title: Delphi method

text: One successful example of a (partially) web-based policy Delphi is the five-round Delphi exercise (with 1,454 contributions) for the creation of the eLAC Action Plans in Latin America. It is believed to be the most extensive online participatory policy-making foresight exercise in the history of intergovernmental processes in the developing world at this time. In addition to the specific policy guidance provided, the authors list the following lessons learned include "(1) the potential of Policy Delphi methods to introduce transparency and accountability into public decision-making, especially in developing countries; (2) the utility of foresight exercises to foster multi-agency networking in the development community; (3) the usefulness of embedding foresight exercises into established mechanisms of representative democracy and international multilateralism, such as the United Nations; (4) the potential of online tools to facilitate participation in resource-scarce developing countries; and (5) the resource-efficiency stemming from the scale of international foresight exercises, and therefore its adequacy for resource-scarce regions."


title: Delphi method

text: The guidance for developing reporting guidelines in 2010 recommended using the Delphi method for developing reporting guidelines. However, less than 30% of the reporting guidelines were developed with the Delphi method according to the systematic reviews in 2015 and 2020. The Delphi approach has been successfully employed to improve agreement between experts in iterative rating exercises on clinical test results using inter-rater kappa statistics as an outcome measure.


title: Delphi method

text: A number of Delphi forecasts are conducted using web sites that allow the process to be conducted in real-time. For instance, the TechCast Project uses a panel of 100 experts worldwide to forecast breakthroughs in all fields of science and technology. Another example is the Horizon Project, where educational futurists collaborate online using the Delphi method to come up with the technological advancements to look out for in education for the next few years.


title: Delphi method

text: Traditionally the Delphi method has aimed at a consensus of the most probable future by iteration. Other versions, such as the Policy Delphi, is instead a decision support method aiming at structuring and discussing the diverse views of the preferred future.


title: Delphi method

text: In Europe, more recent web-based experiments have used the Delphi method as a communication technique for interactive decision-making and e-democracy.


title: Delphi method

text: The Argument Delphi, developed by Osmo Kuusi, focuses on ongoing discussion and finding relevant arguments rather than focusing on the output. The Disaggregative Policy Delphi, developed by Petri Tapio, uses cluster analysis as a systematic tool to construct various scenarios of the future in the latest Delphi round. The respondent's view on the probable and the preferable future are dealt with as separate cases. The computerization of Argument Delphi is relatively difficult because of several problems like argument resolution, argument aggregation and argument evaluation. The computerization of Argument Delphi, developed by Sadi Evren Seker, proposes solutions to such problems.


title: Delphi method

text: Today the Delphi method is a widely accepted forecasting tool and has been used successfully for thousands of studies in areas varying from technology forecasting to drug abuse.


title: Delphi method

text: Overall the track record of the Delphi method is mixed. There have been many cases when the method produced poor results. Still, some authors attribute this to poor application of the method and not to the weaknesses of the method itself. It must also be realized that in areas such as science and technology forecasting, the degree of uncertainty is so great that exact and always correct predictions are impossible, so a high degree of error is to be expected.


title: Delphi method

text: A particular weakness of the Delphi method is that future developments are not always predicted correctly by consensus of experts. This shortcoming concerning the issue of ignorance is important. If panelists are misinformed about a topic, the use of Delphi may only add confidence to their ignorance.


title: Delphi method

text: One of the initial problems of the method was its inability to make complex forecasts with multiple factors. Potential future outcomes were usually considered as if they had no effect on each other. Later on, several extensions to the Delphi method were developed to address this problem, such as cross impact analysis, that takes into consideration the possibility that the occurrence of one event may change probabilities of other events covered in the survey. Still the Delphi method can be used most successfully in forecasting single scalar indicators.


title: Delphi method

text: Delphi has characteristics similar to prediction markets as both are structured approaches that aggregate diverse opinions from groups. Yet, there are differences that may be decisive for their relative applicability for different problems.


title: Delphi method

text: Some advantages of prediction markets derive from the possibility to provide incentives for participation.


title: Delphi method

text: More recent research has also focused on combining both, the Delphi technique and prediction markets. More specifically, in a research study at Deutsche Börse elements of the Delphi method had been integrated into a prediction market.


title: Division (mathematics)

text: Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication.


title: Division (mathematics)

text: At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture).


title: Division (mathematics)

text: The division with remainder or Euclidean division of two natural numbers provides an integer "quotient", which is the number of times the second number is completely contained in the first number, and a "remainder", which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. For example, if 21 apples are divided between 4 people, everyone receives 5 apples again, and 1 apple remains.


title: Division (mathematics)

text: For division to always yield one number rather than a quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers. In these enlarged number systems, division is the inverse operation to multiplication, that is means , as long as is not zero. If , then this is a division by zero, which is not defined. In the 21-apples example, everyone would receive 5 apple and a quarter of an apple, thus avoiding any leftover.


title: Division (mathematics)

text: Both forms of division appear in various algebraic structures, different ways of defining mathematical structure. Those in which a Euclidean division (with remainder) is defined are called Euclidean domains and include polynomial rings in one indeterminate (which define multiplication and addition over single-variabled formulas). Those in which a division (with a single result) by all nonzero elements is defined are called fields and division rings. In a ring the elements by which division is always possible are called the units (for example, 1 and −1 in the ring of integers). Another generalization of division to algebraic structures is the quotient group, in which the result of "division" is a group rather than a number.


title: Division (mathematics)

text: The simplest way of viewing division is in terms of quotition and partition: from the quotition perspective, means the number of 5s that must be added to get 20. In terms of partition, means the size of each of 5 parts into which a set of size 20 is divided. For example, 20 apples divide into five groups of four apples, meaning that "twenty divided by five is equal to four". This is denoted as , or . What is being divided is called the "dividend", which is divided by the "divisor", and the result is called the "quotient". In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient.


title: Division (mathematics)

text: Unlike the other basic operations, when dividing natural numbers there is sometimes a remainder that will not go evenly into the dividend; for example, leaves a remainder of 1, as 10 is not a multiple of 3. Sometimes this remainder is added to the quotient as a fractional part, so is equal to or , but in the context of integer division, where numbers have no fractional part, the remainder is kept separately (or exceptionally, discarded or rounded). When the remainder is kept as a fraction, it leads to a rational number. The set of all rational numbers is created by extending the integers with all possible results of divisions of integers.


title: Division (mathematics)

text: Unlike multiplication and addition, division is not commutative, meaning that is not always equal to . Division is also not, in general, associative, meaning that when dividing multiple times, the order of division can change the result. For example, , but (where the use of parentheses indicates that the operations inside parentheses are performed before the operations outside parentheses).


title: Division (mathematics)

text: Division is traditionally considered as left-associative. That is, if there are multiple divisions in a row, the order of calculation goes from left to right:


title: Division (mathematics)

text: This is unlike the case in multiplication, which is both left-distributive and right-distributive, and thus distributive.


title: Division (mathematics)

text: Division is often shown in algebra and science by placing the "dividend" over the "divisor" with a horizontal line, also called a fraction bar, between them. For example, ""a" divided by "b"" can written as:


title: Division (mathematics)

text: which can also be read out loud as "divide "a" by "b"" or ""a" over "b"". A way to express division all on one line is to write the "dividend" (or numerator), then a slash, then the "divisor" (or denominator), as follows:


title: Division (mathematics)

text: This is the usual way of specifying division in most computer programming languages, since it can easily be typed as a simple sequence of ASCII characters. (It is also the only notation used for quotient objects in abstract algebra.) Some mathematical software, such as MATLAB and GNU Octave, allows the operands to be written in the reverse order by using the backslash as the division operator:


title: Division (mathematics)

text: A typographical variation halfway between these two forms uses a solidus (fraction slash), but elevates the dividend and lowers the divisor:


title: Division (mathematics)

text: Any of these forms can be used to display a fraction. A fraction is a division expression where both dividend and divisor are integers (typically called the "numerator" and "denominator"), and there is no implication that the division must be evaluated further. A second way to show division is to use the division sign (÷, also known as obelus though the term has additional meanings), common in arithmetic, in this manner:


title: Division (mathematics)

text: This form is infrequent except in elementary arithmetic. ISO 80000-2-9.6 states it should not be used. This division sign is also used alone to represent the division operation itself, as for instance as a label on a key of a calculator. The obelus was introduced by Swiss mathematician Johann Rahn in 1659 in "Teutsche Algebra". The ÷ symbol is used to indicate subtraction in some European countries, so its use may be misunderstood.


title: Division (mathematics)

text: This notation was introduced by Gottfried Wilhelm Leibniz in his 1684 "Acta eruditorum". Leibniz disliked having separate symbols for ratio and division. However, in English usage the colon is restricted to expressing the related concept of ratios.


title: Division (mathematics)

text: Since the 19th century, US textbooks have used formula_13 or formula_14 to denote "a" divided by "b", especially when discussing long division. The history of this notation is not entirely clear because it evolved over time.


title: Division (mathematics)

text: Division is often introduced through the notion of "sharing out" a set of objects, for example a pile of lollies, into a number of equal portions. Distributing the objects several at a time in each round of sharing to each portion leads to the idea of 'chunking' a form of division where one repeatedly subtracts multiples of the divisor from the dividend itself.


title: Division (mathematics)

text: By allowing one to subtract more multiples than what the partial remainder allows at a given stage, more flexible methods, such as the bidirectional variant of chunking, can be developed as well.


title: Division (mathematics)

text: More systematically and more efficiently, two integers can be divided with pencil and paper with the method of short division, if the divisor is small, or long division, if the divisor is larger. If the dividend has a fractional part (expressed as a decimal fraction), one can continue the procedure past the ones place as far as desired. If the divisor has a fractional part, one can restate the problem by moving the decimal to the right in both numbers until the divisor has no fraction, which can make the problem easier to solve (e.g., 10/2.5 = 100/25 = 4).


title: Division (mathematics)

text: Logarithm tables can be used to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result.


title: Division (mathematics)

text: Division can be calculated with a slide rule by aligning the divisor on the C scale with the dividend on the D scale. The quotient can be found on the D scale where it is aligned with the left index on the C scale. The user is responsible, however, for mentally keeping track of the decimal point.


title: Division (mathematics)

text: Modern calculators and computers compute division either by methods similar to long division, or by faster methods; see Division algorithm.


title: Division (mathematics)

text: In modular arithmetic (modulo a prime number) and for real numbers, nonzero numbers have a multiplicative inverse. In these cases, a division by may be computed as the product by the multiplicative inverse of . This approach is often associated with the faster methods in computer arithmetic.


title: Division (mathematics)

text: Euclidean division is the mathematical formulation of the outcome of the usual process of division of integers. It asserts that, given two integers, "a", the "dividend", and "b", the "divisor", such that "b" ≠ 0, there are unique integers "q", the "quotient", and "r", the remainder, such that "a" = "bq" + "r" and 0 ≤ "r" < , where denotes the absolute value of "b".


title: Division (mathematics)

text: Integers are not closed under division. Apart from division by zero being undefined, the quotient is not an integer unless the dividend is an integer multiple of the divisor. For example, 26 cannot be divided by 11 to give an integer. Such a case uses one of five approaches:


title: Division (mathematics)

text: Dividing integers in a computer program requires special care. Some programming languages treat integer division as in case 5 above, so the answer is an integer. Other languages, such as MATLAB and every computer algebra system return a rational number as the answer, as in case 3 above. These languages also provide functions to get the results of the other cases, either directly or from the result of case 3.


title: Division (mathematics)

text: Names and symbols used for integer division include div, /, \, and %. Definitions vary regarding integer division when the dividend or the divisor is negative: rounding may be toward zero (so called T-division) or toward −∞ (F-division); rarer styles can occur – see modulo operation for the details.


title: Division (mathematics)

text: Divisibility rules can sometimes be used to quickly determine whether one integer divides exactly into another.


title: Division (mathematics)

text: The result of dividing two rational numbers is another rational number when the divisor is not 0. The division of two rational numbers "p"/"q" and "r"/"s" can be computed as


title: Division (mathematics)

text: All four quantities are integers, and only "p" may be 0. This definition ensures that division is the inverse operation of multiplication.


title: Division (mathematics)

text: Division of two real numbers results in another real number (when the divisor is nonzero). It is defined such that "a"/"b" = "c" if and only if "a" = "cb" and "b" ≠ 0.


title: Division (mathematics)

text: Dividing two complex numbers (when the divisor is nonzero) results in another complex number, which is found using the conjugate of the denominator:


title: Division (mathematics)

text: This process of multiplying and dividing by formula_22 is called 'realisation' or (by analogy) rationalisation. All four quantities "p", "q", "r", "s" are real numbers, and "r" and "s" may not both be 0.


title: Division (mathematics)

text: One can define the division operation for polynomials in one variable over a field. Then, as in the case of integers, one has a remainder. See Euclidean division of polynomials, and, for hand-written computation, polynomial long division or synthetic division.


title: Division (mathematics)

text: One can define a division operation for matrices. The usual way to do this is to define , where denotes the inverse of "B", but it is far more common to write out explicitly to avoid confusion. An elementwise division can also be defined in terms of the Hadamard product.


title: Division (mathematics)

text: Because matrix multiplication is not commutative, one can also define a left division or so-called "backslash-division" as . For this to be well defined, need not exist, however does need to exist. To avoid confusion, division as defined by is sometimes called "right division" or "slash-division" in this context.


title: Division (mathematics)

text: Note that with left and right division defined this way, is in general not the same as , nor is the same as . However, it holds that and .


title: Division (mathematics)

text: To avoid problems when and/or do not exist, division can also be defined as multiplication by the pseudoinverse. That is, and , where and denote the pseudoinverses of "A" and "B".


title: Division (mathematics)

text: In abstract algebra, given a magma with binary operation ∗ (which could nominally be termed multiplication), left division of "b" by "a" (written ) is typically defined as the solution "x" to the equation , if this exists and is unique. Similarly, right division of "b" by "a" (written ) is the solution "y" to the equation . Division in this sense does not require ∗ to have any particular properties (such as commutativity, associativity, or an identity element).


title: Division (mathematics)

text: "Division" in the sense of "cancellation" can be done in any magma by an element with the cancellation property. Examples include matrix algebras and quaternion algebras. A quasigroup is a structure in which division is always possible, even without an identity element and hence inverses. In an integral domain, where not every element need have an inverse, "division" by a cancellative element "a" can still be performed on elements of the form "ab" or "ca" by left or right cancellation, respectively. If a ring is finite and every nonzero element is cancellative, then by an application of the pigeonhole principle, every nonzero element of the ring is invertible, and "division" by any nonzero element is possible. To learn about when "algebras" (in the technical sense) have a division operation, refer to the page on division algebras. In particular Bott periodicity can be used to show that any real normed division algebra must be isomorphic to either the real numbers R, the complex numbers C, the quaternions H, or the octonions O.


title: Division (mathematics)

text: Division of any number by zero in most mathematical systems is undefined, because zero multiplied by any finite number always results in a product of zero. Entry of such an expression into most calculators produces an error message. However, in certain higher level mathematics division by zero is possible by the zero ring and algebras such as wheels. In these algebras, the meaning of division is different from traditional definitions.


title: In Your Area World Tour

text: The In Your Area World Tour (also known as Blackpink World Tour [In Your Area]) was the first worldwide concert tour and the second overall by South Korean girl group Blackpink. The tour began on November 10, 2018, in Seoul, South Korea, and ended on February 22, 2020, in Fukuoka, Japan, in support of their albums "Square Up" (2018) and "Kill This Love" (2019). The group held 36 shows in 26 cities in 17 countries around the world. The tour is the highest-grossing tour by a Korean girl group.


title: In Your Area World Tour

text: On September 12, it was announced that the group would hold their first concert in Seoul titled "Blackpink 2018 Tour [In Your Area] Seoul x BC Card" on November 11 and November 12 at the Olympic Gymnastics Arena. It was revealed that the title of the tour 'In Your Area' was chosen by the members themselves. Pre-order tickets became available to the group's fan club members on September 14 via Auction Ticket, while tickets were made available to the general public on September 18. Each member of the group played an active role in pitching ideas for the concert. All 20,000 tickets for the two concerts were quickly sold out.


title: In Your Area World Tour

text: During the two-day concerts at Seoul, member Jennie performed her debut solo song "Solo", which was released later on November 12, 2018, for the first time ever. Blackpink released a 14-track live album that was recorded during the Seoul concerts, "Blackpink 2018 Tour In Your Area Seoul", on August 30, 2019.


title: In Your Area World Tour

text: On October 31, 2018, Blackpink announced their first tour dates for the Asia leg, with dates in Bangkok, Jakarta, Manila, Singapore, and Kuala Lumpur commencing in mid-January 2019. On January 28, 2019, Blackpink officially announced the concert dates and venues for the European leg. The tour kicked off in Amsterdam on May 18, 2019. The group later shared the tour's North America stops, on February 11, 2019, via social media. The North America leg kicked off in Los Angeles on April 17, in between the two weekends of Coachella where the group performed. On February 22, 2019, it was reported that all 60,000 tickets for the group's first North America tour were sold out. Blackpink announced tour dates for Australia on February 25. Kia Motors served as the tour's official sponsor.


title: In Your Area World Tour

text: On April 15, the group announced they would hold a total of four dome concerts in three cities in Japan, starting with Tokyo on December 4, 2019. On 22 January 2020, it was announced that the tour's last concert at Fukuoka Dome will be broadcast live in 96 movie theaters in Japan to repay the enthusiastic support from fans. A live album, DVD and Blu-ray of the Tokyo Dome concert, "Blackpink 2019–2020 World Tour In Your Area – Tokyo Dome –", was released on May 6, 2020. The DVD ranked first on Oricon DVD Weekly Chart (May 4–10).


title: In Your Area World Tour

text: The concert began with a montage of a Rubik's Cube spelling out "Blackpink" and the names of the group's members on the main stage's screen. The cube then turned into an explosion of pink glitter and rising smokes as all members of Blackpink started rising to the stage and performing "Ddu-Du Ddu-Du" in light pink outfits. The quartet was then lifted on stage platforms to perform "Forever Young" with an outer space-like backdrop on screen. After performing the two verses and the second chorus on the main stage, Blackpink was raised on the platforms again and joined by backup dancers as they sang the final part of the song. The group then greeted and introduced themselves to the audience after the platforms were lowered back to the main stage surface level. Afterward, Blackpink performed "Stay" on chairs on the main stage and walked to the B-stage during the final chorus. The group proceeded to sing "Whistle" on the B-stage for a majority of the song before being accompanied by backup dancers and returning to the main stage for the ending part. The group was then lowered down below the stage by lifts for a costume change to prepare for their respective solo stages.


title: In Your Area World Tour

text: Depending on the tour leg, the order of the solo performances changes. In the first Asian leg, Jisoo would commence the portion by coming out on a platform made of disco balls to sing a cover of "Clarity" by Zedd. Her stage would be followed by Lisa dancing to a medley of songs, both solo and with a group of backup dancers. In Seoul, Lisa danced to "I Like It", "Faded" (by Tink) and "Attention"; the dance number was changed to "Take Me" and "Swalla" from the Bangkok date on January 11, 2019, onwards. Subsequently, after Lisa, Rosé rose to the stage along with Dante Jackson from The Band Six on the piano and sang a cover medley of "Let It Be" by the Beatles, "You and I" by former label mate Park Bom and "Only Look At Me" by Taeyang. From April 17, 2019, to the rest of the tour, Rosé opened the solo stages instead of Jisoo. The solo stage portion then concluded with Jennie performing "Solo" with multiple backup dancers whilst a dance hall setting was on display on the screen. The Band Six played an interlude after Jennie went backstage for her costume change. With an exception to Jennie's performance, the solo segment was revamped for the final leg in Japan. Rosé sang a cover of Lewis Capaldi's "Someone You Loved", Lisa's dance number was changed to a medley of "Good Thing" and "Señorita" while Jisoo performed a cover of AKMU's "How Can I Love the Heartbreak, You're the One I Love".


title: In Your Area World Tour

text: After the release of "Kill This Love" EP in April 2019, Blackpink opened Act III of the concert with "Kill This Love", dressed in street style outfits. The main screen featured different scenes from the song's official music video, served as the performance backdrop. A group of backup dancers joined Blackpink for the ending beat drop of the song in marching band outfits before leaving the stage for the quartet to perform "Don't Know What To Do" on their own. The group spent some time afterward to talk and interact with the audience. Next, "Kiss and Make Up" was performed with each member standing on their respective raised and moving platform while the screen was showing tropical patterns and imagery. The Band Six and backup dancers later returned to the main stage to accompany Blackpink, now back down on stage level, performing "Really" and "See U Later". They all exited the stage when a video interlude featuring Blackpink racing and drifting in Kia motorcars started playing on the screens.


title: In Your Area World Tour

text: Blackpink, in sparkly costumes, returned to the stage from below and performed "Playing with Fire" to a gate-like setting on the screen. The background changed to kaleidoscope-like graphics when the group sang "Kick It". They moved to the B-stage and proceeded to perform the final two songs "Boombayah" and "As If It's Your Last" there, after a small talk with the audience.


title: In Your Area World Tour

text: For the encore, the group reappeared on stage in more casual and sporty clothes to perform a remix version of "Ddu-Du Ddu-Du". Following that performance, Blackpink introduced members of the band and the backup dancer group to the audience and thanked them before casually enjoying an instrumental performance of The Band Six themselves. Only the group remained on stage afterward to sing the final song "Hope Not"; they said goodbye to the audience before exiting the stage on a lift lowering them back down to the pit.


title: In Your Area World Tour

text: The concert received generally positive reviews from the critics. "Variety" drew comparisons between the all-dancing concert to Beyonce's 2018 Coachella performance, calling it "within the realm of earthly aspirational possibility" with "semi-rigid, semi-relaxed synchronization" and "major charm offensive from four quintessential Girls Next Door". Evan Real writing for "The Hollywood Reporter" said the girl group delivered "impressive vocals, dancing" that "not even the stage's extravagant light display or frequent bursts of fireworks could pull the group's focus from their exceptionally polished routine". "Billboard" described the concert as "hugely engaging" and applauded Blackpink's "remarkably natural aura" as opposed to the usual rigidity that K-Pop concerts usually have thanks to the group's improvisations and audience interaction, but also fell short during the solo segment, as they called Lisa's dance number "as baffling as it was boring" and Jisoo's cover of Clarity "uncomfortably close to a filler". "The Guardian" also shared a similar sentiment about the solo segment and gave the concert three stars out of five, saying while the show had "brilliant moments throughout", it didn't "take enough risks". However, Jan Lee of "The Straits Times" felt the solo performances were enjoyable and the concert's energy was infectious as he described the members of Blackpink as "exuberant, charming and visually stunning onstage", though he felt the concert in general needed more original material from Blackpink.


title: In Your Area World Tour

text: The In Your Area World Tour became the most successful tour by a Korean female group in history. It recorded a 96.6% rate of seat occupancy for the first 32 concerts, excluding the concerts in Japan. Among them, 22 concerts in cities including Bangkok, Jakarta, Manila, Singapore, Kuala Lumpur, Los Angeles, Chicago, Hamilton, Newark, Fort Worth, Paris, Macau, and Melbourne were sold out. All four dome concerts for the Japan leg were also sold out.


title: In Your Area World Tour

text: The North American setlist was performed at the May 1, 2019 concert at the Prudential Center in Newark. It does not represent all shows throughout the tour.


title: In Your Area World Tour

text: Two live albums were released for the In Your Area World Tour: "Blackpink 2018 Tour 'In Your Area' Seoul", and "Blackpink 2019–2020 World Tour in Your Area – Tokyo Dome".


title: In Your Area World Tour

text: Blackpink 2018 Tour 'In Your Area' Seoul is the second live album of the South Korean music group Blackpink, released on August 8, 2019, on DVD and August 30, 2019, on digital and streaming platforms.


title: In Your Area World Tour

text: Blackpink 2019–2020 World Tour in Your Area – Tokyo Dome is the third live album of the South Korean music group Blackpink, released on May 14, 2020.


title: Joseph Schumpeter

text: Joseph Alois Schumpeter (; February 8, 1883 – January 8, 1950) was an Austrian-born political economist. He served briefly as Finance Minister of German-Austria in 1919. In 1932, he emigrated to the United States to become a professor at Harvard University, where he remained until the end of his career, and in 1939 obtained American citizenship.


title: Joseph Schumpeter

text: Schumpeter was one of the most influential economists of the early 20th century, and popularized the term "creative destruction", which was coined by Werner Sombart.


title: Joseph Schumpeter

text: Schumpeter was born in Triesch, Habsburg Moravia (now Třešť in the Czech Republic, then part of Austria-Hungary) in 1883 to German-speaking Catholic parents. Both of his grandmothers were Czech. Schumpeter did not acknowledge his Czech ancestry; he considered himself an ethnic German. His father owned a factory, but he died when Joseph was only four years old. In 1893, Joseph and his mother moved to Vienna. Schumpeter was a loyal supporter of Franz Joseph I of Austria.


title: Joseph Schumpeter

text: After attending school at the Theresianum, Schumpeter began his career studying law at the University of Vienna under the Austrian capital theorist Eugen von Böhm-Bawerk, taking his PhD in 1906. In 1909, after some study trips, he became a professor of economics and government at the University of Czernowitz in modern-day Ukraine. In 1911, he joined the University of Graz, where he remained until World War I.


title: Joseph Schumpeter

text: In 1918, Schumpeter was a member of the Socialization Commission established by the Council of the People's Deputies in Germany. In March 1919, he was invited to take office as Minister of Finance in the Republic of German-Austria. He proposed a capital levy as a way to tackle the war debt and opposed the socialization of the Alpine Mountain plant. In 1921, he became president of the private Biedermann Bank. He was also a board member at the Kaufmann Bank. Problems at those banks left Schumpeter in debt. His resignation was a condition of the takeover of the Biedermann Bank in September 1924.


title: Joseph Schumpeter

text: From 1925 to 1932, Schumpeter held a chair at the University of Bonn, Germany. He lectured at Harvard in 1927–1928 and 1930. In 1931, he was a visiting professor at The Tokyo College of Commerce. In 1932, Schumpeter moved to the United States and soon began what would become extensive efforts to help central European economist colleagues displaced by Nazism. Schumpeter also became known for his opposition to Marxism and socialism that he thought would lead to dictatorship, and even criticized President Franklin Roosevelt's New Deal. In 1939, Schumpeter became a US citizen. In the beginning of World War II, the FBI investigated him and his wife, Elizabeth Boody (a prominent scholar of Japanese economics) for pro-Nazi leanings, but found no evidence of Nazi sympathies.


title: Joseph Schumpeter

text: At Harvard, Schumpeter was considered a memorable character, erudite, and even showy in the classroom. He became known for his heavy teaching load and his personal and painstaking interest in his students. He served as the faculty advisor of the Graduate Economics Club and organized private seminars and discussion groups. Some colleagues thought his views outdated by Keynesianism which was fashionable; others resented his criticisms, particularly of their failure to offer an assistant professorship to Paul Samuelson, but recanted when they thought him likely to accept a position at Yale University. This period of his life was characterized by hard work and comparatively little recognition of his massive 2-volume book "Business Cycles." However, Schumpeter persevered, and in 1942 published what became the most popular of all his works, "Capitalism, Socialism and Democracy", reprinted many times and in many languages in the following decades, as well as cited thousands of times.


title: Joseph Schumpeter

text: The source of Schumpeter's dynamic, change-oriented, and innovation-based economics was the historical school of economics. Although his writings could be critical of that perspective, Schumpeter's work on the role of innovation and entrepreneurship can be seen as a continuation of ideas originated by the historical school, especially the work of Gustav von Schmoller and Werner Sombart. Despite being born in Austria and having trained with many of the same economists, some argue he cannot be categorized with the Austrian School of economics without major qualifications while others maintain the opposite.


title: Joseph Schumpeter

text: The Austrian sociologist Rudolf Goldscheid's concept of fiscal sociology influenced Schumpeter's analysis of the tax state. A 2012 paper showed that Schumpeter's writings displayed the influence of Francis Galton's work.


title: Joseph Schumpeter

text: According to Christopher Freeman (2009), "the central point of his whole life work [is]: that capitalism can only be understood as an evolutionary process of continuous innovation and 'creative destruction'".


title: Joseph Schumpeter

text: Schumpeter's scholarship is apparent in his posthumous "History of Economic Analysis", although some of his judgments seem idiosyncratic and sometimes cavalier. For instance, Schumpeter thought that the greatest 18th century economist was Turgot rather than Adam Smith, and he considered Léon Walras to be the "greatest of all economists", beside whom other economists' theories were "like inadequate attempts to catch some particular aspects of Walrasian truth". Schumpeter criticized John Maynard Keynes and David Ricardo for the "Ricardian vice". According to Schumpeter, both Ricardo and Keynes reasoned in terms of abstract models, where they would freeze all but a few variables. Then they could argue that one caused the other in a simple monotonic fashion. This led to the belief that one could easily deduce policy conclusions directly from a highly abstract theoretical model.


title: Joseph Schumpeter

text: In this book, Joseph Schumpeter recognized the implication of a gold monetary standard compared to a fiat monetary standard. In "History of Economic Analysis", Schumpeter stated the following: "An 'automatic' gold currency is part and parcel of a laissez-faire and free-trade economy. It links every nation's money rates and price levels with the money rates and price levels of all the other nations that are 'on gold.' However, gold is extremely sensitive to government expenditure and even to attitudes or policies that do not involve expenditure directly, for example, in foreign policy, certain policies of taxation, and, in general, precisely all those policies that violate the principles of [classical] liberalism. "This" is the reason why gold is so unpopular now and also why it was so popular in a bourgeois era."


title: Joseph Schumpeter

text: Schumpeter's relationships with the ideas of other economists were quite complex in his most important contributions to economic analysis – the theory of business cycles and development. Following neither Walras nor Keynes, Schumpeter starts in "The Theory of Economic Development" with a treatise of circular flow which, excluding any innovations and innovative activities, leads to a stationary state. The stationary state is, according to Schumpeter, described by Walrasian equilibrium. The hero of his story is the entrepreneur.


title: Joseph Schumpeter

text: The entrepreneur disturbs this equilibrium and is the prime cause of economic development, which proceeds in a cyclic fashion along with several time scales. In fashioning this theory connecting innovations, cycles, and development, Schumpeter kept alive the Russian Nikolai Kondratiev's ideas on 50-year cycles, Kondratiev waves.


title: Joseph Schumpeter

text: Schumpeter suggested a model in which the four main cycles, Kondratiev (54 years), Kuznets (18 years), Juglar (9 years), and Kitchin (about 4 years) can be added together to form a composite waveform. A Kondratiev wave could consist of three lower-degree Kuznets waves. Each Kuznets wave could, itself, be made up of two Juglar waves. Similarly two (or three) Kitchin waves could form a higher degree Juglar wave. If each of these were in phase; more importantly, if the downward arc of each was simultaneous so that the nadir of each was coincident, it would explain disastrous slumps and consequent depressions. As far as the segmentation of the Kondratiev Wave, Schumpeter never proposed such a fixed model. He saw these cycles varying in time – although in a tight time frame by coincidence – and for each to serve a specific purpose.


title: Joseph Schumpeter

text: In Schumpeter's theory, Walrasian equilibrium is not adequate to capture the key mechanisms of economic development. Schumpeter also thought that the institution enabling the entrepreneur to buy the resources needed to realize his vision was a well-developed capitalist financial system, including a whole range of institutions for granting credit. One could divide economists among (1) those who emphasized "real" analysis and regarded money as merely a "veil" and (2) those who thought monetary institutions are important and money could be a separate driving force. Both Schumpeter and Keynes were among the latter.


title: Joseph Schumpeter

text: Schumpeter's most popular book in English is probably "Capitalism, Socialism and Democracy". While he agrees with Karl Marx that capitalism will collapse and be replaced by socialism, Schumpeter predicts a different way this will come about. While Marx predicted that capitalism would be overthrown by a violent proletarian revolution, which actually occurred in the least capitalist countries, Schumpeter believed that capitalism would gradually weaken by itself and eventually collapse. Specifically, the success of capitalism would lead to corporatism and to values hostile to capitalism, especially among intellectuals.


title: Joseph Schumpeter

text: "Intellectuals" are a social class in a position to critique societal matters for which they are not directly responsible and to stand up for the interests of other classes. Intellectuals tend to have a negative outlook on capitalism, even while relying on it for prestige because their professions rely on antagonism toward it. The growing number of people with higher education is a great advantage of capitalism, according to Schumpeter. Yet, unemployment and a lack of fulfilling work will lead to intellectual critique, discontent, and protests.


title: Joseph Schumpeter

text: Parliaments will increasingly elect social democratic parties, and democratic majorities will vote for restrictions on entrepreneurship. Increasing workers' self-management, industrial democracy and regulatory institutions would evolve non-politically into "liberal capitalism". Thus, the intellectual and social climate needed for thriving entrepreneurship will be replaced by some form of "laborism". This will exacerbate "creative destruction" (a borrowed phrase to denote an endogenous replacement of old ways of doing things by new ways), which will ultimately undermine and destroy the capitalist structure.


title: Joseph Schumpeter

text: Schumpeter emphasizes throughout this book that he is analyzing trends, not engaging in political advocacy.


title: Joseph Schumpeter

text: William Fellner, in the book "Schumpeter's Vision: Capitalism, Socialism and Democracy After 40 Years", noted that Schumpeter saw any political system in which the power was fully monopolized as fascist.


title: Joseph Schumpeter

text: In the same book, Schumpeter expounded on a theory of democracy that sought to challenge what he called the "classical doctrine". He disputed the idea that democracy was a process by which the electorate identified the common good, and politicians carried this out for them. He argued this was unrealistic, and that people's ignorance and superficiality meant that in fact they were largely manipulated by politicians, who set the agenda. Furthermore, he claimed that even if the common good was possible to find, it would still not make clear the means needed to reach its end, since citizens do not have the requisite knowledge to design government policy. This made a 'rule by the people' concept both unlikely and undesirable. Instead, he advocated a minimalist model, much influenced by Max Weber, whereby democracy is the mechanism for competition between leaders, much like a market structure. Although periodic votes by the general public legitimize governments and keep them accountable, the policy program is very much seen as their own and not that of the people, and the participatory role of individuals is usually severely limited.


title: Joseph Schumpeter

text: Schumpeter defined democracy as the method by which people elect representatives in competitive elections to carry out their will. This definition has been described as simple, elegant and parsimonious, making it clearer to distinguish political systems that either fulfill or fail these characteristics. This minimalist definition stands in contrast to broader definitions of democracy, which may emphasize aspects such as "representation, accountability, equality, participation, justice, dignity, rationality, security, freedom". Within such a minimalist definition, states which other scholars say have experienced democratic backsliding and which lack civil liberties, a free press, the rule of law and a constrained executive, would still be considered democracies. For Schumpeter, the formation of a government is the endpoint of the democratic process, which means that for the purposes of his democratic theory, he has no comment on what kinds of decisions that the government can take to be a democracy. Schumpeter faced pushback on his theory from other democratic theorists, such as Robert Dahl, who argued that there is more to democracy than simply the formation of government through competitive elections.


title: Joseph Schumpeter

text: Schumpeter's view of democracy has been described as "elitist", as he criticizes the rationality and knowledge of voters, and expresses a preference for politicians making decisions. Democracy is therefore in a sense a means to ensure circulation among elites. However, studies by Natasha Piano (of the University of Chicago) emphasize that Schumpeter had substantial disdain for elites as well.


title: Joseph Schumpeter

text: Schumpeter was probably the first scholar to theorize about entrepreneurship, and the field owed much to his contributions. His fundamental theories are often referred to as Mark I and Mark II. In Mark I, Schumpeter argued that the innovation and technological change of a nation come from the entrepreneurs or wild spirits. He coined the word "Unternehmergeist", German for "entrepreneur-spirit", and asserted that "... the doing of new things or the doing of things that are already being done in a new way" stemmed directly from the efforts of entrepreneurs.


title: Joseph Schumpeter

text: Schumpeter developed Mark II while a professor at Harvard. Many social economists and popular authors of the day argued that large businesses had a negative effect on the standard of living of ordinary people. Contrary to this prevailing opinion, Schumpeter argued that the agents that drive innovation and the economy are large companies that have the capital to invest in research and development of new products and services and to deliver them to customers more cheaply, thus raising their standard of living. In one of his seminal works, "Capitalism, Socialism and Democracy", Schumpeter wrote:


title: Joseph Schumpeter

text: Schumpeter was the most influential thinker to argue that long cycles are caused by innovation and are an incident of it. His treatise on how business cycles developed were based on Kondratiev's ideas which attributed the causes very differently. Schumpeter's treatise brought Kondratiev's ideas to the attention of English-speaking economists. Kondratiev fused important elements that Schumpeter missed. Yet, the Schumpeterian variant of the long-cycles hypothesis, stressing the initiating role of innovations, commands the widest attention today.


title: Joseph Schumpeter

text: In Schumpeter's view, technological innovation is the cause of both cyclical instability and economic growth. Fluctuations in innovation cause fluctuations in investment and those cause cycles in economic growth. Schumpeter sees innovations as clustering around certain points in time periods that he refers to as "neighborhoods of equilibrium", when entrepreneurs perceive that risk and returns warrant innovative commitments. These clusters lead to long cycles by generating periods of acceleration in aggregate growth.


title: Joseph Schumpeter

text: The technological view of change needs to demonstrate that changes in the rate of innovation govern changes in the rate of new investments and that the combined impact of innovation clusters takes the form of fluctuation in aggregate output or employment. The process of technological innovation involves extremely complex relations among a set of key variables: inventions, innovations, diffusion paths, and investment activities. The impact of technological innovation on aggregate output is mediated through a succession of relationships that have yet to be explored systematically in the context of the long wave. New inventions are typically primitive, their performance is usually poorer than existing technologies and the cost of their production is high. A production technology may not yet exist, as is often the case in major chemical and pharmaceutical inventions. The speed with which inventions are transformed into innovations and diffused depends on actual and expected trajectory of performance improvement and cost reduction.


title: Joseph Schumpeter

text: Schumpeter identified innovation as the critical dimension of economic change. He argued that economic change revolves around innovation, entrepreneurial activities, and market power. He sought to prove that innovation-originated market power can provide better results than the invisible hand and price competition. He argued that technological innovation often creates temporary monopolies, allowing abnormal profits that would soon be competed away by rivals and imitators. These temporary monopolies were necessary to provide the incentive for firms to develop new products and processes.


title: Joseph Schumpeter

text: The World Bank's "Doing Business" report was influenced by Schumpeter's focus on removing impediments to creative destruction. The creation of the report is credited in part to his work.


title: Joseph Schumpeter

text: Schumpeter was married three times. His first wife was Gladys Ricarde Seaver, an Englishwoman nearly 12 years his senior (married 1907, separated 1913, divorced 1925). His best man at his wedding was his friend and Austrian jurist Hans Kelsen. His second was Anna Reisinger, 20 years his junior and daughter of the concierge of the apartment where he grew up. As a divorced man, he and his bride converted to Lutheranism to marry. They married in 1925, but within a year, she died in childbirth. The loss of his wife and newborn son came only weeks after Schumpeter's mother had died. Five years after arriving to the US, in 1937, at the age of 54, Schumpeter married the American economic historian Dr. Elizabeth Boody (1898–1953), who helped him popularize his work and edited what became their magnum opus, the posthumously published "History of Economic Analysis". Elizabeth assisted him with his research and English writing until his death.


title: Joseph Schumpeter

text: Schumpeter claimed that he had set himself three goals in life: to be the greatest economist in the world, to be the best horseman in all of Austria, and the greatest lover in all of Vienna. He said he had reached two of his goals, but he never said which two, although he is reported to have said that there were too many fine horsemen in Austria for him to succeed in all his aspirations.


title: Joseph Schumpeter

text: Schumpeter died in his home in Taconic, Connecticut, at the age of 66, on the night of January 7, 1950.


title: Joseph Schumpeter

text: For some time after his death, Schumpeter's views were most influential among various heterodox economists, especially Europeans, who were interested in industrial organization, evolutionary theory, and economic development, and who tended to be on the other end of the political spectrum from Schumpeter and were also often influenced by Keynes, Karl Marx, and Thorstein Veblen. Robert Heilbroner was one of Schumpeter's most renowned pupils, who wrote extensively about him in "The Worldly Philosophers". In the journal "Monthly Review", John Bellamy Foster wrote of that journal's founder Paul Sweezy, one of the leading Marxist economists in the United States and a graduate assistant of Schumpeter's at Harvard, that Schumpeter "played a formative role in his development as a thinker". Other outstanding students of Schumpeter's include the economists Nicholas Georgescu-Roegen and Hyman Minsky and John Kenneth Galbraith and former chairman of the Federal Reserve, Alan Greenspan. Future Nobel Laureate Robert Solow was his student at Harvard, and he expanded on Schumpeter's theory.


title: Joseph Schumpeter

text: Today, Schumpeter has a following outside standard textbook economics, in areas such as economic policy, management studies, industrial policy, and the study of innovation. Schumpeter was probably the first scholar to develop theories about entrepreneurship. For instance, the European Union's innovation program, and its main development plan, the Lisbon Strategy, are influenced by Schumpeter. The International Joseph A. Schumpeter Society awards the Schumpeter Prize.


title: Joseph Schumpeter

text: The Schumpeter School of Business and Economics opened in October 2008 at the University of Wuppertal, Germany. According to University President Professor Lambert T. Koch, "Schumpeter will not only be the name of the Faculty of Management and Economics, but this is also a research and teaching programme related to Joseph A. Schumpeter."


title: Joseph Schumpeter

text: On September 17, 2009, "The Economist" inaugurated a column on business and management named "Schumpeter". The publication has a history of naming columns after significant figures or symbols in the covered field, including naming its British affairs column after former editor Walter Bagehot and its European affairs column after Charlemagne. The initial Schumpeter column praised him as a "champion of innovation and entrepreneurship" whose writing showed an understanding of the benefits and dangers of business that proved to be far ahead of its time.


title: Candaulism

text: Candaulism, or candaulesism, is a paraphilic sexual practice or fantasy in which one person exposes their partner, or images of their partner, to other people for their voyeuristic pleasure. Candaulism is also associated with voyeurism and exhibitionism.


title: Candaulism

text: The term may also be applied to the practice of undressing or otherwise exposing a female partner to others. Similarly, the term may also be applied to the posting of personal images of a female partner on the internet or urging her to wear clothing which reveals her physical attractiveness to others, such as wearing very brief clothing, such as a microskirt, tight-fitting or see-through clothing, or a low-cut top.


title: Candaulism

text: The term is derived from an account in "The Histories" of Herodotus. King Candaules of ancient Lydia, according to the story, conceived a plot to show his unaware naked wife to his servant Gyges. After discovering Gyges while he was watching her naked, Candaules' wife ordered him to choose between killing himself or killing her husband in order to repair the vicious mischief.


title: Candaulism

text: The term was first used in psychology by Richard von Krafft-Ebing in his 1886 book "Psychopathia Sexualis".


title: Candaulism

text: Isidor Sadger hypothesized that the candaulist completely identifies with his partner's body, and deep in his mind is showing himself. Candaulism is also associated with voyeurism and exhibitionism. An alternative definition proposes it as a practice involving one person observing, often from concealment, two others having sexual relations.


title: Candaulism

text: In the 1782 case of Sir Richard Worsley against George Bissett for "criminal conversation"—that is, adultery with Lady Worsley—it was revealed that Sir Richard assisted Bissett to spy on Lady Worsley taking a bath.


title: Candaulism

text: The art collector and connoisseur Charles Saatchi has considered the influence of candaulism upon the work of Salvador Dalí, citing episodes recorded by the artist's biographers in which Dalí's wife Gala was displayed to other men.


title: Candaulism

text: Robert Hanssen was an American FBI agent arrested in 2001 for spying for the Soviet Union and the Russian Federation. It was disclosed that he had taken explicit photographs of his wife and sent them to a friend. Later Hanssen invited his friend to clandestinely observe Hanssen having sex with Hanssen's wife during the friend's occasional visits to the Hanssen household. Initially, his friend watched through a window from outside the house. Later, Hanssen appropriated video equipment from the FBI to set up closed-circuit television to allow his friend to watch from his guest bedroom.


title: Beignet

text: Beignet ( , , ; ) is a type of "fritter", or deep-fried pastry, usually made from yeast dough in France, possibly made from pâte à choux and called Pets-de-nonne, nun's fart, in France, but may also be made from other types of dough, including yeast dough. In France there are many different versions of them, at least 20. They can vary in shape, the flour used for the dough, and the filling. It is popular in French, Italian, and French-American cuisines.


title: Beignet

text: The term beignet can be applied to two varieties, depending on the type of pastry. The French-style beignet in the United States has the specific meaning of deep-fried choux pastry.


title: Beignet

text: Beignets can also be made with yeast pastry, which might be called "boules de Berlin" in French, referring to Berliner doughnuts, which lack the typical doughnut hole, filled with fruit or jam.


title: Beignet

text: Louisiana-style beignets are square or rectangular fried pastries made from leavened dough rather than choux pastry. In New Orleans, they are best known as a breakfast served with powdered sugar on top. They are traditionally prepared to be eaten fresh and hot before consumption. Variations of fried dough can be found across cuisines internationally; however, the origin of the term "beignet" is specifically French. In the United States, beignets have been popular within New Orleans Creole cuisine and may also be served as a dessert. They were brought to New Orleans in the 18th century by French colonists, from "the old mother country", also brought by Acadians, and became a large part of home-style Creole cooking. Variations often include banana or plantain – popular fruits in the port city – or berries.


title: FC Barcelona 2–8 FC Bayern Munich

text: The 2019–20 UEFA Champions League quarter-final match between Barcelona and Bayern Munich was played on 14 August 2020 at the Estádio da Luz in Lisbon, Portugal. Bayern, who later went on to become champions, won the match 8–2, making it the first time Barcelona had conceded eight goals in a game since 1946, when they lost 8–1 to Sevilla in the 1946 Copa del Generalísimo.


title: FC Barcelona 2–8 FC Bayern Munich

text: In the 1998–99 UEFA Champions League group stage, Bayern defeated Barca in both matches, 1–0 at home and 2–1 away en route to Bayern topping Group D while Barcelona finished third and failed to reach the knockout stage.


title: FC Barcelona 2–8 FC Bayern Munich

text: Bayern and Barca had met in four knockout ties since 2008–09 UEFA Champions League, which yielded 26 goals prior to this game. Each time the eventual winner of the Bayern-Barca knockout tie went on not only to win the UEFA Champions League, but also complete the continental treble, which also occurred in 2009, 2013 and 2015.


title: FC Barcelona 2–8 FC Bayern Munich

text: Barcelona won 5–1 on aggregate in the quarter-finals of 2008–09 edition. Barca's 4–0 win at Camp Nou in the first leg, with all goals scored in the first half, led Bayern Munich president Franz Beckenbauer to remark "What I saw in the first half is, without doubt, the worst football in Bayern's history". Barca manager Pep Guardiola was sent off in the first leg for protesting a yellow card given to Lionel Messi, and had to watch the second leg from the stands. This defeat, as well as 0–1 home loss in a Bundesliga match against Schalke 04, eventually led to the sacking of Bayern manager Jürgen Klinsmann.


title: FC Barcelona 2–8 FC Bayern Munich

text: The semi-finals of the 2012–13 competition saw Arjen Robben and Thomas Müller inspire Bayern to a 7–0 aggregate victory, to become the biggest win of the semi-finals on aggregate, including a 3–0 win at the Camp Nou which was Barcelona's last home defeat in European competition until a 3–0 loss on 8 December 2020 to Juventus.


title: FC Barcelona 2–8 FC Bayern Munich

text: The 2014–15 UEFA Champions League semi-finals saw Lionel Messi and Neymar as the key players in a 5–3 aggregate win over Bayern, a 3–0 win at the Camp Nou and then a 3–2 defeat at the Allianz Arena. Bayern's manager at the time was Pep Guardiola, who had previously managed Barca from 2008 to 2012.


title: FC Barcelona 2–8 FC Bayern Munich

text: Both teams qualified for the knockout phase as winners of their respective groups. Both teams had also changed their coaches during the season, Bayern replaced Niko Kovač with Hansi Flick in November 2019, while Barcelona replaced Ernesto Valverde with Quique Setién in January 2020. Barcelona had faced Borussia Dortmund, Inter Milan and Slavia Prague; while Bayern, who faced Tottenham Hotspur, Olympiacos and Red Star Belgrade, won all six of their group matches, including an emphatic 7–2 win at the Tottenham Hotspur Stadium, scoring 24 goals and conceding just five. Barcelona faced Napoli in the round of 16 and won 4–2 on aggregate; while Bayern Munich beat Chelsea 7–1 on aggregate, with the second leg matches of both teams played behind closed doors due to the impact of the COVID-19 pandemic.


title: FC Barcelona 2–8 FC Bayern Munich

text: The match was played on 14 August 2020 at the Estádio da Luz in Lisbon, Portugal, as part of a single-elimination tournament, following UEFA's decision to complete the 2019–20 UEFA Champions League and 2019–20 UEFA Europa League seasons, which had been halted since March due to the COVID-19 pandemic, at neutral venues. In the opening 10 minutes, Thomas Müller fired Bayern Munich ahead following a one-two with Robert Lewandowski. Shortly after, David Alaba sliced a cross from Jordi Alba into his own net – with an unsuccessful save attempt from Manuel Neuer – to level the scores. Barcelona themselves missed two opportunities: Luis Suárez was denied by Neuer and Lionel Messi hit the post with a curling cross-shot. The following minutes took the match away from Barcelona, as Ivan Perišić smashed in a deflected shot in the 21st minute for Bayern, fed by a pass from Serge Gnabry, after a passing error from Sergi Roberto. Gnabry himself scored with a half volley straight shot from a chip through-ball by Leon Goretzka in the 27th minute, and Müller quickly added the fourth four minutes later from a cross by Joshua Kimmich.


title: FC Barcelona 2–8 FC Bayern Munich

text: In the 57th minute, a neat turn and finish from the centre of the box to the bottom-right corner by Suárez gave the Spanish side a glimmer of hope, but that proved premature, as Kimmich's side-footed finish in the 63rd minute, connecting with a delivery from Alphonso Davies – who had beaten his marker, Nélson Semedo, at the edge of the box – made the scoreline 5–2 to the Germans. Bayern scored three goals in the closing 10 minutes of the match as in-form striker Lewandowski, who had been quiet for most of the second half, headed his 14th goal of the campaign from a close-range cross by Philippe Coutinho in the 82nd minute. Then Coutinho, who was on loan to Bayern from Barcelona, made the scoreline 8–2 in the final moments of the match: first by taking advantage of a pass from Müller in the 85th minute with a right-footed shot from the centre of the box to the bottom-left corner, followed by a left-footed shot from very close range to the bottom-left corner from a headed pass by substitute Lucas Hernandez in the 89th minute.


title: FC Barcelona 2–8 FC Bayern Munich

text: Barcelona suffered their heaviest loss in 69 years; this was the first time they had conceded more than five goals in a UEFA Champions League game, and their worst concession since the 8–1 defeat to Sevilla in the round of 16 of the 1946 Copa del Generalísimo. Bayern Munich, on the other hand, continued their run of winning all UEFA Champions League matches they played in the season, and would go on to lift the title. The eight goals Bayern scored was the most a side had scored in a European Cup knockout match since Real Madrid defeated FC Swarovski Tirol 9–1 in the last 16 tie in 1990.


title: FC Barcelona 2–8 FC Bayern Munich

text: Bayern striker Robert Lewandowski became the first player to score in eight or more consecutive UEFA Champions League matches since Cristiano Ronaldo in April 2018 (eleven games), while Bayern's coach Hansi Flick became only the third manager in Champions League history to win his first six matches in charge, after Fabio Capello in 1992–93 and Luis Fernández in 1994–95. The match was also compared to the 2014 FIFA World Cup semi-final match between Brazil and Germany as Thomas Müller opened the scoring in the 7–1 routing of Brazil, which Jérôme Boateng and Manuel Neuer also took part in. Flick had been the assistant coach of Germany in that match as well.


title: FC Barcelona 2–8 FC Bayern Munich

text: Barcelona defender Gerard Piqué stated that the club needed structural changes on all levels, while club president Josep Maria Bartomeu described it as a "disaster". Three days after the game, Barcelona sacked manager Quique Setién. He was followed the next day by the club's sporting director Eric Abidal. Setién was replaced on 19 August by Ronald Koeman, who had played for the club from 1989 to 1995 and was their assistant manager under Louis van Gaal from 1998 to 2000.


title: FC Barcelona 2–8 FC Bayern Munich

text: Partly owing to this heavy defeat, Barcelona captain Lionel Messi demanded to leave Barcelona, explained his decision owed to the club's failing to compete for the Champions League title after three previous debacles in the competition (0–3 against Juventus in 2016–17 quarter-finals, 0–3 against Roma in 2017–18 quarter-finals, and 0–4 against Liverpool in 2018–19 semi-finals), by saying: "I looked further afield and I want to compete at the highest level, win titles, compete in the Champions League. You can win or lose in it, because it is very difficult, but you have to compete. At least compete for it and let us not fall apart in Rome, Liverpool and Lisbon. All that led me to think about that decision that I wanted to carry out." Although Messi ended up staying in the summer, the defeat proved to be the final involvement that Ivan Rakitić, Nélson Semedo, Luis Suárez and Arturo Vidal would have with the club, as all four players departed Barcelona during the following transfer window.


title: FC Barcelona 2–8 FC Bayern Munich

text: Bayern Munich went on to win their sixth title in the competition, overtaking Barcelona's total, following a 3–0 win over Lyon in the semi-finals and a 1–0 victory against Paris Saint-Germain in the final. This win would also secure the club's second continental treble, becoming only the second European side – after Barcelona themselves – to achieve this feat on multiple occasions.


title: FC Barcelona 2–8 FC Bayern Munich

text: Both teams would meet each other again twice later, first as part of the 2021–22 UEFA Champions League group stage, which saw Bayern Munich emerge victorious again with a 3–0 score in both matches, the second of which ultimately sent Barcelona to the UEFA Europa League for the first time in seventeen years, which further aggravated the perception of a crisis occurring within the team. "Marca" pointed that Barcelona's relegation to the Europa League was the culmination of "a glorious cycle that was coming to an end," after the team had suffered a total of ten losses by at least a three-goal margin since 2017, calling the 2–8 defeat to Bayern "the worst." Both the teams went on to meet once again in the group stage for a second consecutive time only to see Barcelona continuing their misery against Bayern after losing 2–0 away from home and 3–0 at home which also saw them getting knocked out of the Champions League twice in a row. It is the first time that Barcelona have been eliminated from the group stage twice in a row in 24 years (in the 1997–98 and 1998–99 seasons respectively, the latter also involved Bayern Munich in that season's group stage).


title: Band gap

text: In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (in electron volts) between the top of the valence band and the bottom of the conduction band in insulators and semiconductors. It is the energy required to promote a valence electron bound to an atom to become a conduction electron, which is free to move within the crystal lattice and serve as a charge carrier to conduct electric current. It is closely related to the HOMO/LUMO gap in chemistry. If the valence band is completely full and the conduction band is completely empty, then electrons cannot move within the solid because there are no available states. If the electrons are not free to move within the crystal lattice, then there is no generated current due to no net charge carrier mobility. However, if some electrons transfer from the valence band (mostly full) to the conduction band (mostly empty), then current "can" flow (see carrier generation and recombination). Therefore, the band gap is a major factor determining the electrical conductivity of a solid. Substances with large band gaps are generally insulators, those with smaller band gaps are semiconductors, while conductors either have very small band gaps or none, because the valence and conduction bands overlap to form a continuous band.


title: Band gap

text: Every solid has its own characteristic energy-band structure. This variation in band structure is responsible for the wide range of electrical characteristics observed in various materials.


title: Band gap

text: Depending on the dimension, the band structure and spectroscopy can vary. The different types of dimensions are as listed: one dimension, two dimensions, and three dimensions.


title: Band gap

text: In semiconductors and insulators, electrons are confined to a number of bands of energy, and forbidden from other regions because there are no allowable electronic states for them to occupy. The term "band gap" refers to the energy difference between the top of the valence band and the bottom of the conduction band. Electrons are able to jump from one band to another. However, in order for a valence band electron to be promoted to the conduction band, it requires a specific minimum amount of energy for the transition. This required energy is an intrinsic characteristic of the solid material. Electrons can gain enough energy to jump to the conduction band by absorbing either a phonon (heat) or a photon (light).


title: Band gap

text: A semiconductor is a material with an intermediate-sized, non-zero band gap that behaves as an insulator at T=0K, but allows thermal excitation of electrons into its conduction band at temperatures that are below its melting point. In contrast, a material with a large band gap is an insulator. In conductors, the valence and conduction bands may overlap, so there is no longer a bandgap with forbidden regions of electronic states.


title: Band gap

text: The conductivity of intrinsic semiconductors is strongly dependent on the band gap. The only available charge carriers for conduction are the electrons that have enough thermal energy to be excited across the band gap and the electron holes that are left off when such an excitation occurs.


title: Band gap

text: Band-gap engineering is the process of controlling or altering the band gap of a material by controlling the composition of certain semiconductor alloys, such as GaAlAs, InGaAs, and InAlAs. It is also possible to construct layered materials with alternating compositions by techniques like molecular-beam epitaxy. These methods are exploited in the design of heterojunction bipolar transistors (HBTs), laser diodes and solar cells.


title: Band gap

text: The distinction between semiconductors and insulators is a matter of convention. One approach is to think of semiconductors as a type of insulator with a narrow band gap. Insulators with a larger band gap, usually greater than 4 eV, are not considered semiconductors and generally do not exhibit semiconductive behaviour under practical conditions. Electron mobility also plays a role in determining a material's informal classification.


title: Band gap

text: The band-gap energy of semiconductors tends to decrease with increasing temperature. When temperature increases, the amplitude of atomic vibrations increase, leading to larger interatomic spacing. The interaction between the lattice phonons and the free electrons and holes will also affect the band gap to a smaller extent. The relationship between band gap energy and temperature can be described by Varshni's empirical expression (named after Y. P. Varshni),


title: Band gap

text: Furthermore, lattice vibrations increase with temperature, which increases the effect of electron scattering. Additionally, the number of charge carriers within a semiconductor will increase, as more carriers have the energy required to cross the band-gap threshold and so conductivity of semiconductors also increases with increasing temperature.


title: Band gap

text: In a regular semiconductor crystal, the band gap is fixed owing to continuous energy states. In a quantum dot crystal, the band gap is size dependent and can be altered to produce a range of energies between the valence band and conduction band. It is also known as quantum confinement effect.


title: Band gap

text: Band gaps also depend on pressure. Band gaps can be either direct or indirect, depending on the electronic band structure of the material.


title: Band gap

text: It was mentioned earlier that the dimensions have different band structure and spectroscopy. For non-metallic solids, which are one dimensional, have optical properties that are dependent on the electronic transitions between valence and conduction bands. In addition, the spectroscopic transition probability is between the initial and final orbital and it depends on the integral.φ is the initial orbital, φ is the final orbital, ʃ φûεφ is the integral, ε is the electric vector, and u is the dipole moment.


title: Band gap

text: Two-dimensional structures of solids behave because of the overlap of atomic orbitals. The simplest two-dimensional crystal contains identical atoms arranged on a square lattice. Energy splitting occurs at the Brillouin zone edge for one-dimensional situations because of a weak periodic potential, which produces a gap between bands. The behavior of the one-dimensional situations does not occur for two-dimensional cases because there are extra freedoms of motion. Furthermore, a bandgap can be produced with strong periodic potential for two-dimensional and three-dimensional cases.


title: Band gap

text: Based on the their band structure, materials are characterised with a direct band gap or indirect band gap. In the free-electron model, k is the momentum of a free electron and assumes unique values within the Brillouin zone that outlines the periodicity of the crystal lattice. If the momentum of the lowest energy state in the conduction band and the highest energy state of the valence band of a material have the same value, then the material has a direct bandgap. If they are not the same, then the material has an indirect band gap and the electronic transition must undergo momentum transfer to satisfy conservation. Such indirect "forbidden" transitions still occur, however at very low probabilities and weaker energy. For materials with a direct band gap, valence electrons can be directly excited into the conduction band by a photon whose energy is larger than the bandgap. In contrast, for materials with an indirect band gap, a photon and phonon must both be involved in a transition from the valence band top to the conduction band bottom, involving a momentum change. Therefore, direct bandgap materials tend to have stronger light emission and absorption properties and tend to be better suited for photovoltaics (PVs), light-emitting diodes (LEDs), and laser diodes; however, indirect bandgap materials are frequently used in PVs and LEDs when the materials have other favorable properties.


title: Band gap

text: LEDs and laser diodes usually emit photons with energy close to and slightly larger than the band gap of the semiconductor material from which they are made. Therefore, as the band gap energy increases, the LED or laser color changes from infrared to red, through the rainbow to violet, then to UV.


title: Band gap

text: The optical band gap (see below) determines what portion of the solar spectrum a photovoltaic cell absorbs. A semiconductor will not absorb photons of energy less than the band gap; and the energy of the electron-hole pair produced by a photon is equal to the bandgap energy. A luminescent solar converter uses a luminescent medium to downconvert photons with energies above the band gap to photon energies closer to the band gap of the semiconductor comprising the solar cell.


title: Band gap

text: Below are band gap values for some selected materials. For a comprehensive list of band gaps in semiconductors, see List of semiconductor materials.


title: Band gap

text: In materials with a large exciton binding energy, it is possible for a photon to have just barely enough energy to create an exciton (bound electron–hole pair), but not enough energy to separate the electron and hole (which are electrically attracted to each other). In this situation, there is a distinction between "optical band gap" and "electronic band gap" (or "transport gap"). The optical bandgap is the threshold for photons to be absorbed, while the transport gap is the threshold for creating an electron–hole pair that is "not" bound together. The optical bandgap is at lower energy than the transport gap.


title: Band gap

text: In almost all inorganic semiconductors, such as silicon, gallium arsenide, etc., there is very little interaction between electrons and holes (very small exciton binding energy), and therefore the optical and electronic bandgap are essentially identical, and the distinction between them is ignored. However, in some systems, including organic semiconductors and single-walled carbon nanotubes, the distinction may be significant.


title: Band gap

text: In photonics, band gaps or stop bands are ranges of photon frequencies where, if tunneling effects are neglected, no photons can be transmitted through a material. A material exhibiting this behaviour is known as a photonic crystal. The concept of hyperuniformity has broadened the range of photonic band gap materials, beyond photonic crystals. By applying the technique in supersymmetric quantum mechanics, a new class of optical disordered materials has been suggested, which support band gaps perfectly equivalent to those of crystals or quasicrystals.


title: World Boxing Association

text: The World Boxing Association (WBA), formerly known as the National Boxing Association (NBA), is the oldest and one of four major organizations which sanction professional boxing bouts, alongside the World Boxing Council (WBC), International Boxing Federation (IBF) and World Boxing Organization (WBO). The WBA awards its world championship title at the professional level. Founded in the United States in 1921 by 13 state representatives as the NBA, in 1962 it changed its name in recognition of boxing's growing popularity worldwide and began to gain other nations as members.


title: World Boxing Association

text: By 1975, a majority of votes were held by Latin American nations and the organization headquarters had moved to Panama. After being located during the 1990s and early 2000s in Venezuela, the organization offices returned to Panama in 2007. It is the oldest of the four major organizations recognized by the International Boxing Hall of Fame (IBHOF), which sanction world championship boxing bouts, alongside the WBC, IBF and WBO.


title: World Boxing Association

text: The World Boxing Association can be traced back to the original National Boxing Association, organized in 1921. The first bout it recognized was the Jack Dempsey–Georges Carpentier heavyweight championship bout in New Jersey.


title: World Boxing Association

text: The NBA was formed by representatives from 13 American states, including Sam Milner, to counterbalance the influence that the New York State Athletic Commission (NYSAC) wielded. The NBA and the NYSAC sometimes crowned different "world champions" in the same division, leading to confusion about who was the real champion.


title: World Boxing Association

text: Originally more comparable to the present American Association of Boxing Commissions than to its offspring and successor, the NBA sanctioned title bouts, published lists of outstanding challengers, withdrew titular recognition, but did not attempt to appoint its own title bout officials or otherwise impose its will on championship fights. It also did not conduct purse bids or collect "sanctioning fees."


title: World Boxing Association

text: The NBA officially became the WBA on 23 August 1962. Gilberto Mendoza was the President of the WBA from 1982 until his death in 2016, after which Gilberto Mendoza Jr. took over as president. In the 1990s, the WBA moved its central offices from Panama City, Panama, to Caracas, Venezuela. In January 2007, it returned its offices to Panama.


title: World Boxing Association

text: As has been the case with all major boxing sanctioning organizations, the WBA has been plagued with charges of corrupt practices. In a 1981 "Sports Illustrated" article, a boxing judge claimed he was influenced by WBA President Gilberto Mendoza to judge certain fighters competing for their titles more favorably. The same article also discussed a variety of bribes paid to WBA officials to obtain championship bout opportunities, or higher placement within the organization's rankings. In a 1982 interview, boxing promoter Bob Arum claimed that he had to pay off WBA officials to obtain rankings for his fighters. Further support for allegations of this nature came in the 1980s and 1990s as two other organizations would have similar corruption exposed, including the conviction and imprisonment of IBF President Bob Lee and Graciano Rocchigiani's successful civil prosecution of the WBC that resulted in the organization briefly filing for bankruptcy before reaching a settlement that saved it from collapse.


title: World Boxing Association

text: Until the fall of 2021, the WBA recognized up to four world champions in any given weight division, to the point of rendering it technically impossible under certain conditions for a WBA world champion to even hold sole recognition from the organization as its champion in a division.


title: World Boxing Association

text: The most prominent designation is that of the WBA Super champion, which was created in 2000 following a suggestion by Lennox Lewis after he was forced to relinquish his WBA heavyweight title prior to his defense against Michael Grant. This distinction was initially reserved for WBA champions who are simultaneously recognized by the WBC, IBF or WBO. A WBA Super champion is afforded special consideration by the organization with respect to meeting mandatory defense obligations to maintain championship recognition, but it also has opened the door for the organization to recognize a separate world champion, commonly referred to as the Regular champion; creating confusion among fans as to who holds the de facto championship title. Some world champions have been upgraded to WBA Super champion status without winning another organization's title, among them Floyd Mayweather Jr., Chris John, Anselmo Moreno and Manny Pacquiao; or upon defending their WBA title five or more times. Upon awarding a WBA Super championship, the regular world champion status is deemed vacant, whereupon it is filled by the organization as a separate championship. On March 5, 2021, Claressa Shields became the inaugural WBA Super women's champion at light middleweight.


title: World Boxing Association

text: The WBA further complicated this from time to time by recognizing an interim champion, ostensibly in cases where a designated world champion is, for some reason, prohibited from making a timely defense of their title. Under such conditions, the interim title holder is to be the next person to compete for one of the full championship titles once the champion is in a position to compete. In practice, however, this actually occurred rarely if ever and in 2019 the organization began awarding the WBA Gold title, for which no provision exists even within the organization's own governing documents. As of December 2019 for example, they simultaneously recognized a WBA Super champion (Anthony Joshua), WBA champion (Manuel Charr), WBA interim champion (Trevor Bryan) and WBA Gold champion (Robert Helenius) in the heavyweight division.


title: World Boxing Association

text: There have even been instances where different WBA world champions have defended versions of the same title, in the same weight class, on the same date in different events.


title: World Boxing Association

text: Following the controversial decision in the Gabriel Maestre vs. Mykal Fox fight on August 7, 2021 amid immense public pressure, the WBA finally began eliminating all interim titles in the attempt to return to a single champion per weight division.


title: World Boxing Association

text: The organization has further garnered negative attention with respect to its ranking of boxers, in spite of having adopted a complex, documented rating formula in the 2000s. In 2015 for example, Ali Raymi had been rated number six when, in his service as a colonel in the Yemeni armed forces, he was killed. His death didn't significantly hinder his rating position in the WBA however, as in a subsequent ranking he had only dropped to number eleven.


title: World Boxing Association

text: In August 2021, a letter sent by the ABC stating that the WBA having multiple titles is "misleading to the public and the boxers". The ABC also stated that if the WBA fails to do a satisfactory action regarding the issue, they would recommend to its members:


title: World Boxing Association

text: The WBA in turn responded by declaring all of their "Interim" titles vacant. They then ordered tournaments to determine a single champion of their weight classes.


title: World Boxing Association

text: At minimumweight, "Regular" champion Vic Saludar was ordered to face former "Interim" champion Erick Rosa on August 26th 2021, with Rosa winning the "Regular" title via split decision on 21st December. it wasn’t until September 29th 2022 until the WBA officially ordered Rosa against "Super" champion Knockout CP Freshmart, with the fight set to take place in the first quarter of 2023 to determine the sole champion.


title: World Boxing Association

text: At light flyweight, "Super" champion Hiroto Kyoguchi and "Regular" champion Esteban Bermudez had already been ordered to fight prior to the ABC letter on June 10th 2021, but complications meant it wasn’t until January 28th 2022 when purse bids were due to be held, however injury to Kyoguchi meant the WBA instead approved the rematch between Bermudez and former regular champion Carlos Cañizales 2 days earlier on January 26th. Bermudez vs Cañizales did not end up happening due to the latter’s short-lived decision to move up to flyweight, and thus Kyoguchi-Bermudez took place on June 10th, with Kyoguchi winning by TKO. Former "Interim" champion Daniel Matellon was ordered to face Cañizales on September 30th in a final eliminator for the "Super" title, with the winner becoming mandatory to Kenshiro Teraji, who defeated Kyoguchi by TKO in November, in a fight to determine the sole champion.


title: World Boxing Association

text: At flyweight, the removal of "Interim" champions meant Artem Dalakian was left as sole champion of the division. Despite never being upgraded to "Super" champion, Dalakian had been the WBA’s primary champion since winning the title in 2018, due to the absence of a Super champion since 2015. Dalakian was ordered to face former "Interim" champion Luis Concepción on August 19th 2021, whom he defeated by TKO on November 20th to remain sole champion.


title: World Boxing Association

text: At super flyweight, "Super" champion Juan Francisco Estrada was ordered to face "Regular" champion Joshua Franco on February 9th, with the fight going to purse bid on April 19th. Despite it being announced on May 17th that the fight would take place on July 16th, Estrada was disowned and stripped by the Championships Commitee on August 11th, leaving Franco as the sole champion of the division.


title: World Boxing Association

text: At bantamweight, "Regular" champion Guillermo Rigondeaux was stripped of his title on August 14th 2021 after facing then WBO champion John Riel Casimero. The WBA announced its refusal to sanction the fight on July 23rd, in respect of restrictions placed on "Regular" titles by the WBO, and declared Rigondeaux would have to request to be ranked in order to follow through with the fight, in which his "Regular" title would be declared vacant. "Super" champion Naoya Inoue then became sole champion.


title: World Boxing Association

text: At super bantamweight, Brandon Figueroa was stripped of his "Regular" title on December 2nd 2021 after facing Stephen Fulton in a WBC and WBO unification on November 27th. This was due to restrictions imposed by the WBO who refuse to sanction fights involving the "Regular" title, with the WBA respecting this and announcing on August 17th (before the ABC letter) that Figueroa would be stripped. This came after Figueroa was allowed to unify in his previous fight with then WBC champion Luis Nery on May 15th, as the WBC do not impose the same restrictions on the Regular title. This left "Super" champion Murodjohn Akhmadaliev as sole champion. Former "Interim" champion Ra’eese Aleem did not move forward any with WBA sanctioned fight and was subsequently dropped from the initial mandatory position.


title: World Boxing Association

text: At featherweight, "Regular" champion Leigh Wood was ordered to face former "Interim" champion Michael Conlan on August 27th 2021, with Wood winning by KO on 12th March 2022. On April 6th, the WBA ordered the bout between Wood and "Super" champion Léo Santa Cruz. On July 19th, the WBA rejected a request from Santa Cruz to unify with WBC champion Rey Vargas, insisting he had to fight Wood, which Santa Cruz accepted 2 days later on July 21st. On August 12th, it was announced that Santa Cruz and Wood had reached an agreement, and thus purse bids were cancelled. On August 24th, the WBA announced they had approved the previously rejected unification between Santa Cruz and Vargas, as well as a title defence for Wood against Mauricio Lara, with the winners set to fight each other. Wood, who was due to fight Lara on September 24th, pulled out with an injury on September 19th, and on September 30th the WBA ruled Wood must face Santa Cruz in his comeback fight, and refused to grant any additional exceptions. Purse bids were scheduled for December 12th, however did not take place due to Santa Cruz relinquishing his "Super" title and leaving Wood as the sole champion of the division.


title: World Boxing Association

text: At super featherweight, Gervonta Davis vacated his "Super" title on August 28th 2021, leaving then "Regular" champion Roger Gutiérrez as the sole champion. Gutiérrez had been ordered to face former "Interim" champion Chris Colbert on August 15th, but following Gutierrez’s withdrawal, replacement Héctor Garcia defeated Colbert via unanimous decision to become mandatory challenger on 26th February 2022. The WBA thus ordered Gutiérrez vs Garcia on June 27th, with Garcia winning a unanimous decision victory to become champion on 20th August 2022.


title: World Boxing Association

text: At lightweight, "Regular" champion Gervonta Davis was due to face former "Interim" champion Rolando Romero on December 5th 2021, but following withdrawal from Romero instead faced Isaac Cruz, winning by unanimous decision. The WBA then formally ordered Davis Vs Romero on January 24th 2022, with Davis winning via TKO on May 28th to retain the "Regular" title. As of December 2022, a fight between Davis and "Super" champion Devin Haney has not been ordered.


title: World Boxing Association

text: At super lightweight, Gervonta Davis vacated his "Regular" title on December 8th 2021, leaving then "Super" champion Josh Taylor as sole champion. Taylor was then ordered to face former "Interim" champion Alberto Puello on March 9th 2022, but was stripped on May 14th for failing to sign the contract. Puello was then ordered to face Batyr Akhmedov on June 12th following a panel to determine the next challenger, with Puello winning via split decision on August 20th to become champion.


title: World Boxing Association

text: At welterweight, the WBA ordered a 4-man box off on September 16th 2021, consisting of "Super" champion Yordenis Ugas against Eimantas Stanionis and "Regular" champion Jamal James against Radzhab Butaev, with the winners set to face each other to determine one champion. On October 20th, the WBA initally rejected permission from Ugas to unify with WBC and IBF champion Errol Spence Jr., while Butaev defeated James via TKO on October 30th to become "Regular" champion. On February 8th 2022, it was announced that Ugas and Spence Jr. would indeed unify on April 16th, followed by the announcement of Butaev vs Stanionis on the undercard on February 21st. On April 16th, Stanionis defeated Butaev via split decision to become "Regular" champion, while Spence Jr. defeated Ugas via TKO to become "Super" champion. Following this on November 21st, the WBA granted special permission for Spence Jr. to defend his titles against former unified champion Keith Thurman, while Stanionis was instead ordered to face Vergil Ortiz Jr., with the winners set to meet. Former "Interim" champion Gabriel Maestre was not included in the WBA’s box off, and subsequently did not receive any title shot.


title: World Boxing Association

text: At super welterweight, "Regular" champion Erislandy Lara was forced to vacate on August 31st 2021, leaving "Super" champion Jermell Charlo as sole champion.


title: World Boxing Association

text: At middleweight, "Super" champion Gennady Golovkin was ordered to face Regular champion Erislandy Lara on September 23rd 2022. Former "Interim" champion Chris Eubank Jr. did not move forward with any WBA sanctioned fight and was thus dropped from the initial mandatory position.


title: World Boxing Association

text: At super middleweight, there has been no fights ordered for any WBA "World" title since the title reduction plan as of December 2022. Canelo Álvarez and David Morrell are the "Super" and "Regular" champions, respectively.


title: World Boxing Association

text: At light heavyweight, the removal of "Interim" champions meant "Super" champion Dmitry Bivol became sole champion. Former "Interim" champion Robin Krasniqi lost in a rematch to Dominic Boesel on 10th October, 2021, with Boesel becoming #1 challenger for Bivol. Boesel fought #2 ranked Gilberto Ramirez in a final eliminator to determine the mandatory challenger on 14th May 2022, with Ramirez winning by knockout. Bivol Vs Ramirez was then ordered on 11th July, with Bivol winning via unanimous decision on 5th November.


title: World Boxing Association

text: At cruiserweight, "Super" champion Arsen Goulamirian and "Regular" champion Ryad Merhy had been ordered to fight on July 19th 2022 (a rematch of their 2018 "Interim" title fight). Merhy instead pursued a fight with WBC champion Illunga Makabu, however after concerns with making the cruiserweight limit, Makabu vs Merhy was called off on August 8th, and Merhy sent a formal letter to the WBA vacating his title 4 days later on August 12th, leaving Goulamirian as the sole champion.


title: World Boxing Association

text: At heavyweight, "Regular" champion Trevor Bryan was ordered to face former "Interim" champion Daniel Dubois on January 31st 2022, with Dubois winning via KO on June 11th. Following this, Dubois was ordered to face "Super" champion Oleksandr Usyk on December 12th.


title: World Boxing Association

text: As of December 2022, 11 divisions; Light flyweight, Flyweight, Super flyweight, Bantamweight, Super bantamweight, Featherweight, Super featherweight, Super lightweight, Super welterweight, Light heavyweight and Cruiserweight now only consist of one, sole champion.


title: World Boxing Association

text: Since 2015, the WBA awards a customized version of their WBA Super champion belt to big fights involving a WBA championship. The WBA called this the "Man of Triumph" belt, named after the trophy awarded to the winner of the Mayweather vs. Pacquiao fight. The plate of the belt has the images of the two boxers fighting. Floyd Mayweather Jr. received the first gold-plated version of the belt while Manny Pacquiao was awarded a one-time rhodium-plated version. Other recipients of the custom gold-plated belt are Anthony Joshua, Vasyl Lomachenko, Manny Pacquiao, Oleksandr Usyk, Canelo Álvarez and Callum Smith.


title: World Boxing Association

text: The WBA signed a cooperation agreement with the amateur governing body International Boxing Association in 2022.


title: Land of the Lustrous

text: "Land of the Lustrous" is set in a far, distant future where the Earth had been struck six times by meteorites, ravaging it in the process. All of the remaining land was reduced to a single coast, whereas nearly all life was destroyed. Over vast stretches of time, a new race of sentient lifeforms emerged; immortal jewels that take the form of people. Phosphophyllite (Phos) is weak (with one of the lowest hardnesses) and considered useless by their peers. Phos asks their aloof but wise colleague Cinnabar for help after they receive an assignment to create a natural history encyclopedia, thus beginning their friendship and personal growth. Meanwhile, the "jewel people" are at war with the Lunarians (Moon people) who want to take advantage of their luxury value.