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835f43d1ac371419c2d771253bdbb78bb313c522 | richards was born at burton-on-trent, the third child | richards was born at burton-on-trent, the third child of robert with two brothers and a sister. his eldest brother died in world war i and the other brother took over the family business as a butcher. richards took an interest in natural history and astronomy at young age. he attended the burton-on-trent grammar school... | wikipedia |
db855f7c6349a27a98de29f774c893173569dc02 | francis john richards frs (1 october 1901 – | francis john richards frs (1 october 1901 – 2 january 1965) was an english plant physiologist who specialized in quantitative studies on the mineral nutrition requirements of crops. he first described the general form of the generalised logistic function in 1959. | wikipedia |
33785bbd1acd6aa8a9e4680a63de95342ac612d4 | a voice prosthesis is an artificial device, usually | a voice prosthesis is an artificial device, usually made of silicone that is used in conjunction with voice therapy to help laryngectomized patients to speak. during a total laryngectomy, the entire voice box (larynx) is removed and the windpipe (trachea) and food pipe (esophagus) are separated from each other. during ... | wikipedia |
27eaf3969f592cb7f07c9b0f6041422e89581966 | there are two ways of inserting the voice | there are two ways of inserting the voice prosthesis: through the mouth and throat with the help of a guide wire, or directly through the tracheostoma (anterograde) manner. nowadays, most voice prosthesis are placed anterograde, through the stoma. | wikipedia |
f0887cb4e8a4af134950fe88dab4d07399c67c22 | the voice quality when speaking with a voice | the voice quality when speaking with a voice prosthesis is influenced by pulmonary support, airflow resistance of the voice prosthesis, and airflow resistance of the new voice source. although the voice prosthesis is only responsible for part of the total resistance – the neoglottis is responsible for the other part – ... | wikipedia |
39d91351d5e417ff39c0752488274e40784bd019 | the device lifetime can range from a couple | the device lifetime can range from a couple of weeks up to two years, depending on individual circumstances. the lifetime is influenced by daily food intake, especially dairy products, but also radiotherapy and gerd (gastro esophageal reflux disease) affects the voice prosthesis and its lifetime. the cause of the proth... | wikipedia |
2099ec8b45c08325c4cceaed26d597bbcfc3e361 | a voice prosthesis has to be replaced regularly, | a voice prosthesis has to be replaced regularly, because after a certain time, the valve flap of the voice prosthesis does not close properly anymore, due to yeast and other natural sediments. this causes leakage of saliva or drinks, which enters the wind pipe and makes the person concerned cough. if not resolved by cl... | wikipedia |
f103360e8d103aeeef1c84edfd17cca959dee1a8 | it is important to clean the voice prosthesis | it is important to clean the voice prosthesis regularly, as the silicone material is exposed to yeast (candida) and bacteria in the food pipe, which is normally present in these areas. if yeast begins growing on or in the area of the valve flap of the voice prosthesis, it may not close well enough anymore. when this ha... | wikipedia |
ee9918f900cf42961049eaf87dd41ac889d23000 | there are even special, problem-solving voice prosthesis, e.g. | there are even special, problem-solving voice prosthesis, e.g. for laryngectomized patients with very short device life times (less than 4 to 8 weeks) of their current prosthesis. those extremely short device life times may be caused by excessive candida growth, so that the valve of the prosthesis does not close proper... | wikipedia |
f4f39f6ecaef33013ced652c338b307a7b62b2ef | the size of a voice prosthesis varies in | the size of a voice prosthesis varies in length, depending on the thickness of the wall between the foodpipe and the windpipe and thereby the length of the te puncture. the according length of the voice prosthesis ranges usually between 4 and 22 mm. another parameter is the outer diameter of the shaft of the voice pros... | wikipedia |
4828c2de4faccc0b84c41619a30a5f976dfc3c22 | the general design of voice prosthesis is quite | the general design of voice prosthesis is quite consistent, even though there are unique characteristics. a voice prosthesis has retaining flanges at each end, the 'tracheal flange' and 'esophageal flange'. those flanges can vary in size and rigidity, e.g. indwelling prostheses have larger and more rigid flanges for st... | wikipedia |
a246496560c334cab276621d7dc5982964ee1b1e | the two main categories voice prosthesis can be | the two main categories voice prosthesis can be divided into are 'non-indwelling' and 'indwelling' voice prostheses. 'non-indwelling' voice prostheses can be replaced by the patients themselves, whereas 'indwelling' prostheses have to be replaced by a medical professional. a non-indwelling voice prosthesis has a safety... | wikipedia |
0ac3c1bc0587b29546adb87ba3863d07ddcbe020 | in 1972, the very first voice prosthesis for | in 1972, the very first voice prosthesis for voice rehabilitation after total laryngectomy was described in an article in polish by mozolewski. since then, many efforts have taken place in this area of rehabilitation. there are several manufacturers that have voice prosthesis in their product portfolio, e.g. blom-singe... | wikipedia |
28db5ab6e520ff6b3aa5e1ad5007bc89cdeb8ea6 | in 1869, the first artificial voice box (larynx) | in 1869, the first artificial voice box (larynx) was built by czermak. in 1873 theodor billroth made a total laryngectomy (in steps) and implanted an artificial voice box. a new development, using modern materials, took place in france by debry. | wikipedia |
befc24fce72bd52e140109b900f1ae08aa6a7807 | a voice prosthesis (plural prostheses) is an artificial | a voice prosthesis (plural prostheses) is an artificial device, usually made of silicone that is used in conjunction with voice therapy to help laryngectomized patients to speak. during a total laryngectomy, the entire voice box (larynx) is removed and the windpipe (trachea) and food pipe (esophagus) are separated from... | wikipedia |
216cf295b7444c26ace8394d56895cd287ecd3ee | viktor mikhailovich kolotov was a soviet and ukrainian | viktor mikhailovich kolotov was a soviet and ukrainian footballer who played as a midfielder. he was born in the settlement of yudino, kazan municipality. today the settlement is included in the kirov raion of kazan city. after becoming a coach he extended his welcomed stay in kyiv. together with dynamo kyiv he became ... | wikipedia |
471e958f3f368f9e5b3d6008d62bbd4bada46f43 | he was born in the settlement of yudino, | he was born in the settlement of yudino, kazan municipality. today the settlement is included in the kirov raion of kazan city. after becoming a coach he extended his welcomed stay in kyiv. together with dynamo kyiv he became the four-time champion of the ussr as well as the two-time holder of the ussr cup. also in eur... | wikipedia |
73fa4772cbc2fd52711049d9a58997a3183eb20e | viktor mikhailovich kolotov (russian: Виктор Михайлович Колотов; ukrainian: | viktor mikhailovich kolotov (russian: Виктор Михайлович Колотов; ukrainian: Віктор Михайлович Колотов; 3 july 1949 – 3 january 2000) was a soviet and ukrainian footballer who played as a midfielder. | wikipedia |
92efd3a5ee805de1f64937c45879406652d3e4a1 | kempe has represented sweden at the junior and | kempe has represented sweden at the junior and senior levels in international competitions. he represented sweden at the 2018 iihf world championship, where they won a gold medal, and at the 2024 iihf world championship, where they won a bronze medal. | wikipedia |
436fb040e25e76cc7a3b054b9ef1964a0e8cc0e9 | kempe's nickname is "juice." the name originated during | kempe's nickname is "juice." the name originated during the monarch's playoff run to the 2015 calder cup, in which the 18-year-old kempe scored eight goals. his teammates and coaches described him as "having the juice" due to his impressive performance. | wikipedia |
db0d7cfb92bdebb23d046d1d7fe96a6696de5405 | kempe was born in kramfors, sweden, where he | kempe was born in kramfors, sweden, where he also grew up. his older brother, mario, is also a professional ice hockey player who played 52 nhl games with the arizona coyotes. kempe and mario briefly overlapped in the kings organization when mario signed a one-year two-way contract with the kings on 5 july 2019. the br... | wikipedia |
200daf35c05923ca9d33b8a5a0c73ccda0bc483c | on 10 july 2022, kempe signed a four-year, | on 10 july 2022, kempe signed a four-year, $22 million extension with the kings. kempe would once again lead the kings in goals scored, adding 41 goals to his total, and becoming the first kings player since luc robitaille to score 40 goals in a season. | wikipedia |
8860856fcadba68578f3c4f58c485637062cfcfc | entering his sixth season with the kings, 2021–22 | entering his sixth season with the kings, 2021–22 would be a breakout year for kempe, who posted new career highs scoring 35 goals and 54 points. he would also participate in his first nhl all-star game, held in las vegas; he is the only player from the kings named to the all stars this season. | wikipedia |
5bfb55f9661fa2818213af20acf2f190039852e1 | due to the covid-19 pandemic, the 2020–21 season | due to the covid-19 pandemic, the 2020–21 season was reduced to 56 games and began on 13 january 2021. during the shortened season, kempe was on pace to set new career highs in goals and assists. he earned praise from head coach todd mclellan for being a versatile player who was able to play different positions wheneve... | wikipedia |
1abb95f784dd83eb657296a9058ff1a30619f6df | kempe struggled at the start of the 2019–20, | kempe struggled at the start of the 2019–20, resulting in him being demoted to the fourth line and playing limited ice time. through the first 17 games of the season, kempe scored one goal and three assists. he was made a healthy scratch for a november game against the minnesota wild before returning to the lineup as a... | wikipedia |
4f68f8b1477035910cc8666f7cbb1a664626d9e1 | kempe returned to the kings lineup for the | kempe returned to the kings lineup for the 2018–19 season, where he was expected to play as a winger on their second line with ilya kovalchuk and jeff carter. due to injuries throughout the lineup, kempe began playing alongside rookies matt luff and austin wagner on the kings third line. after scoring three goals and f... | wikipedia |
310d500f5c1c9ae0cdaaf6706d9fc6759cd438d2 | when attending the kings 2017 training camp, kempe | when attending the kings 2017 training camp, kempe was put on a line with justin auger and kyle clifford. after qualifying for the kings 2017–18 opening night roster, kempe switched from no. 39 to no. 9. he had worn the no. 9 growing up when playing soccer, in honour of fernando torres, and 10 when playing hockey. kemp... | wikipedia |
dbf29b316cced1af9fe929f09a172dca14505f1f | kempe began the 2016–17 season with the reign | kempe began the 2016–17 season with the reign after attending the los angeles kings training camp. as a centreman, kempe struggled at the start of the season, scoring three goals and two assists over 16 games. he was switched back to left wing on 3 december to improve his offensive play. he slowly improved through the ... | wikipedia |
084dd0527af1b1d2126e075cbf5ec3dbf4cc2546 | after attending the kings 2015 training camp, kempe | after attending the kings 2015 training camp, kempe was re-assigned to the reign for the 2015–16 season. as he was coming to the nhl from europe, he was eligible to spend the full 2015–16 season in the ahl if he failed to qualify for the nhl team. due to injuries throughout the lineup, kempe spent the majority of the s... | wikipedia |
c0e80b3b90b1ac980a59b3981ed8c6d5dbc73bac | following the conclusion of his season with modo, | following the conclusion of his season with modo, kempe signed an amateur try-out agreement with the kings american hockey league (ahl) affiliate, the manchester monarchs for the remainder of their regular season and the 2015 calder cup playoffs. he also signed a three-year, entry-level contract with the kings for the ... | wikipedia |
2657897123eda96ea1010d93b3cbda1147ee0ba5 | kempe made his swedish hockey league (shl) debut | kempe made his swedish hockey league (shl) debut playing with modo hockey during the 2013–14 season. at the end of the season, kempe was selected in the first round (29th overall) by the los angeles kings in the 2014 nhl entry draft. he returned to modo for the 2014–15 season. | wikipedia |
7017a1cd00b363da298ea99868cf6830cb842d65 | adrian kempe (born 13 september 1996) is a | adrian kempe (born 13 september 1996) is a swedish professional ice hockey player for the los angeles kings of the national hockey league (nhl). kempe was selected by the kings in the first round (29th overall) of the 2014 nhl entry draft. | wikipedia |
368891875d8173d97069b03cda4af018653c4161 | jonas olov johansson is a swedish professional ice | jonas olov johansson is a swedish professional ice hockey goaltender currently under contract with the tampa bay lightning of the national hockey league (nhl). johansson was selected by the buffalo sabres in the third round, 61st overall, at the 2014 nhl entry draft. along with buffalo, johansson has previously played ... | wikipedia |
bcd6ebfbef9abd8f299112b84e045b5f76b25c93 | at the completion of the season with the | at the completion of the season with the avalanche and as a pending free agent, johansson initially opted to return to sweden in signing a two-year contract with färjestad bk of the shl on 9 may 2023. however, in little under a month later on 7 june 2023, his contract with färjestad bk was mutually cancelled with johan... | wikipedia |
ba4aa8e0415f04d5cbc8d9310db8fc5bd89c3a06 | as a free agent from the panthers, johansson | as a free agent from the panthers, johansson opted to return to former club, the colorado avalanche, agreeing to a one-year, two-way contract on 13 july 2022. after attending training camp with the avalanche, johansson was placed on waivers during the pre-season. he was claimed the following day by divisional rival in ... | wikipedia |
dc787c121adb70b1cd6134c718ff018257b1941c | on 29 june 2021, johansson as a pending | on 29 june 2021, johansson as a pending free agent opted to continue within the avalanche organization, agreeing to a one-year, two-way contract extension. on 13 december, johansson was claimed off waivers by the florida panthers. | wikipedia |
35ea0ab190925954500d6bacf7bdd53225ab3381 | on 20 march 2021, johansson was traded to | on 20 march 2021, johansson was traded to the colorado avalanche in exchange for a sixth-round draft pick. the trade was delayed by a day as the sabres waited to receive the results of several covid-19 tests. following the trade, sabres beat writer john vogl called johansson the worst goaltender he had seen in nineteen... | wikipedia |
64a92b143580bbc1eed4f83a8b308401837bf4fe | with the following north american season delayed due | with the following north american season delayed due to the covid-19 pandemic, on 31 october 2020, johansson was loaned by the sabres to german club, krefeld pinguine of the deutsche eishockey liga (del), until the commencement of nhl training camp. before joining krefeld, the del was later delayed due to the pandemic ... | wikipedia |
62f77a5beae1bd541b0fda065ac41bc18ff6e128 | johansson made his nhl debut on 4 february | johansson made his nhl debut on 4 february 2020, in relief of carter hutton in a game against the colorado avalanche. his first nhl start came on 6 february, making 18 saves on 21 shots in a shootout loss to the detroit red wings. johansson recorded his first nhl win on 23 february 2020, 2–1 against the winnipeg jets. | wikipedia |
926f9da5e202110c4511e9fe3537f5878972ac7a | johansson won a silver medal with team sweden | johansson won a silver medal with team sweden at the 2014 world junior ice hockey championships in a backup role, and he made his swedish hockey league debut playing with brynäs if during the 2013–14 shl season. | wikipedia |
68f0811bcd7081b7d1ec9d833190fb3817a5e019 | jonas olov johansson (born 19 september 1995) is | jonas olov johansson (born 19 september 1995) is a swedish professional ice hockey goaltender currently under contract with the tampa bay lightning of the national hockey league (nhl). johansson was selected by the buffalo sabres in the third round, 61st overall, at the 2014 nhl entry draft. along with buffalo, johanss... | wikipedia |
5b2c3406b375b7762300f74adfd693402dbee168 | an ideal solution or ideal mixture is a | an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. the enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zero the enthalpy of mixing is, the more "ideal" the behavior of the solution becomes. the... | wikipedia |
44892e2536116e1723aff6c69ae358c96500ee65 | in contrast to ideal solutions, where volumes are | in contrast to ideal solutions, where volumes are strictly additive and mixing is always complete, the volume of a non-ideal solution is not, in general, the simple sum of the volumes of the component pure liquids and solubility is not guaranteed over the whole composition range. by measurement of densities, thermodyna... | wikipedia |
e9becc8545c36f8a9e00b368035218912c9d14b2 | where (p i) pure {\displaystyle (p_{i})_{\text{pure}}} is the | where (p i) pure {\displaystyle (p_{i})_{\text{pure}}} is the equilibrium vapor pressure of pure component i {\displaystyle i} and x i {\displaystyle x_{i}\,} is the mole fraction of component i {\displaystyle i} in solution. | wikipedia |
1a311f1db3a5aa73ed99a52c36d45cdb8ffb4eb3 | where Δ μ i, m i x = | where Δ μ i, m i x = r t ln x i {\displaystyle \delta \mu _{i,\mathrm {mix} }=rt\ln x_{i}} is the change in chemical potential of i {\displaystyle i} on mixing. if the chemical potential of pure liquid i {\displaystyle i} is denoted μ i ∗ {\displaystyle \mu _{i}^{*}}, then the chemical potential of i {\displaystyle i} ... | wikipedia |
dcd672a45e5dbc23ebeb95d1a72b7a6a2706a8d5 | where m denotes molar, i.e., change in gibbs | where m denotes molar, i.e., change in gibbs free energy per mole of solution, and x i {\displaystyle x_{i}} is the mole fraction of component i {\displaystyle i}. note that this free energy of mixing is always negative (since each x i ∈ {\displaystyle x_{i}\in }, each ln x i {\displaystyle \ln x_{i}} or its limit for ... | wikipedia |
9809e3ec97fb2050ae022712db84c6ce6845916a | solvent–solute interactions are the same as solute–solute and | solvent–solute interactions are the same as solute–solute and solvent–solvent interactions, on average. consequently, the enthalpy of mixing (solution) is zero and the change in gibbs free energy on mixing is determined solely by the entropy of mixing. hence the molar gibbs free energy of mixing is | wikipedia |
ae3bb53badaf16e95a2bad18569386212bb44168 | at last we can calculate the molar entropy | at last we can calculate the molar entropy of mixing since g i ∗ = h i ∗ − t s i ∗ {\displaystyle g_{i}^{*}=h_{i}^{*}-ts_{i}^{*}} and g i ¯ = h i ¯ − t s i ¯ {\displaystyle {\bar {g_{i}}}={\bar {h_{i}}}-t{\bar {s_{i}}}} | wikipedia |
8e9e559ececaf0580177835534e026f8b694d339 | since the gibbs free energy per mole of | since the gibbs free energy per mole of the mixture g m {\displaystyle g_{m}} is g m = ∑ i x i g i {\displaystyle g_{m}=\sum _{i}x_{i}{g_{i}}} then | wikipedia |
7f83f4229a0e7c06dd1a9557a854fcfd65123507 | since u i ¯ = h i ¯ | since u i ¯ = h i ¯ − p v i ¯ {\displaystyle {\bar {u_{i}}}={\bar {h_{i}}}-p{\bar {v_{i}}}} and u i ∗ = h i ∗ − p v i ∗ {\displaystyle u_{i}^{*}=h_{i}^{*}-pv_{i}^{*}}, similarly | wikipedia |
a8d23cc27b3bf5bb88e3083e90b44d5820aa8a5d | which in turn means that h i ¯ | which in turn means that h i ¯ = h i ∗ {\displaystyle {\bar {h_{i}}}=h_{i}^{*}} and that the enthalpy of the mix is equal to the sum of its component enthalpies. | wikipedia |
e193a7991d24ab783275b83d25623302174d1ef2 | remembering that (∂ g t ∂ t) p | remembering that (∂ g t ∂ t) p = − h t 2 {\displaystyle \left({\frac {\partial {\frac {g}{t}}}{\partial t}}\right)_{p}=-{\frac {h}{t^{2}}}} we get: | wikipedia |
87f1533e701b08f8cda33d8ab04a0ee6138956bf | since all this, done as a pure substance, | since all this, done as a pure substance, is valid in an ideal mix just adding the subscript i {\displaystyle i} to all the intensive variables and changing v {\displaystyle v} to v i ¯ {\displaystyle {\bar {v_{i}}}}, with optional overbar, standing for partial molar volume: | wikipedia |
22c5eca659467551f64f88fa3d4033823d2250a8 | however, the vapor above the solution may not | however, the vapor above the solution may not actually behave as a mixture of ideal gases. some authors therefore define an ideal solution as one for which each component obeys the fugacity analogue of raoult's law f i = x i f i ∗ {\displaystyle f_{i}=x_{i}f_{i}^{*}}. here f i {\displaystyle f_{i}} is the fugacity of c... | wikipedia |
4b2dded80772aaea6e005f87ac13f5f77c0edff5 | this definition depends on vapor pressure, which is | this definition depends on vapor pressure, which is a directly measurable property, at least for volatile components. the thermodynamic properties may then be obtained from the chemical potential μ (which is the partial molar gibbs energy g) of each component. if the vapor is an ideal gas, | wikipedia |
ccb3eaddbcafa2bf65f4aa7c86eeaae3fb995218 | different related definitions of an ideal solution have | different related definitions of an ideal solution have been proposed. the simplest definition is that an ideal solution is a solution for which each component obeys raoult's law p i = x i p i ∗ {\displaystyle p_{i}=x_{i}p_{i}^{*}} for all compositions. here p i {\displaystyle p_{i}} is the vapor pressure of component ... | wikipedia |
484c1a4ce2c28e8aba910a2216de796bea5f07eb | if the molecules are almost identical chemically, e.g., | if the molecules are almost identical chemically, e.g., 1-butanol and 2-butanol, then the solution will be almost ideal. since the interaction energies between a and b are almost equal, it follows that there is only a very small overall energy (enthalpy) change when the substances are mixed. the more dissimilar the nat... | wikipedia |
f0405b55f56daeaf252d727eca2d774eb34618db | more formally, for a mix of molecules of | more formally, for a mix of molecules of a and b, then the interactions between unlike neighbors (u) and like neighbors u and u must be of the same average strength, i.e., 2 u = u + u and the longer-range interactions must be nil (or at least indistinguishable). if the molecular forces are the same between aa, ab and b... | wikipedia |
d6bf10b69b45cb154f0bfb6c32e5e06ae0c795de | ideality of solutions is analogous to ideality for | ideality of solutions is analogous to ideality for gases, with the important difference that intermolecular interactions in liquids are strong and cannot simply be neglected as they can for ideal gases. instead we assume that the mean strength of the interactions are the same between all the molecules of the solution. | wikipedia |
243ebcba6349f0baccbed89f3379b04a260c0603 | an ideal solution or ideal mixture is a | an ideal solution or ideal mixture is a solution that exhibits thermodynamic properties analogous to those of a mixture of ideal gases. the enthalpy of mixing is zero as is the volume change on mixing by definition; the closer to zero the enthalpy of mixing is, the more "ideal" the behavior of the solution becomes. the... | wikipedia |
da38098f844ba36c60571d057a1d4be37722b590 | in june 2016, england played a three-test series | in june 2016, england played a three-test series against australia as part of the 2016 mid-year rugby union tests. they played the wallabies across the three weeks of the june international window, 11 june–25 june, and contested the cook cup, which england had previously won eight times to australia's twelve. the serie... | wikipedia |
b44f9bccc3aba7ad4dcdbf891953ad64fc8ba3cd | on 12 june, matt to'omua joined the squad | on 12 june, matt to'omua joined the squad as un-listed member of the squad after recovering from his knee surgery. liam gill (rugby)|liam gill also joined the squad after david pocock was ruled out of the rest of the series. | wikipedia |
e40d404259573267f018d4864cf981502c35e4c6 | on 3 june 2016, michael cheika named a | on 3 june 2016, michael cheika named a final 33-man squad for the test series, with adam coleman, liam gill, james hanson, leroy houston, eto nabuli and joe powell missing out on the final cut. | wikipedia |
51072ee6b53002309cde2f54f2a88b1fe2e7a8d4 | on 22 may, eddie jones named a 32-man | on 22 may, eddie jones named a 32-man squad for england's tour of australia. an additional 5 players (dave attwood, luther burrell, ollie devoto, matt kvesic, tommy taylor) were also named ahead of the test match against wales on 29 may, the day after the aviva premiership final between saracens and exeter chiefs. ben ... | wikipedia |
e073aba6b55e4a4ae6f3c87e24476df6f241cef6 | england won all three matches, the first time | england won all three matches, the first time they had won a test series in australia. after defeating the hosts in the second match, england retained the cook cup and achieved second place in the world rugby rankings, while australia dropped to fourth. australia had not been "whitewashed" in a home series since losing... | wikipedia |
e30e88a3afce847de66ba1e82272c5b01d4a38e2 | in june 2016, england played a three-test series | in june 2016, england played a three-test series against australia as part of the 2016 mid-year rugby union tests. they played the wallabies across the three weeks of the june international window, 11 june–25 june, and contested the cook cup, which england had previously won eight times to australia's twelve. the serie... | wikipedia |
974600e43d8a89c9b019e1e1e00843311a9ec416 | in mathematics and computer science, horner's method is | in mathematics and computer science, horner's method is an algorithm for polynomial evaluation. although named after william george horner, this method is much older, as it has been attributed to joseph-louis lagrange by horner himself, and can be traced back many hundreds of years to chinese and persian mathematicians... | wikipedia |
d6572f4e6f0b50214fca49e4d6576e3f21a83df7 | ulrich libbrecht concluded: it is obvious that this | ulrich libbrecht concluded: it is obvious that this procedure is a chinese invention... the method was not known in india. he said, fibonacci probably learned of it from arabs, who perhaps borrowed from the chinese. the extraction of square and cube roots along similar lines is already discussed by liu hui in connectio... | wikipedia |
9072e0a8cad5176c336e1bf53ceb54aa21ac830b | "... who can deny the fact of horner's | "... who can deny the fact of horner's illustrious process being used in china at least nearly six long centuries earlier than in europe... we of course don't intend in any way to ascribe horner's invention to a chinese origin, but the lapse of time sufficiently makes it not altogether impossible that the europeans cou... | wikipedia |
c9bb00655d4190cca8202adac5bef72c9bc31028 | qin jiushao, in his shu shu jiu zhang | qin jiushao, in his shu shu jiu zhang (mathematical treatise in nine sections; 1247), presents a portfolio of methods of horner-type for solving polynomial equations, which was based on earlier works of the 11th century song dynasty mathematician jia xian; for example, one method is specifically suited to bi-quintics, ... | wikipedia |
16da89d1b681ea0db6a797a812ab0e36a76ddf82 | unlike his english contemporaries, horner drew on the | unlike his english contemporaries, horner drew on the continental literature, notably the work of arbogast. horner is also known to have made a close reading of john bonneycastle's book on algebra, though he neglected the work of paolo ruffini. | wikipedia |
c72007b7fa52371227356b90f3f6db7b9a353ff4 | horner's paper, titled "a new method of solving | horner's paper, titled "a new method of solving numerical equations of all orders, by continuous approximation", was read before the royal society of london, at its meeting on july 1, 1819, with a sequel in 1823. horner's paper in part ii of philosophical transactions of the royal society of london for 1819 was warmly ... | wikipedia |
3bf2b17a5ab1c626f96c373524bafd4ddce3ab3c | at completion, we have p (x) = b | at completion, we have p (x) = b 0, p (y) − p (x) y − x = d 1, p (y) = b 0 + (y − x) d 1. {\displaystyle {\begin{aligned}p(x)&=b_{0},\\{\frac {p(y)-p(x)}{y-x}}&=d_{1},\\p(y)&=b_{0}+(y-x)d_{1}.\end{aligned}}} this computation of the divided difference is subject to less round-off error than evaluating p (x) {\displaysty... | wikipedia |
1380841e1226dca775c352ff9eb9156b1e96b17f | horner's method can be modified to compute the | horner's method can be modified to compute the divided difference (p (y) − p (x)) / (y − x). {\displaystyle (p(y)-p(x))/(y-x).} given the polynomial (as before) p (x) = ∑ i = 0 n a i x i = a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ⋯ + a n x n, {\displaystyle p(x)=\sum _{i=0}^{n}a_{i}x^{i}=a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}+\cd... | wikipedia |
27ac7101daabced9ff00d2c32e8dad3b3fd356e3 | from the above we know that the largest | from the above we know that the largest root of this polynomial is 7 so we are able to make an initial guess of 8. using newton's method the first zero of 7 is found as shown in black in the figure to the right. next p (x) {\displaystyle p(x)} is divided by (x − 7) {\displaystyle (x-7)} to obtain p 5 (x) = x 5 + 11 x 4... | wikipedia |
81900d2aade5e8dc293479065de4f7e8a78d3a07 | from the above we know that the largest | } which is shown in green and found to have a zero at − 3. this polynomial is further reduced to p 2 (x) = x 2 + 13 x + 40 {\displaystyle p_{2}(x)=x^{2}+13x+40} which is shown in blue and yields a zero of − 5. the final root of the original polynomial may be found by either using the final zero as an initial guess for ... | wikipedia |
3ef2d0a5d43c2615f0e961bc7655cb89a9ca09fb | consider the polynomial p 6 (x) = (x | consider the polynomial p 6 (x) = (x + 8) (x + 5) (x + 3) (x − 2) (x − 3) (x − 7) {\displaystyle p_{6}(x)=(x+8)(x+5)(x+3)(x-2)(x-3)(x-7)} which can be expanded to p 6 (x) = x 6 + 4 x 5 − 72 x 4 − 214 x 3 + 1127 x 2 + 1602 x − 5040. {\displaystyle p_{6}(x)=x^{6}+4x^{5}-72x^{4}-214x^{3}+1127x^{2}+1602x-5040.} | wikipedia |
a8d767e25dbb760f549d3380bc1989b86d76a467 | these two steps are repeated until all real | these two steps are repeated until all real zeros are found for the polynomial. if the approximated zeros are not precise enough, the obtained values can be used as initial guesses for newton's method but using the full polynomial rather than the reduced polynomials. | wikipedia |
da57923105f1005b7fb72b8e86f56817142696de | using the long division algorithm in combination with | using the long division algorithm in combination with newton's method, it is possible to approximate the real roots of a polynomial. the algorithm works as follows. given a polynomial p n (x) {\displaystyle p_{n}(x)} of degree n {\displaystyle n} with zeros z n < z n − 1 < ⋯ < z 1, {\displaystyle z_{n}<z_{n-1}<\cdots <... | wikipedia |
7ee5edf2782894faf7dec7abee6cf7a1cd57e534 | horner's method can be used to convert between | horner's method can be used to convert between different positional numeral systems – in which case x is the base of the number system, and the a coefficients are the digits of the base- x representation of a given number – and can also be used if x is a matrix, in which case the gain in computational efficiency is eve... | wikipedia |
2c5ca5ec977a01635719417b28ec9c203e14915f | the method is particularly fast on processors supporting | the method is particularly fast on processors supporting a single-instruction shift-and-addition-accumulate. compared to a c floating-point library, horner's method sacrifices some accuracy, however it is nominally 13 times faster (16 times faster when the " canonical signed digit " (csd) form is used) and uses only 20... | wikipedia |
4f74dd7afe8f556c16d28e4ea23195d8e87ae61f | in binary (base-2) math, multiplication by a power | in binary (base-2) math, multiplication by a power of 2 is merely a register shift operation. thus, multiplying by 2 is calculated in base-2 by an arithmetic shift. the factor (2) is a right arithmetic shift, a (0) results in no operation (since 2 = 1 is the multiplicative identity element), and a (2) results in a left... | wikipedia |
4cf0cd3976fb452b2011f5d9b26bb6d522c845d0 | the denominators all equal one (or the term | the denominators all equal one (or the term is absent), so this reduces to = d 0 (m + 2 d 1 (m + 2 d 2 (m + 2 d 3 (m)))), {\displaystyle =d_{0}(m+2{d_{1}}(m+2{d_{2}}(m+2{d_{3}}(m)))),} or equivalently (as consistent with the "method" described above) = d 3 (m + 2 − 1 d 2 (m + 2 − 1 d 1 (m + d 0 (m)))). {\displaystyle =... | wikipedia |
4e6abaf48fb914381536dc8787aee93e8ed42215 | in general, for a binary number with bit | in general, for a binary number with bit values (d 3 d 2 d 1 d 0 {\displaystyle d_{3}d_{2}d_{1}d_{0}}) the product is (d 3 2 3 + d 2 2 2 + d 1 2 1 + d 0 2 0) m = d 3 2 3 m + d 2 2 2 m + d 1 2 1 m + d 0 2 0 m. {\displaystyle (d_{3}2^{3}+d_{2}2^{2}+d_{1}2^{1}+d_{0}2^{0})m=d_{3}2^{3}m+d_{2}2^{2}m+d_{1}2^{1}m+d_{0}2^{0}m.}... | wikipedia |
6e6848a23d38c04a63c7417b32a70f61f434a7d2 | for example, to find the product of two | for example, to find the product of two numbers (0.15625) and m: (0.15625) m = (0.00101 b) m = (2 − 3 + 2 − 5) m = (2 − 3) m + (2 − 5) m = 2 − 3 (m + (2 − 2) m) = 2 − 3 (m + 2 − 2 (m)). {\displaystyle {\begin{aligned}(0.15625)m&=(0.00101_{b})m=\left(2^{-3}+2^{-5}\right)m=\left(2^{-3})m+(2^{-5}\right)m\\&=2^{-3}\left(m+... | wikipedia |
fbec1a9dcc262ee8e9ebbb7ca1aebbb8810d3751 | horner's method is a fast, code-efficient method for | horner's method is a fast, code-efficient method for multiplication and division of binary numbers on a microcontroller with no hardware multiplier. one of the binary numbers to be multiplied is represented as a trivial polynomial, where (using the above notation) a i = 1 {\displaystyle a_{i}=1}, and x = 2 {\displaysty... | wikipedia |
c6da8b6ed7867feac5e0bc75d76d78f996dbcfc4 | more generally, the summation can be broken into | more generally, the summation can be broken into k parts: p (x) = ∑ i = 0 n a i x i = ∑ j = 0 k − 1 x j ∑ i = 0 ⌊ n / k ⌋ a k i + j x k i = ∑ j = 0 k − 1 x j p j (x k) {\displaystyle p(x)=\sum _{i=0}^{n}a_{i}x^{i}=\sum _{j=0}^{k-1}x^{j}\sum _{i=0}^{\lfloor n/k\rfloor }a_{ki+j}x^{ki}=\sum _{j=0}^{k-1}x^{j}p_{j}(x^{k})} ... | wikipedia |
1db54bbea00157fea0ec66333d43690159ec5c6d | if, however, one is evaluating a single polynomial | if, however, one is evaluating a single polynomial of very high order, it may be useful to break it up as follows: p (x) = ∑ i = 0 n a i x i = a 0 + a 1 x + a 2 x 2 + a 3 x 3 + ⋯ + a n x n = (a 0 + a 2 x 2 + a 4 x 4 + ⋯) + (a 1 x + a 3 x 3 + a 5 x 5 + ⋯) = (a 0 + a 2 x 2 + a 4 x 4 + ⋯) + x (a 1 + a 3 x 2 + a 5 x 4 + ⋯)... | wikipedia |
8b81cfb67f354f89e02cd97d9b3cee182bc19356 | if, however, one is evaluating a single polynomial | }+a_{2}x^{2}+a_{4}x^{4}+\cdots \right)+x\left(a_{1}+a_{3}x^{2}+a_{5}x^{4}+\cdots \right)\\&=\sum _{i=0}^{\lfloor n/2\rfloor }a_{2i}x^{2i}+x\sum _{i=0}^{\lfloor n/2\rfloor }a_{2i+1}x^{2i}\\&=p_{0}(x^{2})+xp_{1}(x^{2}).\end{aligned}}} | wikipedia |
928e5dabceb9fbcd7dc4bb79827b48adc324d12e | a disadvantage of horner's rule is that all | a disadvantage of horner's rule is that all of the operations are sequentially dependent, so it is not possible to take advantage of instruction level parallelism on modern computers. in most applications where the efficiency of polynomial evaluation matters, many low-order polynomials are evaluated simultaneously (for... | wikipedia |
d67eeee1fa5be85a26e803e94bffdc6c2c0ea4f0 | this assumes that the polynomial is evaluated in | this assumes that the polynomial is evaluated in monomial form and no preconditioning of the representation is allowed, which makes sense if the polynomial is evaluated only once. however, if preconditioning is allowed and the polynomial is to be evaluated many times, then faster algorithms are possible. they involve a... | wikipedia |
d944181ddfcd94270a787fc1e3f18238c0267253 | horner's method is optimal, in the sense that | horner's method is optimal, in the sense that any algorithm to evaluate an arbitrary polynomial must use at least as many operations. alexander ostrowski proved in 1954 that the number of additions required is minimal. victor pan proved in 1966 that the number of multiplications is minimal. however, when x {\displaysty... | wikipedia |
1d2ee687618c32af1fe124b77f476edeb777d9f4 | if numerical data are represented in terms of | if numerical data are represented in terms of digits (or bits), then the naive algorithm also entails storing approximately 2 n {\displaystyle 2n} times the number of bits of x {\displaystyle x}: the evaluated polynomial has approximate magnitude x n {\displaystyle x^{n}}, and one must also store x n {\displaystyle x^{... | wikipedia |
9d90601787b97c472177a41385fbb7b73f1c1234 | evaluation using the monomial form of a degree | evaluation using the monomial form of a degree n {\displaystyle n} polynomial requires at most n {\displaystyle n} additions and (n 2 + n) / 2 {\displaystyle (n^{2}+n)/2} multiplications, if powers are calculated by repeated multiplication and each monomial is evaluated individually. the cost can be reduced to n {\disp... | wikipedia |
a7027c73cc964f37abedd4d1a8c20b860a6b98de | the third row is the sum of the | the third row is the sum of the first two rows, divided by 2. each entry in the second row is the product of 1 with the third-row entry to the left. the answer is f 1 (x) f 2 (x) = 2 x 3 − 2 x 2 − x + 1 − 4 2 x − 1. {\displaystyle {\frac {f_{1}(x)}{f_{2}(x)}}=2x^{3}-2x^{2}-x+1-{\frac {4}{2x-1}}.} | wikipedia |
2517d3585d75005708f3d8c0985fc968acefa366 | let f 1 (x) = 4 x 4 | let f 1 (x) = 4 x 4 − 6 x 3 + 3 x − 5 {\displaystyle f_{1}(x)=4x^{4}-6x^{3}+3x-5} and f 2 (x) = 2 x − 1 {\displaystyle f_{2}(x)=2x-1}. divide f 1 (x) {\displaystyle f_{1}(x)} by f 2 (x) {\displaystyle f_{2}\,(x)} using horner's method. | wikipedia |
e477912725f8e8e1791de0b396b80a89758ff68f | as a consequence of the polynomial remainder theorem, | as a consequence of the polynomial remainder theorem, the entries in the third row are the coefficients of the second-degree polynomial, the quotient of f (x) {\displaystyle f(x)} on division by x − 3 {\displaystyle x-3}. the remainder is 5. this makes horner's method useful for polynomial long division. | wikipedia |
87483a002bf82997b630ee4523d10f1e6aee22a1 | in this example, if a 3 = 2, | in this example, if a 3 = 2, a 2 = − 6, a 1 = 2, a 0 = − 1 {\displaystyle a_{3}=2,a_{2}=-6,a_{1}=2,a_{0}=-1} we can see that b 3 = 2, b 2 = 0, b 1 = 2, b 0 = 5 {\displaystyle b_{3}=2,b_{2}=0,b_{1}=2,b_{0}=5}, the entries in the third row. so, synthetic division (which was actually invented and published by ruffini 10 y... | wikipedia |
9a2eda1e01a3792a0ba3f8359f142c3dfe77b5f4 | the entries in the third row are the | the entries in the third row are the sum of those in the first two. each entry in the second row is the product of the x -value (3 in this example) with the third-row entry immediately to the left. the entries in the first row are the coefficients of the polynomial to be evaluated. then the remainder of f (x) {\display... | wikipedia |
3471e08bf85db244e39c364eb02138ec2556fde7 | evaluate f (x) = 2 x 3 − | evaluate f (x) = 2 x 3 − 6 x 2 + 2 x − 1 {\displaystyle f(x)=2x^{3}-6x^{2}+2x-1} for x = 3 {\displaystyle x=3}. | wikipedia |
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