title: Operation Yellow Ribbon

text: Some airports were awarded for how they handled the crisis. The British Columbia Aviation Council presented its 2001 Airport Management Award to Vancouver International Airport, citing its professional and compassionate handling of the situation, while the Canadian Public Relations Society (Nova Scotia) presented Halifax International an Amethyst Award in the Crisis Communications category to honour the authority's crisis communication response to the situation.


title: Operation Yellow Ribbon

text: On September 11, 2002, about 2,500 people gathered at Gander International Airport for Canada's memorial service to mark the first anniversary of the attacks, over which Chrétien, Collenette, and Cellucci and other provincial and local officials presided. Chrétien addressed them: "9/11 will live long in memory as a day of terror and grief. But thanks to the countless acts of kindness and compassion done for those stranded visitors here in Gander and right across Canada it will live forever in memory as a day of comfort and of healing" and closed his speech by commending Operation Yellow Ribbon, "You did yourselves proud, ladies and gentlemen, and you did Canada proud."


title: Operation Yellow Ribbon

text: It was dramatized in the CBC miniseries "Diverted" and is the subject of the Broadway musical "Come from Away", written by the Canadian writing team of Irene Sankoff and David Hein. The musical follows the stories of several passengers, Newfoundlanders, and flight crews in the days following 9/11. The show ran on Broadway at the Schoenfeld Theatre starting in 2017, and is scheduled to close on October 2, 2022. It received seven nominations in the 2017 71st Tony Awards, including best musical. It won a Tony Award for Best Direction of a Musical. Gander's part in Operation Yellow Ribbon is examined in the 2018 film "You Are Here", which won the Canadian Screen Award for best documentary.


title: Operation Yellow Ribbon

text: The efforts of Gander Center and Gander Air Traffic control during Operation Yellow Ribbon were showcased on a Discovery Channel documentary entitled "9/11: CLEARED FOR CHAOS."


title: Bolbbalgan4

text: Bolbbalgan4 (), also known as BOL4 or Blushing Youth, is a South Korean musical act formed by Shofar Music in 2016. They appeared on "Superstar K6" in 2014 before signing a contract with their current agency. BOL4 was originally a duo consisting of Ahn Ji-young and Woo Ji-yoon. They debuted with the single "Fight Day" from the mini-album "Red Ickle" on April 22, 2016. The first syllable of the Korean word "puberty" is pronounced the same as the Sino-Korean numeral four (), and accordingly the group name is sometimes shortened to BOL4.


title: Bolbbalgan4

text: The duo went on a temporary hiatus due to Ahn's music classes requirements in the first half of 2018. Bolbbalgan4 signed with King Records and debuted in Japan on June 5, 2019, with the mini-album "Red Planet (Japan Edition)".


title: Bolbbalgan4

text: On April 2, 2020, Shofar Music announced that Woo Ji-yoon had left the duo, and Ahn Ji-young will continue to promote as Bolbbalgan4.


title: Bolbbalgan4

text: Jiyoung and Jiyoon were both raised in Yeongju, North Gyeongsang Province, and were classmates. They had previously competed SuperStarK6 in 2014. Since they were young they had dreamed of becoming singers. The name of their duo was built on the grounds that they wanted to make the kind of pure, honest music that can only be found in adolescence. Jiyoon portrays the "blushing" part of the name because she is often shy, while Jiyoung portrays "youth" because she acts like an adolescent girl.


title: 2021–22 Men's FIH Pro League

text: The 2021–22 Men's FIH Pro League was the third edition of the Men's FIH Pro League, a field hockey championship for men's national teams. The tournament started in October 2021 and finished in June 2022.


title: 2021–22 Men's FIH Pro League

text: The home and away principle was kept but this principle was split over two consecutive seasons and work according to the following example:


title: 2021–22 Men's FIH Pro League

text: If one of the two matches played between two teams was cancelled, the winner of the other match would have received double points.


title: 2021–22 Men's FIH Pro League

text: Originally, nine teams were scheduled to compete in a round-robin tournament, being played from October 2021 to June 2022. On 17 September 2021, both New Zealand and Australia withdrew due to the COVID-19 pandemic and the travel restrictions coming with it. Canada and South Africa joined on 8 December 2021. On 17 January 2022, Canada withdrew due to the COVID-19 Omicron variant and the travel restrictions coming with it, six weeks after being named New Zealand substitute. France was announced as Canada's substitute on 25 January 2022.


title: Yahweh ben Yahweh

text: Yahweh ben Yahweh (born Hulon Mitchell Jr.; October 27, 1935 – May 7, 2007) was an American religious leader, black separatist and founder of the Nation of Yahweh, a new religious movement headquartered in Florida that had thousands of black American devotees at its peak. He preached that Jesus is black but white devils are in charge temporarily, and was accused of teaching hate. Yahweh was later indicted on three counts of federal racketeering and extortion charges, of which he was found not guilty. However, he was convicted of conspiracy to commit murder.


title: Yahweh ben Yahweh

text: Yahweh ben Yahweh was born Hulon Mitchell Jr. on October 27, 1935. One of 15 children born to Hulon Mitchell Sr., the minister of the Antioch Church of God in Christ in Enid, Oklahoma, and Pearl O. Mitchell ( Leatherman), pianist for the same congregation.


title: Yahweh ben Yahweh

text: After leaving Oklahoma, Mitchell joined the military and then attended law school. He moved to Atlanta, Georgia, where in the 1960s he joined the Nation of Islam (NOI) and took the name Hulon X. After leaving the NOI in the late 1960s, he became a faith healing Christian preacher and named himself Father Mitchell, fashioning himself after Father Divine and Samuel "Father Jehovia" Morris, two African-American ministers and self-proclaimed divine connections to God who were active during the early 20th century. Mitchell arrived in Miami, Florida in 1978, where he gathered members of the city's Black Hebrew Israelite congregations and founded the Nation of Yahweh.


title: Yahweh ben Yahweh

text: Broadly classified as a branch of the Black Hebrew Israelite movement, Mitchell's doctrine emphasized the belief that God and all of the prophets of the Bible were black and that blacks would gain the knowledge of their true history through Mitchell himself. He also characterized whites and Jews as infidels and oppressors. Mitchell emphasized loyalty to himself as the son of God, Yahweh.


title: Yahweh ben Yahweh

text: Mitchell's business and charity efforts earned him respect in the community. Then-Miami mayor Xavier Suárez declared "Yahweh ben Yahweh Day" on October 7, 1990, a month before Ben Yahweh's indictment.


title: Yahweh ben Yahweh

text: Although Yahweh ben Yahweh's followers remained devoted to him, he was in trouble with the law by the 1990s. Between 1990 and 2001, he served eleven years of an eighteen-year sentence on a Racketeer Influenced and Corrupt Organizations Act (RICO) conviction after he and several other Nation of Yahweh members were convicted of conspiracy for ex followers role in more than a dozen murders. Robert Rozier, a former NFL player and a devotee of Mitchell, confessed to seven of these murders.


title: Yahweh ben Yahweh

text: Ben Yahweh faced conviction only for conspiracy to murder. A primary component of the prosecution's case was Rozier, who testified in return for a lighter sentence. Rozier later entered the Witness Protection Program, but returned to prison on a sentence of 25 years to life under California's three strikes law, following a check kiting conviction. Mitchell had the Federal Bureau of Prisons ID# 22031-034.


title: Yahweh ben Yahweh

text: Ben Yahweh was released on parole in 2001 and returned to Miami, but his activities were strongly restricted until a few months before his death. He was prohibited from reconnecting with his old congregation.


title: Yahweh ben Yahweh

text: To ensure this, he was restricted from any form of speech by Internet, telephone, computer, radio or television that could place him in contact with any Nation of Yahweh members.


title: Yahweh ben Yahweh

text: In 2006, as he became increasingly ill with prostate cancer, ben Yahweh’s attorney, Jayne Weintraub, petitioned the U.S. District Court for his release from parole to permit him to "die with dignity".


title: Yahweh ben Yahweh

text: Mitchell died on May 7, 2007 at the age of 71. The location was not disclosed. "Yahweh will be remembered and mourned by the millions of people that he touched through prayer and teachings", his lawyers, Jayne Weintraub and Steven Potolsky, said in a joint statement.


title: Yahweh ben Yahweh

text: The story of the police investigation and prosecution of Yahweh ben Yahweh is the subject of an episode of "The FBI Files" entitled "Temple of Fear" (Season 3, Episode 10) as well as an Investigation Discovery Channel episode of "Most Infamous" (Season 2, Episode1).


title: Yahweh ben Yahweh

text: One of Mitchell's siblings is his younger sister, Leona Mitchell, a soprano who sang at the Metropolitan Opera.


title: Nitrite

text: The nitrite ion has the chemical formula . Nitrite (mostly sodium nitrite) is widely used throughout chemical and pharmaceutical industries. The nitrite anion is a pervasive intermediate in the nitrogen cycle in nature. The name nitrite also refers to organic compounds having the –ONO group, which are esters of nitrous acid.


title: Nitrite

text: Sodium nitrite is made industrially by passing a mixture of nitrogen oxides into aqueous sodium hydroxide or sodium carbonate solution:


title: Nitrite

text: The product is purified by recrystallization. Alkali metal nitrites are thermally stable up to and beyond their melting point (441 °C for KNO). Ammonium nitrite can be made from dinitrogen trioxide, NO, which is formally the anhydride of nitrous acid:


title: Nitrite

text: The nitrite ion has a symmetrical structure (C symmetry), with both N–O bonds having equal length and a bond angle of about 115°. In valence bond theory, it is described as a resonance hybrid with equal contributions from two canonical forms that are mirror images of each other. In molecular orbital theory, there is a sigma bond between each oxygen atom and the nitrogen atom, and a delocalized pi bond made from the p orbitals on nitrogen and oxygen atoms which is perpendicular to the plane of the molecule. The negative charge of the ion is equally distributed on the two oxygen atoms. Both nitrogen and oxygen atoms carry a lone pair of electrons. Therefore, the nitrite ion is a Lewis base.


title: Nitrite

text: Nitrous acid is also highly volatile – in the gas phase it exists predominantly as a "trans"-planar molecule. In solution, it is unstable with respect to the disproportionation reaction:


title: Nitrite

text: This reaction is slow at 0 °C. Addition of acid to a solution of a nitrite in the presence of a reducing agent, such as iron(II), is a way to make nitric oxide (NO) in the laboratory.


title: Nitrite

text: The formal oxidation state of the nitrogen atom in nitrite is +3. This means that it can be either oxidized to oxidation states +4 and +5, or reduced to oxidation states as low as −3. Standard reduction potentials for reactions directly involving nitrous acid are shown in the table below:


title: Nitrite

text: Oxidation reactions usually result in the formation of the nitrate ion, with nitrogen in oxidation state +5. For example, oxidation with permanganate ion can be used for quantitative analysis of nitrite (by titration):


title: Nitrite

text: The product of reduction reactions with nitrite ion are varied, depending on the reducing agent used and its strength. With sulfur dioxide, the products are NO and NO; with tin(II) (Sn) the product is hyponitrous acid (HNO); reduction all the way to ammonia (NH) occurs with hydrogen sulfide. With the hydrazinium cation () the product of nitrite reduction is hydrazoic acid (HN), an instable and explosive compound:


title: Nitrite

text: This reaction is unusual in that it involves compounds with nitrogen in four different oxidation states.


title: Nitrite

text: Nitrite is detected and analyzed by the Griess Reaction, involving the formation of a deep red-colored azo dye upon treatment of a -containing sample with sulfanilic acid and naphthyl-1-amine in the presence of acid.


title: Nitrite

text: Nitrite is an ambidentate ligand and can form a wide variety of coordination complexes by binding to metal ions in several ways. Two examples are the red nitrito complex [Co(NH)(ONO)] is metastable, isomerizing to the yellow nitro complex [Co(NH)(NO)]. Nitrite is processed by several enzymes, all of which utilize coordination complexes.


title: Nitrite

text: In nitrification, ammonium is converted to nitrite. Important species include "Nitrosomonas". Other bacterial species such as "Nitrobacter", are responsible for the oxidation of the nitrite into nitrate.


title: Nitrite

text: Nitrite can be reduced to nitric oxide or ammonia by many species of bacteria. Under hypoxic conditions, nitrite may release nitric oxide, which causes potent vasodilation. Several mechanisms for nitrite conversion to NO have been described, including enzymatic reduction by xanthine oxidoreductase, nitrite reductase, and NO synthase (NOS), as well as nonenzymatic acidic disproportionation reactions.


title: Nitrite

text: Azo dyes and other colorants are prepared by the process called diazotization, which requires nitrite.


title: Nitrite

text: Sodium nitrite is used to speed up the curing of meat and also impart an attractive colour. A 2018 study by the British Meat Producers Association determined that legally permitted levels of nitrite have no effect on the growth of the "Clostridium botulinum" bacteria which causes botulism, in line with the UK's Advisory Committee on the Microbiological Safety of Food opinion that nitrites are not required to prevent "Clostridium botulinum" growth and extend shelf life. In the U.S., meat cannot be labeled as "cured" without the addition of nitrite. In some countries, cured-meat products are manufactured without nitrate or nitrite, and without nitrite from vegetable source. Parma ham, produced without nitrite since 1993, was reported in 2018 to have caused no cases of botulism.


title: Nitrite

text: In mice, food rich in nitrites together with unsaturated fats can prevent hypertension, which is one explanation for the apparent health effect of the Mediterranean diet. However, adding nitrites to meat has been shown to generate known carcinogens; the World Health Organization (WHO) advises that eating of nitrite processed meat a day would raise the risk of getting bowel cancer by 18% over a lifetime.


title: Nitrite

text: The recommended maximum limits by the World Health Organization in drinking water are 3 mg L and 50 mg L for nitrite and nitrate ions, respectively.


title: Nitrite

text: In a reaction with the meat's myoglobin, nitrite gives the product a desirable pink-red "fresh" color, such as with corned beef. In the US, nitrite has been formally used since 1925. According to scientists working for the industry group American Meat Institute, this use of nitrite started in the Middle Ages. Historians and epidemiologists argue that the widespread use of nitrite in meat-curing is closely linked to the development of industrial meat-processing. French investigative journalist Guillaume Coudray asserts that the meat industry chooses to cure its meats with nitrite even though it is established that this chemical gives rise to cancer-causing nitroso-compounds.


title: Nitrite

text: Nitrites in the form of Sodium Nitrite and Amyl Nitrite are components of many cyanide antidote kits. Both of these compounds bind to haemoglobin and oxidizes the Fe ions to Fe ions forming methaemoglobin. Methaemoglobin in turn binds to cyanide (CN) creating cyanmethaemoglobin, effectively removing cyanide from the Complex IV of the Electron transport chain (ETC) in mitochondria, which is the primary site of disruption caused by cyanide. Another mechanism by which nitrites are useful in treating cyanide toxicity is the generation of Nitric oxide (NO). NO displaces the CN from the Cytochrome c Oxidase (ETC complex IV), making it available for methaemoglobin to bind.


title: Nitrite

text: In organic chemistry, alkyl nitrites are esters of nitrous acid and contain the nitrosoxy functional group. Nitro compounds contain the C–NO group. Nitrites have the general formula RONO, where R is an aryl or alkyl group. Amyl nitrite and other alkyl nitrites have a vasodilating action and must be handled in the laboratory with caution. They are sometimes used in medicine for the treatment of heart diseases. A classic named reaction for the synthesis of alkyl nitrites is the Meyer synthesis in which alkyl halides react with metallic nitrites to a mixture to nitroalkanes and nitrites.


title: Nitrite

text: Nitrites salts can react with secondary amines to produce "N"-nitrosamines, which are suspected to cause stomach cancer. The World Health Organization (WHO) advises that each of processed meat eaten a day would raise the risk of getting bowel cancer by 18% over a lifetime; processed meat refers to meat that has been transformed through fermentation, nitrite curing, salting, smoking, or other processes to enhance flavour or improve preservation. The World Health Organization's review of more than 400 studies concluded, in 2015, that there was sufficient evidence that processed meats caused cancer, particularly colon cancer; the WHO's International Agency for Research on Cancer (IARC) classified processed meats as carcinogenic to humans (Group 1).


title: Nitrite

text: Nitrite (ingested) under conditions that result in endogenous nitrosation, specifically the production of nitrosamine, has been classified as ""Probably carcinogenic to humans"" (Group 2A) by the IARC.


title: Harmonic function

text: In mathematics, mathematical physics and the theory of stochastic processes, a harmonic function is a twice continuously differentiable function formula_1 where is an open subset of that satisfies Laplace's equation, that is,


title: Harmonic function

text: The descriptor "harmonic" in the name harmonic function originates from a point on a taut string which is undergoing harmonic motion. The solution to the differential equation for this type of motion can be written in terms of sines and cosines, functions which are thus referred to as "harmonics". Fourier analysis involves expanding functions on the unit circle in terms of a series of these harmonics. Considering higher dimensional analogues of the harmonics on the unit "n"-sphere, one arrives at the spherical harmonics. These functions satisfy Laplace's equation and over time "harmonic" was used to refer to all functions satisfying Laplace's equation.


title: Harmonic function

text: Harmonic functions that arise in physics are determined by their singularities and boundary conditions (such as Dirichlet boundary conditions or Neumann boundary conditions). On regions without boundaries, adding the real or imaginary part of any entire function will produce a harmonic function with the same singularity, so in this case the harmonic function is not determined by its singularities; however, we can make the solution unique in physical situations by requiring that the solution approaches 0 as r approaches infinity. In this case, uniqueness follows by Liouville's theorem.


title: Harmonic function

text: The singular points of the harmonic functions above are expressed as "charges" and "charge densities" using the terminology of electrostatics, and so the corresponding harmonic function will be proportional to the electrostatic potential due to these charge distributions. Each function above will yield another harmonic function when multiplied by a constant, rotated, and/or has a constant added. The inversion of each function will yield another harmonic function which has singularities which are the images of the original singularities in a spherical "mirror". Also, the sum of any two harmonic functions will yield another harmonic function.


title: Harmonic function

text: The set of harmonic functions on a given open set can be seen as the kernel of the Laplace operator and is therefore a vector space over linear combinations of harmonic functions are again harmonic.


title: Harmonic function

text: If is a harmonic function on , then all partial derivatives of are also harmonic functions on . The Laplace operator and the partial derivative operator will commute on this class of functions.


title: Harmonic function

text: In several ways, the harmonic functions are real analogues to holomorphic functions. All harmonic functions are analytic, that is, they can be locally expressed as power series. This is a general fact about elliptic operators, of which the Laplacian is a major example.


title: Harmonic function

text: The uniform limit of a convergent sequence of harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider the sequence on defined by formula_13 this sequence is harmonic and converges uniformly to the zero function; however note that the partial derivatives are not uniformly convergent to the zero function (the derivative of the zero function). This example shows the importance of relying on the mean value property and continuity to argue that the limit is harmonic.


title: Harmonic function

text: The real and imaginary part of any holomorphic function yield harmonic functions on (these are said to be a pair of harmonic conjugate functions). Conversely, any harmonic function on an open subset of is "locally" the real part of a holomorphic function. This is immediately seen observing that, writing formula_14 the complex function formula_15 is holomorphic in because it satisfies the Cauchy–Riemann equations. Therefore, locally has a primitive , and is the real part of up to a constant, as is the real part of formula_16


title: Harmonic function

text: Although the above correspondence with holomorphic functions only holds for functions of two real variables, harmonic functions in variables still enjoy a number of properties typical of holomorphic functions. They are (real) analytic; they have a maximum principle and a mean-value principle; a theorem of removal of singularities as well as a Liouville theorem holds for them in analogy to the corresponding theorems in complex functions theory.


title: Harmonic function

text: Harmonic functions are infinitely differentiable in open sets. In fact, harmonic functions are real analytic.


title: Harmonic function

text: Harmonic functions satisfy the following "maximum principle": if is a nonempty compact subset of , then restricted to attains its maximum and minimum on the boundary of . If is connected, this means that cannot have local maxima or minima, other than the exceptional case where is constant. Similar properties can be shown for subharmonic functions.


title: Harmonic function

text: If is a ball with center and radius which is completely contained in the open set formula_17 then the value of a harmonic function formula_18 at the center of the ball is given by the average value of on the surface of the ball; this average value is also equal to the average value of in the interior of the ball. In other words,


title: Harmonic function

text: Conversely, all locally integrable functions satisfying the (volume) mean-value property are both infinitely differentiable and harmonic.


title: Harmonic function

text: denotes the characteristic function of the ball with radius about the origin, normalized so that formula_21 the function is harmonic on if and only if


title: Harmonic function

text: Sketch of the proof. The proof of the mean-value property of the harmonic functions and its converse follows immediately observing that the non-homogeneous equation, for any


title: Harmonic function

text: Since is continuous in , formula_27 converges to as showing the mean value property for in . Conversely, if is any formula_28 function satisfying the mean-value property in , that is,


title: Harmonic function

text: so that is formula_31 because the -fold iterated convolution of is of class formula_32 with support . Since and are arbitrary, is formula_33 too. Moreover,


title: Harmonic function

text: for all so that in by the fundamental theorem of the calculus of variations, proving the equivalence between harmonicity and mean-value property.


title: Harmonic function

text: This statement of the mean value property can be generalized as follows: If is any spherically symmetric function supported in such that formula_35 then formula_36 In other words, we can take the weighted average of about a point and recover . In particular, by taking to be a function, we can recover the value of at any point even if we only know how acts as a distribution. See Weyl's lemma.


title: Harmonic function

text: The following principle of removal of singularities holds for harmonic functions. If is a harmonic function defined on a dotted open subset formula_39 of , which is less singular at than the fundamental solution (for ), that is


title: Harmonic function

text: then extends to a harmonic function on (compare Riemann's theorem for functions of a complex variable).


title: Harmonic function

text: Theorem: If is a harmonic function defined on all of which is bounded above or bounded below, then is constant.


title: Harmonic function

text: Edward Nelson gave a particularly short proof of this theorem for the case of bounded functions, using the mean value property mentioned above:


title: Harmonic function

text: Given two points, choose two balls with the given points as centers and of equal radius. If the radius is large enough, the two balls will coincide except for an arbitrarily small proportion of their volume. Since is bounded, the averages of it over the two balls are arbitrarily close, and so assumes the same value at any two points.


title: Harmonic function

text: The proof can be adapted to the case where the harmonic function is merely bounded above or below. By adding a constant and possibly multiplying by –1, we may assume that is non-negative. Then for any two points and , and any positive number , we let formula_41 We then consider the balls and where by the triangle inequality, the first ball is contained in the second.


title: Harmonic function

text: (Note that since is independent of , we denote it merely as .) In the last expression, we may multiply and divide by and use the averaging property again, to obtain


title: Harmonic function

text: tends to 1. Thus, formula_46 The same argument with the roles of and reversed shows that formula_47, so that formula_48


title: Harmonic function

text: Another proof uses the fact that given a Brownian motion in such that formula_49 we have formula_50 for all . In words, it says that a harmonic function defines a martingale for the Brownian motion. Then a probabilistic coupling argument finishes the proof.


title: Harmonic function

text: A function (or, more generally, a distribution) is weakly harmonic if it satisfies Laplace's equation


title: Harmonic function

text: in a weak sense (or, equivalently, in the sense of distributions). A weakly harmonic function coincides almost everywhere with a strongly harmonic function, and is in particular smooth. A weakly harmonic distribution is precisely the distribution associated to a strongly harmonic function, and so also is smooth. This is Weyl's lemma.


title: Harmonic function

text: There are other weak formulations of Laplace's equation that are often useful. One of which is Dirichlet's principle, representing harmonic functions in the Sobolev space as the minimizers of the Dirichlet energy integral


title: Harmonic function

text: with respect to local variations, that is, all functions formula_53 such that formula_54 holds for all formula_55 or equivalently, for all formula_56


title: Harmonic function

text: Harmonic functions can be defined on an arbitrary Riemannian manifold, using the Laplace–Beltrami operator . In this context, a function is called "harmonic" if


title: Harmonic function

text: Many of the properties of harmonic functions on domains in Euclidean space carry over to this more general setting, including the mean value theorem (over geodesic balls), the maximum principle, and the Harnack inequality. With the exception of the mean value theorem, these are easy consequences of the corresponding results for general linear elliptic partial differential equations of the second order.


title: Harmonic function

text: A function that satisfies is called subharmonic. This condition guarantees that the maximum principle will hold, although other properties of harmonic functions may fail. More generally, a function is subharmonic if and only if, in the interior of any ball in its domain, its graph lies below that of the harmonic function interpolating its boundary values on the ball.


title: Harmonic function

text: One generalization of the study of harmonic functions is the study of harmonic forms on Riemannian manifolds, and it is related to the study of cohomology. Also, it is possible to define harmonic vector-valued functions, or harmonic maps of two Riemannian manifolds, which are critical points of a generalized Dirichlet energy functional (this includes harmonic functions as a special case, a result known as Dirichlet principle). This kind of harmonic map appears in the theory of minimal surfaces. For example, a curve, that is, a map from an interval in to a Riemannian manifold, is a harmonic map if and only if it is a geodesic.


title: Harmonic function

text: If and are two Riemannian manifolds, then a harmonic map formula_58 is defined to be a critical point of the Dirichlet energy


title: Harmonic function

text: in which formula_60 is the differential of , and the norm is that induced by the metric on and that on on the tensor product bundle formula_61


title: Harmonic function

text: Important special cases of harmonic maps between manifolds include minimal surfaces, which are precisely the harmonic immersions of a surface into three-dimensional Euclidean space. More generally, minimal submanifolds are harmonic immersions of one manifold in another. Harmonic coordinates are a harmonic diffeomorphism from a manifold to an open subset of a Euclidean space of the same dimension.


title: Quincy Jones production discography

text: Quincy Jones is an American record producer, musical arranger, film composer, impresario, conductor, and trumpeter. Jones has charted 6 singles and 6 albums in the top 40 and won 4 Platinum Awards and 7 Gold Awards only in the United States. Jones is one of few producers to have number one records in three consecutive decades (1960s, 1970s, and 1980s).


title: Test tube

text: A test tube, also known as a culture tube or sample tube, is a common piece of laboratory glassware consisting of a finger-like length of glass or clear plastic tubing, open at the top and closed at the bottom.


title: Test tube

text: Test tubes intended for general chemical work are usually made of glass, for its relative resistance to heat. Tubes made from expansion-resistant glasses, mostly borosilicate glass or fused quartz, can withstand high temperatures up to several hundred degrees Celsius.


title: Test tube

text: Chemistry tubes are available in a multitude of lengths and widths, typically from 10 to 20 mm wide and 50 to 200 mm long. The top often features a flared lip to aid pouring out the contents.


title: Test tube

text: A chemistry test tube typically has a flat bottom, a round bottom, or a conical bottom. Some test tubes are made to accept a ground glass stopper or a screw cap. They are often provided with a small ground glass or white glaze area near the top for labelling with a pencil.


title: Test tube

text: Test tubes are widely used by chemists to handle chemicals, especially for qualitative experiments and assays. Their spherical bottom and vertical sides reduce mass loss when pouring, make them easier to wash out, and allow convenient monitoring of the contents. The long, narrow neck of test tube slows down the spreading of gases to the environment.


title: Test tube

text: Test tubes are convenient containers for heating small amounts of liquids or solids with a Bunsen burner or alcohol burner. The tube is usually held by its neck with a clamp or tongs. By tilting the tube, the bottom can be heated to hundreds of degrees in the flame, while the neck remains relatively cool, possibly allowing vapours to condense on its walls. A boiling tube is a large test tube intended specifically for boiling liquids.


title: Test tube

text: A test tube filled with water and upturned into a water-filled beaker is often used to capture gases, e.g. in electrolysis demonstrations.


title: Test tube

text: Culture tubes are test tubes used in biology and related sciences for handling and culturing all kinds of live organisms, such as molds, bacteria, seedlings, plant cuttings, etc.. Some racks for culture tubes are designed to hold the tubes in a nearly horizontal position, so as to maximize the surface of the culture medium inside.


title: Test tube

text: Culture tubes for biology are usually made of clear plastic (such as polystyrene or polypropylene) by injection molding and are often discarded after use. Plastic test tubes with a screwtop cap are often called "Falcon tubes" after a line manufactured by Becton Dickinson.


title: Test tube

text: Some sources consider that the presence of a lip is what distinguishes a test tube from a culture tube.


title: Test tube

text: In clinical medicine, sterile test tubes with air removed, called vacutainers, are used to collect and hold samples of physiological fluids such as blood, urine, pus, and synovial fluid. These tubes are commonly sealed with a rubber stopper and often have a specific additive placed in the tube with the stopper color indicating the additive. For example, a "blue-top tube" is a 5 ml test tube containing sodium citrate as an anticoagulant, used to collect blood for coagulation and glucose-6-phosphate dehydrogenase testing. Small vials used in medicine may have a snap-top (also called a hinge cap) molded as part of the vial.


title: Test tube

text: Test tubes are sometimes put to casual uses outside of lab environments, e.g. as flower vases, glassware for certain weak shots, or containers for spices. They can also be used for raising queen ants during their first months of development.


title: Test tube

text: A boiling tube is a small cylindrical vessel used to strongly heat substances in the flame of a Bunsen burner. A boiling tube is essentially a scaled-up test tube, being about 50% larger.


title: Test tube

text: They are designed to be wide enough to allow substances to boil violently as opposed to a test tube, which is too narrow; a boiling liquid can explode out of the end of test tubes when they are heated, as there is no room for bubbles of gas to escape independently of the surrounding liquid. This phenomenon is called bumping.


title: Test tube

text: An ignition tube is used in much the same way as a boiling tube, except it is not as large and thick-walled. It is primarily used to hold small quantities of substances which are undergoing direct heating by a Bunsen burner or other heat source. This type of tube is used in the sodium fusion test.


title: Test tube

text: Ignition tubes are often difficult to clean due to the small bore. When used to heat substances strongly, some char may stick to the walls as well. They are usually disposable.


title: Covert operation

text: A covert operation is a military operation intended to conceal the identity of (or allow plausible deniability by) the party that instigated the operation. Covert operations should not be confused with clandestine operations, which are performed in secret and meant to stay secret.


title: Covert operation

text: Covert operations aim to secretly fulfill their mission objectives without anyone knowing who sponsored or carried out the operation, or in some cases, without anyone knowing that the operation has even occurred.


title: Covert operation

text: According to a 2018 study by University of Chicago political scientist Austin Carson, covert operations may have the beneficial effect of preventing escalation of disputes into full-blown wars. He argues that keeping military operations secret can limit escalation dynamics, as well as insulate leaders from domestic pressures while simultaneously allowing them communicating their interest to the adversary in keeping a war contained. He finds that covert operations are frequently detected by other major powers.


title: Covert operation

text: Under U.S. law, the Central Intelligence Agency (CIA) must lead covert operations unless the president finds that another agency should do so and properly informs Congress. Normally, the CIA is the U.S. government agency legally allowed to carry out covert action. The CIA's authority to conduct covert action comes from the National Security Act of 1947. President Ronald Reagan issued Executive Order 12333 titled "United States Intelligence Activities" in 1984. This order defined covert action as "special activities", both political and military, that the US Government could legally deny. The CIA was also designated as the sole authority under the 1991 Intelligence Authorization Act and in Title 50 of the United States Code Section 413(e). The CIA must have a "Presidential Finding" issued by the President of the United States in order to conduct these activities under the Hughes-Ryan amendment to the 1991 Intelligence Authorization Act. These findings are then monitored by the oversight committees in both the U.S. Senate and the House of Representatives. As a result of this framework, William J. Daugherty writes that the CIA "receives more oversight from the Congress than any other agency in the federal government". The Special Activities Division (SAD) is a division of the CIA's Directorate of Operations, responsible for Covert Action and "Special Activities". These special activities include covert political influence and paramilitary operations.


title: Covert operation

text: Covert operations and clandestine operations are distinct. The "Department of Defense Dictionary of Military and Associated Terms" (Joint Publication JP1-02), defines "covert operation" as "an operation that is so planned and executed as to conceal the identity of or permit plausible denial by the sponsor. A covert operation differs from a clandestine operation in that emphasis is placed on concealment of a sponsor rather than on concealment of the operation". The United States Department of Defense definition has been used by the United States and NATO since World War II.


title: Covert operation

text: In a covert operation, the identity of the sponsor is concealed, while in a clandestine operation the operation itself is concealed. Put differently, "clandestine" means "hidden", while "covert" means "deniable". The term "stealth" refers both to a broad set of tactics aimed at providing and preserving the element of surprise and reducing enemy resistance and to a set of technologies (stealth technology) to aid in those tactics. While secrecy and stealthiness are often desired in clandestine and covert operations, the terms "secret" and "stealthy" are not used to formally describe types of missions.


title: Covert operation

text: Covert operations are employed in situations where openly operating against a target would be disadvantageous. Operations may be directed at or conducted with allies and friends to secure their support for controversial components of foreign policy throughout the world. Covert operations may include sabotage, assassinations, support for coups d'état, or support for subversion. Tactics include the use of a false flag or front group.


title: Covert operation

text: The activity of organizations engaged in covert operations is in some instances similar to or overlaps with, the activity of front organizations. While covert organizations are generally of a more official military or paramilitary nature, like the DVS German Air Transport School in the Nazi era, the line between both becomes muddled in the case of front organizations engaged in terrorist activities and organized crime.


title: Covert operation

text: Undercover operations (such as sting operations or infiltration of organized crime groups) are conducted by law enforcement agencies to deter and detect crime and to gather information for future arrest and prosecution. The FBI's domestic operations were defined on September 29, 2008, by the "Attorney General's Guidelines for Domestic FBI Operations".


title: Covert operation

text: Covert operations have often been the subject of popular films ("Zero Dark Thirty", "Argo", "The Falcon and The Snowman", "The Kremlin Letter"), novels, TV series, and comics.


title: Covert operation

text: The Company is a fictional covert organization featured in the American TV series "Prison Break". Also other series that deal with covert operations are "", "Alias", "Burn Notice", "The Unit", "The State Within", "Covert Affairs", "Air Wolf", "24", "The West Wing", "The Blacklist", "Scandal, Strike Back series, and Vagabond."


title: Tony Martin (American singer)

text: Alvin Morris (December 25, 1913 – July 27, 2012), known professionally as Tony Martin, was an American actor and popular singer.


title: Tony Martin (American singer)

text: His career spanned over seven decades, and he scored dozens of hits between the late-1930s and mid-1950s with songs such as "Walk Hand in Hand", "I Love Paris", "Stranger in Paradise" and "I Get Ideas". He was married to actress and dancer Cyd Charisse for 60 years, from 1948 until her death in 2008.


title: Tony Martin (American singer)

text: Alvin Morris was born on December 25, 1913, in San Francisco, the son of Hattie (née Smith) and Edward Clarence Morris. His family was Jewish, and all of his grandparents had emigrated from Eastern Europe. He was raised in Oakland, California. At the age of ten, he received a saxophone as a gift from his grandmother. He went to Oakland High School and St Mary's College.


title: Tony Martin (American singer)

text: In his grammar school glee club, he became an instrumentalist and singer, playing both saxophone and clarinet. He formed his first band, named "The Red Peppers," when he was at Oakland Technical High School, eventually joining the band of a local orchestra leader, Tom Gerun, as a saxophone player sitting alongside the future bandleader Woody Herman. He attended Saint Mary's College of California during the mid-1930s. After college, he left Gerun's band to go to Hollywood to try films. It was at that time that he adopted the stage name of Tony Martin.


title: Tony Martin (American singer)

text: On radio, Martin sang and was master of ceremonies on "Tune-Up Time", with Andre Kostelanetz, on CBS in the early 1940s. NBC broadcast "The Tony Martin Show", a 15-minute variety program, from 1954 to 1956 prior to the evening newscast. One of his guests was Dinah Shore, soon starring in her own hour-long NBC variety program.


title: Tony Martin (American singer)

text: He was a featured vocalist on the George Burns and Gracie Allen radio program. On the show Allen playfully flirted with Tony, often threatening to fire him. Allen would say things like, "Oh, Tony, you look so tired, why don't you rest your lips on mine?"


title: Tony Martin (American singer)

text: In films, Martin was first cast in a number of bit parts, including a role as a sailor in "Follow the Fleet" (1936), starring Fred Astaire and Ginger Rogers. He eventually signed with 20th Century-Fox and then Metro-Goldwyn-Mayer in which he starred in a number of musicals. Between 1938 and 1942, he made a number of hit records for Decca. In 1941, Martin received equal billing with the Marx Brothers in their final film for MGM, "The Big Store", in an effort to lure pop music fans and as an indication of MGM's lack of interest in the comedy team. In the film he played a rising singer and performed "Tenement Symphony," which was written by Hal Borne, who became his long-time musical director. Martin was the last surviving actor to co-star with the Marx Brothers.


title: Tony Martin (American singer)

text: Martin joined the United States Navy in 1942 as a chief specialist, the equivalent of a chief petty officer. He was dismissed from the service that year for "unfitness" after he testified at the court martial of a Naval procurement officer. He enlisted as a specialist after the officer twice failed to obtain a commission for him. Martin said that he had given the officer an auto worth $950 to "facilitate" his enlistment. At the time of his dismissal, the Navy said that removal for unfitness was not equivalent to a dishonorable discharge and "does not carry degradation."


title: Tony Martin (American singer)

text: After leaving the Navy, Martin asked his local draft board for immediate induction into the service. He was drafted into the Army and assigned to the United States Army Air Forces. He was assigned to Capt. Glenn Miller's band at the request of Miller, who considered him the best singer in the armed services. Martin later said he felt as though he had "stumbled into heaven through the side door." Martin was later promoted to technical sergeant in the Air Transport Command and stationed in India, where Brig. Gen. William H. Tunner, commanding the Hump Airlift, put him to work as an entertainer, forming a troupe of amateur talent from the command and taking it around the various bases to perform.


title: Tony Martin (American singer)

text: After the war, Martin signed with Mercury Records, then a small independent label run out of Chicago, Illinois. He cut 25 records in 1946 and 1947 for Mercury, including a 1946 recording of "To Each His Own," which became a million-seller. It was awarded a gold disc by the RIAA. This prompted RCA Victor to offer him a record contract, which he signed in 1947 after satisfying his contract obligations to Mercury.


title: Tony Martin (American singer)

text: He continued to appear in film musicals during the 1940s and 1950s. His rendition of "Lover Come Back to Me" with Joan Weldon in "Deep in My Heart" – based on the music of Sigmund Romberg and starring José Ferrer - was one of the highlights of that film. He also starred as Gaylord Ravenal in the "Show Boat" segment from the 1946 film "Till the Clouds Roll By".


title: Tony Martin (American singer)

text: In 1958, he became the highest paid performer in Las Vegas, signing a five-year deal at the Desert Inn, earning $25,000 a week.


title: Tony Martin (American singer)

text: In an unlikely pairing, Martin recorded for the Motown Records label in the mid-1960s, scoring a minor hit with the record "Talkin' To Your Picture".


title: Tony Martin (American singer)

text: In the 1970s, Martin was a television spokesperson for the Lady Brevoni brand of pantyhose sold in supermarkets.


title: Tony Martin (American singer)

text: Martin was a stockholder in the Parvin-Dohrmann Corporation, a hotel and casino company that owned the Flamingo Las Vegas.


title: Tony Martin (American singer)

text: In 1937, he married actress and singer Alice Faye, with whom he had appeared in several films. They divorced in 1940.


title: Tony Martin (American singer)

text: In 1948, Martin married actress and dancer Cyd Charisse. They remained married for 60 years until her death on June 17, 2008. Martin adopted Charisse's son Nicky from her first marriage. They had one son together, Tony Martin, Jr. (August 28, 1950 – April 10, 2011), who predeceased his father.


title: Tony Martin (American singer)

text: Martin died on the evening of July 27, 2012, of natural causes. He was 98 years old. Martin was buried at the Hillside Memorial Park Cemetery in Culver City, California.


title: Aditi Prabhudeva

text: Sudeepana Banakar Prabhudeva (born 13 January 1994), popularly known by her stage name Aditi Prabhudeva, is an Indian actress who predominantly appears in Kannada cinema.


title: SU-100

text: The SU-100 ("Samokhodnaya Ustanovka" 100) was a Soviet tank destroyer armed with the D-10S 100 mm anti-tank gun in a casemate superstructure. It was used extensively during the last year of World War II and saw service for many years afterwards with the armies of Soviet allies around the world.


title: SU-100

text: The SU-85 was developed from the chassis of the T-34 tank replacing the turret with a larger, fixed superstructure that allowed a larger gun to be fitted: the 85 mm D-5 gun, providing dramatically upgraded firepower compared to the T-34's 76.2 mm models. Introduced to service in 1943, the SU-85 was quickly rendered obsolete as a new tank design featured the same gun on the T-34-85.


title: SU-100

text: This prompted the design of a more advanced turretless tank destroyer with an even more powerful cannon. Development was conducted under supervision of L. I. Gorlitskiy, chief designer of all medium Soviet self-propelled guns. The work started in February 1944 and the first prototype of the SU-100, "Object 138", was delivered in March. After intensive testing with different models of 100 mm gun Soviet engineers approved the D-10S gun for mass production. This gun was developed in Constructors Bureau of Artillery Factory No. 9 under the guidance of F. F. Petrov. After the Second World War this gun was installed on T-54 and T-55 tanks; these vehicles and their derivatives were in service forty years after initial development.


title: SU-100

text: It was built at the UZTM (Russian abbreviation УЗТМ for Уральский Завод Тяжелого Машиностроения – Ural Heavy Machinery Factory, also called "Uralmash") in Yekaterinburg. The SU-100 quickly proved itself to be able to penetrate around of vertical armor from a range of and the sloped front armor of the German Panther from (with APCBC round).


title: SU-100

text: The hull of the SU-100 had major improvements over the SU-85; the thickness of the front armour was increased from with a constructional armour slope of 55 degrees, making armour as effective as 125mm, which forced the Panzer IV and StuG III to all but the closest ranges and the Tiger I having to close in at less than 1km. Additional improvements were the commander's workplace, as it now was made in a small sponson on the right side of the hull; combined with the commander's cupola this improved the commander's effectiveness. Its German "Jagdpanzer"-family counterparts — the Jagdpanzer IV, Jagdpanther and Jagdtiger, by comparison, lacked this key piece of observational equipment. On the other hand, the SU-100's optics were little inferior (4x optics vs German 5x optics). For better ventilation two ventilator units were installed, instead of only one as in the SU-85. Mass production began in September 1944.


title: SU-100

text: The SU-100 was introduced in October 1944 and quickly became popular with Soviet tank crews as its gun could penetrate virtually any German tank then in service until being outmatched by the Tiger II. The gun was excellent, being able to penetrate the Tiger I at 2 km with APCBC rounds while its APHE rounds could penetrate a max of 218 mm of armour. The SU-100 especially saw extensive service during the last year of the war. It was used "en masse" in Hungary in March 1945, when Soviet forces defeated the German Operation Frühlingserwachen offensive at Lake Balaton. And although not intended for it, the SU-100 was also used in the Battle of Berlin because its gun could deal with heavy fortifications. However, its lack of a machine gun made it need aircraft and infantry support. By July 1945, 2 335 SU-100s had been built.


title: SU-100

text: The vehicle remained in service with the Red Army well after the war; production continued in the Soviet Union until 1947 and into the 1950s in Czechoslovakia. It was withdrawn from Soviet service in 1967 but many vehicles were transferred to reserve stocks. Some exist to this day in the Russian Army holding facilities.


title: SU-100

text: Many Warsaw Pact countries also used the SU-100, as did Soviet allies such as Egypt, Angola and Cuba. A few SU-100 were delivered to Yugoslavia after the war, under the designation M-44. The SU-100 saw service in the fighting that accompanied the 1956 Suez Crisis, in which the Egyptians used SU-100s against Israel's M4 Sherman tanks. The vehicle was also utilized in the 1967 Six-Day War and the 1973 Yom Kippur War. It was modified slightly to adapt it to the sandy conditions of the Middle East, thus creating the SU-100M variant . Exported SU-100s continued in service until the 1970s, and in some countries, even later. Yugoslavs used them during the civil war; however, due to lack of spare parts they were quickly retired, despite their satisfactory performance. The SU-100 remains in use by the Vietnam People's Army and the Korean People's Army Ground Force.


title: SU-100

text: SU-100s entered service with the People's Liberation Army (PLA) of China after 1 December 1950 when Soviet forces left Dalian. The armaments in Dalian were sold to China, including 99 SU-100s, 18 IS-2 heavy tanks, and 224 T-34s, with which PLA formed its 1st Mechanised Division.


title: SU-100

text: In April 2015, a SU-100 self-propelled gun was photographed being used in Yemen as part of the ongoing conflict. Video evidence uploaded to YouTube in November 2016 showed an apparent SU-100 being knocked out by an anti-tank guided missile in Yemen.


title: Beach Bunny (band)

text: Beach Bunny is an American rock band formed in 2015 by Lili Trifilio in Chicago, Illinois. The group achieved widespread popularity after their song "Prom Queen" went viral on TikTok.


title: Beach Bunny (band)

text: Beach Bunny began as a bedroom-based solo project in 2015 when Lili Trifilio recorded a song titled "6 Weeks". The same year, Trifilio released her first EP, titled "Animalism". She released her second EP titled "Pool Party" in 2016. In 2017, she released her third EP titled "Crybaby", and Beach Bunny expanded to a full four-piece lineup shortly after. In 2018, Beach Bunny released her fourth EP, titled "Prom Queen".


title: Beach Bunny (band)

text: On October 31, 2019, Trifilio and the band announced that they had signed to Mom + Pop Music and released their first full-length album, "Honeymoon", on February 14, 2020. The album was produced by Joe Reinhart at Electrical Audio; the Chicago studio owned by Steve Albini, and subsequently mixed at Reinhart's Headroom Studios. "Honeymoon" was met with widespread critical acclaim, appearing on the Best Albums of 2020 lists in both "The New York Times", and "Rolling Stone". The album contained the song "Cloud 9", which became the band's second song to go viral on TikTok, where it was used in 2 million videos.


title: Beach Bunny (band)

text: In November 2020, the band released a new single titled "Good Girls (Don't Get Used)". Their fifth EP, "Blame Game", was released in 2021.


title: Beach Bunny (band)

text: In October 2021, the band released the single "Oxygen". This was followed by the single "Fire Escape" in March 2022, along with the announcement of their sophomore album "Emotional Creature", released on July 22, 2022.


title: Mere Brother Ki Dulhan

text: Mere Brother Ki Dulhan () is a 2011 Indian Hindi-language romantic comedy film written and directed by Ali Abbas Zafar in his directorial debut and produced by Aditya Chopra for Yash Raj Films. It stars Imran Khan, Katrina Kaif, Ali Zafar, and Tara D'Souza. In the film, Dimple Dixit (Kaif) and Luv Agnihotri (Zafar) are due to get married, but difficulties arise when Dimple and Kush (Khan) develop feelings for each other in the days leading up to the wedding.


title: Mere Brother Ki Dulhan

text: "Mere Brother Ki Dulhan" entered development in August 2010 after Zafar, then known as an assistant director, wrote three separate screenplays for Yash Raj. Khan and Kaif's involvement was announced soon thereafter, marking Khan's first film for Yash Raj and Kaif and Zafar's second, after "New York" (2009). Casting was rounded out with the hirings of Zafar and D'Souza in their initial Bollywood roles and principal photography began in September 2010 and lasted until that November, with filming locations including Haryana, Uttar Pradesh, Uttarakhand, Punjab, and Himachal Pradesh. Upon release, the film received plagiarism allegations, drawing comparisons to "Mere Yaar Ki Shaadi Hai" (2002) and "Dan in Real Life" (2007).


title: Mere Brother Ki Dulhan

text: "Mere Brother Ki Dulhan" was set for release in July 2011, but was unexpectedly postponed. It was theatrically released in India by Sony Pictures Networks on September 9 the same year. "Mere Brother Ki Dulhan" grossed worldwide, making it the ninth highest grossing Indian language film of 2011. It received positive reviews from critics, with particular praise directed towards Kaif's performance as well as its screenplay, soundtrack and humor.


title: Mere Brother Ki Dulhan

text: At the 57th Filmfare Awards, "Mere Brother Ki Dulhan" received 2 nominations – Best Actress (Kaif) and Best Music Director (Sohail Sen).


title: Mere Brother Ki Dulhan

text: After breaking up with his girlfriend, Piyali Patel in London, Luv Agnihotri insists his younger brother Kush, an assistant film director and photographer in Mumbai, to find him a bride. Kush reaches home to meet his army veteran father, Col. (Retd.) Swank Agnihotri and homemaker mother Kanak and travels with them all over India to find a bride suitable for Luv but in vain. His friends come up with an idea to advertise this in a newspaper. A certain Dilip Dixit from Agra responds to the advertisement, claiming that he is looking for a suitable groom for his daughter. However, when Kush travels with his parents to Agra to meet the Dixit family, he is shocked to find out that the prospective bride is none other than Dimple "D" Dixit, who he had previously met during a chance encounter on a college outing five years ago.


title: Mere Brother Ki Dulhan

text: Obnoxious and loud, Dimple is everything that Kush is not, but he pleads not to create a scene and asks her to consider the alliance. After meeting Luv, Dimple agrees to marry him. Her brother Ajay wants them to get married at a place in Agra from where the Taj Mahal is visible. However, during the wedding preparations, Kush realizes he has feelings for Dimple, and she initially responds by slapping him as to why he didn't tell her before. Later, they try to elope, but it doesn't work out, and they return, planning to distract Luv. Eventually, on the eve of the wedding, Dimple brings Piyali, a mutual friend, to Agra, and Luv, figuring out he still has feelings for Piyali, elopes the next day. They get married according to religious customs, with Luv sending letters to the Agnihotri and Dixit families explaining the reasons behind his elopement.


title: Mere Brother Ki Dulhan

text: After reading the letters, Dilip and Swarnik have a bitter fight but figure that the only way to protect their respect and pride is to get Kush and Dimple married. However, Kush maintains a condition that he will marry Dimple only if Luv and Piyali are accepted. The family agrees, with both couples enjoying a proper, lavish wedding. They live happily ever after together.


title: Mere Brother Ki Dulhan

text: Yash Raj Films announced the then-untitled project on 5 August 2010. Ali Abbas Zafar, who was an assistant director on a number of Yash Raj Films productions such as "Jhoom Barabar Jhoom", "Tashan", "New York" and "Badmaash Company", made his feature writing and directing debut with this film, which has been described as a "comedy of errors" by lead actor Imran Khan. After "Band Baaja Baaraat" (2010), this marks the second Yash Raj Films production in a row to be helmed by a first-time director who was previously an assistant director. Zafar is originally from Dehradun, where much of the story is set. After years of working with Yash Raj Films, he submitted three love stories to producer Aditya Chopra, who eventually greenlit "Mere Brother Ki Dulhan", enabling Zafar to start writing his 150-page long script. Ali Abbas Zafar is an alumnus of The Players, the acclaimed theatre society of Kirori Mal College, University of Delhi, where he acted in different plays including an adaptation of William Golding's "Lord of the Flies".


title: Mere Brother Ki Dulhan

text: Like many Bollywood films, "Mere Brother Ki Dulhan" has suffered allegations that it is a rip-off of an American film even before filming wrapped. According to these sources, the film rips off "Dan in Real Life" (2007), in which Steve Carell's character also falls in love with his brother's girlfriend (played by Dane Cook and Juliette Binoche respectively). The film has also drawn comparison to an earlier Yash Raj Films production, "Mere Yaar Ki Shaadi Hai" (2002).


title: Mere Brother Ki Dulhan

text: Katrina Kaif and Imran Khan play the romantic leads in the film, and their involvement was announced in the same press release as the initial production company announcement. This is the first time they've been paired together. They were initially to star together in "7 Days in Paris" for director Sanjay Gadhvi, but the film has been indefinitely postponed. some media publications have alleged that their casting was an attempt by Yash Raj Films to end a recent string of box-office flops and disappointments. While the film was Imran Khan's first for Yash Raj Films, Katrina Kaif had previously worked with them (and then assistant director Ali Abbas Zafar) on the critical and commercial hit "New York" (2009). She was able to take the role thanks to the postponement of "Dostana 2" to which she was already committed. Her role has been reported in the media as different from the characters she had played in the past. It was then given to Ali Zafar (no relation to the director), an actor who'd received rave reviews for his debut film "Tere Bin Laden" (2010) and who confirmed his participation via his Twitter account. A popular singer, Zafar will also perform his character's singing in the film and described his casting as "a dream come true" and his role as a "parallel lead role". The film additionally stars a new actress Tara D'Souza who is a former Kingfisher model.


title: Mere Brother Ki Dulhan

text: On 17 October 2010, several media outlets reported on the casting of Preity Zinta in an unspecified "glamorous role". The actress however quickly denied the report on her official Twitter page.


title: Mere Brother Ki Dulhan

text: Filming started on 25 September 2010 and was scheduled to be completed by November. and Pataudi, before moving on to Chandigarh, Agra, Dehradun, Mussoorie, Haridwar, Dhanaulti, Punjab and Himachal Pradesh for a total of 45 days of filming in northern India and finally finishing the film in Mumbai. Juggling between this film and the final shots of "Tees Maar Khan" and "Zindagi Na Milegi Dobara", Kaif joined the shoot on 27 September.


title: Mere Brother Ki Dulhan

text: A bloody incident happened very early in the shoot, on 29 September, while the crew was filming at Pataudi Palace. The scene being shot, comic in nature, involved Imran Khan pulling Katrina Kaif towards him while pointing a gun towards other cast members. However, Khan miscalculated the move and instead sent the gun barrel crashing into Kaif's nose, causing it to bleed profusely. Kaif was quoted as saying "I am pretty bruised but the staff feels it's good luck for the film. But it was a funny scene so I think it was worth it" and "Please don't make it seem as if Imran was careless or something. These things happen. We were shooting one of the really madcap scenes where the actors' limbs acquire a life of their own. Imran's hand landed on my face" Another incident of sorts was reported by the media in early October and involves an emotional scene where Kaif's character slaps Khan's. Kaif would have been content to slap Khan once, however, he insisted on sixteen takes so that the director would have a variety of slaps to choose from. Kaif was involved in another accident a few weeks later while filming in Nabha. Her hair got caught in a fan, and it was thanks to co-star Ali Zafar's quick action that the incident didn't turn more serious. Zafar and a spot boy named Raju did however sustain minor injuries and bruises. The film's title, "Mere Brother Ki Dulhan", was revealed on 2 October along with a few promo pictures. Ali Zafar stated that Kaif promised him that if the film made over 600 million at the box office, she would do a music video with him.


title: Mere Brother Ki Dulhan

text: Yash Raj Films were first aiming for a July 2011 release, but the release date was later pushed to 16 September 2011. The studio drastically changed their marketing tactics with this film by revealing the title and two stills a week into filming, whereas they have previously been very secretive about sharing such information until about a couple of months before the theatrical release. It was released in Pakistan on 9 September 2011.


title: Mere Brother Ki Dulhan

text: The film received positive reviews from critics, with particular praise directed towards Kaif's performance.


title: Mere Brother Ki Dulhan

text: Taran Adarsh of "Bollywood Hungama" awarded it 4 out of 5 stars and wrote, "On the whole, "Mere Brother Ki Dulhan" is a delectably wholesome, heartening, feel-good entertainer." Shivesh Kumar of "IndiaWeekly" awarded the movie 4 out of 5 stars. "Daily Bhaskar" awarded the movie 3 out of 5 stars and wrote, "Surely a treat for Katrina's fans, as it will be an experience to witness her talent." Komal Nahta of "Koimoi" gave it 3 out of 5 stars and said, ""Mere Brother Ki Dulhan" has reasonable entertainment value, very good music, exciting song picturisations which will all result in a good run at the box-office", but " The screenplay dips at a few places; a few comic scenes seem forced." Sukanya Verma of "Rediff" rated it 3.5 out of 5 stars and said, "At the end of the day, "Mere Brother Ki Dulhan" is a pretty ordinary effort. It's the kind of movie where everyone looks catalogue cool and beams with enthusiasm to make the going-ons appear droll and exciting." Kaveree Bamzai of "India Today" also gave it 3.5 stars and wrote, "A large part of the film is a spoof—from "Dabangg" to "My Name Is Khan". Some of it also an ode—from "Padosan" to "Mughal e Azam". Some of it works, a lot of it doesn't." Gaurav Malani of "The Times of India" wrote, "The screenplay fails to tap the little potential that the story offers (esp. in the second half) pretty much like the film fails to exploit the talent of Ali Zafar. The writing is shallow and resorts to a convenient climax." Krita Coelho of "Gulf News" wrote, " Watch if you're a sucker for a sweet Bollywood romance." Reuters wrote, "If you are willing to ignore some flaws", "Mere Brother Ki Dulhan" "is a fun good one-time watch." Rahul Gangwani from "Filmfare" gave it 3 out of 5 stars and called it K"not" recommend however he praised the performance of the lead actress and added: "the film ultimately belongs to Katrina Kaif. She sparkles, sizzles and infuses energy into the film. Watch out for the scene where she breaks into the shehnai rendition from Ashutosh Gowariker Swades." Rajeev Masand in his review for "CNN-IBN" called the film "too predictable" and said: "The film doesn't always work because it relies too heavily on silly stereotypes and clichés, and because you can see exactly where it's going from the moment you settle into your seat. I'm going with two out of five for director Ali Abbas Zafar's "Mere Brother Ki Dulhan". Aside from a few enjoyable moments, this film recycles so much that you've already seen before." Hamara Bollywood gave the film 4 out of 5 stars and said that Katrina Kaif's performance alone 'is worth paying the admission price.'


title: Mere Brother Ki Dulhan

text: "Mere Brother Ki Dulhan" has had a good opening with first day of 75.0 million net, It had a good first weekend of 255.0 million net. the film held up well on Monday with business of the 37.5 million net mark, taking its four-day business to Rs 290 million net. It grossed net in the first week of its release. Thus it became the ninth highest-grossing film of 2011. At the end of its theatrical run the film grossed Cr in India and a world-wide gross of against a budget of .


title: Mere Brother Ki Dulhan

text: The score and soundtrack of the film was composed by Sohail Sen, best known for being the man behind the music of "What's Your Raashee?" (2009). Lyrics are penned by Irshad Kamil, the first working between Sohail Sen and Irshad Kamil. Ali Zafar sings one song in the film. "Madhubala", the song picturized on Katrina Kaif was a tribute to yesteryear's popular actress Madhubala. The music was released on 9 August 2011. The album contains six original tracks and two remixes.


title: Mere Brother Ki Dulhan

text: The soundtrack of the film received positive reviews from music critics. Joginder Tuteja of "Bollywood Hungama" rated the album favorably, awarding it 3.5/5, stating ""Mere Brother Ki Dulhan" is a winning album by all means and has in it to be widely popular in days to come. As expected, the entire soundtrack follows a fun approach without anything becoming overtly mushy or mellow. Composer Sohail Sen can be assured that he would now have a successful soundtrack to his name as well that would find a wide audience for itself." This is the music director's third work so far, the first two being "What's Your Raashee" and "Khelein Hum Jee Jaan Sey" (2010). Nikhil Hemrajani of "Hindustan Times" wrote, "That all eight songs in "Mere Brother Ki Dulhan"'s ("MBKD") soundtrack are high-energy thumpers probably makes sense for the coming festive season. But there's nothing special about the music, so to speak."


title: Livermorium

text: Livermorium is a synthetic chemical element with the symbol Lv and has an atomic number of 116. It is an extremely radioactive element that has only been created in a laboratory setting and has not been observed in nature. The element is named after the Lawrence Livermore National Laboratory in the United States, which collaborated with the Joint Institute for Nuclear Research (JINR) in Dubna, Russia to discover livermorium during experiments conducted between 2000 and 2006. The name of the laboratory refers to the city of Livermore, California, where it is located, which in turn was named after the rancher and landowner Robert Livermore. The name was adopted by IUPAC on May 30, 2012. Four isotopes of livermorium are known, with mass numbers between 290 and 293 inclusive; the longest-lived among them is livermorium-293 with a half-life of about 60 milliseconds. A fifth possible isotope with mass number 294 has been reported but not yet confirmed.


title: Livermorium

text: In the periodic table, it is a p-block transactinide element. It is a member of the 7th period and is placed in group 16 as the heaviest chalcogen, but it has not been confirmed to behave as the heavier homologue to the chalcogen polonium. Livermorium is calculated to have some similar properties to its lighter homologues (oxygen, sulfur, selenium, tellurium, and polonium), and be a post-transition metal, though it should also show several major differences from them.


title: Livermorium

text: The first search for element 116, using the reaction between Cm and Ca, was performed in 1977 by Ken Hulet and his team at the Lawrence Livermore National Laboratory (LLNL). They were unable to detect any atoms of livermorium. Yuri Oganessian and his team at the Flerov Laboratory of Nuclear Reactions (FLNR) in the Joint Institute for Nuclear Research (JINR) subsequently attempted the reaction in 1978 and met failure. In 1985, in a joint experiment between Berkeley and Peter Armbruster's team at GSI, the result was again negative, with a calculated cross section limit of 10–100 pb. Work on reactions with Ca, which had proved very useful in the synthesis of nobelium from the Pb+Ca reaction, nevertheless continued at Dubna, with a superheavy element separator being developed in 1989, a search for target materials and starting of collaborations with LLNL being started in 1990, production of more intense Ca beams being started in 1996, and preparations for long-term experiments with 3 orders of magnitude higher sensitivity being performed in the early 1990s. This work led directly to the production of new isotopes of elements 112 to 118 in the reactions of Ca with actinide targets and the discovery of the 5 heaviest elements on the periodic table: flerovium, moscovium, livermorium, tennessine, and oganesson.


title: Livermorium

text: In 1995, an international team led by Sigurd Hofmann at the Gesellschaft für Schwerionenforschung (GSI) in Darmstadt, Germany attempted to synthesise element 116 in a radiative capture reaction (in which the compound nucleus de-excites through pure gamma emission without evaporating neutrons) between a lead-208 target and selenium-82 projectiles. No atoms of element 116 were identified.


title: Livermorium

text: In late 1998, Polish physicist Robert Smolańczuk published calculations on the fusion of atomic nuclei towards the synthesis of superheavy atoms, including elements 118 and 116. His calculations suggested that it might be possible to make these two elements by fusing lead with krypton under carefully controlled conditions.


title: Livermorium

text: In 1999, researchers at Lawrence Berkeley National Laboratory made use of these predictions and announced the discovery of elements 118 and 116, in a paper published in "Physical Review Letters", and very soon after the results were reported in "Science". The researchers reported to have performed the reaction


title: Livermorium

text: The following year, they published a retraction after researchers at other laboratories were unable to duplicate the results and the Berkeley lab itself was unable to duplicate them as well. In June 2002, the director of the lab announced that the original claim of the discovery of these two elements had been based on data fabricated by principal author Victor Ninov.


title: Livermorium

text: Livermorium was first synthesized on July 19, 2000, when scientists at Dubna (JINR) bombarded a curium-248 target with accelerated calcium-48 ions. A single atom was detected, decaying by alpha emission with decay energy 10.54 MeV to an isotope of flerovium. The results were published in December 2000.


title: Livermorium

text: The daughter flerovium isotope had properties matching those of a flerovium isotope first synthesized in June 1999, which was originally assigned to Fl, implying an assignment of the parent livermorium isotope to Lv. Later work in December 2002 indicated that the synthesized flerovium isotope was actually Fl, and hence the assignment of the synthesized livermorium atom was correspondingly altered to Lv.


title: Livermorium

text: Two further atoms were reported by the institute during their second experiment during April–May 2001. In the same experiment they also detected a decay chain which corresponded to the first observed decay of flerovium in December 1998, which had been assigned to Fl. No flerovium isotope with the same properties as the one found in December 1998 has ever been observed again, even in repeats of the same reaction. Later it was found that Fl has different decay properties and that the first observed flerovium atom may have been its nuclear isomer Fl. The observation of Fl in this series of experiments may indicate the formation of a parent isomer of livermorium, namely Lv, or a rare and previously unobserved decay branch of the already-discovered state Lv to Fl. Neither possibility is certain, and research is required to positively assign this activity. Another possibility suggested is the assignment of the original December 1998 atom to Fl, as the low beam energy used in that original experiment makes the 2n channel plausible; its parent could then conceivably be Lv, but this assignment would still need confirmation in the Cm(Ca,2n)Lv reaction.


title: Livermorium

text: The team repeated the experiment in April–May 2005 and detected 8 atoms of livermorium. The measured decay data confirmed the assignment of the first-discovered isotope as Lv. In this run, the team also observed the isotope Lv for the first time. In further experiments from 2004 to 2006, the team replaced the curium-248 target with the lighter curium isotope curium-245. Here evidence was found for the two isotopes Lv and Lv.


title: Livermorium

text: In May 2009, the IUPAC/IUPAP Joint Working Party reported on the discovery of copernicium and acknowledged the discovery of the isotope Cn. This implied the "de facto" discovery of the isotope Lv, from the acknowledgment of the data relating to its granddaughter Cn, although the livermorium data was not absolutely critical for the demonstration of copernicium's discovery. Also in 2009, confirmation from Berkeley and the Gesellschaft für Schwerionenforschung (GSI) in Germany came for the flerovium isotopes 286 to 289, immediate daughters of the four known livermorium isotopes. In 2011, IUPAC evaluated the Dubna team experiments of 2000–2006. Whereas they found the earliest data (not involving Lv and Cn) inconclusive, the results of 2004–2006 were accepted as identification of livermorium, and the element was officially recognized as having been discovered.


title: Livermorium

text: The synthesis of livermorium has been separately confirmed at the GSI (2012) and RIKEN (2014 and 2016). In the 2012 GSI experiment, one chain tentatively assigned to Lv was shown to be inconsistent with previous data; it is believed that this chain may instead originate from an isomeric state, Lv. In the 2016 RIKEN experiment, one atom that may be assigned to Lv was seemingly detected, alpha decaying to Fl and Cn, which underwent spontaneous fission; however, the first alpha from the livermorium nuclide produced was missed, and the assignment to Lv is still uncertain though plausible.


title: Livermorium

text: Using Mendeleev's nomenclature for unnamed and undiscovered elements, livermorium is sometimes called "eka-polonium". In 1979 IUPAC recommended that the placeholder systematic element name "ununhexium" ("Uuh") be used until the discovery of the element was confirmed and a name was decided. Although widely used in the chemical community on all levels, from chemistry classrooms to advanced textbooks, the recommendations were mostly ignored among scientists in the field, who called it "element 116", with the symbol of "E116", "(116)", or even simply "116".


title: Livermorium

text: According to IUPAC recommendations, the discoverer or discoverers of a new element have the right to suggest a name. The discovery of livermorium was recognized by the Joint Working Party (JWP) of IUPAC on 1 June 2011, along with that of flerovium. According to the vice-director of JINR, the Dubna team originally wanted to name element 116 "moscovium", after the Moscow Oblast in which Dubna is located, but it was later decided to use this name for element 115 instead. The name "livermorium" and the symbol "Lv" were adopted on May 23, 2012. The name recognises the Lawrence Livermore National Laboratory, within the city of Livermore, California, US, which collaborated with JINR on the discovery. The city in turn is named after the American rancher Robert Livermore, a naturalized Mexican citizen of English birth. The naming ceremony for flerovium and livermorium was held in Moscow on October 24, 2012.


title: Livermorium

text: Other than nuclear properties, no properties of livermorium or its compounds have been measured; this is due to its extremely limited and expensive production and the fact that it decays very quickly. Properties of livermorium remain unknown and only predictions are available.


title: Livermorium

text: Livermorium is expected to be near an island of stability centered on copernicium (element 112) and flerovium (element 114). Due to the expected high fission barriers, any nucleus within this island of stability exclusively decays by alpha decay and perhaps some electron capture and beta decay. While the known isotopes of livermorium do not actually have enough neutrons to be on the island of stability, they can be seen to approach the island, as the heavier isotopes are generally the longer-lived ones.


title: Livermorium

text: Superheavy elements are produced by nuclear fusion. These fusion reactions can be divided into "hot" and "cold" fusion, depending on the excitation energy of the compound nucleus produced. In hot fusion reactions, very light, high-energy projectiles are accelerated toward very heavy targets (actinides), giving rise to compound nuclei at high excitation energy (~40–50 MeV) that may either fission or evaporate several (3 to 5) neutrons. In cold fusion reactions (which use heavier projectiles, typically from the fourth period, and lighter targets, usually lead and bismuth), the produced fused nuclei have a relatively low excitation energy (~10–20 MeV), which decreases the probability that these products will undergo fission reactions. As the fused nuclei cool to the ground state, they require emission of only one or two neutrons. Hot fusion reactions tend to produce more neutron-rich products because the actinides have the highest neutron-to-proton ratios of any elements that can presently be made in macroscopic quantities.


title: Livermorium

text: Important information could be gained regarding the properties of superheavy nuclei by the synthesis of more livermorium isotopes, specifically those with a few neutrons more or less than the known ones – Lv, Lv, Lv, Lv, Lv, and Lv. This is possible because there are many reasonably long-lived isotopes of curium that can be used to make a target. The light isotopes can be made by fusing curium-243 with calcium-48. They would undergo a chain of alpha decays, ending at transactinide isotopes that are too light to achieve by hot fusion and too heavy to be produced by cold fusion.


title: Livermorium

text: The synthesis of the heavy isotopes Lv and Lv could be accomplished by fusing the heavy curium isotope curium-250 with calcium-48. The cross section of this nuclear reaction would be about 1 picobarn, though it is not yet possible to produce Cm in the quantities needed for target manufacture. After a few alpha decays, these livermorium isotopes would reach nuclides at the line of beta stability. Additionally, electron capture may also become an important decay mode in this region, allowing affected nuclei to reach the middle of the island. For example, it is predicted that Lv would alpha decay to Fl, which would undergo successive electron capture to Nh and then Cn which is expected to be in the middle of the island of stability and have a half-life of about 1200 years, affording the most likely hope of reaching the middle of the island using current technology. A drawback is that the decay properties of superheavy nuclei this close to the line of beta stability are largely unexplored.


title: Livermorium

text: Other possibilities to synthesize nuclei on the island of stability include quasifission (partial fusion followed by fission) of a massive nucleus. Such nuclei tend to fission, expelling doubly magic or nearly doubly magic fragments such as calcium-40, tin-132, lead-208, or bismuth-209. Recently it has been shown that the multi-nucleon transfer reactions in collisions of actinide nuclei (such as uranium and curium) might be used to synthesize the neutron-rich superheavy nuclei located at the island of stability, although formation of the lighter elements nobelium or seaborgium is more favored. One last possibility to synthesize isotopes near the island is to use controlled nuclear explosions to create a neutron flux high enough to bypass the gaps of instability at Fm and at mass number 275 (atomic numbers 104 to 108), mimicking the r-process in which the actinides were first produced in nature and the gap of instability around radon bypassed. Some such isotopes (especially Cn and Cn) may even have been synthesized in nature, but would have decayed away far too quickly (with half-lives of only thousands of years) and be produced in far too small quantities (about 10 the abundance of lead) to be detectable as primordial nuclides today outside cosmic rays.


title: Livermorium

text: In the periodic table, livermorium is a member of group 16, the chalcogens. It appears below oxygen, sulfur, selenium, tellurium, and polonium. Every previous chalcogen has six electrons in its valence shell, forming a valence electron configuration of nsnp. In livermorium's case, the trend should be continued and the valence electron configuration is predicted to be 7s7p; therefore, livermorium will have some similarities to its lighter congeners. Differences are likely to arise; a large contributing effect is the spin–orbit (SO) interaction—the mutual interaction between the electrons' motion and spin. It is especially strong for the superheavy elements, because their electrons move much faster than in lighter atoms, at velocities comparable to the speed of light. In relation to livermorium atoms, it lowers the 7s and the 7p electron energy levels (stabilizing the corresponding electrons), but two of the 7p electron energy levels are stabilized more than the other four. The stabilization of the 7s electrons is called the inert pair effect, and the effect "tearing" the 7p subshell into the more stabilized and the less stabilized parts is called subshell splitting. Computation chemists see the split as a change of the second (azimuthal) quantum number "l" from 1 to and for the more stabilized and less stabilized parts of the 7p subshell, respectively: the 7p subshell acts as a second inert pair, though not as inert as the 7s electrons, while the 7p subshell can easily participate in chemistry. For many theoretical purposes, the valence electron configuration may be represented to reflect the 7p subshell split as 7s7p7p.


title: Livermorium

text: Inert pair effects in livermorium should be even stronger than in polonium and hence the +2 oxidation state becomes more stable than the +4 state, which would be stabilized only by the most electronegative ligands; this is reflected in the expected ionization energies of livermorium, where there are large gaps between the second and third ionization energies (corresponding to the breaching of the unreactive 7p shell) and fourth and fifth ionization energies. Indeed, the 7s electrons are expected to be so inert that the +6 state will not be attainable. The melting and boiling points of livermorium are expected to continue the trends down the chalcogens; thus livermorium should melt at a higher temperature than polonium, but boil at a lower temperature. It should also be denser than polonium (α-Lv: 12.9 g/cm; α-Po: 9.2 g/cm); like polonium it should also form an α and a β allotrope. The electron of a hydrogen-like livermorium atom (oxidized so that it only has one electron, Lv) is expected to move so fast that it has a mass 1.86 times that of a stationary electron, due to relativistic effects. For comparison, the figures for hydrogen-like polonium and tellurium are expected to be 1.26 and 1.080 respectively.


title: Livermorium

text: Livermorium is projected to be the fourth member of the 7p series of chemical elements and the heaviest member of group 16 in the periodic table, below polonium. While it is the least theoretically studied of the 7p elements, its chemistry is expected to be quite similar to that of polonium. The group oxidation state of +6 is known for all the chalcogens apart from oxygen which cannot expand its octet and is one of the strongest oxidizing agents among the chemical elements. Oxygen is thus limited to a maximum +2 state, exhibited in the fluoride OF. The +4 state is known for sulfur, selenium, tellurium, and polonium, undergoing a shift in stability from reducing for sulfur(IV) and selenium(IV) through being the most stable state for tellurium(IV) to being oxidizing in polonium(IV). This suggests a decreasing stability for the higher oxidation states as the group is descended due to the increasing importance of relativistic effects, especially the inert pair effect. The most stable oxidation state of livermorium should thus be +2, with a rather unstable +4 state. The +2 state should be about as easy to form as it is for beryllium and magnesium, and the +4 state should only be achieved with strongly electronegative ligands, such as in livermorium(IV) fluoride (LvF). The +6 state should not exist at all due to the very strong stabilization of the 7s electrons, making the valence core of livermorium only four electrons. The lighter chalcogens are also known to form a −2 state as oxide, sulfide, selenide, telluride, and polonide; due to the destabilization of livermorium's 7p subshell, the −2 state should be very unstable for livermorium, whose chemistry should be essentially purely cationic, though the larger subshell and spinor energy splittings of livermorium as compared to polonium should make Lv slightly less unstable than expected.


title: Livermorium

text: Livermorium hydride (LvH) would be the heaviest chalcogen hydride and the heaviest homolog of water (the lighter ones are HS, HSe, HTe, and PoH). Polane (polonium hydride) is a more covalent compound than most metal hydrides because polonium straddles the border between metal and metalloid and has some nonmetallic properties: it is intermediate between a hydrogen halide like hydrogen chloride (HCl) and a metal hydride like stannane (SnH). Livermorane should continue this trend: it should be a hydride rather than a livermoride, but still a covalent molecular compound. Spin-orbit interactions are expected to make the Lv–H bond longer than expected from periodic trends alone, and make the H–Lv–H bond angle larger than expected: this is theorized to be because the unoccupied 8s orbitals are relatively low in energy and can hybridize with the valence 7p orbitals of livermorium. This phenomenon, dubbed "supervalent hybridization", has some analogues in non-relativistic regions in the periodic table; for example, molecular calcium difluoride has 4s and 3d involvement from the calcium atom. The heavier livermorium dihalides are predicted to be linear, but the lighter ones are predicted to be bent.


title: Livermorium

text: Unambiguous determination of the chemical characteristics of livermorium has not yet been established. In 2011, experiments were conducted to create nihonium, flerovium, and moscovium isotopes in the reactions between calcium-48 projectiles and targets of americium-243 and plutonium-244. The targets included lead and bismuth impurities and hence some isotopes of bismuth and polonium were generated in nucleon transfer reactions. This, while an unforeseen complication, could give information that would help in the future chemical investigation of the heavier homologs of bismuth and polonium, which are respectively moscovium and livermorium. The produced nuclides bismuth-213 and polonium-212m were transported as the hydrides BiH and PoH at 850 °C through a quartz wool filter unit held with tantalum, showing that these hydrides were surprisingly thermally stable, although their heavier congeners McH and LvH would be expected to be less thermally stable from simple extrapolation of periodic trends in the p-block. Further calculations on the stability and electronic structure of BiH, McH, PoH, and LvH are needed before chemical investigations take place. Moscovium and livermorium are expected to be volatile enough as pure elements for them to be chemically investigated in the near future, a property livermorium would then share with its lighter congener polonium, though the short half-lives of all presently known livermorium isotopes means that the element is still inaccessible to experimental chemistry.


title: Kamadhenu

text: Kamadhenu (, , ), also known as Surabhi (, or , ), is a divine bovine-goddess described in Hinduism as the mother of all cows. She is a miraculous cow of plenty who provides her owner whatever he desires and is often portrayed as the mother of other cattle. In iconography, she is generally depicted as a white cow with a female head and breasts, the wings of a bird, and the tail of a peafowl or as a white cow containing various deities within her body. Kamadhenu is not worshipped independently as a goddess. Rather, she is honored by the Hindu veneration of cows, who are regarded her earthly embodiments.


title: Kamadhenu

text: Hindu scriptures provide diverse accounts of the birth of Kamadhenu. While some narrate that she emerged from the churning of the cosmic ocean, others describe her as the daughter of the creator god Daksha, and as the wife of the sage Kashyapa. Still other scriptures narrate that Kamadhenu was in the possession of either Jamadagni or Vashista (both ancient sages), and that kings who tried to steal her from the sage ultimately faced dire consequences for their actions. Kamadhenu plays the important role of providing milk and milk products to be used in her sage-master's oblations; she is also capable of producing fierce warriors to protect him. In addition to dwelling in the sage's hermitage, she is also described as dwelling in Goloka - the realm of the cows - and Patala, the netherworld.


title: Kamadhenu

text: Kamadhenu is often addressed by the proper name "Surabhi" or "Shurbhi", which is also used as a synonym for an ordinary cow. Professor Jacobi considers the name Surabhi—"the fragrant one"—to have originated from the peculiar smell of cows. According to the Monier Williams Sanskrit–English Dictionary (1899), Surabhi means fragrant, charming, pleasing, as well as cow and earth. It can specifically refer to the divine cow Kamadhenu, the mother of cattle who is also sometimes described as a "Matrika" ("mother") goddess. Other proper names attributed to Kamadhenu are "Sabala" ("the spotted one") and "Kapila" ("the red one").


title: Kamadhenu

text: The epithets "Kamadhenu" (कामधेनु), "Kamaduh" (कामदुह्) and "Kamaduha" (कामदुहा) literally mean the cow "from whom all that is desired is drawn"—"the cow of plenty". In the "Mahabharata" and "Devi Bhagavata Purana", in the context of the birth of Bhishma, the cow Nandini is given the epithet Kamadhenu. In other instances, Nandini is described as the cow-daughter of Surabhi-Kamadhenu. The scholar Vettam Mani considers Nandini and Surabhi to be synonyms of Kamadhenu.


title: Kamadhenu

text: According to Indologist Madeleine Biardeau, Kamadhenu or Kamaduh is the generic name of the sacred cow, who is regarded as the source of all prosperity in Hinduism. Kamadhenu is regarded as a form of Devi (the Hindu Divine Mother) and is closely related to the fertile Mother Earth (Prithvi), who is often described as a cow in Sanskrit. The sacred cow denotes "purity and non-erotic fertility, ... sacrificing and motherly nature, [and] sustenance of human life".


title: Kamadhenu

text: Frederick M. Smith describes Kamadhenu as a "popular and enduring image in Indian art". All the gods are believed to reside in the body of Kamadhenu—the generic cow. Her four legs are the scriptural Vedas; her horns are the triune gods Brahma (tip), Vishnu (middle) and Shiva (base); her eyes are the sun and moon gods, her shoulders the fire-god Agni and the wind-god Vayu and her legs the Himalayas. Kamadhenu is often depicted in this form in poster art.


title: Kamadhenu

text: Another representation of Kamadhenu shows her with the body of a white Zebu cow, crowned woman's head, colourful eagle wings and a peacock's tail. According to the Philadelphia Museum of Art, this form is influenced by the iconography of the Islamic Buraq, who is portrayed with a horse's body, wings, and a woman's face. Contemporary poster art also portrays Kamadhenu in this form.


title: Kamadhenu

text: A cow, identified with Kamadhenu, is often depicted accompanying the god Dattatreya. In relation to the deity's iconography, she denotes the Brahminical aspect and Vaishnava connection of the deity contrasting with the accompanying dogs—symbolizing a non-Brahminical aspect. She also symbolizes the "Panch Bhuta" (the five classical elements) in the icon. Dattatreya is sometimes depicted holding the divine cow in one of his hands.


title: Kamadhenu

text: The "Mahabharata" (Adi Parva book) records that Kamadhenu-Surabhi rose from the churning of the cosmic ocean ("Samudra Manthana") by the gods and demons to acquire "Amrita" (ambrosia, elixir of life). As such, she is regarded the offspring of the gods and demons, created when they churned the cosmic milk ocean and then given to the Saptarishi, the seven great seers. She was ordered by the creator-god Brahma to give milk, and supply it and "ghee" ("clarified butter") for ritual fire-sacrifices.


title: Kamadhenu

text: The "Anushasana Parva" book of the epic narrates that Surabhi was born from the belch of "the creator" ("Prajapati") Daksha after he drank the "Amrita" that rose from the Samudra Manthana. Further, Surabhi gave birth to many golden cows called "Kapila cows", who were called the mothers of the world. The "Satapatha Brahmana" also tells a similar tale: "Prajapati" created Surabhi from his breath. The "Udyoga Parva" Book of the "Mahabharata" narrates that the creator-god Brahma drank so much "Amrita" that he vomited some of it, from which emerged Surabhi.


title: Kamadhenu

text: According to the "Ramayana", Surabhi is the daughter of sage Kashyapa and his wife Krodhavasha, the daughter of Daksha. Her daughters Rohini and Gandharvi are the mothers of cattle and horses respectively. Still, it is Surabhi who is described as the mother of all cows in the text. However, in the "Puranas", such as "Vishnu Purana" and "Bhagavata Purana", Surabhi is described as the daughter of Daksha and the wife of Kashyapa, as well as the mother of cows and buffaloes.


title: Kamadhenu

text: The "Matsya Purana" notes two conflicting descriptions of Surabhi. In one chapter, it describes Surabhi as the consort of Brahma and their union produced the cow Yogishvari, She is then described as the mother of cows and quadrupeds. In another instance, she is described as a daughter of Daksha, wife of Kashyapa and the mother of cows. The "Harivamsa", an appendix of the "Mahabharata", calls Surabhi the mother of Amrita (ambrosia), Brahmins, cows and Rudras.