CH=CH2 + CO2

Styrene was first prepared by this method.

Polymerization
The presence of the vinyl group allows styrene to polymerize. Commercially significant products include polystyrene, acrylonitrile butadiene styrene (ABS), styrene-butadiene (SBR) rubber, styrene-butadiene latex, SIS (styrene-isoprene-styrene), S-EB-S (styrene-ethylene/butylene-styrene), styrene-divinylbenzene (S-DVB), styrene-acrylonitrile resin (SAN), and unsaturated polyesters used in resins and thermosetting compounds. These materials are used in rubber, plastic, insulation, fiberglass, pipes, automobile and boat parts, food containers, and carpet backing.

Autopolymerisation
As a liquid or a gas, pure styrene will polymerise spontaneously to polystyrene, without the need of external initiators. This is known as autopolymerisation. At 100 °C it will autopolymerise at a rate of ~2% per hour, and more rapidly than this at higher temperatures. As the autopolymerisation reaction is exothermic it can be self-accelerating, with a real risk of a thermal runaway, potentially leading to an explosion. Examples include the 2019 explosion of the tanker Stolt Groenland, explosions at the Phillips Petroleum Company in 1999 and 2000 and overheating styrene tanks leading to the 2020 Visakhapatnam gas leak, which killed several people. The autopolymerisation reaction can only be kept in check by the continuous addition of polymerisation inhibitors.

Health effects
Styrene is regarded as a "known carcinogen", especially in case of eye contact, but also in case of skin contact, of ingestion and of inhalation, according to several sources. Styrene is largely metabolized into styrene oxide in humans, resulting from oxidation by cytochrome P450. Styrene oxide is considered toxic, mutagenic, and possibly carcinogenic. Styrene oxide is subsequently hydrolyzed in vivo to styrene glycol by the enzyme epoxide hydrolase. The US Environmental Protection Agency (EPA) has described styrene to be "a suspected toxin to the gastrointestinal tract, kidney, and respiratory system, among others".

On 10 June 2011, the US National Toxicology Program has described styrene as "reasonably anticipated to be a human carcinogen". However, a STATS author describes a review that was done on scientific literature and concluded that "The available epidemiologic evidence does not support a causal relationship between styrene exposure and any type of human cancer". Despite this claim, work has been done by Danish researchers to investigate the relationship between occupational exposure to styrene and cancer. They concluded, "The findings have to be interpreted with caution, due to the company based exposure assessment, but the possible association between exposures in the reinforced plastics industry, mainly styrene, and degenerative disorders of the nervous system and pancreatic cancer, deserves attention". In 2012, the Danish EPA concluded that the styrene data do not support a cancer concern for styrene. The US EPA does not have a cancer classification for styrene, but it has been the subject of their Integrated Risk Information System (IRIS) program.

The National Toxicology Program of the US Department of Health and Human Services has determined that styrene is "reasonably anticipated to be a human carcinogen". Various regulatory bodies refer to styrene, in various contexts, as a possible or potential human carcinogen. The International Agency for Research on Cancer considers styrene to be "probably carcinogenic to humans".

The neurotoxic properties of styrene have also been studied and reported effects include effects on vision (although unable to reproduce in a subsequent study ) and on hearing functions. Studies on rats have yielded contradictory results, but epidemiologic studies have observed a synergistic interaction with noise in causing hearing difficulties.

title: Styrene


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Champions (role-playing game)

Champions is a role-playing game published by Hero Games designed to simulate a superhero comic book world. It was originally created by George MacDonald and Steve Peterson in collaboration with Rob Bell, Bruce Harlick and Ray Greer. The latest edition of the game uses the sixth edition of the Hero System, as revised by Steve Long, and was written by Aaron Allston. It was released in early 2010.

Description
Champions, first published in 1981, was inspired by Superhero: 2044 and The Fantasy Trip as one of the first published role-playing games in which character generation was based on a point-buy system instead of random dice rolls. A player decides what kind of character to play, and designs the character using a set number of "character points," often abbreviated as "CP." The limited number of character points generally defines how powerful the character will be. Points can be used in many ways: to increase personal characteristics, such as strength or intelligence; to buy special skills, such as martial arts or computer programming; or to build superpowers, such as supersonic flight or telepathy. This point system was praised by reviewers for the balance it gave character generation over random dice rolls. The stats in Champions are Strength, Constitution, Body, Dexterity, Intelligence, Ego, and Presence.

Players are required not only to design a hero's powers, but also the hero's skills, disadvantages, and other traits. Thus, Champions characters are built with friends, enemies, and weaknesses, along with powers and abilities with varying scales of character point value for each. This design approach intends to make all the facets of Champions characters balanced in relation to each other regardless of the specific abilities and character features. Characters are rewarded with more character points after each adventure, which are then used to buy more abilities, or eliminate disadvantages.

The system
Players can design custom superpowers using the Champions rules system. Rather than offering a menu of specific powers, Champions powers are defined by their effects. (An energy blast is the same power regardless of whether it represents a laser beam, ice powers, or mystical spells.) The Champions rulebook includes rules governing many different types of generic powers which can then be modified to fit a player's idea.

This allows players to simulate situations found in superhero stories. Like most comic book heroes, characters and villains are frequently knocked out of the fight but seldom killed. There are special rules for throwing heavy objects like aircraft carriers.

History and other genres
The Champions system was adapted to a fantasy genre under the title Fantasy Hero (the first playtest edition of Fantasy Hero appeared before Champions was published), with similar advantages and disadvantages to the original Champions game. In 1984, the rules for Champions began being adapted into generic role-playing game system called the Hero System, although no formal and separate generic release of this as a standalone system would occur until 1990; instead the Champions rules would be edited down, expanded, and otherwise adapted on an individual basis for a variety of different genre treatments, such as pulp and modern espionage. Champions now exists as a genre sourcebook for the Hero System. Books for other genres have also appeared over the years, including Star Hero, Dark Champions, Pulp Hero, and Ninja Hero.

Archetypes
While Champions does not use "character classes" as some RPGs do, it does define common superhero archetypes as found in comic books. These are based variably on how they use their powers in combat, motivation, or the powers' origin. As listed in the Champions genre book, they are:

 * Brick – slower hand-to-hand fighter who relies more on raw strength and tougher defenses (Incredible Hulk / Colossus)
 * Energy Projector – primary combat ability is a ranged attack, which, despite the name, is not necessarily energy-based (Cyclops / Starfire)
 * Gadgeteer – abilities based on technological devices (Brainiac 5 / Forge)
 * Martial Artist (or martist for short) – lightly armored hand-to-hand combatant who fights with skill, quickness, and agility (Daredevil / Wolverine / Batman)
 * Mentalist – abilities target the mind, not the physical foe (Professor X / Jean Grey)
 * Metamorph – abilities involving changes in shape and/or size (Plastic Man / Mystique)
 * Mystic – trained in the use of magic, or with abilities or items with magical properties (Doctor Fate / Doctor Strange)
 * Patriot – an embodiment of his or her nation (Captain America / Captain Britain)
 * Powered Armor – a variant of a Gadgeteer, who uses an "all-in-one" gadget worn as armor (Iron Man / Cyborg)
 * Sink – with primary abilities being drains or transfers, a "Sink" can diminish, nullify or steal another characters powers, abilities or stats, either temporarily or permanently. (Rogue / Parasite)
 * Speedster – with abilities based around movement (Flash / Quicksilver)
 * Weaponmaster – with expertise at using a particular type of weapon (Green Arrow / Swordsman)

It is possible for a character to fall into multiple categories, such as Superman (brick/energy projector/speedster/patriot), Batman (martial artist/gadgeteer), or Spider-Man (martial artist/speedster/gadgeteer). It is also common for characters not to fall into any easily defined category—these categories are simply to provide easy definition and really have no impact on normative game play and do not imply stricture nor benefit within the rules.

The Champions Team
The Champions superhero team is presented as an example of how to build a well-balanced team in terms of game mechanics, including the hero Flare. Their enemies include Foxbat and Doctor Destroyer.

 * 4th edition
 * Defender – inventor wearing powered armor
 * Jaguar – werecat
 * Obsidian – alien prince brick
 * Quantum – mutant energy projector
 * Seeker – martial artist
 * Solitaire – mystic

 * 5th edition
 * Defender – an inventor wearing powered armor
 * Ironclad – super-strong and super-tough alien
 * Nighthawk – grim inventor/martial artist
 * Sapphire – flying energy projector
 * Witchcraft – sorceress

 * 6th edition
 * Defender – inventor wearing powered armor
 * Ironclad – super-strong and super-tough alien
 * Kinetik – speedster
 * Sapphire – flying energy projector
 * Witchcraft – sorceress

Setting
Much of the game is set in Millennium City. After its destruction by Dr. Destroyer, Detroit was rebuilt using the newest technologies and renamed.

MMORPG
A massively multiplayer online role-playing game based on the license was announced by Cryptic Studios, who had developed the popular City of Heroes and then reinvented Marvel Universe Online to Marvel Heroes. The game was released in September 2009. The game takes place in the established Champions universe and features classic Champions heroes and villains as NPCs.

Flextiles game supplement

Flextiles is a 1983 role-playing supplement for Champions. It is published by Hero. Craig Sheeley for Space Gamer. commented in a review that "...the Flextile concept is a good idea, but not at the price Flextiles sell for now. Cut the cost [...] and they'd be much better."

Reception
In the January 1982 edition of Ares, Eric Goldberg noted the "sketchy" design of the first edition, and yet believed that "in many ways, it is sufficient... What enables the designers to get away with this minimalist approach is an unswerving devotion to the philosophy and to the spirit of the superhero comic, which itself has never pretended to be terribly complex."

In the April–May 1982 edition of White Dwarf, Dave Morris liked the first edition combat system, calling it "a good simulation of comic-book battles". But Morris questioned whether players would enjoy playing superheroes rather than more ordinary characters found in most other role-playing games. He gave the game an average rating of 7 out of 10, saying, "All the same, the occasional bout of world-saving might be enjoyable, and Champions is worth buying on this basis alone."

Reviews for two editions of the game appeared in Dragon:
 * In the January 1982 edition, Scott Bennie liked the well-written and concise text of the first edition, but noticed many gaps and holes in the rules, including a lack of any system for buying equipment. Nevertheless, Bennie gave the game a thumbs up, saying, "Despite these flaws, I heartily recommend Champions. The more serious gamer will undoubtedly be put off by the silliness, and not everyone has a comic-book mind. But if you like this sort of thing, Champions is for you!"
 * In the October 1990 edition, Allen Varney disliked the slow pace of the 4th edition combat system. But he concluded with a strong recommendation, saying, "Fans of previous editions will delight in the new consistency and versatility. Experienced players of other games, discontent with the arbitrary restrictions of their current system, should also find the HERO SYSTEM rules a superb investment. Lastly, for comic-book fans who want to simulate every maneuver they see in their favorite stories, the Champions game remains, after almost 10 years, the system to beat."

Reviews for various editions of the game appeared in The Space Gamer:
 * In the September 1981 edition, Aaron Allston recommended the first edition of the game for those interested in the superhero theme, saying "If the subject matter interests you, I'd wholeheartedly recommend this product."
 * In the September–October 1983 edition, Russell Grant Collins wasn't sure if readers should buy the second edition: "Should you buy this material? I think so, if you are interested in superhero RPGs. If you hated the original Champions rules for more than their slight omissions and loopholes, don't bother. The changes aren't all that significant. If you're happy with the old version, weigh your decision carefully."
 * In the March–April 1985 edition, Allen Varney recommended the third edition for everyone, saying, "Champions is the only superhero RPG I would recommend; and this edition of Champions is the one to buy."
 * In the October–November 1989 edition, Dave Rogers reviewed the fourth edition of Champions and recommended it, saying, "even if you have all the Hero Games products ever printed, it still has something new to offer. Now, it's the only role-playing game you'll ever need."

Ken Cliffe reviewed the 4th edition of Champions for White Wolf, rating it 3 out of 5 overall, and stated that "I recommend this book to anyone already familiar with the hero system, and suggest the Champions game to anyone who enjoys exact, complicated role-playing. To those looking for slick, fun role-playing, I say look to other SHRPGs and other game systems."

In February 1989's issue of The Games Machine, John Woods reviewed the 4th edition of the game and called the rules "a model of clarity", although he criticized the lack of an index. He concluded with a strong recommendation, saying, "One of the best aspects of this type of game is that you don’t need anything more than the rulebook and a little imagination to start playing a fast moving game where the future of the world lies in your hands!"

In his 1990 book The Complete Guide to Role-Playing Games, game critic Rick Swan commented, "In addition to being one of the oldest superhero RPGs, Champions is easily the biggest and arguably the best." Swan noted that the character generation system "gives players near-total freedom in assembling the superhero of their dreams." However, he found that the combat system "is the game's weakest features, a seemingly endless array of numbers, formulas and tables that's all but certain to discourage first-timers." Swan concluded by giving the game an excellent rating of 3.5 out of 4, saying, "Of all the superhero RPGs, Champions remains the connoisseur's choice."

In a 1996 reader poll taken by Arcane magazine to determine the 50 most popular roleplaying games of all time, Champions was ranked 27th. Editor Paul Pettengale commented: "It wasn't the first superhero RPG and it never had licensed links to any big-name comics – but it's still the classic of the genre. It popularised the now-commonplace 'points-design' approach to character creation; in fact, it's probably the most flexible, detailed points-based system ever, which makes it rather overwhelming for some new players, and combat can be a little slow. But once you've learned how to use it, no other game catches the feeling of superhero action in quite the same way."

Champions was included in the 2007 book Hobby Games: The 100 Best. Game designer Bill Bridges described Champions as "the superhero roleplaying game. While it wasn't the first game on the market that let you play superheroes and duke it out with supervillains, using earth-shattering powers, it was the most innovative. The major roleplaying games of the time involved characters stalking monsters in dungeons; the heroes in Champions delivered knockout blows to archnemeses—all while speaking the requisite inspiring soliloquies."

In his 2023 book Monsters, Aliens, and Holes in the Ground, RPG historian Stu Horvath noted that Champions was a pioneer in two respects. It "is the first entirely new game to embrace the idea of non-random character generation through a point-buy system, and it marks a significant expansion of the concept." The second new concept was "the idea of disadvantages."

Reviews

 * Different Worlds No. 17
 * Pyramid (for Hero System 5th Edition)
 * InQuest No. 27, July 1997 (for 5th edition)
 * Computer and Video Games

Awards

 * At the 1999 Origins Awards, Champions was installed in the Adventure Gaming Hall of Fame
 * Three Champions adventures won ENnie Awards:
 * In 2004, in the "Best Non-D20 Adventure" category, Champions Battlegrounds won a gold medal, and Shades of Black won a Silver Medal
 * In 2005, Villainy Amok won a silver medal for "Best Adventure"

Comics
Starting in June 1986, a comic book limited series was published by Eclipse Comics based on characters from the first Champions campaign. The Eclipse series included character sheets that allowed readers to incorporate characters used in the comic books into their own Champions campaigns; this practice was also used in the Villains and Vigilantes comic book limited series (also published by Eclipse in 1986–1987).

Soon after Eclipse's initial limited series, an ongoing Champions series was published by Hero Comics (later Hero Graphics, later still Heroic Publishing) from 1987 to 1993.

As of 2024, Heroic Publishing was still publishing comics about some of the Champions characters (under the title League of Champions), although the publisher had long since parted ways with the makers of the game.

title: Champions (role-playing game)


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