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In biochemistry , isozymes (also known as isoenzymes or more generally as multiple forms of enzymes ) are enzymes that differ in amino acid sequence but catalyze the same chemical reaction. Isozymes usually have different kinetic parameters (e.g. different K M values), or are regulated differently. They permit the fine-tuning of metabolism to meet the particular needs of a given tissue or developmental stage.
In many cases, isozymes are encoded by homologous genes that have diverged over time. Strictly speaking, enzymes with different amino acid sequences that catalyse the same reaction are isozymes if encoded by different genes, or allozymes if encoded by different alleles of the same gene ; the two terms are often used interchangeably.
Isozymes were first described by R. L. Hunter and Clement Markert (1957) who defined them as different variants of the same enzyme having identical functions and present in the same individual . [ 1 ] This definition encompasses (1) enzyme variants that are the product of different genes and thus represent different loci (described as isozymes ) and (2) enzymes that are the product of different alleles of the same gene (described as allozymes ). [ 2 ]
Isozymes are usually the result of gene duplication , but can also arise from polyploidisation or nucleic acid hybridization . Over evolutionary time, if the function of the new variant remains identical to the original, then it is likely that one or the other will be lost as mutations accumulate, resulting in a pseudogene . However, if the mutations do not immediately prevent the enzyme from functioning, but instead modify either its function, or its pattern of expression , then the two variants may both be favoured by natural selection and become specialised to different functions. [ 3 ] For example, they may be expressed at different stages of development or in different tissues. [ 4 ]
Allozymes may result from point mutations or from insertion-deletion ( indel ) events that affect the coding sequence of the gene. As with any other new mutations, there are three things that may happen to a new allozyme:
An example of an isozyme is glucokinase , a variant of hexokinase which is not inhibited by glucose 6-phosphate . Its different regulatory features and lower affinity for glucose (compared to other hexokinases), allow it to serve different functions in cells of specific organs, such as control of insulin release by the beta cells of the pancreas , or initiation of glycogen synthesis by liver cells. Both these processes must only occur when glucose is abundant.
1.) The enzyme lactate dehydrogenase is a tetramer made of two different sub-units, the H-form and the M-form. These combine in different combinations depending on the tissue: [ 7 ]
Heat (at 60 °C)
serum in humans
2.) Isoenzymes of creatine phosphokinase: [ 7 ] Creatine kinase (CK) or creatine phosphokinase (CPK) catalyses the interconversion of phospho creatine to creatine .
CPK exists in 3 isoenzymes. Each isoenzymes is a dimer of 2 subunits M (muscle), B (brain) or both [ 7 ]
3.) Isoenzymes of alkaline phosphatase: [ 7 ] Six isoenzymes have been identified. The enzyme is a monomer, the isoenzymes are due to the differences in the carbohydrate content (sialic acid residues). The most important ALP isoenzymes are α 1 -ALP, α 2 -heat labile ALP, α 2 -heat stable ALP, pre-β ALP and γ-ALP. Increase in α 2 -heat labile ALP suggests hepatitis whereas pre-β ALP indicates bone diseases.
Isozymes (and allozymes) are variants of the same enzyme. Unless they are identical in their biochemical properties, for example their substrates and enzyme kinetics , they may be distinguished by a biochemical assay . However, such differences are usually subtle, particularly between allozymes which are often neutral variants . This subtlety is to be expected, because two enzymes that differ significantly in their function are unlikely to have been identified as isozymes .
While isozymes may be almost identical in function, they may differ in other ways. In particular, amino acid substitutions that change the electric charge of the enzyme are simple to identify by gel electrophoresis , and this forms the basis for the use of isozymes as molecular markers . To identify isozymes, a crude protein extract is made by grinding animal or plant tissue with an extraction buffer, and the components of extract are separated according to their charge by gel electrophoresis. Historically, this has usually been done using gels made from potato starch , but acrylamide gels provide better resolution.
All the proteins from the tissue are present in the gel, so that individual enzymes must be identified using an assay that links their function to a staining reaction. For example, detection can be based on the localised precipitation of soluble indicator dyes such as tetrazolium salts which become insoluble when they are reduced by cofactors such as NAD or NADP , which generated in zones of enzyme activity. This assay method requires that the enzymes are still functional after separation ( native gel electrophoresis ), and provides the greatest challenge to using isozymes as a laboratory technique.
Isoenzymes differ in kinetics (they have different K M and V max values).
Population genetics is essentially a study of the causes and effects of genetic variation within and between populations, and in the past, isozymes have been amongst the most widely used molecular markers for this purpose. Although they have now been largely superseded by more informative DNA -based approaches (such as direct DNA sequencing , single nucleotide polymorphisms and microsatellites ), they are still among the quickest and cheapest marker systems to develop, and remain (as of 2005 [update] ) an excellent choice for projects that only need to identify low levels of genetic variation, e.g. quantifying mating systems . | https://en.wikipedia.org/wiki/Isozyme |
Israel Nathan Herstein (March 28, 1923 – February 9, 1988) [ 1 ] was a mathematician, appointed as professor at the University of Chicago in 1962. He worked on a variety of areas of algebra , including ring theory , with over 100 research papers and over a dozen books.
Herstein was born in Lublin , Poland , in 1923. His family emigrated to Canada in 1926, and he grew up in a harsh and underprivileged environment where, according to him, "you either became a gangster or a college professor." [ 2 ] During his school years he played football, ice hockey, golf, tennis, and pool . He also worked as a steeplejack and as a barker at a fair. He received his B.S. degree from the University of Manitoba and his M.A. from the University of Toronto . He received his Ph.D. from Indiana University Bloomington in 1948. His advisor was Max Zorn . He held positions at the University of Kansas , Ohio State University , University of Pennsylvania , and Cornell University before permanently settling at the University of Chicago in 1962. He was a Guggenheim Fellow for the academic year 1960–1961.
He is known for his lucid style of writing, as exemplified by his Topics in Algebra , an undergraduate introduction to abstract algebra that was first published in 1964, with a second edition in 1975. A more advanced text is his Noncommutative Rings [ 3 ] in the Carus Mathematical Monographs series. His primary interest was in noncommutative ring theory , but he also wrote papers on finite groups , linear algebra , and mathematical economics .
He had 30 Ph.D. students, traveled and lectured widely, and spoke Italian, Hebrew, Polish, and Portuguese. He died from cancer in Chicago , Illinois , in 1988. His doctoral students include Miriam Cohen , Wallace S. Martindale , Susan Montgomery , Karen Parshall and Claudio Procesi . | https://en.wikipedia.org/wiki/Israel_Nathan_Herstein |
The Israeli Astronomical Association ( IAA ) is an Israeli nonprofit organization. Its purpose is to deepen and distribute the awareness for the field of astronomy among the Israeli public.
The Israeli Astronomical Association was established first as an amateur fellowship on May 28, 1951, by a group of astronomy fans immigrating from Germany and Czechoslovakia , among them Dr Heilbruner and Dr Zaichik. Dr Zaichik was the first chairman of the association and kept his position for many years until his retirement due to personal health matters.
The decision to make the association national was made in 1953 in the chamber of David Ben-Gurion , the country's prime minister, in order to promote astronomical knowledge and related science fields in the newly formed state of Israel .
The association was then allocated a territory in Givat Ram in Jerusalem by the Israel Land Administration . The same area was later designated for the development of the Hebrew University of Jerusalem . A planetarium was built for the exclusive use of the association with the financial help of the Williams family from the Palestine bank (later was known as Bank Leumi , Israel National Bank) in 1956.
The main goal of the association was—and still is—the distribution knowledge of the astronomy amongst the Israeli public. This purpose is carried out by organizing conventions, courses, lectures, star parties and observations, as well as publishing the magazine Astronomy (previously All the Stars of Light and The Stars in their Month ). This magazine is one-of-a-kind in Hebrew ever since.
In 1953 the association built an observatory in the suburb of Talabia in Jerusalem and started branching all over the country—Tel Aviv, Ramat Gan, Haifa and the Galilee. These branches are no longer active and others will take their place. All the activities of its members were made and are still being made fully voluntarily.
Due to a temporal setback on the activities of the association and the transference of its center of gravity to Givatayim, The Hebrew University of Jerusalem took hold of the planetarium building in 1986, which by then was in the university's expanding territory. The takeover included Albert Einstein's telescope which was given to the association in 1962 from the "Ben Shemen" school. The university turned most of the planetarium site into its office spaces, which brought the association and the Williams family to file two lawsuits against The Hebrew University of Jerusalem (1574/98, 8514/90). These lawsuits were supposed to return the management of the planetarium back to the hands of the association as well as using the planetarium for astronomical purposes. Unfortunately it was decided that in spite of the forceful take-over by the university, the observatory will remain in their custody. Currently the association does not have the resources to maintain the battle and neither the observatory nor the planetarium in Givat Ram do function in their designated purposes.
In 1967, following the Six-Day War , the association inaugurated the Givatayim Observatory in the city of Giv'atayim in the center of Israel. Giv'atayim was the choice of preference due to the height of the place allocated for the observatory, far above the sea level and in distance from its humidity (relative to the surroundings at the time). The observatory was established with the funds of the municipality of Giv'atayim, the association and donations from abroad raised by the observatory manager at the time, Eng. Yossi Fooks. For 25 years the observatory was solely managed by the association. Dince 1994 it had co-management with the municipality of Giv'atayim. The chairmen of the association were sometimes the managers of the observatory at the same time. Among them: Haim Levi, Dr. Noah Brosch (presently the director of the Wise Observatory of Tel Aviv University ), Dr. Isaac Shlosman (presently Astrophysics Professor at the University of Kentucky), Ilan Manulis (presently the director of the Technoda Observatory) and Dr. Igal Patel who is the chairman of the association as well as manager of the observatory for over 20 years (ever since 1987).
The association operates as a nonprofit organization with hundreds of members. The majority of the activities are focused on the observatory in Giv'atayim. Nevertheless, the association holds country wide astronomical activities with organized observations on the south side of Israel, astronomical weekends, conventions of astronomy and seminars.
The journal of the association Astronomy is published several times a year. The association also publishes a yearly almanac with all the astronomical phenomena expected to be seen in Israeli skies.
A guideline for the association is that all of its members—including the functionaries—are all volunteers. The activities of the association are financed by membership fees (as for the year 2014, membership fees are 100 NIS per year), incomes raised from the activities and from time to time it is also supported by the ministry of science and other donating bodies (the most recent is the Pelephone company on 1999).
The association holds ties with similar groups abroad and with national as well as international research institutions.
During the past as well as present, the association holds observation divisions. The two prominent divisions are:
Nowadays, only Ofer Gabzo holds the relevant knowledge inside the association. | https://en.wikipedia.org/wiki/Israeli_Astronomical_Association |
In probability theory , Isserlis's theorem or Wick's probability theorem is a formula that allows one to compute higher-order moments of the multivariate normal distribution in terms of its covariance matrix. It is named after Leon Isserlis .
This theorem is also particularly important in particle physics , where it is known as Wick's theorem after the work of Wick (1950) . [ 1 ] Other applications include the analysis of portfolio returns, [ 2 ] quantum field theory [ 3 ] and generation of colored noise. [ 4 ]
If ( X 1 , … , X n ) {\displaystyle (X_{1},\dots ,X_{n})} is a zero-mean multivariate normal random vector, then E [ X 1 X 2 ⋯ X n ] = ∑ p ∈ P n 2 ∏ { i , j } ∈ p E [ X i X j ] = ∑ p ∈ P n 2 ∏ { i , j } ∈ p Cov ( X i , X j ) , {\displaystyle \operatorname {E} [\,X_{1}X_{2}\cdots X_{n}\,]=\sum _{p\in P_{n}^{2}}\prod _{\{i,j\}\in p}\operatorname {E} [\,X_{i}X_{j}\,]=\sum _{p\in P_{n}^{2}}\prod _{\{i,j\}\in p}\operatorname {Cov} (\,X_{i},X_{j}\,),} where the sum is over all the pairings of { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} , i.e. all distinct ways of partitioning { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} into pairs { i , j } {\displaystyle \{i,j\}} , and the product is over the pairs contained in p {\displaystyle p} . [ 5 ] [ 6 ]
More generally, if ( Z 1 , … , Z n ) {\displaystyle (Z_{1},\dots ,Z_{n})} is a zero-mean complex -valued multivariate normal random vector, then the formula still holds.
The expression on the right-hand side is also known as the hafnian of the covariance matrix of ( X 1 , … , X n ) {\displaystyle (X_{1},\dots ,X_{n})} .
If n = 2 m + 1 {\displaystyle n=2m+1} is odd, there does not exist any pairing of { 1 , … , 2 m + 1 } {\displaystyle \{1,\ldots ,2m+1\}} . Under this hypothesis, Isserlis's theorem implies that E [ X 1 X 2 ⋯ X 2 m + 1 ] = 0. {\displaystyle \operatorname {E} [\,X_{1}X_{2}\cdots X_{2m+1}\,]=0.} This also follows from the fact that − X = ( − X 1 , … , − X n ) {\displaystyle -X=(-X_{1},\dots ,-X_{n})} has the same distribution as X {\displaystyle X} , which implies that E [ X 1 ⋯ X 2 m + 1 ] = E [ ( − X 1 ) ⋯ ( − X 2 m + 1 ) ] = − E [ X 1 ⋯ X 2 m + 1 ] = 0 {\displaystyle \operatorname {E} [\,X_{1}\cdots X_{2m+1}\,]=\operatorname {E} [\,(-X_{1})\cdots (-X_{2m+1})\,]=-\operatorname {E} [\,X_{1}\cdots X_{2m+1}\,]=0} .
In his original paper, [ 7 ] Leon Isserlis proves this theorem by mathematical induction, generalizing the formula for the 4 th {\displaystyle 4^{\text{th}}} order moments, [ 8 ] which takes the appearance
If n = 2 m {\displaystyle n=2m} is even, there exist ( 2 m ) ! / ( 2 m m ! ) = ( 2 m − 1 ) ! ! {\displaystyle (2m)!/(2^{m}m!)=(2m-1)!!} (see double factorial ) pair partitions of { 1 , … , 2 m } {\displaystyle \{1,\ldots ,2m\}} : this yields ( 2 m ) ! / ( 2 m m ! ) = ( 2 m − 1 ) ! ! {\displaystyle (2m)!/(2^{m}m!)=(2m-1)!!} terms in the sum. For example, for 4 th {\displaystyle 4^{\text{th}}} order moments (i.e. 4 {\displaystyle 4} random variables) there are three terms. For 6 th {\displaystyle 6^{\text{th}}} -order moments there are 3 × 5 = 15 {\displaystyle 3\times 5=15} terms, and for 8 th {\displaystyle 8^{\text{th}}} -order moments there are 3 × 5 × 7 = 105 {\displaystyle 3\times 5\times 7=105} terms.
We can evaluate the characteristic function of gaussians by the Isserlis theorem: E [ e − i X ] = ∑ k ( − i ) k k ! E [ X k ] = ∑ k ( − i ) 2 k ( 2 k ) ! E [ X 2 k ] = ∑ k ( − i ) 2 k ( 2 k ) ! ( 2 k ) ! k ! 2 k E [ X 2 ] k = e − 1 2 E [ X 2 ] {\displaystyle E[e^{-iX}]=\sum _{k}{\frac {(-i)^{k}}{k!}}E[X^{k}]=\sum _{k}{\frac {(-i)^{2k}}{(2k)!}}E[X^{2k}]=\sum _{k}{\frac {(-i)^{2k}}{(2k)!}}{\frac {(2k)!}{k!2^{k}}}E[X^{2}]^{k}=e^{-{\frac {1}{2}}E[X^{2}]}}
Since both sides of the formula are multilinear in X 1 , . . . , X n {\displaystyle X_{1},...,X_{n}} , if we can prove the real case, we get the complex case for free.
Let Σ i j = Cov ( X i , X j ) {\displaystyle \Sigma _{ij}=\operatorname {Cov} (X_{i},X_{j})} be the covariance matrix, so that we have the zero-mean multivariate normal random vector ( X 1 , . . . , X n ) ∼ N ( 0 , Σ ) {\displaystyle (X_{1},...,X_{n})\sim N(0,\Sigma )} . Since both sides of the formula are continuous with respect to Σ {\displaystyle \Sigma } , it suffices to prove the case when Σ {\displaystyle \Sigma } is invertible.
Using quadratic factorization − x T Σ − 1 x / 2 + v T x − v T Σ v / 2 = − ( x − Σ v ) T Σ − 1 ( x − Σ v ) / 2 {\displaystyle -x^{T}\Sigma ^{-1}x/2+v^{T}x-v^{T}\Sigma v/2=-(x-\Sigma v)^{T}\Sigma ^{-1}(x-\Sigma v)/2} , we get
1 ( 2 π ) n det Σ ∫ e − x T Σ − 1 x / 2 + v T x d x = e v T Σ v / 2 {\displaystyle {\frac {1}{\sqrt {(2\pi )^{n}\det \Sigma }}}\int e^{-x^{T}\Sigma ^{-1}x/2+v^{T}x}dx=e^{v^{T}\Sigma v/2}}
Differentiate under the integral sign with ∂ v 1 , . . . , v n | v 1 , . . . , v n = 0 {\displaystyle \partial _{v_{1},...,v_{n}}|_{v_{1},...,v_{n}=0}} to obtain
E [ X 1 ⋯ X n ] = ∂ v 1 , . . . , v n | v 1 , . . . , v n = 0 e v T Σ v / 2 {\displaystyle E[X_{1}\cdots X_{n}]=\partial _{v_{1},...,v_{n}}|_{v_{1},...,v_{n}=0}e^{v^{T}\Sigma v/2}} .
That is, we need only find the coefficient of term v 1 ⋯ v n {\displaystyle v_{1}\cdots v_{n}} in the Taylor expansion of e v T Σ v / 2 {\displaystyle e^{v^{T}\Sigma v/2}} .
If n {\displaystyle n} is odd, this is zero. So let n = 2 m {\displaystyle n=2m} , then we need only find the coefficient of term v 1 ⋯ v n {\displaystyle v_{1}\cdots v_{n}} in the polynomial 1 m ! ( v T Σ v / 2 ) m {\displaystyle {\frac {1}{m!}}(v^{T}\Sigma v/2)^{m}} .
Expand the polynomial and count, we obtain the formula. ◻ {\displaystyle \square }
An equivalent formulation of the Wick's probability formula is the Gaussian integration by parts . If ( X 1 , … X n ) {\displaystyle (X_{1},\dots X_{n})} is a zero-mean multivariate normal random vector, then
E ( X 1 f ( X 1 , … , X n ) ) = ∑ i = 1 n Cov ( X 1 , X i ) E ( ∂ X i f ( X 1 , … , X n ) ) . {\displaystyle \operatorname {E} (X_{1}f(X_{1},\ldots ,X_{n}))=\sum _{i=1}^{n}\operatorname {Cov} (X_{1},X_{i})\operatorname {E} (\partial _{X_{i}}f(X_{1},\ldots ,X_{n})).} This is a generalization of Stein's lemma .
The Wick's probability formula can be recovered by induction, considering the function f : R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } defined by f ( x 1 , … , x n ) = x 2 … x n {\displaystyle f(x_{1},\ldots ,x_{n})=x_{2}\ldots x_{n}} . Among other things, this formulation is important in Liouville conformal field theory to obtain conformal Ward identities , BPZ equations [ 9 ] and to prove the Fyodorov-Bouchaud formula . [ 10 ]
For non-Gaussian random variables, the moment- cumulants formula [ 11 ] replaces the Wick's probability formula. If ( X 1 , … X n ) {\displaystyle (X_{1},\dots X_{n})} is a vector of random variables , then E ( X 1 … X n ) = ∑ p ∈ P n ∏ b ∈ p κ ( ( X i ) i ∈ b ) , {\displaystyle \operatorname {E} (X_{1}\ldots X_{n})=\sum _{p\in P_{n}}\prod _{b\in p}\kappa {\big (}(X_{i})_{i\in b}{\big )},} where the sum is over all the partitions of { 1 , … , n } {\displaystyle \{1,\ldots ,n\}} , the product is over the blocks of p {\displaystyle p} and κ ( ( X i ) i ∈ b ) {\displaystyle \kappa {\big (}(X_{i})_{i\in b}{\big )}} is the joint cumulant of ( X i ) i ∈ b {\displaystyle (X_{i})_{i\in b}} .
Consider X = ( X 1 , … , X d ) {\displaystyle X=(X_{1},\dots ,X_{d})} uniformly distributed on the unit sphere S d − 1 {\displaystyle S^{d-1}} , so that ‖ X ‖ = 1 {\displaystyle \|X\|=1} almost surely. In this setting, the following holds.
If n {\displaystyle n} is odd, E [ X i 1 X i 2 ⋯ X i n ] = 0. {\displaystyle \operatorname {E} {\bigl [}X_{i_{1}}\,X_{i_{2}}\,\cdots \,X_{i_{n}}{\bigr ]}\;=\;0.\!}
If n = 2 k {\displaystyle n=2k} is even, E [ X i 1 ⋯ X i 2 k ] = 1 d ( d + 2 ) ( d + 4 ) ⋯ ( d + 2 k − 2 ) ∑ p ∈ P 2 k 2 ∏ { r , s } ∈ p δ i r , i s , {\displaystyle \operatorname {E} {\bigl [}X_{i_{1}}\,\cdots \,X_{i_{2k}}{\bigr ]}\;=\;{\frac {1}{d\,{\bigl (}d+2{\bigr )}{\bigl (}d+4{\bigr )}\cdots {\bigl (}d+2k-2{\bigr )}}}\sum _{p\in P_{2k}^{2}}\prod _{\{r,s\}\in p}\delta _{\,i_{r},i_{s}},} where P 2 k 2 {\displaystyle P_{2k}^{2}} is the set of all pairings of { 1 , … , 2 k } {\displaystyle \{1,\ldots ,2k\}} , δ i , j {\displaystyle \delta _{i,j}} is the Kronecker delta .
Since there are | P 2 k 2 | = ( 2 k − 1 ) ! ! {\displaystyle |P_{2k}^{2}|=(2k-1)!!} delta-terms, we get on the diagonal: E [ X 1 2 k ] = ( 2 k − 1 ) ! ! d ( d + 2 ) ( d + 4 ) ⋯ ( d + 2 k − 2 ) . {\displaystyle \operatorname {E} [\,X_{1}^{2k}\,]\;=\;{\frac {(2k-1)!!}{d\,{\bigl (}d+2{\bigr )}{\bigl (}d+4{\bigr )}\cdots {\bigl (}d+2k-2{\bigr )}}}.} Here, ( 2 k − 1 ) ! ! {\displaystyle (2k-1)!!} denotes the double factorial .
These results are discussed in the context of random vectors and irreducible representations in the work by Kushkuley (2021). [ 12 ] | https://en.wikipedia.org/wiki/Isserlis's_theorem |
The issue-based information system (IBIS) is an argumentation -based approach to clarifying wicked problems —complex, ill-defined problems that involve multiple stakeholders . [ 1 ] Diagrammatic visualization using IBIS notation is often called issue mapping . [ 2 ] : ix
IBIS was invented by Werner Kunz and Horst Rittel in the 1960s. According to Kunz and Rittel, "Issue-Based Information Systems (IBIS) are meant to support coordination and planning of political decision processes. IBIS guides the identification , structuring , and settling of issues raised by problem-solving groups, and provides information pertinent to the discourse ." [ 1 ]
Subsequently, the understanding of planning and design as a process of argumentation (of the designer with himself or with others) has led to the use of IBIS in design rationale , [ 3 ] [ 4 ] where IBIS notation is one of a number of different kinds of rationale notation. [ 5 ] The simplicity of IBIS notation, and its focus on questions, makes it especially suited for representing conversations during the early exploratory phase of problem solving, when a problem is relatively ill-defined. [ 6 ] : 204
The basic structure of IBIS is a graph . It is therefore quite suitable to be manipulated by computer, as in a graph database . [ 7 ]
The elements of IBIS are: issues (questions that need to be answered), each of which are associated with (answered by) alternative positions (possible answers or ideas), which are associated with arguments which support or object to a given position; arguments that support a position are called "pros", and arguments that object to a position are called "cons". [ 1 ] [ 8 ] In the course of the treatment of issues, new issues come up which are treated likewise. [ 9 ] [ 10 ]
IBIS elements are usually represented as nodes , and the associations between elements are represented as directed edges (arrows). [ 11 ]
In 1988, Douglas E. Noble and Horst Rittel described the overall purpose of IBIS as follows:
Issue-Based Information Systems are used as a means of widening the coverage of a problem. By encouraging a greater degree of participation, particularly in the earlier phases of the process, the designer is increasing the opportunity that difficulties of his proposed solution, unseen by him, will be discovered by others. Since the problem observed by a designer can always be treated as merely a symptom of another higher-level problem , the argumentative approach also increases the likelihood that someone will attempt to attack the problem from this point of view. Another desirable characteristic of the Issue-Based Information System is that it helps to make the design process 'transparent'. Transparency here refers to the ability of observers as well as participants to trace back the process of decision-making. [ 3 ]
IBIS notation has been used, along with function analysis diagram (FAD) notation, as an aid for root cause analysis . [ 12 ] [ 13 ]
IBIS notation is used in issue mapping, [ 2 ] : ix an argument visualization technique closely related to argument mapping . [ 6 ] An issue map aims to comprehensively diagram the rhetorical structure of a conversation (or a series of conversations) as seen by the participants in the conversation, as opposed to an ideal conceptual structure such as, for example, a causal loop diagram , flowchart , or structure chart . [ 2 ] : 264
Issue mapping is the basis of a meeting facilitation technique called dialogue mapping . [ 14 ] [ 15 ] [ 16 ] In dialogue mapping, a person called a facilitator uses IBIS notation to record a group conversation, while it is happening, on a "shared display" (usually a video projector). The facilitator listens to the conversation, and summarizes the ideas mentioned in the conversation on the shared display using IBIS notation, and if possible "validates" the map often by checking with the group to make sure each recorded element accurately represents the group's thinking. [ 16 ] Dialogue mapping, like a few other facilitation methods, has been called "nondirective" because it does not require participants or leaders to agree on an agenda or a problem definition. [ 17 ] Users of dialogue mapping have reported that dialogue mapping, under certain conditions, can improve the efficiency of meetings by reducing unnecessary redundancy and digressions in conversations, among other benefits. [ 16 ] [ 18 ]
A dialogue map does not aim to be as formal as, for example, a logic diagram or decision tree , but rather aims to be a comprehensive display of all the ideas that people shared during a conversation. [ 16 ] Other decision algorithms can be applied to a dialogue map after it has been created, [ 19 ] although dialogue mapping is also well suited to situations that are too complex and context-dependent for an algorithmic approach to decision-making . [ 16 ] Some researchers and practitioners have combined IBIS with numerical decision-making software based on multi-criteria decision making . [ 20 ] [ 21 ] [ 22 ] [ 23 ]
Rittel's interest lay in the area of public policy and planning, which is also the context in which he and his colleagues defined wicked problems . [ 24 ] So it is no surprise that Kunz and Rittel envisaged IBIS as the "type of information system meant to support the work of cooperatives like governmental or administrative agencies or committees, planning groups, etc., that are confronted with a problem complex in order to arrive at a plan for decision". [ 1 ]
When Kunz and Rittel's paper was written, there were three manual, paper-based IBIS-type systems in use—two in government agencies and one in a university. [ 1 ] [ 25 ]
A renewed interest in IBIS-type systems came about in the following decade, when advances in technology made it possible to design relatively inexpensive, computer-based IBIS-type systems. [ 3 ] [ 7 ] [ 26 ] By 1983, Raymond McCall and colleagues had implemented a version of IBIS called PHIBIS (procedurally hierarchical IBIS) in personal computer software called MIKROPLIS (microcomputer-based planning and information system), which was described as an information system for "professional problem solvers—including planners, designers and scientists". [ 27 ] [ 28 ] In 1987, Douglas E. Noble completed a computer-supported IBIS program as part of his doctoral dissertation. [ 3 ] Another IBIS computer program developed in the late 1980s was called HyperIBIS. [ 29 ] Jeff Conklin and co-workers adapted the IBIS structure for use in software engineering, creating the gIBIS (graphical IBIS) hypertext system in the late 1980s. [ 7 ] [ 26 ] Around 1990, a program called Author's Argumentation Assistant (AAA) combined the PHIBIS model with the Toulmin model of argumentation in "a hypertext-based authoring tool for argumentative texts". [ 30 ] In the 1990s, architecture researchers experimented with enhancing IBIS with a fuzzy reasoning system . [ 31 ] [ 32 ]
Several other graphical IBIS-type systems were developed once it was realised that such systems facilitated collaborative design and problem solving . [ 4 ] These efforts culminated in the creation of the open source Compendium (software) tool which supports—among other things—a graphical IBIS notation. [ 4 ] [ 33 ] [ 34 ] Another IBIS tool that integrates with Microsoft SharePoint is called Glyma. [ 2 ] : 290 Similar tools which do not rely on a database for storage include DRed (Design Rationale editor) [ 35 ] and designVUE. [ 36 ]
Since the mid-2000s, there has been a renewed interest in IBIS-type systems, particularly in the context of sensemaking and collaborative problem solving in a variety of social and technical contexts. [ 2 ] [ 37 ] [ 6 ] [ 38 ] [ 39 ] Of particular note is the facilitation method called dialogue mapping which uses the IBIS notation to map out a design (or any other) dialogue as it evolves. [ 15 ] [ 16 ]
In 2021, researchers reported that IBIS notation is used in D-Agree, a discussion support platform with artificial intelligence –based facilitation. [ 40 ] The discussion trees in D-Agree, inspired by IBIS, contain a combination of four types of elements: issues, ideas, pros, and cons. [ 40 ] [ 41 ] The software extracts a discussion's structure in real time based on IBIS, automatically classifying all the sentences. [ 40 ] [ 41 ] | https://en.wikipedia.org/wiki/Issue-based_information_system |
Issues in Environmental Science and Technology is a book series by the Royal Society of Chemistry , published twice a year. Each issue's content focuses on a specific theme topic. The series is written by worldwide experts in various specialist fields, and covers broader aspects of the science (such as economics and politics) as well as the narrower chemistry of environmental science. It aims to assess possible practical solutions to perceived environmental problems. [ 1 ] The Editors Commission will review articles from authors that may come from industry, public service and academia.
The current Editors are RE Hester, University of York , England and RM Harrison, University of Birmingham , England. | https://en.wikipedia.org/wiki/Issues_in_Environmental_Science_and_Technology |
Issues relating to biofuel are social, economic, environmental and technical problems that may arise from biofuel production and use. Social and economic issues include the " food vs fuel " debate and the need to develop responsible policies and economic instruments to ensure sustainable biofuel production. Farming for biofuels feedstock can be detrimental to the environment if not done sustainably. Environmental concerns include deforestation , biodiversity loss and soil erosion as a result of land clearing for biofuels agriculture. While biofuels can contribute to reduction in global carbon emissions , indirect land use change for biofuel production can have the inverse effect. Technical issues include possible modifications necessary to run the engine on biofuel, as well as energy balance and efficiency.
The International Resource Panel outlined the wider and interrelated factors that need to be considered when deciding on the relative merits of pursuing one biofuel over another. [ 1 ] The IRP concluded that not all biofuels perform equally in terms of their effect on climate, energy security and ecosystems, and suggested that environmental and social effects need to be assessed throughout the entire life-cycle.
The International Energy Agency 's World Energy Outlook 2006 concludes that rising oil demand, if left unchecked,
would accentuate the consuming countries' vulnerability to a severe supply disruption and resulting price shock. The report suggested that biofuels may one day offer a viable alternative, but also that "the implications of the use of biofuels for global security as well as for economic, environmental, and public health need to be further evaluated". [ 2 ]
According to Francisco Blanch, a commodity strategist for Merrill Lynch , crude oil would be trading 15 per cent higher and gasoline would be as much as 25 per cent more expensive, if it were not for biofuels. [ 3 ] Gordon Quaiattini, president of the Canadian Renewable Fuels Association , argued that a healthy supply of alternative energy sources will help to combat gasoline price spikes. [ 4 ]
Food vs fuel is the debate regarding the risk of diverting farmland or crops for biofuels production in detriment of the food supply on a global scale. Essentially the debate refers to the possibility that by farmers increasing their production of these crops, often through government subsidy incentives, their time and land is shifted away from other types of non-biofuel crops driving up the price of non-biofuel crops due to the decrease in production. [ 5 ] Therefore, it is not only that there is an increase in demand for the food staples, like corn and cassava, that sustain the majority of the world's poor but this also has the potential to increase the price of the remaining crops that these individuals would otherwise need to utilize to supplement their diets. A recent study for the International Centre for Trade and Sustainable Development shows that market-driven expansion of ethanol in the US increased maize prices by 21 percent in 2009, in comparison with what prices would have been had ethanol production been frozen at 2004 levels. [ 5 ] A November 2011 study states that biofuels, their production, and their subsidies are leading causes of agricultural price shocks. [ 6 ] The counter-argument includes considerations of the type of corn that is utilized in biofuels, often field corn not suitable for human consumption; the portion of the corn that is used in ethanol, the starch portion; and the negative effect higher prices for corn and grains have on government welfare for these products. The "food vs. fuel" or "food or fuel" debate is internationally controversial, with disagreement about how significant this is, what is causing it, what the effect is, and what can or should be done about it. [ 7 ] [ 8 ] [ 9 ] [ 10 ] The world is facing three global crises, energy, food and environment. Changing the trend of recreation or population growth can impact each one of these. By increasing the world population, the ratio of energy and food demands will increase as well. So, it can put these two energy and food industries in completion of supplying. Developing the techniques and utilizing the food crops for biofuel production, especially in shortage areas, can adverse the competition between the food and biofuel industries. [ 11 ] It can be cay that harvesting and producing biofuels crop on a large scale can put local food communities at risk, such as challenges to access lands and portions of the food. [ 12 ] If the food economy cannot place safe and stable, protocols such as Kyoto can not meet their purposes and help control emissions. [ 11 ]
Researchers at the Overseas Development Institute have argued that biofuels could help to reduce poverty in the developing world, through increased employment , wider economic growth multipliers and by stabilising oil prices (many developing countries are net importers of oil). [ 13 ] However, this potential is described as 'fragile', and is reduced where feedstock production tends to be large scale, or causes pressure on limited agricultural resources: capital investment, land, water, and the net cost of food for the poor.
With regards to the potential for poverty reduction or exacerbation, biofuels rely on many of the same policy, regulatory or investment shortcomings that impede agriculture as a route to poverty reduction . Since many of these shortcomings require policy improvements at a country level rather than a global one, they argue for a country-by-country analysis of the potential poverty effects of biofuels. This would consider, among other things, land administration systems, market coordination and prioritizing investment in biodiesel , as this 'generates more labour, has lower transportation costs and uses simpler technology'. [ 14 ] Also necessary are reductions in the tariffs on biofuel imports regardless of the country of origin, especially due to the increased efficiency of biofuel production in countries such as Brazil. [ 13 ]
Responsible policies and economic instruments would help to ensure that biofuel commercialization, including the development of new cellulosic technologies , is sustainable . Responsible commercialization of biofuels represents an opportunity to enhance sustainable economic prospects in Africa, Latin America and impoverished Asia. [ 4 ]
Large-scale deforestation of mature trees (which help remove CO 2 through photosynthesis — much better than sugar cane or most other biofuel feedstock crops do) contributes to soil erosion , un- sustainable global warming atmospheric greenhouse gas levels, loss of habitat , and a reduction of valuable biodiversity (both on land as in oceans [ 15 ] ). [ 16 ] Demand for biofuel has led to clearing land for palm oil plantations. [ 17 ] In Indonesia alone, over 9,400,000 acres (38,000 km 2 ) of forest have been converted to plantations since 1996. [ 18 ]
A portion of the biomass should be retained onsite to support the soil resource. Normally this will be in the form of raw biomass, but processed biomass is also an option. If the exported biomass is used to produce syngas , the process can be used to co-produce biochar , a low-temperature charcoal used as a soil amendment to increase soil organic matter to a degree not practical with less recalcitrant forms of organic carbon. For co-production of biochar to be widely adopted, the soil amendment and carbon sequestration value of co-produced charcoal must exceed its net value as a source of energy. [ 19 ]
Some commentators claim that removal of additional cellulosic biomass for biofuel production will further deplete soils. [ 20 ]
Increased use of biofuels puts increasing pressure on water resources in at least two ways: water use for the irrigation of crops used as feedstocks for biodiesel production; and water use in the production of biofuels in refineries, mostly for boiling and cooling.
In many parts of the world supplemental or full irrigation is needed to grow feedstocks. For example, if in the production of corn (maize) half the water needs of crops are met through irrigation and the other half through rainfall, about 860 liters of water are needed to produce one liter of ethanol. [ 21 ] However, in the United States only 5-15% of the water required for corn comes from irrigation while the other 85-95% comes from natural rainfall.
In the United States, the number of ethanol factories has almost tripled from 50 in 2000 to about 140 in 2008. A further 60 or so are under construction, and many more are planned. Projects are being challenged by residents at courts in Missouri (where water is drawn from the Ozark Aquifer ), Iowa, Nebraska, Kansas (all of which draw water from the non-renewable Ogallala Aquifer ), central Illinois (where water is drawn from the Mahomet Aquifer ) and Minnesota. [ 22 ]
For example, the four ethanol crops: corn, sugarcane, sweet sorghum and pine yield net energy. However, increasing production in order to meet the U.S. Energy Independence and Security Act mandates for renewable fuels by 2022 would take a heavy toll in the states of Florida and Georgia. The sweet sorghum, which performed the best of the four, would increase the amount of freshwater withdrawals from the two states by almost 25%. [ 23 ]
Formaldehyde , acetaldehyde and other aldehydes are produced when alcohols are oxidized . When only a 10% mixture of ethanol is added to gasoline (as is common in American E10 gasohol and elsewhere), aldehyde emissions increase 40%. [ citation needed ] Some study results are conflicting on this fact however, and lowering the sulfur content of biofuel mixes lowers the acetaldehyde levels. [ 24 ] Burning biodiesel also emits aldehydes and other potentially hazardous aromatic compounds which are not regulated in emissions laws. [ 25 ]
Many aldehydes are toxic to living cells. Formaldehyde irreversibly cross-links protein amino acids , which produces the hard flesh of embalmed bodies. At high concentrations in an enclosed space, formaldehyde can be a significant respiratory irritant causing nose bleeds, respiratory distress, lung disease, and persistent headaches. [ 26 ] Acetaldehyde, which is produced in the body by alcohol drinkers and found in the mouths of smokers and those with poor oral hygiene, is carcinogenic and mutagenic . [ 27 ]
The European Union has banned products that contain formaldehyde , due to its documented carcinogenic characteristics. The U.S. Environmental Protection Agency has labeled Formaldehyde as a probable cause of cancer in humans.
Brazil burns significant amounts of ethanol biofuel. Gas chromatograph studies were performed of ambient air in São Paulo, Brazil, and compared to Osaka, Japan, which does not burn ethanol fuel. Atmospheric Formaldehyde was 160% higher in Brazil, and Acetaldehyde was 260% higher. [ 28 ]
Despite its occasional proclamation as a "green" fuel, first-generation biofuels, primarily ethanol, are not without their own GHG emissions . While ethanol does produce fewer overall GHG emissions than gasoline, its production is still an energy intensive process with secondary effects. Gasoline generally produces 8.91 kg CO 2 per gallon, compared to 8.02 kg CO 2 per gallon for E10 ethanol and 1.34 kg CO 2 per gallon for E85 ethanol. Based on a study by Dias de Oliveira et al. (2005), corn-based ethanol requires 65.02 gigajoules (GJ) of energy per hectare (ha) and produces approximately 1236.72 kg per ha of carbon dioxide (CO 2 ), while sugar cane-based ethanol requires 42.43 GJ/ha and produces 2268.26 kg/ha of CO 2 under the assumption of non-carbon neutral energy production. These emissions accrue from agricultural production, crop cultivation, and ethanol processing. Once the ethanol is blended with gasoline, it results in carbon-savings of approximately 0.89 kg of CO 2 per gallon consumed (U.S. D.O.E., 2011a). [ 29 ]
From a production standpoint, miscanthus can produce 742 gallons of ethanol per acre of land, which is nearly twice as much as corn (399 gal/acre, assuming average yield of 145 bushels per acre under normal corn-soybean rotation) and nearly three times as much as corn stover (165 gal/acre) and switchgrass (214 gal/acre). Production costs are a big impediment to large-scale implementation of 2nd Generation bio-fuels, and their market demand will depend primarily on their price competitiveness relative to corn ethanol and gasoline. At this time, costs of conversion of cellulosic fuels, at $1.46 per gallon, were roughly twice that of corn-based ethanol, at $0.78 per gallon. Cellulosic biofuels from corn stover and miscanthus were 24% and 29% more expensive than corn ethanol, respectively, and switchgrass biofuel is more than twice as expensive as corn ethanol.
[ 29 ]
[ 29 ]
Biofuels and other forms of renewable energy aim to be carbon neutral or even carbon negative . Carbon neutral means that the carbon released during the use of the fuel, e.g. through burning to power transport or generate electricity, is reabsorbed and balanced by the carbon absorbed by new plant growth. These plants are then harvested to make the next batch of fuel. Carbon neutral fuels lead to no net increases in human contributions to atmospheric carbon dioxide levels, reducing the human contributions to global warming . A carbon negative aim is achieved when a portion of the biomass is used for carbon sequestration . [ 30 ] Calculating exactly how much greenhouse gas (GHG) is produced in burning biofuels is a complex and inexact process, which depends very much on the method by which the fuel is produced and other assumptions made in the calculation.
The carbon emissions ( carbon footprint ) produced by biofuels are calculated using a technique called Life Cycle Analysis (LCA). This uses a "cradle to grave" or "well to wheels" approach to calculate the total amount of carbon dioxide and other greenhouse gases emitted during biofuel production, from putting seed in the ground to using the fuel in cars and trucks. Many different LCAs have been done for different biofuels, with widely differing results. Several well-to-wheel analysis for biofuels has shown that first generation biofuels can reduce carbon emissions, with savings depending on the feedstock used, and second generation biofuels can produce even higher savings when compared to using fossil fuels. [ 31 ] [ 32 ] [ 33 ] [ 34 ] [ 35 ] [ 36 ] [ 37 ] However, those studies did not take into account emissions from nitrogen fixation , or additional carbon emissions due to indirect land use changes . In addition, many LCA studies fail to analyze the effect of substitutes that may come into the market to replace current biomass-based products. In the case of Crude Tall Oil, a raw material used in the production of pine chemicals and now being diverted for use in biofuel, an LCA study [ 38 ] found that the global carbon footprint of pine chemicals produced from CTO is 50 percent lower than substitute products used in the same situation offsetting any gains from utilizing a biofuel to replace fossil fuels. Additionally the study showed that fossil fuels are not reduced when CTO is diverted to biofuel use and the substitute products consume disproportionately more energy. This diversion will negatively affect an industry that contributes significantly to the world economy, [ 39 ] globally producing more than 3 billion pounds of pine chemicals annually in complex, high technology refineries and providing jobs directly and indirectly for tens of thousands of workers.
A paper published in February 2008 in Sciencexpress by a team led by Searchinger from Princeton University concluded that once considered indirect land use changes effects in the life cycle assessment of biofuels used to substitute gasoline, instead of savings both corn and cellulosic ethanol increased carbon emissions as compared to gasoline by 93 and 50 percent respectively. [ 40 ] A second paper published in the same issue of Sciencexpress, by a team led by Fargione from The Nature Conservancy , found that a carbon debt is created when natural lands are cleared and being converted to biofuel production and to crop production when agricultural land is diverted to biofuel production, therefore this carbon debt applies to both direct and indirect land use changes. [ 41 ]
The Searchinger and Fargione studies gained prominent attention in both the popular media [ 42 ] [ 43 ] [ 44 ] [ 45 ] [ 46 ] [ 47 ] [ 48 ] and in scientific journals . The methodology, however, drew some criticism, with Wang and Haq from Argonne National Laboratory posted a public letter and send their criticism about the Searchinger paper to Letters to Science . [ 49 ] [ 50 ] Another criticism by Kline and Dale from Oak Ridge National Laboratory was published in Letters to Science. They argued that Searchinger et al. and Fargione et al. "... do not provide adequate support for their claim that biofuels cause high emissions due to land-use change . [ 51 ] The U.S. biofuel industry also reacted, claiming in a public letter, that the " Searchinger study is clearly a "worst-case scenario" analysis... " and that this study " relies on a long series of highly subjective assumptions... ". [ 52 ]
The modifications necessary to run internal combustion engines on biofuel depend on the type of biofuel used, as well as the type of engine used. For example, gasoline engines can run without any modification at all on biobutanol . Minor modifications are however needed to run on bioethanol or biomethanol . Diesel engines can run on the latter fuels, as well as on vegetable oils (which are cheaper). However, the latter is only possible when the engine has been foreseen with indirect injection . If no indirect injection is present, the engine hence needs to be fitted with this.
A number of environmental NGOs campaign against the production of biofuels as a large-scale alternative to fossil fuels. For example, Friends of the Earth state that "the current rush to develop agrofuels (or biofuels) on a large scale is ill-conceived and will contribute to an already unsustainable trade whilst not solving the problems of climate change or energy security". [ 53 ] Some mainstream environmental groups support biofuels as a significant step toward slowing or stopping global climate change. [ 54 ] [ 55 ] However, supportive environmental groups generally hold the view that biofuel production can threaten the environment if it is not done sustainably. This finding has been backed by reports of the UN , [ 56 ] the IPCC , [ 57 ] and some other smaller environmental and social groups as the EEB [ 58 ] and the Bank Sarasin, [ 59 ] which generally remain negative about biofuels.
As a result, governmental [ 60 ] and environmental organizations are turning against biofuels made in a non-sustainable way (hereby preferring certain oil sources as jatropha and lignocellulose over palm oil ) [ 61 ] and are asking for global support for this. [ 62 ] [ 63 ] Also, besides supporting these more sustainable biofuels, environmental organizations are redirecting to new technologies that do not use internal combustion engines such as hydrogen and compressed air . [ 64 ]
Several standard-setting and certification initiatives have been set up on the topic of biofuels. The "Roundtable on Sustainable Biofuels" is an international initiative which brings together farmers, companies, governments, non-governmental organizations, and scientists who are interested in the sustainability of biofuels production and distribution. During 2008, the Roundtable is developing a series of principles and criteria for sustainable biofuels production through meetings, teleconferences, and online discussions. [ 65 ] In a similar vein, the Bonsucro standard has been developed as a metric-based certificate for products and supply chains, as a result of an ongoing multi-stakeholder initiative focussing on the products of sugar cane , including ethanol fuel. [ 66 ]
The increased manufacture of biofuels will require increasing land areas to be used for agriculture. Second and third generation biofuel processes can ease the pressure on land, because they can use waste biomass, and existing (untapped) sources of biomass such as crop residues and potentially even marine algae.
In some regions of the world, a combination of increasing demand for food, and increasing demand for biofuel, is causing deforestation and threats to biodiversity. The best reported example of this is the expansion of oil palm plantations in Malaysia and Indonesia, where rainforest is being destroyed to establish new oil palm plantations. It is an important fact that 90% of the palm oil produced in Malaysia is used by the food industry; [ 67 ] therefore biofuels cannot be held solely responsible for this deforestation. There is a pressing need for sustainable palm oil production for the food and fuel industries; palm oil is used in a wide variety of food products. The Roundtable on Sustainable Biofuels is working to define criteria, standards and processes to promote sustainably produced biofuels. [ 68 ] Palm oil is also used in the manufacture of detergents, and in electricity and heat generation both in Asia and around the world (the UK burns palm oil in coal-fired power stations to generate electricity). [ citation needed ]
Significant area is likely to be dedicated to sugar cane in future years as demand for ethanol increases worldwide. The expansion of sugar cane plantations will place pressure on environmentally sensitive native ecosystems including rainforest in South America. [ 69 ] In forest ecosystems, these effects themselves will undermine the climate benefits of alternative fuels, in addition to representing a major threat to global biodiversity. [ 70 ]
Although biofuels are generally considered to improve net carbon output, biodiesel and other fuels do produce local air pollution, including nitrogen oxides , the principal cause of smog . [ citation needed ] | https://en.wikipedia.org/wiki/Issues_relating_to_biofuels |
The Istanbul Canal ( Turkish : Kanal İstanbul pronounced [kɑnɑɫ isˈtɑnbuɫ] ) is a project for an artificial sea-level waterway planned by Turkey in East Thrace , connecting the Black Sea to the Sea of Marmara , and thus to the Aegean and Mediterranean seas. The Istanbul Canal would bisect the current European side of Istanbul and thus form an island between Asia and Europe (the island would have a shoreline with the Black Sea, Sea of Marmara, the new canal and the Bosporus ). [ 1 ] The new waterway would bypass the current Bosporus.
The canal aims to minimise shipping traffic in the Bosporus. It is projected to have a capacity of 160 vessel transits a day – similar to the current volume of traffic through the Bosporus, where traffic congestion leaves ships queuing for days to transit the strait. Some analysts have speculated that the main reason for construction of the canal is to bypass the Montreux Convention , which limits the number and tonnage of warships from non-Black Sea powers that could enter the sea via the Bosporus, as well as prohibiting tolls on traffic passing through it. [ 2 ] Indeed, in January 2018, the Turkish Prime Minister Binali Yıldırım announced that the Istanbul Canal would not be subject to the Montreux Convention. [ 2 ]
The Istanbul Canal project also includes the construction of ports (a large container terminal in the Black Sea, close to the Istanbul Airport ), logistic centres and artificial islands to be integrated with the canal, as well as new earthquake-resistant residential areas along the channel. [ 3 ] The artificial islands are to be built using soil dug for the canal. Transport projects to be integrated with the canal project include the Halkali-Kapikule high-speed train, the Turkish State Railways project, the Yenikapi-Sefakoy-Beylikduzu and Mahmutbey-Esenyurt metro lines in Istanbul and the D-100 highway crossing, Tem highway and Sazlibosna highway.
Financing the canal is expected to be via a build-operate-transfer model, but could also be funded through public-private partnerships . The government is expecting to generate US$8 billion in revenue per year from the Istanbul Canal, in part from a service fee for transits. [ 4 ] Critics, such as Korkut Boratav , have questioned this number and said that the net revenues could be negative. [ 5 ] Other criticisms include the need to direct resources for focusing on earthquake readiness and addressing economic issues, [ 6 ] [ 7 ] and potential negative environmental impacts. [ 8 ]
A canal linking the Black Sea with the Sea of Marmara has been proposed at least seven times. [ 9 ]
The first proposal was made by the Ottoman sultan Suleiman the Magnificent (reigned 1520–1566). His architect, Mimar Sinan , was said to have devised plans for the project. The project was abandoned for unknown reasons. [ 9 ]
On March 6, 1591, during the reign of Sultan Murad III , an imperial ferman (order) was issued and work on the project recommenced, but, again for unknown reasons, the project was stopped.
In 1654, during the reign of Sultan Mehmed IV , pressure for the recommencement of the canal was applied, but to no avail.
Sultan Mustafa III (reigned 1757–1774) attempted twice in 1760, but the project could not go ahead because of a lack of funds.
During the reign of Sultan Mahmud II (reigned 1808–1839), an Imperial Ottoman Committee was established to examine the project once again. A report was prepared in 1813, but no concrete steps were taken.
The Energy Ministry 's Consultant Yüksel Önem suggested constructing an alternative waterway to the Bosporus in the 1985 magazine of the Turkish Standards Institution and in the Science and Technical Magazine of the Scientific and Technological Research Council of Turkey in 1990. [ 10 ]
In 1991, Nusret Avcı, head of the Istanbul Metropolitan Municipality Environment Commission, proposed that a canal 23 km (14 mi) long be constructed between Silivri and Karacaköy . He suggested that this channel would significantly reduce hazards of maritime traffic and pollution in the Bosporus. [ 11 ]
Finally, on January 17, 1994, shortly before the local elections , the leader of the Democratic Left Party (DSP) Bülent Ecevit proposed a canal connecting the Black Sea with the Sea of Marmara. [ 9 ] [ 12 ]
Canal Istanbul was announced by President Recep Tayyip Erdoğan in June 2021. [ 13 ] It would be large enough to accommodate VLCC class vessels. [ 14 ]
The stated purpose of the project is to reduce the large marine traffic through the Bosporus and minimise the risks and dangers associated particularly with tankers. [ 15 ]
About 41,000 vessels of all sizes pass yearly through the Istanbul Strait, among them 8,000 tankers carrying 145 million tons of crude oil . International pressure is growing to increase the marine traffic tonnage through the Turkish straits, which brings risks for the security of marine navigation during the passage. [ 16 ] The Bosporus sees nearly three times the traffic of the Suez Canal . The canal will further help prevent the pollution caused by cargo vessels passing through or mooring in the Sea of Marmara before the southern entrance of the Bosporus. [ 17 ]
According to data of Ministry of Transport and Infrastructure, there was a decrease in total amount of vessels, but an increase in the amount of very large vessels and the total gross tonnage. The data are shown in the following table: [ 18 ]
On January 15, 2018, the route of the project was declared. The final route for Istanbul Canal was selected after studies on five alternative routes. The Ministry of Transport announced that the project will pass through Lake Küçükçekmece near the Marmara Sea. It will pass through the districts of Avcılar and Başakşehir before reaching the Black Sea in the Arnavutköy district north of the city. Seven kilometers of the route passes through Küçükçekmece, 3.1 kilometers goes through Avcılar, 6.5 kilometers goes through Başakşehir, and the major 28.6-kilometer part of the route goes through Arnavutköy.
The waterway will have a length of 45 km (28 mi), with a depth of 20.75 m (68.1 ft). Its width will be 360 m (1,180 ft) on the surface and 275 m (902 ft) wide at the bottom.
The largest ship sizes that can pass through the canal were determined as 275–350 meters long, 49 meters wide, draft of 17 meters and an air draft of 58 meters. [ 19 ]
On September 23, 2010, Hıncal Uluç , a columnist with the daily Sabah , wrote an article named "A Crazy Project from the Prime Minister" without mentioning the content of the project. In this article, Uluç wrote his reaction to his phone call with Prime Minister Erdogan, stating that, "I had the phone in my hand and froze. This is the most crazy project I've ever heard about Istanbul. If anyone would have asked me to come up with thousand projects, it still wouldn't have crossed my mind. It's that crazy." This article led to creating hype around the project, dubbing it the "Crazy Project" ( Turkish : Çılgın Proje ). [ 20 ]
It appeared that the Justice and Development Party (AKP) government had started discreet studies on the project earlier and that concrete steps were taken for the revival of this project. The project was mentioned by Minister of Transport Binali Yıldırım in May 2009 at the parliament. [ 16 ] On April 27, 2011, the then-prime minister Recep Tayyip Erdoğan officially announced the Kanal İstanbul project during a rally held in connection with the upcoming 2011 general elections [ 15 ] [ 21 ] [ 22 ]
Studies relating to the project were completed within two years. The canal was initially planned to be in service at the latest in 2023, the 100th anniversary of the foundation of the Republic. [ 17 ]
On 22 January 2013, the Turkish Government announced that research studies about the canal would commence in May 2013. [ 23 ] In April 2013, the first stage of the Kanal İstanbul project, which includes the construction of various network bridges and highways, commenced. [ 24 ] [ 25 ]
By December 2019, construction had not yet commenced. President Erdoğan indicated that a request for tender for the project would be published in early 2020. Meanwhile, Ekrem İmamoğlu , elected as the mayor of Istanbul in 2019 from the opposition party CHP , is opposed to the project. [ 26 ]
In January 2020, the Environment and Urbanization Ministry approved the final version of the Environmental Impact Assessment (EIA) report of the Istanbul Canal project. [ 3 ] Construction work is scheduled to begin in mid-2021. [ 27 ] The project is expected to take seven years to complete.
On June 26, 2021, construction started on Sazlıdere Bridge , which Erdogan also stated was the start of the canal construction. [ 28 ]
Turkish President Recep Tayyip Erdogan and Istanbul Metropolitan Municipality officials have stated that Istanbul Canal will cost an estimated ₺75 billion (US$10 billion) to build. [ 29 ] [ 30 ] The central government has put forward a build-operate-transfer model as its main preference, but will use funds from the national budget if needed. [ 31 ] Approximately 8,000–10,000 people are expected to be employed during the construction phase of the project, while 500-800 are to be employed during the operational phase. [ 32 ]
A multidisciplinary evaluation study on Canal Istanbul by a scientific team formed by IMM has been published as a book. The book, edited by Prof. Dr. Naci Görür , Prof. Dr. Derin Orhon and Prof. Dr. Seval Sözen, mainly discussed the environmental impacts of Canal Istanbul and whether these impacts were adequately addressed in the EIA report . The points that are not adequately explained in the EIA report can be summarized as follows: [ 33 ]
The Black Sea is 50 cm higher than the Marmara and less salty. [ 34 ] Simulations predict that, unlike the Bosphorus, which flows both ways, water would rarely flow north through the canal but almost always south, which would make the top 25m of the Marmara less salty. [ 35 ] However the ecosystems of both seas could be affected. [ 36 ] The project has been criticized for destroying agricultural and forest land and a walking trail, and potentially contaminating groundwater with salt and increasing flooding. [ 37 ] Other environmental criticism includes potential changes to the salinity of Marmara Sea, leading to Istanbul smelling of hydrogen sulfide . [ 38 ]
Some critics have stated that Turkey aims to bypass the Montreux Convention Regarding the Regime of the Straits , in order to attain greater autonomy with respect to the passage of military ships (which are limited in number, tonnage, and weaponry) from the Black Sea to the Sea of Marmara . [ 39 ] [ 40 ]
In 2013, Stratfor characterized the announced US$12 billion construction budget and initial operating date of 2023 as being "not realistic for a project of this magnitude." [ 41 ]
The city government of Istanbul and local groups are opposed to the project because it would eliminate Lake Durusu , [ clarification needed ] which is used for a fifth of the city's drinking water, and because they expect it will cause overcrowding as the local population increases. [ 42 ] Observers said the plan to charge transit fees to oil and gas tankers is unrealistic, as long as free passage is guaranteed through the Bosporous. [ 37 ] However, Article 3 of the Montreux convention does allow sanitary inspections before transiting the Bosphorus, leading to speculation that Turkey might apply lengthy sanitary inspections, making the canal a faster alternative. Along with members of the royal family of Qatar, Berat Albayrak , the former Turkish Minister of Finance and son-in-law of President Erdoğan, purchased property along the route, meaning he would personally benefit financially from the resulting real-estate development. [ 42 ] Ekrem Imamoglu, Istanbul's mayor, said that limited financial resources should be used for getting Istanbul ready for an earthquake and solving economic problems, [ 43 ] and that all buildings that have an earthquake risk in Istanbul could be rebuilt with Istanbul Canal's budget. [ 44 ] According to a survey in Istanbul by MAK, 80.4% of the respondents were against Istanbul Canal project, while only 7.9% supported it. [ 45 ]
In April 2021, ten retired Turkish navy admirals were arrested over public criticism of the Istanbul Canal project. The arrests followed a day after a group of 104 senior former navy officials signed an open letter warning that the proposed canal could, by invalidating the Montreux Convention, harm Turkish security. [ 46 ]
The project has been described as a 'testing ground for anticipatory policy-making'. [ 47 ] Should the world move decisively away from fossil fuels in the coming decades, the problem of traffic congestion in the Bosporus Strait will dissipate, removing one of the justifications for the canal. [ 47 ] | https://en.wikipedia.org/wiki/Istanbul_Canal |
ITU Faculty of Naval Architecture and Ocean Engineering was founded as an individual department in School of Mechanical Engineering in 1943. It was reorganized in 1971 as a separate school. [ 2 ] Faculty has its own library in addition to Mustafa Inan Library. [ 3 ]
The faculty has two departments today: | https://en.wikipedia.org/wiki/Istanbul_Technical_University_Faculty_of_Naval_Architecture_and_Ocean_Engineering |
István Fáry (30 June 1922 – 2 November 1984) was a Hungarian -born mathematician known for his work in geometry and algebraic topology . [ 1 ] He proved Fáry's theorem that every planar graph has a straight-line embedding in 1948, and the Fáry–Milnor theorem lower-bounding the curvature of a nontrivial knot in 1949.
Fáry was born June 30, 1922, in Gyula, Hungary . After studying for a master's degree at the University of Budapest , he moved to the University of Szeged , where he earned a Ph.D. in 1947. He then studied at the Sorbonne before taking a faculty position at the University of Montreal in 1955. He moved to the University of California, Berkeley in 1958 and became a full professor in 1962. He died on November 2, 1984, in El Cerrito, California . [ 1 ] | https://en.wikipedia.org/wiki/István_Fáry |
Isuzu Motors Ltd. ( Japanese : いすゞ自動車株式会社 , Hepburn : Isuzu Jidōsha Kabushiki-Kaisha ) , commonly known as Isuzu ( Japanese pronunciation: [isɨᵝzɨᵝ] , / i ˈ s u z u / ), is a Japanese multinational automobile manufacturer headquartered in Yokohama , Kanagawa Prefecture . Its principal activity is the production, marketing and sale of Isuzu commercial vehicles and diesel engines .
The company also has a number of subsidiaries and joint ventures, including UD Trucks , Anadolu Isuzu (a Turkish joint venture with Anadolu Group), Sollers-Isuzu (a Russian joint venture with Sollers JSC - Production stopped in March 2022, Isuzu stake transferred to Sollers in July 2023 [ 2 ] ), SML Isuzu (an Indian venture formerly known as Swaraj Mazda ), Jiangxi Isuzu Motors (a Chinese joint venture with Jiangling Motors Company Group ), Isuzu Astra Motor Indonesia , Isuzu Malaysia ( Isuzu HICOM ), Industries Mécaniques Maghrébines , Isuzu Truck (UK) , Isuzu South Africa , Isuzu Philippines , Taiwan Isuzu Motors , Isuzu Vietnam , Isuzu Motors India and BYD Isuzu .
Isuzu has assembly and manufacturing plants in Fujisawa , which have been there since the company was founded under earlier names, as well as in the Tochigi and Hokkaidō prefectures. Isuzu-branded vehicles are sold in most commercial markets worldwide. Isuzu's primary market focus is on commercial diesel-powered truck, buses and construction.
The company is named after the Isuzu River , the kanji of Isuzu (五十鈴), meaning "fifty bells".
Isuzu Motors' history began in 1916, when Tokyo Ishikawajima Shipbuilding and Engineering Co., Ltd. planned a cooperation with the Tokyo Gas and Electric Industrial Company to build automobiles. The next step was taken in 1918, when a technical cooperation with Wolseley Motors Limited was initiated, yielding exclusive rights to the production and sales of Wolseley vehicles in East Asia from knock-down kits . [ 3 ] In 1919 came the first ever Japan-produced passenger car, a Wolseley model, the Fifteen A9 15/40 НР at the Tokyo Ishikawajima Shipyard at the Fukagawa Factory . [ 4 ] The Wolseley sourced CP truck followed two years later; 550 of these were built by 1927. [ 5 ] In 1923 Japan was devastated by the Kanto earthquake which made the fledgling transportation infrastructure that was heavily reliant on government-owned railroads unusable due to the twisted tracks. Heavy construction vehicles were imported from the United States companies GMC and Ford to aid in recovery and reconstruction, and the company sought to contribute by producing locally built construction and heavy duty vehicles. In 1927 the company introduced its 2-ton load capacity "Sumida P-type truck" equipped with an A6 engine and a 1-ton vehicle "Sumida M-type No. 1 bus" equipped with an A4 engine. The name "sumida" was used from the Sumida River as the factory at Fukagawa was close by.
In 1929 IHI Corporation , separated part of its manufacturing business and merged with DAT Automobile Manufacturing Inc. (a predecessor of Nissan ) and changed its name to Jidosha Kogyo Co., Ltd. ( Automobile Industries Co., Ltd. ) The names used for the products of this company, marketed as "Sumida" and "Chiyoda", have special significance in Japan. Chiyoda is a district in Tokyo where the Imperial Palace is located, and Sumida refers to a river that flows through Tokyo approximately 3.59 km (2.23 mi) east of the Imperial Palace. [ 3 ] In 1934 the Tsurumi Factory opened under company name Automobile Industry Co., Ltd. and in 1937 Automobile Industries was reorganized and formed into a new company, Tokyo Automobile Industries Co., Ltd. and was founded with a capital of ¥1,000,000. The company continued to manufacture heavy duty trucks and passenger busses, realizing the need to modernize the transportation infrastructure of Japan, and was one of the primary manufacturers for the Imperial Japanese Army along with Mitsubishi Heavy Industries , and had a corporate allegiance to the Yasuda Zaibatsu . One of the vehicles it produced for the war effort was the Sumida M.2593 armored personnel carrier. In 1942, Hino Heavy Industries was split off from Tokyo Automobile Industries, becoming a separate corporation. [ 6 ] In 1949, the company was renamed Isuzu after the Isuzu River , following a meeting with the Japanese Government's Ministry of International Trade and Industry (MITI).
The word Isuzu translated into English means "fifty bells"—hence the focus on "bell" in both the later Bellel and the Bellett . The name was used from the Isuzu River that flows near to the Ise Grand Shrine , one of Japan's most sacred and revered shrines.
Truck and bus production of the TX40 and TU60 series and the Isuzu Sumida bus resumed in 1945, with the permission of the occupation authorities . [ 7 ] and has remained the primary focus of manufacture for the company, along with diesel engine production. In 1958 a factory was built at Fujisawa, Kanagawa , and in 1959 the Isuzu Elf was introduced as a medium duty cab over commercial truck which is still in production, and was also shared with the Isuzu Journey bus. Isuzu continued to maintain its market presence by providing commercial vehicles by introducing the Isuzu TY in 1966. The company is one of the primary manufacturers of commercial duty trucks and busses for public transportation, to include the Isuzu Cubic , Isuzu Gala and the Isuzu Erga along with the Isuzu Giga .
Beginning in 1953 the Hillman Minx passenger car is produced under license of Rootes Group giving the company a passenger car to compete with other Japanese manufacturers, realizing that their resources were limited and therefore sought out international partnerships. The Minx remained in production until 1962, after the 1961 introduction of Isuzu's first passenger car, the Bellel , [ 3 ] and later the sports coupe Isuzu 117 Coupé . Being a small producer making cars which were somewhat too large and pricey for the Japanese market at the time, Isuzu spent some time looking for a commercial partner. Under pressure from MITI, who were attempting to limit the number of automobile manufacturers in Japan, a cooperation with Fuji Heavy Industries ( Subaru ) began in 1966. This joint sales-service collaboration was seen as the first step towards an eventual merger. [ 8 ] The Subaru 1000 was even shown in Isuzu's 1967 annual vehicle brochure, as a suitable complement to the larger Isuzu lineup. [ 9 ] This tie-up was over by 1968, when an agreement with Mitsubishi was formed. This ended even more quickly, by 1969, and the next year an equally short-lived collaboration was entered with Nissan . [ 10 ] A few months later, in September 1971, what was to prove a more durable capital agreement was signed with General Motors . This would see GM own Isuzu for the next 35 years.
While the company had a long relationship with GM going back to the 1920s, the first investment of GM taking a 34% stake in Isuzu was seen in 1972, when the Chevrolet LUV became the first Isuzu-built vehicle to be sold in the United States. To symbolize the new beginning, Isuzu also developed a new logo for 1974, with two vertical pillars as stylized representations of the first syllable in いすゞ ("Isuzu"). [ 5 ] In 1974 Isuzu introduced the Gemini , which was co-produced with General Motors as the T-body Chevrolet Chevette . A modified version was sold in the United States as Buick's Opel by Isuzu , and in Australia as the Holden Gemini . As a result of the collaboration, certain American GM products were sold to Japanese customers through Isuzu dealerships. Holden's Statesman was also briefly sold (246 examples) with Isuzu badging in Japan during the seventies. [ 11 ] Isuzu exports also increased considerably as a result of being able to use GM networks, from 0.7% of production in 1973 to 35.2% by 1976; this while overall production increased more than fourfold in the same period. [ 10 ] As a result of the GM joint venture, Isuzu engines were also used by existing GM divisions (some USA-market Chevrolet automobiles had Isuzu powertrains e.g. the Chevette and early S10/S15 trucks manufactured prior to 1985).
In 1981 Isuzu began selling consumer and commercial vehicles under their own brand in the United States. The Isuzu P'Up was the first model sold to consumers as an Isuzu, rather than as a Chevrolet or Buick, along with the Isuzu Piazza sports car. Isuzu's then president Toshio Okamoto then initiated a collaboration with small-car expert Suzuki to develop a global small car for GM, the S-car . [ 12 ] A three-way agreement of co-ownership was signed in August 1981, with Isuzu and Suzuki exchanging shares and General Motors taking a 5% share of Suzuki. [ 12 ] Following on from this, in 1985 Isuzu and GM established the IBC Vehicles venture in the United Kingdom, producing locally built versions of Isuzu and Suzuki light vans (the Isuzu Fargo and Suzuki Carry ); to be sold in the European market under Vauxhall's Bedford brand. During this period Isuzu also developed a worldwide presence as an exporter of diesel engines, with their powerplants in use by Opel /Vauxhall, Land Rover , Hindustan , and many others. Two Isuzu model lines (Gemini, Impulse) were marketed as part of the Geo division (Spectrum, Storm) when it was initially launched as a Chevrolet subsidiary. In the domestic Japanese market, OEM deals with other manufacturers were entered to aid the poorly performing passenger car arm. It led to the badging of Suzukis, beginning in 1986, [ 13 ] and Subaru small commercial vehicles as Isuzus ( Geminett , Geminett II ). This OEM tie-up occurred alongside the establishment of SIA (Subaru-Isuzu Automotive), an American joint venture with Fuji Heavy Industries (the parent company of Subaru ). Shortly afterwards, the Lafayette, Indiana plant became operational.
Isuzu ended US sales of the Impulse ( Geo Storm ) in 1992, and the following year it stopped exporting the Stylus (the basis for the Geo Spectrum), the last Isuzu-built car sold in the US.
In 1993 Isuzu began a new vehicle exchange program with Honda , whereby Honda sold the Isuzu Rodeo [ 14 ] and Isuzu Trooper as the Honda Passport and Acura SLX , respectively. In return Isuzu began selling the Honda Odyssey as the Isuzu Oasis. Thus, Honda's lineup gained two SUVs, and Isuzu's lineup gained a minivan. In the Japanese market, the Gemini (Stylus) was now a rebadged Honda Domani and the Aska (originally based on the GM J-car ) was a Honda Accord , while Honda received the 2-door MU as the Jazz and the 4-door Trooper as the Horizon.
Isuzu's United States sales reached a peak in 1996 after the introduction of the Isuzu Hombre pickup, a badge-engineered GM truck (using the sheetmetal of the Brazil-market Chevrolet S10). Isuzu resurrected the beloved Amigo in 1998, before changing the name of the 2-door convertible to Rodeo Sport in 2001 in an attempt to associate it with the better selling 4-door Rodeo. The new Axiom launched in 2001, with the fictional salesman Joe Isuzu from 1980s advertising campaigns brought back to promote it. Isuzu sales began to slide due to the aging of the Rodeo and Trooper , and poor management and a lack of assistance from GM. The Rodeo Sport was discontinued in 2003, while production of the Rodeo and Axiom ceased a year later. By this point sales in North America had slowed to just 27,188, with the discontinued Rodeo and Axiom making up 71% of that total.
In 1998 GM and Isuzu formed DMAX , a joint venture to produce diesel engines . GM raised its stake in Isuzu to 49% the following year, effectively gaining control of the company, and quickly followed this up by appointing an American GM executive to head Isuzu's North American Operations. This marked the first time a non-Japanese executive had held such a high position at Isuzu. In 2001 GM and Isuzu announced plans to share distribution networks and for Chevrolet to market an Isuzu product. [ 15 ]
The production version of the VehiCROSS was introduced to the US in 1999, but met with mixed reviews, as its high price tag, unique styling and two-door configuration did not seem to meet with market demands. Production of the VehiCROSS and other sport utility vehicles, including the Trooper , ended in 2001 as part of a major financial reorganization which eliminated almost 10,000 jobs. [ 15 ] GM had been pushing the company to focus exclusively on producing commercial vehicles and engines. [ 15 ]
The number of Isuzu dealerships in the US began a rapid decline, and by 2005 had only 2 models: the Ascender (a re-badged GMC Envoy) and the i-series pickup truck (a rebadged Chevrolet Colorado). At this point, Isuzu in the US was primarily a distributor of medium duty trucks such as the N-series , sourced both from Japan and US plants in Janesville, Wisconsin and Flint, Michigan. Isuzu had 290 light-vehicle dealers in the US in August 2006, and sold an average of just two Ascenders per dealer per month, and rumors of Isuzu's withdrawal from the US market were rampant. Plans to introduce a new Thai-built SUV for 2007 were shelved when Isuzu Motors Limited decided that a new SUV would be too risky, instead proceeding with the launch of the i-series trucks. Despite extremely low sales figures of 12,177 passenger vehicles for 2005 (with leftover Axiom and Rodeos making up 30% of this), Isuzu Motors America announced its first profit in years, mainly due to restructuring cuts.
In early 2002, Fuji Heavy Industries (Subaru's parent company) bought Isuzu's share of Lafayette, Indiana plant, and Subaru Isuzu Automotive (SIA) became Subaru of Indiana Automotive . After eight years of heavy Honda Passport sales and light Isuzu Oasis sales, Honda and Isuzu cooperatively ended their vehicle exchange agreement in 2001. The Oasis was dropped, and Honda replaced the Passport with the Pilot . Isuzu's last year for passenger vehicles in Canada was 2001, as Isuzus in Canada were mostly sold at Saturn - Saab dealerships. In late 2002 Isuzu initiated a recapitalization and debt-for-equity conversion plan to stave off a bankruptcy. [ 16 ] GM acquired 20% of DMAX, 60% of Isuzu Motors Polska and Isuzu Motors Germany, and the rights to three types of diesel engine technology from Isuzu. [ 17 ] by paying 50 billion yen (about US$425 million). [ 16 ] GM also paid 10 billion yen (about US$85 million) for a 12% stake in the recapitalized company. [ 16 ] GM wrote off its investment in Isuzu in 2001. [ 18 ]
Production of the 7-passenger Ascender ended in February 2006 with the closure of GM's Oklahoma City Assembly plant, leaving Isuzu with the 5-passenger Ascender, built in Moraine, Ohio and the low-selling i-Series as its only retail products. The company sold just 1,504 vehicles in North America in the first two months of 2006. GM ended its equity investment in Isuzu and sold all its shares to Mitsubishi Corporation , Itochu and Mizuho Corporate Bank ; both GM and Isuzu claimed the companies would continue their relationship, but there was no word as of April 12, 2006 on the effect this would have on DMAX operations.
In June 2006 Isuzu and GM agreed to establish a joint venture called "LCV Platform Engineering Corporation (LPEC)" to develop a new pickup. Isuzu said it would use its engineering expertise to develop the pickup and GM would develop derivatives based on the integrated platform. Mitsubishi Corp became Isuzu's largest shareholder in October 2006, after it converted all the preferred shares in Isuzu it had held since 2005 into common stock, increasing its shareholding from 3.5% to 15.65%. [ 19 ]
In November 2006 Toyota purchased a 5.9% shareholding in Isuzu, becoming the third largest shareholder behind Itochu and Mitsubishi Corporation . The two companies agreed to study possible business collaboration focusing on the areas of R&D and production of diesel engines, related emissions-control, and other environmental technologies. In January 2007 Isuzu and General Motors updated the LCV range with a 3.0 litre common rail diesel engine that had far more torque and power than its predecessor. In August 2007 Isuzu and Toyota agreed to develop a 1.6-liter diesel engine for use in Toyota vehicles sold in European markets. At this point, details of development, production and supply of the diesel engine were still under discussion, but in principle, Isuzu would play the leading role, with production scheduled to begin around 2012.
On 30 January 2008, Isuzu announced its complete withdrawal from the US market, [ 20 ] effective 31 January 2009. It would continue to provide support and parts. The decision was due to lack of sales. [ 21 ] Some of the lack of sales was blamed on consumer experiences with low quality engines and service. [ 22 ] Isuzu had been experiencing a slow decline since the late 1990s. In less than 10 years, they had gone from selling a complete line of cars, trucks, and SUVs, into being a specialized SUV maker, and finally selling only a pair of rebadged, General Motors Trucks. [ 23 ] The company continued to sell commercial vehicles in the US. [ 24 ]
Isuzu and Toyota shelved development of a clean diesel engine in December 2008. [ 25 ]
On 29 January 2009, Isuzu and GM announced that they were in talks to transfer the operation of the medium-duty truck production line in Flint, Michigan to Isuzu for a five-year period. In June, however, GM announced that these talks failed to reach an agreement, and GM instead ceased production of the Chevrolet Kodiak and GMC Topkick vehicles on 31 July 2009. [ 26 ]
In July 2016, Isuzu and Mazda agreed to collaborate to produce the next-generation pickup trucks for Mazda outside of North America. [ 27 ] As a result, the third-generation Mazda BT-50 is built by Isuzu in Thailand since 2020.
Isuzu's plant in the Indian state of Andhra Pradesh began operations in 2016. [ 28 ]
In August 2018, Toyota sold off its 5.9% stake in Isuzu. [ 29 ]
In December 2019, Isuzu announced that it had signed a non-binding memorandum of understanding which would eventually see Volvo sell UD Trucks to them. [ 30 ] In November 2020, the companies announced that they have signed the "final agreements", making the memorandum of understanding binding. [ 31 ] In April 2021, Isuzu completed UD Trucks acquisition. [ 32 ]
In March 2021, Isuzu, Hino, and Hino's parent Toyota announced the creation of a strategic partnership between the three companies. Toyota acquired a 4.6% stake in Isuzu while the latter plans to acquire Toyota shares for an equivalent value. The three companies said they would form a new joint venture by April called Commercial Japan Partnership Technologies Corporation with the aim of developing fuel cell and electric light trucks. Toyota would own an 80% stake in the venture while Hino and Isuzu would own 10% each. [ 33 ]
In most of Asia and Africa, Isuzu is known primarily for trucks of all sizes, after Isuzu dropped all sales of sedans and compact cars in the late 1990s due to plummeting sales. In the days when Isuzu sold passenger cars, they were known for focusing on the diesel-engined niche. In 1983, for instance, long before the explosion in diesel sales, diesels represented 63.4% of their passenger car production. [ 34 ] In 2009, Isuzu abandoned the United States consumer market due to lack of sales. Isuzu as a corporation has always been primarily a manufacturer of small to medium compact automobiles and commercial trucks of sizes medium duty and larger, but markets around the world show different needs.
Isuzu Motors America discontinued the sale of passenger vehicles in the United States on January 31, 2009. The company explained to its dealers that it had not been able to secure replacements for the Isuzu Ascender and Isuzu i-Series that would be commercially viable. Isuzu sold 7,098 cars in the year 2007. This action did not affect Isuzu's commercial vehicle or industrial diesel engine operations in the United States. [ 21 ] Isuzu has a contract with Budget Truck Rental to manufacture their rental trucks, shared with Ford , GMC , and Navistar International . [ 35 ]
In Australia, Isuzu was for many years a major supplier of light commercial and domestic vehicles to Holden (General Motors). However, by 2008, Holden was sourcing few Isuzus. At this time Isuzu began to sell the D-Max under the Isuzu name.
Isuzu's entry in the Thai market proved to be one of its most successful. Its presence in the country began in 1966 when it established a manufacturing facility for pick-up trucks in the Samuthprakarn province with a capacity of 155,000 units per year. [ 36 ] The automaker quickly became a market leader so that by 2002, the company transferred its production base from its original location in Fujisawa, Japan to Thailand. Isuzu claimed the largest share of the Thai commercial vehicle market, outperforming its competitors for at least 23 years. [ 36 ] By 2006, the company transferred to an industrial zone in Chachoengsao province to support further production expansion. By 2017, Isuzu has been exporting pick-up trucks, with shipments reaching North America, Latin America, Australia, and Japan. [ 37 ] In the same year, it announced that its profit climbed 7 percent and has doubled its annual truck production to meet overseas demands. [ 38 ]
The Fujisawa Plant was built and opened for production November 1961. It is located at 8 Tsuchidana, Fujisawa, Kanagawa , and is still producing commercial vehicles for domestic Japanese use and international exports. The Toghichi Plant, located at Hakuchu, Ohira-Machi , Tochigi, Tochigi , is where the engines are currently built. There was a factory at Tono Machi, Kawasaki-ku, Kawasaki-shi, Kanagawa Pref. that closed March 2005 that manufactured passenger vehicles.
Mimamori-kun, which means to watch, monitor, or observe in Japanese (literally "Mr. Watcher"), [ 39 ] is a commercial vehicle telematics service developed by Isuzu Motors for monitoring and tracking commercial vehicle operations and movements in Japan. The service uses GPS satellite tracking services, and began February 2004. It is connected to the internet and provides government mandated driver activity logs , and records how long the driver was on-duty and how much time was spent driving. The service also records when the driver took lunch breaks, where the truck stopped and for how long, and when the driver logged off for his duty shift.
The service has been modified for personal use in Japan to keep track of family members, to include the health status of elderly persons and pinpoint the location of children for safety purposes. [ 40 ]
Some of the main features include the wireless Internet Digital Tachograph , the first of its kind in Japan, combined with hands-free communication, voice guidance, and text messages displayed from the dispatch office. The system also has a password-enabled vehicle theft prevention feature that will not let the vehicle start without the driver having entered a password. [ citation needed ]
Diesel engines are a major part of the Isuzu Motor's business with over 20 million engines worldwide. [ clarification needed ] [ 41 ] The diesel power division, known as the PowerTrain Division, of Isuzu Motors America, is located in Plymouth, Michigan. [ 41 ]
From April 2021 onwards, UD Trucks' products are part of the Isuzu company lineup.
As of 2017, Isuzu has been the shirt sponsor of the Wales Rugby Union sports team in the UK ( Europe ). The contract was renewed during 2023, until 2025. [ 47 ] [ 48 ] | https://en.wikipedia.org/wiki/Isuzu |
The Italian Amateur Astronomers Union ( Italian : Unione Astrofili Italiani ; Unione degli Astrofili Italiani ; UAI ), also known as Union of Italian Amateur Astronomers , is an Italian organization active in astronomy research and outreach that was founded in 1967. [ 1 ] Its members are both professional and amateur astronomers . The UAI claims more than two thousands members from the whole Italy and is one of the most important amateur astronomical associations in Europe. [ citation needed ]
The main-belt asteroid 234026 Unioneastrofili , discovered by Luciano Tesi in 1998, was named in honor of the organization. [ 1 ]
This article about an organization or institute connected with astronomy is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Italian_Amateur_Astronomers_Union |
The Italian Chemical Society ( Italian : Società Chimica Italiana ) is the national association in Italy representing the chemical sciences . Its main aim is to promote and support the development of chemistry and scientific research, spreading the knowledge of chemistry and its applications in order to improve the welfare of the country, establishing and maintaining relations with organizations from other countries with similar purposes and promoting the study of this subject at school and university. [ 1 ]
The Italian Chemical Society was formed in 1909 by the union of two existing societies, the Chemical Society of Rome, founded in 1902, and the Chemical Society of Milan, founded in 1895. The two original societies became sections of the new one and a third section was added in 1910, when the Chemical Society of Naples was incorporated. [ 2 ]
During the First World War , the activity of the society experienced a marked decrease and the link among the three sections got was loosened, with the result that, in 1919, the section in Milan claimed its independence and became the Society of Industrial Chemistry ( Societa′ di Chimica Industriale ). [ 2 ]
In 1928, the Society of Industrial Chemistry of Milan and the Society of General and Applied Chemistry of Rome merged into the Italian Association of Chemistry ( Associazione Italiana di Chimica ), which finally assumed the name of Italian Chemical Society on 1 January 1947, maintaining exactly the same structure as before. [ 2 ]
It is the publisher of the journal La Chimica e l'Industria (Chemistry and Industry) and also published, until 1997, the Gazzetta Chimica Italiana (Italian Chemical Bulletin), which converged, together with many other European publications, into the European Journal of Inorganic Chemistry and the European Journal of Organic Chemistry .
As of 2023, the President of the Society is Professor Gianluca Farinola. [ 3 ] | https://en.wikipedia.org/wiki/Italian_Chemical_Society |
The Italian Federation of Chemical Workers ( Italian : Federazione Italiana Lavoratori Chimici , FILC) was a trade union representing workers in the chemical industry in Italy.
The union was founded in 1901, as the Italian Chemical Workers' Federation , and was a founding affiliate of the General Confederation of Labour . It was banned by the fascist government in 1926, but re-established after World War II , when it affiliated to the recently formed Italian General Confederation of Labour . [ 1 ] [ 2 ] By 1954, it had 123,286 members. [ 3 ]
In 1960, the union merged with the Italian Union of Oil Workers, to form the Italian Federation of Chemical and Oil Workers . [ 2 ] | https://en.wikipedia.org/wiki/Italian_Federation_of_Chemical_Workers |
The Italian Federation of Chemical and Allied Workers ( Italian : Federazione Italiana Lavoratori Chimici ed Affini , FILCEA) was a trade union representing chemical and some manufacturing workers in Italy.
The union was founded in December 1968, when the Italian Federation of Chemical and Oil Workers merged with the Federation of Glass and Ceramics. Like its predecessors, it affiliated to the Italian General Confederation of Labour . [ 1 ]
By 1998, the union had 128,566 members, of whom 90% worked in the chemical industry, and most of the remainder in glass and ceramics. [ 2 ] In February 2006, the union merged with the National Federation of Energy Workers , to form the Italian Federation of Chemical, Energy and Manufacturing Workers . [ 1 ] | https://en.wikipedia.org/wiki/Italian_Federation_of_Chemical_and_Allied_Workers |
The Italian Federation of Chemical and Oil Workers ( Italian : Federazione Italiana Lavoratori Chimici e Petroliferi , FILCEP) was a trade union representing workers in the chemical and mining industries in Italy.
The union was founded in 1960, when the Italian Federation of Chemical Workers merged with the Italian Union of Oil Workers and the Italian Federation of Mining Industry Workers. Like its predecessors, it affiliated to the Italian General Confederation of Labour . In December 1968, it merged with the Federation of Glass and Ceramics, to form the Italian Federation of Chemical and Allied Workers . [ 1 ] | https://en.wikipedia.org/wiki/Italian_Federation_of_Chemical_and_Oil_Workers |
The Italian Union of Chemical, Energy and Resource Workers ( Italian : Unione Italiana Lavoratori Chimica Energia Risorse , UILCER) was a trade union representing manufacturing and utility workers in Italy.
The union was founded in the summer of 1994, when the Italian Union of Chemical and Allied Industries merged with the Italian Union of Oil and Gas Workers. Like both its predecessors, it affiliated to the Italian Union of Labour . From 1995, it was led by Romano Bellissima. On 25 March 1999, it merged with the Italian Union of Public Service Workers, to form the Italian Union of Chemical, Energy and Manufacturing Workers . [ 1 ] [ 2 ] [ 3 ] | https://en.wikipedia.org/wiki/Italian_Union_of_Chemical,_Energy_and_Resource_Workers |
The Italian Union of Chemical and Allied Industries ( Italian : Unione Italiana Lavoratori Chimica e Industrie Diverse , UILCID) was a trade union representing workers in the chemical and mining industries in Italy.
The union was founded in 1950, as the Italian Union of Chemical Workers , and was a founding affiliate of the Italian Labour Union . It grew steadily, and by 1953, had 22,006 members. In 1962, it absorbed the National Union of Mine and Quarry Workers, and renamed itself as the "Italian Union of Chemical and Allied Industries", and by 1964, it had 45,237 members. [ 1 ] [ 2 ] [ 3 ]
In the summer of 1994, the union merged with the Italian Union of Oil and Gas Workers, to form the Italian Union of Chemical, Energy and Resource Workers . [ 4 ] [ 5 ] By 1997, the union had 61,815 members, of whom 70% worked in the chemical industry, and most of the remainder in ceramics and glass. [ 6 ] | https://en.wikipedia.org/wiki/Italian_Union_of_Chemical_and_Allied_Industries |
In relation to the history of mathematics , the Italian school of algebraic geometry refers to mathematicians and their work in birational geometry , particularly on algebraic surfaces , centered around Rome roughly from 1885 to 1935. There were 30 to 40 leading mathematicians who made major contributions, about half of those being Italian. The leadership fell to the group in Rome of Guido Castelnuovo , Federigo Enriques and Francesco Severi , who were involved in some of the deepest discoveries, as well as setting the style.
The emphasis on algebraic surfaces — algebraic varieties of dimension two—followed on from an essentially complete geometric theory of algebraic curves (dimension 1). The position in around 1870 was that the curve theory had incorporated with Brill–Noether theory the Riemann–Roch theorem in all its refinements (via the detailed geometry of the theta-divisor ).
The classification of algebraic surfaces was a bold and successful attempt to repeat the division of algebraic curves by their genus g . The division of curves corresponds to the rough classification into the three types: g = 0 ( projective line ); g = 1 ( elliptic curve ); and g > 1 ( Riemann surfaces with independent holomorphic differentials). In the case of surfaces, the Enriques classification was into five similar big classes, with three of those being analogues of the curve cases, and two more ( elliptic fibrations , and K3 surfaces , as they would now be called) being with the case of two-dimension abelian varieties in the 'middle' territory. This was an essentially sound, breakthrough set of insights, recovered in modern complex manifold language by Kunihiko Kodaira in the 1950s, and refined to include mod p phenomena by Zariski , the Shafarevich school and others by around 1960. The form of the Riemann–Roch theorem on a surface was also worked out.
Some proofs produced by the school are not considered satisfactory because of foundational difficulties. These included frequent use of birational models in dimension three of surfaces that can have non-singular models only when embedded in higher-dimensional projective space . In order to avoid these issues, a sophisticated theory of handling a linear system of divisors was developed (in effect, a line bundle theory for hyperplane sections of putative embeddings in projective space). Many modern techniques were found, in embryonic form, and in some cases the articulation of these ideas exceeded the available technical language.
According to Guerraggio & Nastasi (page 9, 2005), Luigi Cremona is "considered the founder of the Italian school of algebraic geometry". Later they explain that in Turin the collaboration of Enrico D'Ovidio and Corrado Segre "would bring, either by their own efforts or those of their students, Italian algebraic geometry to full maturity". A one-time student of Segre, H.F. Baker wrote [ 1 ] that Corrado Segre "may probably be said to be the father of that wonderful Italian school which has achieved so much in the birational theory of algebraical loci." On this topic, Brigaglia & Ciliberto (2004) say "Segre had headed and maintained the school of geometry that Luigi Cremona had established in 1860." Reference to the Mathematics Genealogy Project shows that, in terms of Italian doctorates , the real productivity of the school began with Guido Castelnuovo and Federigo Enriques .
The roll of honour of the school includes the following other Italians: Giacomo Albanese , Eugenio Bertini , Luigi Campedelli, Oscar Chisini , Michele De Franchis , Pasquale del Pezzo , Beniamino Segre , Francesco Severi , Guido Zappa (with contributions also from Gino Fano , Carlo Rosati, Giuseppe Torelli, Giuseppe Veronese ).
Elsewhere it involved H. F. Baker and Patrick du Val (UK), Arthur Byron Coble (USA), Georges Humbert and Charles Émile Picard (France), Lucien Godeaux (Belgium), Hermann Schubert and Max Noether , and later Oscar Zariski (United States), Erich Kähler (Germany), H. G. Zeuthen (Denmark).
These figures were all involved in algebraic geometry, rather than the pursuit of projective geometry as synthetic geometry , which during the period under discussion was a huge (in volume terms) but secondary subject (when judged by its importance as research).
In 1950 Henry Forder mentioned the Italian school in connection with algebraic curves . [ 2 ]
Further development of the theory of plane curves is only fruitful when it is connected with the theory of Riemann surfaces and Abelian functions . This has been a favorite study during the last fifty years, of the Italian geometers, and they have also made contributions of great beauty to a similar theory of surfaces and of “ Varieties ” of higher dimensions. Herein a combination of the theory of integrals on the varieties, and of their topology, yields decisive results. The theory of curves and surfaces is thus connected with modern algebra and topology...
The new algebraic geometry that would succeed the Italian school was distinguished by the intensive use of algebraic topology . The founder of that tendency was Henri Poincaré ; during the 1930s it was developed by Lefschetz , Hodge and Todd . The modern synthesis brought together their work, that of the Cartan school, and of W.L. Chow and Kunihiko Kodaira , with the traditional material.
In the earlier years of the Italian school under Castelnuovo, the standards of rigor were as high as most areas of mathematics. Under Enriques it gradually became acceptable to use somewhat more informal arguments instead of complete rigorous proofs, such as the "principle of continuity" saying that what is true up to the limit is true at the limit, a claim that had neither a rigorous proof nor even a precise statement. At first this did not matter too much, as Enriques's intuition was so good that essentially all the results he claimed were in fact correct, and using this more informal style of argument allowed him to produce spectacular results about algebraic surfaces.
Unfortunately, from about 1930 onwards under Severi's leadership the standards of accuracy declined further, to the point where some of the claimed results were not just inadequately proved, but were incorrect.
For example, in 1934 Severi claimed that the space of rational equivalence classes of cycles on an algebraic surface is finite-dimensional, but Mumford (1968) showed that this is false for surfaces of positive geometric genus, and in 1946 Severi published a paper claiming to prove that a degree-6 surface in 3-dimensional projective space has at most 52 nodes, but the Barth sextic has 65 nodes.
Severi did not accept that his arguments were inadequate, leading to some acrimonious disputes as to the status of some results.
By about 1950 it had become too difficult to tell which of the results claimed were correct, and the informal intuitive school of algebraic geometry collapsed due to its inadequate foundations. [ citation needed ] From about 1950 to 1980 there was considerable effort to salvage as much as possible, and convert it into the rigorous algebraic style of algebraic geometry set up by Weil and Zariski. In particular in the 1960s Kodaira and Shafarevich and his students rewrote the Enriques classification of algebraic surfaces in a more rigorous style, and also extended it to all compact complex surfaces, while in the 1970s Fulton and MacPherson put the classical calculations of intersection theory on rigorous foundations. | https://en.wikipedia.org/wiki/Italian_school_of_algebraic_geometry |
Iterated filtering algorithms are a tool for maximum likelihood inference on partially observed dynamical systems . Stochastic perturbations to the unknown parameters are used to explore the parameter space . Applying sequential Monte Carlo (the particle filter ) to this extended model results in the selection of the parameter values that are more consistent with the data. Appropriately constructed procedures, iterating with successively diminished perturbations, converge to the maximum likelihood estimate. [ 1 ] [ 2 ] [ 3 ] Iterated filtering methods have so far been used most extensively to study infectious disease transmission dynamics. Case studies include cholera , [ 4 ] [ 5 ] Ebola virus , [ 6 ] influenza , [ 7 ] [ 8 ] [ 9 ] [ 10 ] malaria , [ 11 ] [ 12 ] [ 13 ] HIV , [ 14 ] pertussis , [ 15 ] [ 16 ] poliovirus [ 17 ] and measles . [ 5 ] [ 18 ] Other areas which have been proposed to be suitable for these methods include ecological dynamics [ 19 ] [ 20 ] and finance . [ 21 ] [ 22 ]
The perturbations to the parameter space play several different roles. Firstly, they smooth out the likelihood surface, enabling the algorithm to overcome small-scale features of the likelihood during early stages of the global search. Secondly, Monte Carlo variation allows the search to escape from local minima. Thirdly, the iterated filtering update uses the perturbed parameter values to construct an approximation to the derivative of the log likelihood even though this quantity is not typically available in closed form. Fourthly, the parameter perturbations help to overcome numerical difficulties that can arise during sequential Monte Carlo.
The data are a time series y 1 , … , y N {\displaystyle y_{1},\dots ,y_{N}} collected at times t 1 < t 2 < ⋯ < t N {\displaystyle t_{1}<t_{2}<\dots <t_{N}} . The dynamic system is modeled by a Markov process X ( t ) {\displaystyle X(t)} which is generated by a function f ( x , s , t , θ , W ) {\displaystyle f(x,s,t,\theta ,W)} in the sense that
where θ {\displaystyle \theta } is a vector of unknown parameters and W {\displaystyle W} is some random quantity that is drawn independently each time f ( . ) {\displaystyle f(.)} is evaluated. An initial condition X ( t 0 ) {\displaystyle X(t_{0})} at some time t 0 < t 1 {\displaystyle t_{0}<t_{1}} is specified by an initialization function, X ( t 0 ) = h ( θ ) {\displaystyle X(t_{0})=h(\theta )} . A measurement density g ( y n | X n , t n , θ ) {\displaystyle g(y_{n}|X_{n},t_{n},\theta )} completes the specification of a partially observed Markov process. We present a basic iterated filtering algorithm (IF1) [ 1 ] [ 2 ] followed by an iterated filtering algorithm implementing an iterated, perturbed Bayes map (IF2). [ 3 ] [ 23 ]
"pomp: statistical inference for partially-observed Markov processes" : R package. | https://en.wikipedia.org/wiki/Iterated_filtering |
Iterative Viterbi decoding is an algorithm that spots the subsequence S of an observation O = { o 1 , ..., o n } having the highest average probability (i.e., probability scaled by the length of S ) of being generated by a given hidden Markov model M with m states. The algorithm uses a modified Viterbi algorithm as an internal step.
The scaled probability measure was first proposed by John S. Bridle . An early algorithm to solve this problem, sliding window , was proposed by Jay G. Wilpon et al., 1989, with constant cost T = mn 2 /2.
A faster algorithm consists of an iteration of calls to the Viterbi algorithm , reestimating a filler score until convergence.
A basic (non-optimized) version, finding the sequence s with the smallest normalized distance from some subsequence of t is:
The ViterbiDistance() procedure returns the tuple ( e , B , E ), i.e., the Viterbi score " e " for the match of t and the selected entry ( B ) and exit ( E ) points from it. " B " and " E " have to be recorded using a simple modification to Viterbi.
A modification that can be applied to CYK tables, proposed by Antoine Rozenknop, consists in subtracting e from all elements of the initial matrix d . | https://en.wikipedia.org/wiki/Iterative_Viterbi_decoding |
Iterative closest point ( ICP ) [ 1 ] [ 2 ] [ 3 ] [ 4 ] is a point cloud registration algorithm employed to minimize the difference between two clouds of points . ICP is often used to reconstruct 2D or 3D surfaces from different scans, to localize robots and achieve optimal path planning (especially when wheel odometry is unreliable due to slippery terrain), to co-register bone models, etc.
The Iterative Closest Point algorithm keeps one point cloud, the reference or target, fixed, while transforming the other, the source, to best match the reference. The transformation (combination of translation and rotation) is iteratively estimated in order to minimize an error metric, typically the sum of squared differences between the coordinates of the matched pairs. ICP is one of the widely used algorithms in aligning three dimensional models given an initial guess of the rigid transformation required. [ 5 ] The ICP algorithm was first introduced by Chen and Medioni, [ 3 ] and Besl and McKay. [ 2 ]
Inputs: reference and source point clouds, initial estimation of the transformation to align the source to the reference (optional), criteria for stopping the iterations.
Output: refined transformation.
Essentially, the algorithm steps are: [ 5 ]
Zhang [ 4 ] proposes a modified k -d tree algorithm for efficient closest point computation. In this work a statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance, and disappearance, which enables subset-subset matching.
There exist many ICP variants, [ 6 ] from which point-to-point and point-to-plane are the most popular. The latter usually performs better in structured environments. [ 7 ] [ 8 ] | https://en.wikipedia.org/wiki/Iterative_closest_point |
Iterative design is a design methodology based on a cyclic process of prototyping , testing , analyzing, and refining a product or process. Based on the results of testing the most recent iteration of a design, changes and refinements are made. This process is intended to ultimately improve the quality and functionality of a design. In iterative design, interaction with the designed system is used as a form of research for informing and evolving a project, as successive versions, or iterations of a design are implemented.
Iterative design has long been used in engineering fields. One example is the plan–do–check–act cycle implemented in the 1960s. Most New product development or existing product improvement programs have a checking loop which is used for iterative purposes. DMAIC uses the Six Sigma framework and has such a checking function.
Iterative design is connected with the practice of object-oriented programming , and the phrase appeared in computer science literature as early as 1990. [ 1 ] The idea has its roots in spiral development , conceived of by Barry Boehm . [ 2 ]
The iterative design process may be applied throughout the new product development process. However, changes are easiest and less expensive to implement in the earliest stages of development. The first step in the iterative design process is to develop a prototype . The prototype should be evaluated by a focus group or a group not associated with the product in order to deliver non-biased opinions. Information from the focus group should be synthesized and incorporated into the next iteration of the design. The process should be repeated until user issues have been reduced to an acceptable level.
Iterative design is commonly used in the development of human computer interfaces. This allows designers to identify any usability issues that may arise in the user interface before it is put into wide use. Even the best usability experts cannot design perfect user interfaces in a single attempt, so a usability engineering lifecycle should be built around the concept of iteration. [ 3 ]
The typical steps of iterative design in user interfaces are as follows:
Iterative design in user interfaces can be implemented in many ways. One common method of using iterative design in computer software is software testing . While this includes testing the product for functionality outside of the user interface, important feedback on the interface can be gained from subject testing early versions of a program. This allows software companies to release a better quality product to the public, and prevents the need of product modification following its release.
Iterative design in online (website) interfaces is a more continual process, as website modification, after it has been released to the user, is far more viable than in software design. Often websites use their users as test subjects for interface design, making modifications based on recommendations from visitors to their sites.
Iterative design is a way of confronting the reality of unpredictable user needs and behaviors that can lead to sweeping and fundamental changes in a design. User testing will often show that even carefully evaluated ideas will be inadequate when confronted with a user test. Thus, it is important that the flexibility of the iterative design's implementation approach extends as far into the system as possible. Designers must further recognize that user testing results may suggest radical change that requires the designers to be prepared to completely abandon old ideas in favor of new ideas that are more equipped to suit user needs. Iterative design applies in many fields, from making knives to rockets. As an example consider the design of an electronic circuit that must perform a certain task, and must ultimately fit in a small space on a circuit board . It is useful to split these independent tasks into two smaller and simpler tasks, the functionality task, and the space and weight task. A breadboard is a useful way of implementing the electronic circuit on an interim basis, without having to worry about space and weight.
Once the circuit works, improvements or incremental changes may be applied to the breadboard to increase or improve functionality over the original design. When the design is finalized, one can set about designing a proper circuit board meeting the space and weight criteria. Compacting the circuit on the circuit board requires that the wires and components be juggled around without changing their electrical characteristics. This juggling follows simpler rules than the design of the circuit itself, and is often automated . As far as possible off the shelf components are used, but where necessary for space or performance reasons, custom made components may be developed.
Several instances of iterative design are as follows:
One approach to iterative design is to use the highest level of abstraction for developing an early generation product. The principle here is that rapid development may not produce efficient code, but obtaining feedback is more important than technology optimization. Examples of this approach include use of non-functional code, object databases, or low code platforms - these allow quick testing of designs before issues of optimization are addressed.
When properly applied, iterative design will ensure a product or process is the best solution possible. When applied early in the development stage, significant cost savings are possible. [ 4 ]
Other benefits to iterative design include:
The Marshmallow Challenge is an instructive design challenge. It involves the task of constructing the highest possible free-standing structure with a marshmallow on top. The structure must be completed within 18 minutes using only 20 sticks of spaghetti, one yard of tape, and one yard of string. [ 5 ] [ 6 ]
Observation and studies of participants show that kindergartners are regularly able to build higher structures, in comparison to groups of business school graduates. This is explained by the tendency for children to at once stick the marshmallow on top of a simple structure, test the prototype, and continue to improve upon it. Whereas, business school students tend to spend time vying for power, planning, and finally producing a structure to which the marshmallow is added. [ 7 ] The challenge helps to build and develop prototyping, teamwork, leadership and innovation skills and is a popular STEM activity. The challenge was invented by Peter Skillman of Palm, Inc. and popularized by Tom Wujec of Autodesk . [ 8 ] [ 9 ] [ 10 ] [ 11 ] [ 12 ] | https://en.wikipedia.org/wiki/Iterative_design |
Iterons are directly repeated DNA sequences which play an important role in regulation of plasmid copy number in bacterial cells . It is one among the three negative regulatory elements found in plasmids which control its copy number. The others are antisense RNAs and ctRNAs . Iterons complex with cognate replication (Rep) initiator proteins to achieve the required regulatory effect. [ 1 ] [ 2 ]
Iterons have an important role in plasmid replication. An iteron-containing plasmid origin of replication can be found containing about five iterons about 20 base pairs in length total. These iterons provide a saturation site for initiator receptor proteins and promote replication, thus increasing plasmid copy number in a given cell. [ 1 ]
There are four main limiting factors leading to no initiation of replication in iterons: [ 1 ]
Transcriptional auto-repression is thought to reduce initiator synthesis by repressing the formation of the Rep proteins. Since these proteins work to promote binding of replication machinery, replication can be halted in this form. Another factor used to stop replication is known as dimerization. It works to dimerize these Rep proteins, and as a result, monomers of these proteins are no longer in a high enough concentration to initiate replication. [ 2 ] Another limiting factor, titration, occurs after replication, and works to prevent saturation by distributing monomers to daughter origins so that none are fully saturated. Finally, handcuffing refers to pairing origins leading to inactivation. This is mediated by monomers, and inactivation is due to steric hindrance between the origins. [ 1 ] [ 2 ]
Another less prevalent limitation thought to be present in these iterons is the presence of extra repeats. If a plasmid contains an extra supply of iterons outside of the saturation site, this can decrease plasmid copy number. In contrast, removing these extra iterons will increase copy number. [ 1 ]
Plasmids are known to have very similar structure when under control of iterons. This structure consists of an origin of replication upstream of a gene that codes for a replication initiator protein. The iterons themselves are known to cover about half of the origin of replication. [ 2 ] Usually, iterons on the same plasmid are highly conserved, whereas comparing iterons on different plasmids still exhibit homology yet are not as highly conserved. This suggests that iterons could be evolutionarily related. [ 3 ]
The replication initiator protein (Rep) plays a key role in initiation of replication in plasmids. In its monomer form, Rep binds an iteron and promotes replication. The protein itself is known to contain two independent N-terminal and C-terminal globular domains that subsequently bind to two domains of the iteron. The dimer version of the protein is generally inactive in iteron binding; however, it is known to bind to the repE operator . This operator contains half of the iteron sequence, making it able to bind the dimer and promote gene expression. [ 2 ] [ 4 ]
Plasmids containing iterons are all organized very similarly in structure. [ 2 ] The gene for Rep proteins is usually found directly downstream of the origin of replication. [ 5 ] This means that the iterons themselves are known to regulate the synthesis of the rep proteins. [ 6 ] [ 7 ] | https://en.wikipedia.org/wiki/Iteron |
ITN , is a file format designed as an itinerary data format for TomTom devices.
It can be used to describe itineraries using support waypoints . The format is proprietary for TomTom. Its data store location, name, and waypoint type and can in this way be used to interchange data between GPS devices and software packages. Such computer programs allow users, for example, to create and modify itineraries.
The file format assumes that each line in it holds a supporting waypoint:
The type specifies whether how to handle this waypoint:
Latitude and longitude are expressed in fixed point integer numbers using the WGS 84 datum . Please note these numbers are the floating point values times 100,000, e.g. the latitude 52.493601 will be shown as 5249360.
It is allowed to prefix these numbers with + or -.
The following is an ITN file produced by a TomTom hand-held GPS unit. This document does not show all functionality which can be stored in the ITN format but its purpose is to serve as a brief illustration.
TomTom devices as of 2014 will only accept at most 255 waypoints. Devices before that allow 32 or 48 at most, with an exception for the Rider product range, allowing 100 waypoints.
It is unknown what the maximum length of the description field is allowed to be, most applications assume 64 characters. The character encoding of the description is assumed to be Windows-1252 (the Latin alphabet), sometimes called ANSI. This character set allows 224 different characters to be used, supporting most European languages.
TomTom decided in 2015 to deprecate the ITN format in favour of the more versatile GPX format. ITN is still supported as an import format. | https://en.wikipedia.org/wiki/Itinerary_file |
Ituran Location and Control Ltd. is an Israeli company that provides stolen vehicle recovery and tracking services, and markets GPS wireless communications products. Ituran is traded on NASDAQ and is included in the TA-100 Index . Ituran has over 3,200 employees worldwide and is a market leader in Brazil , Argentina , Israel and the United States. As of June 2020, the company has more than 2M subscribers. [ 1 ]
Ituran was established in 1994 by the Tadiran conglomerate to develop and operate a service for locating stolen vehicles using a technology that was originally developed for military use at Tadiran Telematics , a subsidiary of Tadiran Communications . The core technology was originally developed and licensed by Tadiran from Teletrac USA. Teletrac was founded as International Teletrac Systems in 1988. It received initial funding from a unit of AirTouch Communication (formerly known as Pacific Telesis) in exchange for 49% equity of the company. Teletrac contracted Tadiran to build base stations for their US system which were later used under license in deploying the network in Israel.
In 1995, Tadiran decided to sell the Ituran concept to a group of investors headed by Izzy Sheratzky. [ 2 ]
In 1998, the company had an initial public offering on the Tel Aviv Stock Exchange , raising the capital required to develop the service overseas in the United States, Brazil and Argentina . [ 3 ]
In November 1999, Ituran acquired Tadiran Telematics , which manufactured the vehicle tracking systems Ituran was using for its services, for $10 million. The acquisition enabled Ituran to reduce the cost of the systems it sold.
Ituran then changed their company's name to Telematics Wireless.
In 2005, Ituran raised approximately $50 million in an initial public offering on Nasdaq, which gave the company a value of $294 million. [ 4 ]
In April 2007, Ituran acquired the Mapa group for $13 million. The Mapa Group consists of three divisions: geographical databases, map publishing in print and online, satellite navigation and location-based services. [ citation needed ]
In November 2007, Ituran sold Telematics Wireless to Singapore based ST Electronics, part of the ST Engineering corporation, for $90 million. [ citation needed ]
In 2011, Ituran signed an agreement with Pelephone which allows Ituran to use Pelephone's network to set up an MVNO (mobile virtual network operator) venture. [ 5 ]
In 2012, Ituran announced that Ituran Brazil entered into agreement with General Motors Brazil ("GMB") through a company controlled by Ituran (51%).
Ituran Brazil was founded in 1999 and has (as of the end of 2014) more than 310,000 active subscribers.
In May 2018, a severe security vulnerability was discovered in the Ituran system. The vulnerability allowed attackers to easily extract personal information of Ituran customers, including home addresses, phone numbers and car registration numbers. For some users it also allowed real-time tracking using the Ituran application. Following the discovery of the vulnerability, Ituran disabled the self-service portal for its Israeli customers, until the vulnerability is fixed. [ 6 ]
Mapa - Mapping and Publishing ( Hebrew : מפה - מיפוי והוצאה לאור , lit. map) is an Israeli cartographic and book publishing company, purchased in April 2007 by Ituran for $13 million. [ 7 ]
Mapa was founded in 1985 under the name Sifrei Tel Aviv ( lit. Tel Aviv Books). It entered the field of cartography in 1994. Mapa eventually moved solely into cartography, becoming the market leader in map making for the public sector in 1995. It controlled close to 80% of the map making market in 2005. [ 8 ] Mapa has been expanding its horizons since 1996, and now publishes books in all fields. It also exports some books. Mapa's workforce consists of approximately 70 employees. [ when? ] | https://en.wikipedia.org/wiki/Ituran |
itv.com is the main website of ITV plc , the UK's largest commercial television broadcaster which operates 13 out of 15 regions on the ITV network under the ITV1 brand. [ 1 ] The website offers the ITVX streaming service, with sections for ITV News , certain ITV1 programmes and competitions. STV , Which runs the only regions not owned by ITV plc, have their own separate website at stv.tv .
The URL 'www.itv.com' was created on 31 October 1994, but it was registered elsewhere for some years before Carlton and Granada bought the domain name after merging their respective online services, carlton.com and G-Wizz . These companies have since merged to form ITV plc. The original ITV URL was www.itv.co.uk, which now redirects to itv.com. itv.co.uk was and still is registered to the ITV Network Limited as opposed to ITV plc. Previous corporate logos had ".com" added as a logo for the Web site. However, this trend stopped with the 2011 redesign wherein a black ITV logo began being used when referring to the Web site. ITV.com's slogan used to be "total freedom of entertainment".
The 2007 redesign of the website featured a media player through which viewers gain access to whole shows, simulcasts, previews and catchups of broadcast content, much of it within a 30-day window, all for free for the viewer, funded by advertising. Users also have access to the network's programme archive, 'behind-the-scenes' programming, games and user-generated content . The site also makes available some 1,000 hours of exclusive archive content, which will grow over time. In addition, the site also introduces interactive services and community elements. [ 2 ]
Soaps such as Coronation Street and Emmerdale were the first genre to launch on 12 June 2007, followed by Games on 19 June 2007, Drama and Best of ITV on 29 June 2007, Lifestyle on 9 July 2007, Entertainment on 17 July 2007, Sport on 25 July, with every other section launching on 31 July, making the site now fully launched. [ 3 ] Also on 12 June 2007 simulcasts of ITV, ITV2, ITV3 and ITV4 were launched. (However, not all programming will be shown due to rights restrictions.)
In March 2008, the Web site was revamped with changes including the home page and the video player, with a new Catch Up TV section. [ 4 ]
On 10 December 2008 it was announced that itv.com would undergo another redesign to introduce more social media features and a greater emphasis on its most popular TV shows with a "fewer, bigger, better" strategy. The redesign was code named 'Project Penguin', and it followed the announcement of ITV's Catch Up service being rebranded to ITV Player . [ 5 ]
Parts of the site have already had a redesign, including a new look for the home page. The Coronation Street , Loose Women and football sections pages were updated in the early months of 2009. This Morning was relaunched in August. ITV News was relaunched 2010, coinciding with a new Tonight page. On 11 September 2009, video coding was changed from Microsoft Silverlight to Flash, and on 25 September 2009, ITV relaunched its TV classics section. On 19 November ITV Player had a complete overhaul of its site and relaunched with a new Web site with a few new addons, including a search bar, a light dimmer and bigger video players. A Brand New TV Shows directory was relaunched on 10 December, which then led to the old style Drama, Soap, Entertainment pages on the site being replaced with similar pages in the TV Shows directory. On 4 February a brand new weather page launched and on 22 February a brand new ITV News Web site launched. Stories from ITV News correspondents, the latest news programme, news blogs and a meet the team page are all on the brand new Web site. From Summer 2010, the ITV Web site underwent another overhaul, with tweaks to the layout such as centring pages when used on wide-screen displays as well as improved pages for various ITV shows with high-resolution images and videos.
On 4 March 2009, ITV announced that ITV Local would close as a separate business. On 17 March 2009, it did, with the ITV regions integrated into itv.com. The new itv.com/local relaunched during October 2009 and are now prominent in regional news.
On 31 March 2011 ITV.com had another new design. The home page was completely redesigned, as were the channel minisites. The TV guide and TV shows sections incorporated the new page headers and footers whilst becoming centred for better presentation on wide-screen displays. The news option in the navigational bar offers national and regional news. The sports section also become centred, with a redesigned itv.com/f1 site launching soon thereafter. Other sports minisites are expected to redesigned in the same way when their respective new seasons begin. Many programmes minisites relating to current programmes were centred, whilst shows returning for new series saw their sites redesigned with high-resolution background images and increased interactive and video content. This redesign continues to build upon the social networking functionality introduced in previous versions of the site.
The ITV Player relaunched on Monday 22 August 2011 with a new look and new features. ITV has said there will be upcoming improvements to the ITV Player such as dedicated applications for Android and iOS devices. Currently improvements to the reliability, subtitles on some programmes and a dedicated CITV section have since launched.
ITV has signalled their intention to trial a micro-payments feature on their Web site. It is currently unclear what they will charge for, but this could include consumers paying for alternative story lines for soaps and archive content. The video archive section of the site, introduced in the 2007 redesign was removed when the redesign went live.
ITV relaunched its news website in March 2012, [ 6 ] including the sport and weather pages.
As ITV underwent a corporate rebrand in January 2013, the ITV.com website was redesigned to complement the new look.
ITV Mobile was an entertainment portal that offers catch-ups and clips from ITV 's soaps: Coronation Street and Emmerdale , ITV Sport and ITV's entertainment shows: This Morning and The X Factor . It also provided the latest information for regional weather forecasts. In 2006, ITV began streaming ITV1 to customers of 3 in the United Kingdom . The service was priced at 99p per day's viewing of ITV, with a £5 per month for an 18 channel unlimited viewing TV pack. The service also was broadcast alongside other PSB channels on the short lived BT Movio service, which used the DAB network in the UK to transmit video channels. The streaming of ITV on mobile was introduced on Vodafone and Orange in 2007. iOS users could also stream ITV1 and ITV2 to their devices via the ITV Mobile site.
From 2007, ITN and ITV Mobile have produced an ITV News video service. Bulletins were sent to mobiles twice a day, once in the morning and once in the afternoon, two bulletins at the weekend. The service previously charged users £2. The service was eventually replaced with the ITV News website and app [ 7 ] | https://en.wikipedia.org/wiki/Itv.com |
In mathematics , Itô's lemma or Itô's formula (also called the Itô–Döblin formula [ 1 ] ) is an identity used in Itô calculus to find the differential of a time-dependent function of a stochastic process . It serves as the stochastic calculus counterpart of the chain rule . It can be heuristically derived by forming the Taylor series expansion of the function up to its second derivatives and retaining terms up to first order in the time increment and second order in the Wiener process increment. The lemma is widely employed in mathematical finance , and its best known application is in the derivation of the Black–Scholes equation for option values.
This result was discovered by Japanese mathematician Kiyoshi Itô in 1951. [ 2 ]
Suppose we are given the stochastic differential equation d X t = μ t d t + σ t d B t , {\displaystyle dX_{t}=\mu _{t}\ dt+\sigma _{t}\ dB_{t},} where B t is a Wiener process and the functions μ t , σ t {\displaystyle \mu _{t},\sigma _{t}} are deterministic (not stochastic) functions of time. In general, it's not possible to write a solution X t {\displaystyle X_{t}} directly in terms of B t . {\displaystyle B_{t}.} However, we can formally write an integral solution X t = ∫ 0 t μ s d s + ∫ 0 t σ s d B s . {\displaystyle X_{t}=\int _{0}^{t}\mu _{s}\ ds+\int _{0}^{t}\sigma _{s}\ dB_{s}.}
This expression lets us easily read off the mean and variance of X t {\displaystyle X_{t}} (which has no higher moments). First, notice that every d B t {\displaystyle \mathrm {d} B_{t}} individually has mean 0, so the expected value of X t {\displaystyle X_{t}} is simply the integral of the drift function: E [ X t ] = ∫ 0 t μ s d s . {\displaystyle \mathrm {E} [X_{t}]=\int _{0}^{t}\mu _{s}\ ds.}
Similarly, because the d B {\displaystyle dB} terms have variance 1 and no correlation with one another, the variance of X t {\displaystyle X_{t}} is simply the integral of the variance of each infinitesimal step in the random walk: V a r [ X t ] = ∫ 0 t σ s 2 d s . {\displaystyle \mathrm {Var} [X_{t}]=\int _{0}^{t}\sigma _{s}^{2}\ ds.}
However, sometimes we are faced with a stochastic differential equation for a more complex process Y t , {\displaystyle Y_{t},} in which the process appears on both sides of the differential equation. That is, say d Y t = a 1 ( Y t , t ) d t + a 2 ( Y t , t ) d B t , {\displaystyle dY_{t}=a_{1}(Y_{t},t)\ dt+a_{2}(Y_{t},t)\ dB_{t},} for some functions a 1 {\displaystyle a_{1}} and a 2 . {\displaystyle a_{2}.} In this case, we cannot immediately write a formal solution as we did for the simpler case above. Instead, we hope to write the process Y t {\displaystyle Y_{t}} as a function of a simpler process X t {\displaystyle X_{t}} taking the form above. That is, we want to identify three functions f ( t , x ) , μ t , {\displaystyle f(t,x),\mu _{t},} and σ t , {\displaystyle \sigma _{t},} such that Y t = f ( t , X t ) {\displaystyle Y_{t}=f(t,X_{t})} and d X t = μ t d t + σ t d B t . {\displaystyle dX_{t}=\mu _{t}\ dt+\sigma _{t}\ dB_{t}.} In practice, Ito's lemma is used in order to find this transformation. Finally, once we have transformed the problem into the simpler type of problem, we can determine the mean and higher moments of the process.
We derive Itô's lemma by expanding a Taylor series and applying the rules of stochastic calculus.
Suppose X t {\displaystyle X_{t}} is an Itô drift-diffusion process that satisfies the stochastic differential equation
d X t = μ t d t + σ t d B t , {\displaystyle dX_{t}=\mu _{t}\,dt+\sigma _{t}\,dB_{t},}
where B t is a Wiener process .
If f ( t , x ) is a twice-differentiable scalar function, its expansion in a Taylor series is
Δ f ( t ) d t d t = f ( t + d t , x ) − f ( t , x ) = ∂ f ∂ t d t + 1 2 ∂ 2 f ∂ t 2 ( d t ) 2 + ⋯ Δ f ( x ) d x d x = f ( t , x + d x ) − f ( t , x ) = ∂ f ∂ x d x + 1 2 ∂ 2 f ∂ x 2 ( d x ) 2 + ⋯ {\displaystyle {\begin{aligned}{\frac {\Delta f(t)}{dt}}dt&=f(t+dt,x)-f(t,x)\\&={\frac {\partial f}{\partial t}}\,dt+{\frac {1}{2}}{\frac {\partial ^{2}f}{\partial t^{2}}}\,(dt)^{2}+\cdots \\[1ex]{\frac {\Delta f(x)}{dx}}dx&=f(t,x+dx)-f(t,x)\\&={\frac {\partial f}{\partial x}}\,dx+{\frac {1}{2}}{\frac {\partial ^{2}f}{\partial x^{2}}}\,(dx)^{2}+\cdots \end{aligned}}}
Then use the total derivative and the definition of the partial derivative f y = lim d y → 0 Δ f ( y ) d y {\displaystyle f_{y}=\lim _{dy\to 0}{\frac {\Delta f(y)}{dy}}} :
d f = f t d t + f x d x = lim d x → 0 d t → 0 ∂ f ∂ t d t + ∂ f ∂ x d x + 1 2 ( ∂ 2 f ∂ t 2 ( d t ) 2 + ∂ 2 f ∂ x 2 ( d x ) 2 ) + ⋯ . {\displaystyle {\begin{aligned}df&=f_{t}dt+f_{x}dx\\[1ex]&=\lim _{dx\to 0 \atop dt\to 0}{\frac {\partial f}{\partial t}}\,dt+{\frac {\partial f}{\partial x}}\,dx+{\frac {1}{2}}\left({\frac {\partial ^{2}f}{\partial t^{2}}}\,(dt)^{2}+{\frac {\partial ^{2}f}{\partial x^{2}}}\,(dx)^{2}\right)+\cdots .\end{aligned}}}
Substituting x = X t {\displaystyle x=X_{t}} and therefore d x = d X t = μ t d t + σ t d B t {\displaystyle dx=dX_{t}=\mu _{t}\,dt+\sigma _{t}\,dB_{t}} , we get
d f = lim d B t → 0 d t → 0 ∂ f ∂ t d t + ∂ f ∂ x ( μ t d t + σ t d B t ) + 1 2 [ ∂ 2 f ∂ t 2 ( d t ) 2 + ∂ 2 f ∂ x 2 ( μ t 2 ( d t ) 2 + 2 μ t σ t d t d B t + σ t 2 ( d B t ) 2 ) ] + ⋯ . {\displaystyle {\begin{aligned}df=\lim _{dB_{t}\to 0 \atop dt\to 0}\;&{\frac {\partial f}{\partial t}}\,dt+{\frac {\partial f}{\partial x}}\left(\mu _{t}\,dt+\sigma _{t}\,dB_{t}\right)\\&+{\frac {1}{2}}\left[{\frac {\partial ^{2}f}{\partial t^{2}}}\,{\left(dt\right)}^{2}+{\frac {\partial ^{2}f}{\partial x^{2}}}\left(\mu _{t}^{2}\,{\left(dt\right)}^{2}+2\mu _{t}\sigma _{t}\,dt\,dB_{t}+\sigma _{t}^{2}\,{\left(dB_{t}\right)}^{2}\right)\right]+\cdots .\end{aligned}}}
In the limit d t → 0 {\displaystyle dt\to 0} , the terms ( d t ) 2 {\displaystyle (dt)^{2}} and d t d B t {\displaystyle dt\,dB_{t}} tend to zero faster than d t {\displaystyle dt} . ( d B t ) 2 {\displaystyle (dB_{t})^{2}} is O ( d t ) {\displaystyle O(dt)} (due to the quadratic variation of a Wiener process which says B t 2 = O ( t ) {\displaystyle B_{t}^{2}=O(t)} ), so setting ( d t ) 2 , d t d B t {\displaystyle (dt)^{2},dt\,dB_{t}} and ( d x ) 3 {\displaystyle (dx)^{3}} terms to zero and substituting d t {\displaystyle dt} for ( d B t ) 2 {\displaystyle (dB_{t})^{2}} , and then collecting the d t {\displaystyle dt} terms, we obtain
d f = lim d t → 0 ( ∂ f ∂ t + μ t ∂ f ∂ x + σ t 2 2 ∂ 2 f ∂ x 2 ) d t + σ t ∂ f ∂ x d B t {\displaystyle df=\lim _{dt\to 0}\left({\frac {\partial f}{\partial t}}+\mu _{t}{\frac {\partial f}{\partial x}}+{\frac {\sigma _{t}^{2}}{2}}{\frac {\partial ^{2}f}{\partial x^{2}}}\right)dt+\sigma _{t}{\frac {\partial f}{\partial x}}\,dB_{t}}
as required.
Alternatively,
d f = lim d t → 0 ( ∂ f ∂ t + σ t 2 2 ∂ 2 f ∂ x 2 ) d t + ∂ f ∂ x d X t {\displaystyle df=\lim _{dt\to 0}\left({\frac {\partial f}{\partial t}}+{\frac {\sigma _{t}^{2}}{2}}{\frac {\partial ^{2}f}{\partial x^{2}}}\right)dt+{\frac {\partial f}{\partial x}}\,dX_{t}}
Suppose we know that X t , X t + d t {\displaystyle X_{t},X_{t+dt}} are two jointly-Gaussian distributed random variables, and f {\displaystyle f} is nonlinear but has continuous second derivative, then in general, neither of f ( X t ) , f ( X t + d t ) {\displaystyle f(X_{t}),f(X_{t+dt})} is Gaussian, and their joint distribution is also not Gaussian. However, since X t + d t ∣ X t {\displaystyle X_{t+dt}\mid X_{t}} is Gaussian, we might still find f ( X t + d t ) ∣ f ( X t ) {\displaystyle f(X_{t+dt})\mid f(X_{t})} is Gaussian. This is not true when d t {\displaystyle dt} is finite, but when d t {\displaystyle dt} becomes infinitesimal, this becomes true.
The key idea is that X t + d t = X t + μ t d t + d W t {\displaystyle X_{t+dt}=X_{t}+\mu _{t}\,dt+dW_{t}} has a deterministic part and a noisy part. When f {\displaystyle f} is nonlinear, the noisy part has a deterministic contribution. If f {\displaystyle f} is convex, then the deterministic contribution is positive (by Jensen's inequality ).
To find out how large the contribution is, we write X t + d t = X t + μ t d t + σ t d t z {\displaystyle X_{t+dt}=X_{t}+\mu _{t}\,dt+\sigma _{t}{\sqrt {dt}}\,z} , where z {\displaystyle z} is a standard Gaussian, then perform Taylor expansion. f ( X t + d t ) = f ( X t ) + f ′ ( X t ) μ t d t + f ′ ( X t ) σ t d t z + 1 2 f ″ ( X t ) ( σ t 2 z 2 d t + 2 μ t σ t z d t 3 / 2 + μ t 2 d t 2 ) + o ( d t ) = [ f ( X t ) + f ′ ( X t ) μ t d t + 1 2 f ″ ( X t ) σ t 2 d t + o ( d t ) ] + [ f ′ ( X t ) σ t d t z + 1 2 f ″ ( X t ) σ t 2 ( z 2 − 1 ) d t + o ( d t ) ] {\displaystyle {\begin{aligned}f(X_{t+dt})={}&f(X_{t})+f'(X_{t})\mu _{t}\,dt+f'(X_{t})\sigma _{t}{\sqrt {dt}}\,z\\[1ex]&+{\frac {1}{2}}f''(X_{t})\left(\sigma _{t}^{2}z^{2}\,dt+2\mu _{t}\sigma _{t}z\,dt^{3/2}+\mu _{t}^{2}dt^{2}\right)+o(dt)\\[2ex]={}&\left[f(X_{t})+f'(X_{t})\mu _{t}\,dt+{\frac {1}{2}}f''(X_{t})\sigma _{t}^{2}\,dt+o(dt)\right]\\[1ex]&+\left[f'(X_{t})\sigma _{t}{\sqrt {dt}}\,z+{\frac {1}{2}}f''(X_{t})\sigma _{t}^{2}\left(z^{2}-1\right)\,dt+o(dt)\right]\end{aligned}}} We have split it into two parts, a deterministic part, and a random part with mean zero. The random part is non-Gaussian, but the non-Gaussian parts decay faster than the Gaussian part, and at the d t → 0 {\displaystyle dt\to 0} limit, only the Gaussian part remains. The deterministic part has the expected f ( X t ) + f ′ ( X t ) μ t d t {\displaystyle f(X_{t})+f'(X_{t})\mu _{t}\,dt} , but also a part contributed by the convexity: 1 2 f ″ ( X t ) σ t 2 d t {\textstyle {\frac {1}{2}}f''(X_{t})\sigma _{t}^{2}\,dt} .
To understand why there should be a contribution due to convexity, consider the simplest case of geometric Brownian walk (of the stock market): S t + d t = S t ( 1 + d B t ) {\displaystyle S_{t+dt}=S_{t}(1+dB_{t})} . In other words, d ( ln S t ) = d B t {\displaystyle d(\ln S_{t})=dB_{t}} . Let X t = ln S t {\displaystyle X_{t}=\ln S_{t}} , then S t = e X t {\displaystyle S_{t}=e^{X_{t}}} , and X t {\displaystyle X_{t}} is a Brownian walk. However, although the expectation of X t {\displaystyle X_{t}} remains constant, the expectation of S t {\displaystyle S_{t}} grows. Intuitively it is because the downside is limited at zero, but the upside is unlimited. That is, while X t {\displaystyle X_{t}} is normally distributed, S t {\displaystyle S_{t}} is log-normally distributed .
In the following subsections we discuss versions of Itô's lemma for different types of stochastic processes.
In its simplest form, Itô's lemma states the following: for an Itô drift-diffusion process
d X t = μ t d t + σ t d B t {\displaystyle dX_{t}=\mu _{t}\,dt+\sigma _{t}\,dB_{t}}
and any twice differentiable scalar function f ( t , x ) of two real variables t and x , one has
d f ( t , X t ) = ( ∂ f ∂ t + μ t ∂ f ∂ x + σ t 2 2 ∂ 2 f ∂ x 2 ) d t + σ t ∂ f ∂ x d B t . {\displaystyle df(t,X_{t})=\left({\frac {\partial f}{\partial t}}+\mu _{t}{\frac {\partial f}{\partial x}}+{\frac {\sigma _{t}^{2}}{2}}{\frac {\partial ^{2}f}{\partial x^{2}}}\right)dt+\sigma _{t}{\frac {\partial f}{\partial x}}\,dB_{t}.}
This immediately implies that f ( t , X t ) is itself an Itô drift-diffusion process.
In higher dimensions, if X t = ( X t 1 , X t 2 , … , X t n ) T {\displaystyle \mathbf {X} _{t}=(X_{t}^{1},X_{t}^{2},\ldots ,X_{t}^{n})^{T}} is a vector of Itô processes such that
d X t = μ t d t + G t d B t {\displaystyle d\mathbf {X} _{t}={\boldsymbol {\mu }}_{t}\,dt+\mathbf {G} _{t}\,d\mathbf {B} _{t}}
for a vector μ t {\displaystyle {\boldsymbol {\mu }}_{t}} and matrix G t {\displaystyle \mathbf {G} _{t}} , Itô's lemma then states that
d f ( t , X t ) = ∂ f ∂ t d t + ( ∇ X f ) T d X t + 1 2 ( d X t ) T ( H X f ) d X t , = { ∂ f ∂ t + ( ∇ X f ) T μ t + 1 2 Tr [ G t T ( H X f ) G t ] } d t + ( ∇ X f ) T G t d B t {\displaystyle {\begin{aligned}df(t,\mathbf {X} _{t})&={\frac {\partial f}{\partial t}}\,dt+\left(\nabla _{\mathbf {X} }f\right)^{T}\,d\mathbf {X} _{t}+{\frac {1}{2}}\left(d\mathbf {X} _{t}\right)^{T}\left(H_{\mathbf {X} }f\right)\,d\mathbf {X} _{t},\\[4pt]&=\left\{{\frac {\partial f}{\partial t}}+\left(\nabla _{\mathbf {X} }f\right)^{T}{\boldsymbol {\mu }}_{t}+{\frac {1}{2}}\operatorname {Tr} \left[\mathbf {G} _{t}^{T}\left(H_{\mathbf {X} }f\right)\mathbf {G} _{t}\right]\right\}\,dt+\left(\nabla _{\mathbf {X} }f\right)^{T}\mathbf {G} _{t}\,d\mathbf {B} _{t}\end{aligned}}}
where ∇ X f {\displaystyle \nabla _{\mathbf {X} }f} is the gradient of f w.r.t. X , H X f is the Hessian matrix of f w.r.t. X , and Tr is the trace operator .
We may also define functions on discontinuous stochastic processes.
Let h be the jump intensity. The Poisson process model for jumps is that the probability of one jump in the interval [ t , t + Δ t ] is h Δ t plus higher order terms. h could be a constant, a deterministic function of time, or a stochastic process. The survival probability p s ( t ) is the probability that no jump has occurred in the interval [0, t ] . The change in the survival probability is
d p s ( t ) = − p s ( t ) h ( t ) d t . {\displaystyle dp_{s}(t)=-p_{s}(t)h(t)\,dt.}
So
p s ( t ) = exp ( − ∫ 0 t h ( u ) d u ) . {\displaystyle p_{s}(t)=\exp \left(-\int _{0}^{t}h(u)\,du\right).}
Let S ( t ) be a discontinuous stochastic process. Write S ( t − ) {\displaystyle S(t^{-})} for the value of S as we approach t from the left. Write d j S ( t ) {\displaystyle d_{j}S(t)} for the non-infinitesimal change in S ( t ) as a result of a jump. Then
d j S ( t ) = lim Δ t → 0 [ S ( t + Δ t ) − S ( t − ) ] {\displaystyle d_{j}S(t)=\lim _{\Delta t\to 0}\left[S(t+\Delta t)-S(t^{-})\right]}
Let z be the magnitude of the jump and let η ( S ( t − ) , z ) {\displaystyle \eta (S(t^{-}),z)} be the distribution of z . The expected magnitude of the jump is
E [ d j S ( t ) ] = h ( S ( t − ) ) d t ∫ z z η ( S ( t − ) , z ) d z . {\displaystyle \operatorname {E} [d_{j}S(t)]=h(S(t^{-}))\,dt\int _{z}z\eta (S(t^{-}),z)\,dz.}
Define d J S ( t ) {\displaystyle dJ_{S}(t)} , a compensated process and martingale , as
d J S ( t ) = d j S ( t ) − E [ d j S ( t ) ] = S ( t ) − S ( t − ) − ( h ( S ( t − ) ) ∫ z z η ( S ( t − ) , z ) d z ) d t . {\displaystyle {\begin{aligned}dJ_{S}(t)&=d_{j}S(t)-\operatorname {E} [d_{j}S(t)]\\[1ex]&=S(t)-S(t^{-})-\left(h(S(t^{-}))\int _{z}z\eta \left(S(t^{-}),z\right)\,dz\right)\,dt.\end{aligned}}}
Then
d j S ( t ) = E [ d j S ( t ) ] + d J S ( t ) = h ( S ( t − ) ) ( ∫ z z η ( S ( t − ) , z ) d z ) d t + d J S ( t ) . {\displaystyle {\begin{aligned}d_{j}S(t)&=E[d_{j}S(t)]+dJ_{S}(t)\\[1ex]&=h(S(t^{-}))\left(\int _{z}z\eta (S(t^{-}),z)\,dz\right)dt+dJ_{S}(t).\end{aligned}}}
Consider a function g ( S ( t ) , t ) {\displaystyle g(S(t),t)} of the jump process dS ( t ) . If S ( t ) jumps by Δ s then g ( t ) jumps by Δ g . Δ g is drawn from distribution η g ( ) {\displaystyle \eta _{g}()} which may depend on g ( t − ) {\displaystyle g(t^{-})} , dg and S ( t − ) {\displaystyle S(t^{-})} . The jump part of g {\displaystyle g} is
g ( t ) − g ( t − ) = h ( t ) d t ∫ Δ g Δ g η g ( ⋅ ) d Δ g + d J g ( t ) . {\displaystyle g(t)-g(t^{-})=h(t)\,dt\int _{\Delta g}\,\Delta g\eta _{g}(\cdot )\,d\Delta g+dJ_{g}(t).}
If S {\displaystyle S} contains drift, diffusion and jump parts, then Itô's Lemma for g ( S ( t ) , t ) {\displaystyle g(S(t),t)} is
d g ( t ) = ( ∂ g ∂ t + μ ∂ g ∂ S + σ 2 2 ∂ 2 g ∂ S 2 + h ( t ) ∫ Δ g ( Δ g η g ( ⋅ ) d Δ g ) ) d t + ∂ g ∂ S σ d W ( t ) + d J g ( t ) . {\displaystyle {\begin{aligned}dg(t)={}&\left({\frac {\partial g}{\partial t}}+\mu {\frac {\partial g}{\partial S}}+{\frac {\sigma ^{2}}{2}}{\frac {\partial ^{2}g}{\partial S^{2}}}+h(t)\int _{\Delta g}\left(\Delta g\eta _{g}(\cdot )\,d{\Delta }g\right)\,\right)dt\\&+{\frac {\partial g}{\partial S}}\sigma \,dW(t)+dJ_{g}(t).\end{aligned}}}
Itô's lemma for a process which is the sum of a drift-diffusion process and a jump process is just the sum of the Itô's lemma for the individual parts.
Itô's lemma can also be applied to general d -dimensional semimartingales , which need not be continuous. In general, a semimartingale is a càdlàg process, and an additional jump term needs to be added to the Itô's formula.
For any cadlag process Y t , the left limit in t is denoted by Y t− , which is a left-continuous process. The jumps are written as Δ Y t = Y t − Y t− . Then, Itô's lemma states that if X = ( X 1 , X 2 , ..., X d ) is a d -dimensional semimartingale and f is a twice continuously differentiable real valued function on R d then f ( X ) is a semimartingale, and
f ( X t ) = f ( X 0 ) + ∑ i = 1 d ∫ 0 t f i ( X s − ) d X s i + 1 2 ∑ i , j = 1 d ∫ 0 t f i , j ( X s − ) d [ X i , X j ] s + ∑ s ≤ t ( Δ f ( X s ) − ∑ i = 1 d f i ( X s − ) Δ X s i − 1 2 ∑ i , j = 1 d f i , j ( X s − ) Δ X s i Δ X s j ) . {\displaystyle {\begin{aligned}f(X_{t})=f(X_{0})&+\sum _{i=1}^{d}\int _{0}^{t}f_{i}(X_{s-})\,dX_{s}^{i}+{\frac {1}{2}}\sum _{i,j=1}^{d}\int _{0}^{t}f_{i,j}(X_{s-})\,d[X^{i},X^{j}]_{s}\\&+\sum _{s\leq t}\left(\Delta f(X_{s})-\sum _{i=1}^{d}f_{i}(X_{s-})\,\Delta X_{s}^{i}-{\frac {1}{2}}\sum _{i,j=1}^{d}f_{i,j}(X_{s-})\,\Delta X_{s}^{i}\,\Delta X_{s}^{j}\right).\end{aligned}}}
This differs from the formula for continuous semi-martingales by the last term summing over the jumps of X , which ensures that the jump of the right hand side at time t is Δ f ( X t ).
A process S is said to follow a geometric Brownian motion with constant volatility σ and constant drift μ if it satisfies the stochastic differential equation d S t = σ S t d B t + μ S t d t {\displaystyle dS_{t}=\sigma S_{t}\,dB_{t}+\mu S_{t}\,dt} , for a Brownian motion B . Applying Itô's lemma with f ( S t ) = log ( S t ) {\displaystyle f(S_{t})=\log(S_{t})} gives
d f = f ′ ( S t ) d S t + 1 2 f ″ ( S t ) ( d S t ) 2 = 1 S t d S t + 1 2 ( − S t − 2 ) ( S t 2 σ 2 d t ) = 1 S t ( σ S t d B t + μ S t d t ) − σ 2 2 d t = σ d B t + ( μ − σ 2 2 ) d t . {\displaystyle {\begin{aligned}df&=f'(S_{t})\,dS_{t}+{\frac {1}{2}}f''(S_{t})\,{\left(dS_{t}\right)}^{2}\\[4pt]&={\frac {1}{S_{t}}}\,dS_{t}+{\frac {1}{2}}\left(-S_{t}^{-2}\right)\left(S_{t}^{2}\sigma ^{2}\,dt\right)\\[4pt]&={\frac {1}{S_{t}}}\left(\sigma S_{t}\,dB_{t}+\mu S_{t}\,dt\right)-{\frac {\sigma ^{2}}{2}}\,dt\\[4pt]&=\sigma \,dB_{t}+\left(\mu -{\tfrac {\sigma ^{2}}{2}}\right)dt.\end{aligned}}}
It follows that
log ( S t ) = log ( S 0 ) + σ B t + ( μ − σ 2 2 ) t , {\displaystyle \log(S_{t})=\log(S_{0})+\sigma B_{t}+\left(\mu -{\tfrac {\sigma ^{2}}{2}}\right)t,}
exponentiating gives the expression for S ,
S t = S 0 exp ( σ B t + ( μ − σ 2 2 ) t ) . {\displaystyle S_{t}=S_{0}\exp \left(\sigma B_{t}+\left(\mu -{\tfrac {\sigma ^{2}}{2}}\right)t\right).}
The correction term of − σ 2 / 2 corresponds to the difference between the median and mean of the log-normal distribution , or equivalently for this distribution, the geometric mean and arithmetic mean, with the median (geometric mean) being lower. This is due to the AM–GM inequality , and corresponds to the logarithm being concave (or convex upwards), so the correction term can accordingly be interpreted as a convexity correction . This is an infinitesimal version of the fact that the annualized return is less than the average return, with the difference proportional to the variance. See geometric moments of the log-normal distribution for further discussion.
The same factor of σ 2 / 2 appears in the d 1 and d 2 auxiliary variables of the Black–Scholes formula , and can be interpreted as a consequence of Itô's lemma.
The Doléans-Dade exponential (or stochastic exponential) of a continuous semimartingale X can be defined as the solution to the SDE dY = Y dX with initial condition Y 0 = 1 . It is sometimes denoted by Ɛ( X ) .
Applying Itô's lemma with f ( Y ) = log( Y ) gives
d log ( Y ) = 1 Y d Y − 1 2 Y 2 d [ Y ] = d X − 1 2 d [ X ] . {\displaystyle {\begin{aligned}d\log(Y)&={\frac {1}{Y}}\,dY-{\frac {1}{2Y^{2}}}\,d[Y]\\[6pt]&=dX-{\tfrac {1}{2}}\,d[X].\end{aligned}}}
Exponentiating gives the solution
Y t = exp ( X t − X 0 − 1 2 [ X ] t ) . {\displaystyle Y_{t}=\exp \left(X_{t}-X_{0}-{\tfrac {1}{2}}[X]_{t}\right).}
Itô's lemma can be used to derive the Black–Scholes equation for an option . [ 3 ] Suppose a stock price follows a geometric Brownian motion given by the stochastic differential equation dS = S ( σ dB + μ dt ) . Then, if the value of an option at time t is f ( t , S t ) , Itô's lemma gives
d f ( t , S t ) = ( ∂ f ∂ t + 1 2 ( S t σ ) 2 ∂ 2 f ∂ S 2 ) d t + ∂ f ∂ S d S t . {\displaystyle df(t,S_{t})=\left({\frac {\partial f}{\partial t}}+{\frac {1}{2}}\left(S_{t}\sigma \right)^{2}{\frac {\partial ^{2}f}{\partial S^{2}}}\right)\,dt+{\frac {\partial f}{\partial S}}\,dS_{t}.}
The term ∂ f / ∂ S dS represents the change in value in time dt of the trading strategy consisting of holding an amount ∂ f / ∂ S of the stock. If this trading strategy is followed, and any cash held is assumed to grow at the risk free rate r , then the total value V of this portfolio satisfies the SDE
d V t = r ( V t − ∂ f ∂ S S t ) d t + ∂ f ∂ S d S t . {\displaystyle dV_{t}=r\left(V_{t}-{\frac {\partial f}{\partial S}}S_{t}\right)\,dt+{\frac {\partial f}{\partial S}}\,dS_{t}.}
This strategy replicates the option if V = f ( t , S ) . Combining these equations gives the celebrated Black–Scholes equation
∂ f ∂ t + σ 2 S 2 2 ∂ 2 f ∂ S 2 + r S ∂ f ∂ S − r f = 0. {\displaystyle {\frac {\partial f}{\partial t}}+{\frac {\sigma ^{2}S^{2}}{2}}{\frac {\partial ^{2}f}{\partial S^{2}}}+rS{\frac {\partial f}{\partial S}}-rf=0.}
Let X t {\displaystyle \mathbf {X} _{t}} be a two-dimensional Ito process with SDE: d X t = d ( X t 1 X t 2 ) = ( μ t 1 μ t 2 ) d t + ( σ t 1 σ t 2 ) d B t {\displaystyle d\mathbf {X} _{t}=d{\begin{pmatrix}X_{t}^{1}\\X_{t}^{2}\end{pmatrix}}={\begin{pmatrix}\mu _{t}^{1}\\\mu _{t}^{2}\end{pmatrix}}dt+{\begin{pmatrix}\sigma _{t}^{1}\\\sigma _{t}^{2}\end{pmatrix}}\,dB_{t}}
Then we can use the multi-dimensional form of Ito's lemma to find an expression for d ( X t 1 X t 2 ) {\displaystyle d(X_{t}^{1}X_{t}^{2})} .
We have μ t = ( μ t 1 μ t 2 ) {\displaystyle \mu _{t}={\begin{pmatrix}\mu _{t}^{1}\\\mu _{t}^{2}\end{pmatrix}}} and G = ( σ t 1 σ t 2 ) {\displaystyle \mathbf {G} ={\begin{pmatrix}\sigma _{t}^{1}\\\sigma _{t}^{2}\end{pmatrix}}} .
We set f ( t , X t ) = X t 1 X t 2 {\displaystyle f(t,\mathbf {X} _{t})=X_{t}^{1}X_{t}^{2}} and observe that ∂ f ∂ t = 0 {\displaystyle {\frac {\partial f}{\partial t}}=0} , ( ∇ X f ) T = ( X t 2 X t 1 ) {\displaystyle (\nabla _{\mathbf {X} }f)^{T}={\begin{pmatrix}X_{t}^{2}&X_{t}^{1}\end{pmatrix}}} , and H X f = ( 0 1 1 0 ) {\displaystyle H_{\mathbf {X} }f={\begin{pmatrix}0&1\\1&0\end{pmatrix}}}
Substituting these values in the multi-dimensional version of the lemma gives us:
d ( X t 1 X t 2 ) = d f ( t , X t ) = 0 ⋅ d t + ( X t 2 X t 1 ) d X t + 1 2 ( d X t 1 d X t 2 ) ( 0 1 1 0 ) ( d X t 1 d X t 2 ) = X t 2 d X t 1 + X t 1 d X t 2 + d X t 1 d X t 2 {\displaystyle {\begin{aligned}d(X_{t}^{1}X_{t}^{2})&=df(t,\mathbf {X} _{t})\\&=0\cdot dt+{\begin{pmatrix}X_{t}^{2}&X_{t}^{1}\end{pmatrix}}\,d\mathbf {X} _{t}+{\frac {1}{2}}{\begin{pmatrix}dX_{t}^{1}&dX_{t}^{2}\end{pmatrix}}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}dX_{t}^{1}\\dX_{t}^{2}\end{pmatrix}}\\[1ex]&=X_{t}^{2}\,dX_{t}^{1}+X_{t}^{1}\,dX_{t}^{2}+dX_{t}^{1}\,dX_{t}^{2}\end{aligned}}}
This is a generalisation of Leibniz's product rule to Ito processes, which are non-differentiable.
Further, using the second form of the multidimensional version above gives us
d ( X t 1 X t 2 ) = { 0 + ( X t 2 X t 1 ) ( μ t 1 μ t 2 ) + 1 2 Tr [ ( σ t 1 σ t 2 ) ( 0 1 1 0 ) ( σ t 1 σ t 2 ) ] } d t + ( X t 2 σ t 1 + X t 1 σ t 2 ) d B t = ( X t 2 μ t 1 + X t 1 μ t 2 + σ t 1 σ t 2 ) d t + ( X t 2 σ t 1 + X t 1 σ t 2 ) d B t {\displaystyle {\begin{aligned}d(X_{t}^{1}X_{t}^{2})&=\left\{0+{\begin{pmatrix}X_{t}^{2}&X_{t}^{1}\end{pmatrix}}{\begin{pmatrix}\mu _{t}^{1}\\\mu _{t}^{2}\end{pmatrix}}+{\frac {1}{2}}\operatorname {Tr} \left[{\begin{pmatrix}\sigma _{t}^{1}&\sigma _{t}^{2}\end{pmatrix}}{\begin{pmatrix}0&1\\1&0\end{pmatrix}}{\begin{pmatrix}\sigma _{t}^{1}\\\sigma _{t}^{2}\end{pmatrix}}\right]\right\}dt\\[1ex]&\qquad +\left(X_{t}^{2}\sigma _{t}^{1}+X_{t}^{1}\sigma _{t}^{2}\right)dB_{t}\\[2ex]&=\left(X_{t}^{2}\mu _{t}^{1}+X_{t}^{1}\mu _{t}^{2}+\sigma _{t}^{1}\sigma _{t}^{2}\right)dt+\left(X_{t}^{2}\sigma _{t}^{1}+X_{t}^{1}\sigma _{t}^{2}\right)dB_{t}\end{aligned}}}
so we see that the product X t 1 X t 2 {\displaystyle X_{t}^{1}X_{t}^{2}} is itself an Itô drift-diffusion process .
Hans Föllmer provided a non-probabilistic proof of the Itô formula and showed that it holds for all functions with finite quadratic variation. [ 4 ]
Let f ∈ C 2 {\displaystyle f\in C^{2}} be a real-valued function and x : [ 0 , ∞ ] → R {\displaystyle x:[0,\infty ]\to \mathbb {R} } a right-continuous function with left limits and finite quadratic variation [ x ] {\displaystyle [x]} . Then f ( x t ) = f ( x 0 ) + ∫ 0 t f ′ ( x s − ) d x s + 1 2 ∫ ] 0 , t ] f ″ ( x s − ) d [ x ] s + ∑ 0 ≤ s ≤ t [ f ( x s ) − f ( x s − ) − f ′ ( x s − ) Δ x s − 1 2 f ″ ( x s − ) ( Δ x s ) 2 ] . {\displaystyle {\begin{aligned}f(x_{t})=f(x_{0})&+\int _{0}^{t}f'(x_{s-})\,\mathrm {d} x_{s}+{\frac {1}{2}}\int _{]0,t]}f''(x_{s-})\,d[x]_{s}\\&+\sum _{0\leq s\leq t}\left[f(x_{s})-f(x_{s-})-f'(x_{s-})\Delta x_{s}-{\frac {1}{2}}f''(x_{s-})(\Delta x_{s})^{2}\right].\end{aligned}}}
where the quadratic variation of x {\displaystyle x} is defined as a limit along a sequence of partitions D n {\displaystyle D_{n}} of [ 0 , t ] {\displaystyle [0,t]} with step decreasing to zero:
[ x ] ( t ) = lim n → ∞ ∑ t k n ∈ D n ( x t k + 1 n − x t k n ) 2 . {\displaystyle [x](t)=\lim _{n\to \infty }\sum _{t_{k}^{n}\in D_{n}}\left(x_{t_{k+1}^{n}}-x_{t_{k}^{n}}\right)^{2}.}
Rama Cont and Nicholas Perkowski extended the Ito formula to functions with finite p -th variation where p ≥ 2 {\displaystyle p\geq 2} is an arbitrarily large integer. [ 5 ]
Given a continuous function with finite p-th variation
[ x ] p ( t ) = lim n → ∞ ∑ t k n ∈ D n ( x t k + 1 n − x t k n ) p , {\displaystyle [x]^{p}(t)=\lim _{n\to \infty }\sum _{t_{k}^{n}\in D_{n}}{\left(x_{t_{k+1}^{n}}-x_{t_{k}^{n}}\right)}^{p},}
Cont and Perkowski's change of variable formula states that for any f ∈ C p ( R d , R ) {\displaystyle f\in C^{p}(\mathbb {R} ^{d},\mathbb {R} )} :
f ( x t ) = f ( x 0 ) + ∫ 0 t ∇ p − 1 f ( x s − ) d x s + 1 p ! ∫ ] 0 , t ] f p ( x s − ) d [ x ] s p {\displaystyle {\begin{aligned}f(x_{t})={}&f(x_{0})+\int _{0}^{t}\nabla _{p-1}f(x_{s-})\,\mathrm {d} x_{s}+{\frac {1}{p!}}\int _{]0,t]}f^{p}(x_{s-})\,d[x]_{s}^{p}\end{aligned}}}
where the first integral is defined as a limit of compensated left Riemann sums along a sequence of partitions D n {\displaystyle D_{n}} :
∫ 0 t ∇ p − 1 f ( x s − ) d x s := ∑ t k n ∈ D n ∑ k = 1 p − 1 f k ( x t k n ) k ! ( x t k + 1 n − x t k n ) k . {\displaystyle {\begin{aligned}\int _{0}^{t}\nabla _{p-1}f(x_{s-})\,\mathrm {d} x_{s}:={}&\sum _{t_{k}^{n}\in D_{n}}\sum _{k=1}^{p-1}{\frac {f^{k}(x_{t_{k}^{n}})}{k!}}\left(x_{t_{k+1}^{n}}-x_{t_{k}^{n}}\right)^{k}.\end{aligned}}} An extension to the case of fractional regularity (non-integer p {\displaystyle p} ) was obtained by Cont and Jin. [ 6 ]
There exist some extensions to infinite-dimensional spaces (e.g. Pardoux, [ 7 ] Gyöngy-Krylov, [ 8 ] Brzezniak-van Neerven-Veraar-Weis [ 9 ] ). | https://en.wikipedia.org/wiki/Itô's_lemma |
Itô calculus , named after Kiyosi Itô , extends the methods of calculus to stochastic processes such as Brownian motion (see Wiener process ). It has important applications in mathematical finance and stochastic differential equations .
The central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators are now stochastic processes: Y t = ∫ 0 t H s d X s , {\displaystyle Y_{t}=\int _{0}^{t}H_{s}\,dX_{s},} where H is a locally square-integrable process adapted to the filtration generated by X ( Revuz & Yor 1999 , Chapter IV), which is a Brownian motion or, more generally, a semimartingale . The result of the integration is then another stochastic process. Concretely, the integral from 0 to any particular t is a random variable , defined as a limit of a certain sequence of random variables. The paths of Brownian motion fail to satisfy the requirements to be able to apply the standard techniques of calculus. So with the integrand a stochastic process, the Itô stochastic integral amounts to an integral with respect to a function which is not differentiable at any point and has infinite variation over every time interval.
The main insight is that the integral can be defined as long as the integrand H is adapted , which loosely speaking means that its value at time t can only depend on information available up until this time. Roughly speaking, one chooses a sequence of partitions of the interval from 0 to t and constructs Riemann sums . Every time we are computing a Riemann sum, we are using a particular instantiation of the integrator. It is crucial which point in each of the small intervals is used to compute the value of the function. The limit then is taken in probability as the mesh of the partition is going to zero. Numerous technical details have to be taken care of to show that this limit exists and is independent of the particular sequence of partitions. Typically, the left end of the interval is used.
Important results of Itô calculus include the integration by parts formula and Itô's lemma , which is a change of variables formula. These differ from the formulas of standard calculus, due to quadratic variation terms. This can be contrasted to the Stratonovich integral as an alternative formulation; it does follow the chain rule , and does not require Itô's lemma. The two integral forms can be converted to one-another. The Stratonovich integral is obtained as the limiting form of a Riemann sum that employs the average of stochastic variable over each small timestep, whereas the Itô integral considers it only at the beginning.
In mathematical finance , the described evaluation strategy of the integral is conceptualized as that we are first deciding what to do, then observing the change in the prices. The integrand is how much stock we hold, the integrator represents the movement of the prices, and the integral is how much money we have in total including what our stock is worth, at any given moment. The prices of stocks and other traded financial assets can be modeled by stochastic processes such as Brownian motion or, more often, geometric Brownian motion (see Black–Scholes ). Then, the Itô stochastic integral represents the payoff of a continuous-time trading strategy consisting of holding an amount H t of the stock at time t . In this situation, the condition that H is adapted corresponds to the necessary restriction that the trading strategy can only make use of the available information at any time. This prevents the possibility of unlimited gains through clairvoyance : buying the stock just before each uptick in the market and selling before each downtick. Similarly, the condition that H is adapted implies that the stochastic integral will not diverge when calculated as a limit of Riemann sums ( Revuz & Yor 1999 , Chapter IV).
The process Y defined before as Y t = ∫ 0 t H d X ≡ ∫ 0 t H s d X s , {\displaystyle Y_{t}=\int _{0}^{t}H\,dX\equiv \int _{0}^{t}H_{s}\,dX_{s},} is itself a stochastic process with time parameter t , which is also sometimes written as Y = H · X ( Rogers & Williams 2000 ). Alternatively, the integral is often written in differential form dY = H dX , which is equivalent to Y − Y 0 = H · X . As Itô calculus is concerned with continuous-time stochastic processes, it is assumed that an underlying filtered probability space is given ( Ω , F , ( F t ) t ≥ 0 , P ) . {\displaystyle (\Omega ,{\mathcal {F}},({\mathcal {F}}_{t})_{t\geq 0},\mathbb {P} ).} The σ-algebra F t {\displaystyle {\mathcal {F}}_{t}} represents the information available up until time t , and a process X is adapted if X t is F t {\displaystyle {\mathcal {F}}_{t}} -measurable. A Brownian motion B is understood to be an F t {\displaystyle {\mathcal {F}}_{t}} -Brownian motion, which is just a standard Brownian motion with the properties that B t is F t {\displaystyle {\mathcal {F}}_{t}} -measurable and that B t + s − B t is independent of F t {\displaystyle {\mathcal {F}}_{t}} for all s , t ≥ 0 ( Revuz & Yor 1999 ).
The Itô integral can be defined in a manner similar to the Riemann–Stieltjes integral , that is as a limit in probability of Riemann sums ; such a limit does not necessarily exist pathwise. Suppose that B is a Wiener process (Brownian motion) and that H is a right-continuous ( càdlàg ), adapted and locally bounded process. If { π n } {\displaystyle \{\pi _{n}\}} is a sequence of partitions of [0, t ] with mesh width going to zero, then the Itô integral of H with respect to B up to time t is a random variable ∫ 0 t H d B = lim n → ∞ ∑ [ t i − 1 , t i ] ∈ π n H t i − 1 ( B t i − B t i − 1 ) . {\displaystyle \int _{0}^{t}H\,dB=\lim _{n\rightarrow \infty }\sum _{[t_{i-1},t_{i}]\in \pi _{n}}H_{t_{i-1}}(B_{t_{i}}-B_{t_{i-1}}).}
It can be shown that this limit converges in probability .
For some applications, such as martingale representation theorems and local times , the integral is needed for processes that are not continuous. The predictable processes form the smallest class that is closed under taking limits of sequences and contains all adapted left-continuous processes. If H is any predictable process such that ∫ 0 t H 2 ds < ∞ for every t ≥ 0 then the integral of H with respect to B can be defined, and H is said to be B -integrable. Any such process can be approximated by a sequence H n of left-continuous, adapted and locally bounded processes, in the sense that ∫ 0 t ( H − H n ) 2 d s → 0 {\displaystyle \int _{0}^{t}(H-H_{n})^{2}\,ds\to 0} in probability. Then, the Itô integral is ∫ 0 t H d B = lim n → ∞ ∫ 0 t H n d B {\displaystyle \int _{0}^{t}H\,dB=\lim _{n\to \infty }\int _{0}^{t}H_{n}\,dB} where, again, the limit can be shown to converge in probability. The stochastic integral satisfies the Itô isometry E [ ( ∫ 0 t H s d B s ) 2 ] = E [ ∫ 0 t H s 2 d s ] {\displaystyle \mathbb {E} \left[\left(\int _{0}^{t}H_{s}\,dB_{s}\right)^{2}\right]=\mathbb {E} \left[\int _{0}^{t}H_{s}^{2}\,ds\right]} which holds when H is bounded or, more generally, when the integral on the right hand side is finite.
An Itô process is defined to be an adapted stochastic process that can be expressed as the sum of an integral with respect to Brownian motion and an integral with respect to time, X t = X 0 + ∫ 0 t σ s d B s + ∫ 0 t μ s d s . {\displaystyle X_{t}=X_{0}+\int _{0}^{t}\sigma _{s}\,dB_{s}+\int _{0}^{t}\mu _{s}\,ds.}
Here, B is a Brownian motion and it is required that σ is a predictable B -integrable process, and μ is predictable and ( Lebesgue ) integrable. That is, ∫ 0 t ( σ s 2 + | μ s | ) d s < ∞ {\displaystyle \int _{0}^{t}(\sigma _{s}^{2}+|\mu _{s}|)\,ds<\infty } for each t . The stochastic integral can be extended to such Itô processes, ∫ 0 t H d X = ∫ 0 t H s σ s d B s + ∫ 0 t H s μ s d s . {\displaystyle \int _{0}^{t}H\,dX=\int _{0}^{t}H_{s}\sigma _{s}\,dB_{s}+\int _{0}^{t}H_{s}\mu _{s}\,ds.}
This is defined for all locally bounded and predictable integrands. More generally, it is required that Hσ be B -integrable and Hμ be Lebesgue integrable, so that ∫ 0 t ( H 2 σ 2 + | H μ | ) d s < ∞ . {\displaystyle \int _{0}^{t}\left(H^{2}\sigma ^{2}+|H\mu |\right)ds<\infty .} Such predictable processes H are called X -integrable.
An important result for the study of Itô processes is Itô's lemma . In its simplest form, for any twice continuously differentiable function f on the reals and Itô process X as described above, it states that Y t = f ( X t ) {\displaystyle Y_{t}=f(X_{t})} is itself an Itô process satisfying d Y t = f ′ ( X t ) μ t d t + 1 2 f ′ ′ ( X t ) σ t 2 d t + f ′ ( X t ) σ t d B t . {\displaystyle dY_{t}=f^{\prime }(X_{t})\mu _{t}\,dt+{\tfrac {1}{2}}f^{\prime \prime }(X_{t})\sigma _{t}^{2}\,dt+f^{\prime }(X_{t})\sigma _{t}\,dB_{t}.}
This is the stochastic calculus version of the change of variables formula and chain rule . It differs from the standard result due to the additional term involving the second derivative of f , which comes from the property that Brownian motion has non-zero quadratic variation .
The Itô integral is defined with respect to a semimartingale X . These are processes which can be decomposed as X = M + A for a local martingale M and finite variation process A . Important examples of such processes include Brownian motion , which is a martingale , and Lévy processes . For a left continuous, locally bounded and adapted process H the integral H · X exists, and can be calculated as a limit of Riemann sums. Let π n be a sequence of partitions of [0, t ] with mesh going to zero, ∫ 0 t H d X = lim n → ∞ ∑ t i − 1 , t i ∈ π n H t i − 1 ( X t i − X t i − 1 ) . {\displaystyle \int _{0}^{t}H\,dX=\lim _{n\to \infty }\sum _{t_{i-1},t_{i}\in \pi _{n}}H_{t_{i-1}}(X_{t_{i}}-X_{t_{i-1}}).}
This limit converges in probability. The stochastic integral of left-continuous processes is general enough for studying much of stochastic calculus. For example, it is sufficient for applications of Itô's Lemma, changes of measure via Girsanov's theorem , and for the study of stochastic differential equations . However, it is inadequate for other important topics such as martingale representation theorems and local times .
The integral extends to all predictable and locally bounded integrands, in a unique way, such that the dominated convergence theorem holds. That is, if H n → H and | H n | ≤ J for a locally bounded process J , then ∫ 0 t H n d X → ∫ 0 t H d X , {\displaystyle \int _{0}^{t}H_{n}\,dX\to \int _{0}^{t}H\,dX,} in probability. The uniqueness of the extension from left-continuous to predictable integrands is a result of the monotone class lemma .
In general, the stochastic integral H · X can be defined even in cases where the predictable process H is not locally bounded. If K = 1 / (1 + | H |) then K and KH are bounded. Associativity of stochastic integration implies that H is X -integrable, with integral H · X = Y , if and only if Y 0 = 0 and K · Y = ( KH ) · X . The set of X -integrable processes is denoted by L ( X ) .
The following properties can be found in works such as ( Revuz & Yor 1999 ) and ( Rogers & Williams 2000 ):
As with ordinary calculus, integration by parts is an important result in stochastic calculus. The integration by parts formula for the Itô integral differs from the standard result due to the inclusion of a quadratic covariation term. This term comes from the fact that Itô calculus deals with processes with non-zero quadratic variation, which only occurs for infinite variation processes (such as Brownian motion). If X and Y are semimartingales then X t Y t = X 0 Y 0 + ∫ 0 t X s − d Y s + ∫ 0 t Y s − d X s + [ X , Y ] t {\displaystyle X_{t}Y_{t}=X_{0}Y_{0}+\int _{0}^{t}X_{s-}\,dY_{s}+\int _{0}^{t}Y_{s-}\,dX_{s}+[X,Y]_{t}} where [ X , Y ] is the quadratic covariation process.
The result is similar to the integration by parts theorem for the Riemann–Stieltjes integral but has an additional quadratic variation term.
Itô's lemma is the version of the chain rule or change of variables formula which applies to the Itô integral. It is one of the most powerful and frequently used theorems in stochastic calculus. For a continuous n -dimensional semimartingale X = ( X 1 ,..., X n ) and twice continuously differentiable function f from R n to R , it states that f ( X ) is a semimartingale and, d f ( X t ) = ∑ i = 1 n f i ( X t ) d X t i + 1 2 ∑ i , j = 1 n f i , j ( X t ) d [ X i , X j ] t . {\displaystyle df(X_{t})=\sum _{i=1}^{n}f_{i}(X_{t})\,dX_{t}^{i}+{\frac {1}{2}}\sum _{i,j=1}^{n}f_{i,j}(X_{t})\,d[X^{i},X^{j}]_{t}.} This differs from the chain rule used in standard calculus due to the term involving the quadratic covariation [ X i , X j ] . The formula can be generalized to include an explicit time-dependence in f , {\displaystyle f,} and in other ways (see Itô's lemma ).
An important property of the Itô integral is that it preserves the local martingale property. If M is a local martingale and H is a locally bounded predictable process then H · M is also a local martingale. For integrands which are not locally bounded, there are examples where H · M is not a local martingale. However, this can only occur when M is not continuous. If M is a continuous local martingale then a predictable process H is M -integrable if and only if ∫ 0 t H 2 d [ M ] < ∞ , {\displaystyle \int _{0}^{t}H^{2}\,d[M]<\infty ,} for each t , and H · M is always a local martingale.
The most general statement for a discontinuous local martingale M is that if ( H 2 · [ M ]) 1/2 is locally integrable then H · M exists and is a local martingale.
For bounded integrands, the Itô stochastic integral preserves the space of square integrable martingales, which is the set of càdlàg martingales M such that E[ M t 2 ] is finite for all t . For any such square integrable martingale M , the quadratic variation process [ M ] is integrable, and the Itô isometry states that E [ ( H ⋅ M t ) 2 ] = E [ ∫ 0 t H 2 d [ M ] ] . {\displaystyle \mathbb {E} \left[(H\cdot M_{t})^{2}\right]=\mathbb {E} \left[\int _{0}^{t}H^{2}\,d[M]\right].} This equality holds more generally for any martingale M such that H 2 · [ M ] t is integrable. The Itô isometry is often used as an important step in the construction of the stochastic integral, by defining H · M to be the unique extension of this isometry from a certain class of simple integrands to all bounded and predictable processes.
For any p > 1 , and bounded predictable integrand, the stochastic integral preserves the space of p -integrable martingales. These are càdlàg martingales such that E(| M t | p ) is finite for all t . However, this is not always true in the case where p = 1 . There are examples of integrals of bounded predictable processes with respect to martingales which are not themselves martingales.
The maximum process of a càdlàg process M is written as M* t = sup s ≤ t | M s | . For any p ≥ 1 and bounded predictable integrand, the stochastic integral preserves the space of càdlàg martingales M such that E[( M* t ) p ] is finite for all t . If p > 1 then this is the same as the space of p -integrable martingales, by Doob's inequalities .
The Burkholder–Davis–Gundy inequalities state that, for any given p ≥ 1 , there exist positive constants c , C that depend on p , but not M or on t such that c E [ [ M ] t p 2 ] ≤ E [ ( M t ∗ ) p ] ≤ C E [ [ M ] t p 2 ] {\displaystyle c\mathbb {E} \left[[M]_{t}^{\frac {p}{2}}\right]\leq \mathbb {E} \left[(M_{t}^{*})^{p}\right]\leq C\mathbb {E} \left[[M]_{t}^{\frac {p}{2}}\right]} for all càdlàg local martingales M . These are used to show that if ( M* t ) p is integrable and H is a bounded predictable process then E [ ( ( H ⋅ M ) t ∗ ) p ] ≤ C E [ ( H 2 ⋅ [ M ] t ) p 2 ] < ∞ {\displaystyle \mathbb {E} \left[((H\cdot M)_{t}^{*})^{p}\right]\leq C\mathbb {E} \left[(H^{2}\cdot [M]_{t})^{\frac {p}{2}}\right]<\infty } and, consequently, H · M is a p -integrable martingale. More generally, this statement is true whenever ( H 2 · [ M ]) p /2 is integrable.
Proofs that the Itô integral is well defined typically proceed by first looking at very simple integrands, such as piecewise constant, left continuous and adapted processes where the integral can be written explicitly. Such simple predictable processes are linear combinations of terms of the form H t = A 1 { t > T } for stopping times T and F T -measurable random variables A , for which the integral is H ⋅ X t ≡ 1 { t > T } A ( X t − X T ) . {\displaystyle H\cdot X_{t}\equiv \mathbf {1} _{\{t>T\}}A(X_{t}-X_{T}).} This is extended to all simple predictable processes by the linearity of H · X in H .
For a Brownian motion B , the property that it has independent increments with zero mean and variance Var( B t ) = t can be used to prove the Itô isometry for simple predictable integrands, E [ ( H ⋅ B t ) 2 ] = E [ ∫ 0 t H s 2 d s ] . {\displaystyle \mathbb {E} \left[(H\cdot B_{t})^{2}\right]=\mathbb {E} \left[\int _{0}^{t}H_{s}^{2}\,ds\right].} By a continuous linear extension , the integral extends uniquely to all predictable integrands satisfying E [ ∫ 0 t H 2 d s ] < ∞ , {\displaystyle \mathbb {E} \left[\int _{0}^{t}H^{2}\,ds\right]<\infty ,} in such way that the Itô isometry still holds. It can then be extended to all B -integrable processes by localization . This method allows the integral to be defined with respect to any Itô process.
For a general semimartingale X , the decomposition X = M + A into a local martingale M plus a finite variation process A can be used. Then, the integral can be shown to exist separately with respect to M and A and combined using linearity, H · X = H · M + H · A , to get the integral with respect to X . The standard Lebesgue–Stieltjes integral allows integration to be defined with respect to finite variation processes, so the existence of the Itô integral for semimartingales will follow from any construction for local martingales.
For a càdlàg square integrable martingale M , a generalized form of the Itô isometry can be used. First, the Doob–Meyer decomposition theorem is used to show that a decomposition M 2 = N + ⟨ M ⟩ exists, where N is a martingale and ⟨ M ⟩ is a right-continuous, increasing and predictable process starting at zero. This uniquely defines ⟨ M ⟩ , which is referred to as the predictable quadratic variation of M . The Itô isometry for square integrable martingales is then E [ ( H ⋅ M t ) 2 ] = E [ ∫ 0 t H s 2 d ⟨ M ⟩ s ] , {\displaystyle \mathbb {E} \left[(H\cdot M_{t})^{2}\right]=\mathbb {E} \left[\int _{0}^{t}H_{s}^{2}\,d\langle M\rangle _{s}\right],} which can be proved directly for simple predictable integrands. As with the case above for Brownian motion, a continuous linear extension can be used to uniquely extend to all predictable integrands satisfying E [ H 2 · ⟨ M ⟩ t ] < ∞ . This method can be extended to all local square integrable martingales by localization. Finally, the Doob–Meyer decomposition can be used to decompose any local martingale into the sum of a local square integrable martingale and a finite variation process, allowing the Itô integral to be constructed with respect to any semimartingale.
Many other proofs exist which apply similar methods but which avoid the need to use the Doob–Meyer decomposition theorem, such as the use of the quadratic variation [ M ] in the Itô isometry, the use of the Doléans measure for submartingales , or the use of the Burkholder–Davis–Gundy inequalities instead of the Itô isometry. The latter applies directly to local martingales without having to first deal with the square integrable martingale case.
Alternative proofs exist only making use of the fact that X is càdlàg, adapted, and the set { H · X t : | H | ≤ 1 is simple previsible} is bounded in probability for each time t , which is an alternative definition for X to be a semimartingale. A continuous linear extension can be used to construct the integral for all left-continuous and adapted integrands with right limits everywhere (caglad or L-processes). This is general enough to be able to apply techniques such as Itô's lemma ( Protter 2004 ). Also, a Khintchine inequality can be used to prove the dominated convergence theorem and extend the integral to general predictable integrands ( Bichteler 2002 ).
The Itô calculus is first and foremost defined as an integral calculus as outlined above. However, there are also different notions of "derivative" with respect to Brownian motion:
Malliavin calculus provides a theory of differentiation for random variables defined over Wiener space , including an integration by parts formula ( Nualart 2006 ).
The following result allows to express martingales as Itô integrals: if M is a square-integrable martingale on a time interval [0, T ] with respect to the filtration generated by a Brownian motion B , then there is a unique adapted square integrable process α {\displaystyle \alpha } on [0, T ] such that M t = M 0 + ∫ 0 t α s d B s {\displaystyle M_{t}=M_{0}+\int _{0}^{t}\alpha _{s}\,\mathrm {d} B_{s}} almost surely, and for all t ∈ [0, T ] ( Rogers & Williams 2000 , Theorem 36.5). This representation theorem can be interpreted formally as saying that α is the "time derivative" of M with respect to Brownian motion B , since α is precisely the process that must be integrated up to time t to obtain M t − M 0 , as in deterministic calculus.
In physics, usually stochastic differential equations (SDEs), such as Langevin equations , are used, rather than stochastic integrals. Here an Itô stochastic differential equation (SDE) is often formulated via x ˙ k = h k + g k l ξ l , {\displaystyle {\dot {x}}_{k}=h_{k}+g_{kl}\xi _{l},} where ξ j {\displaystyle \xi _{j}} is Gaussian white noise with ⟨ ξ k ( t 1 ) ξ l ( t 2 ) ⟩ = δ k l δ ( t 1 − t 2 ) {\displaystyle \langle \xi _{k}(t_{1})\,\xi _{l}(t_{2})\rangle =\delta _{kl}\delta (t_{1}-t_{2})} and Einstein's summation convention is used.
If y = y ( x k ) {\displaystyle y=y(x_{k})} is a function of the x k , then Itô's lemma has to be used: y ˙ = ∂ y ∂ x j x ˙ j + 1 2 ∂ 2 y ∂ x k ∂ x l g k m g m l . {\displaystyle {\dot {y}}={\frac {\partial y}{\partial x_{j}}}{\dot {x}}_{j}+{\frac {1}{2}}{\frac {\partial ^{2}y}{\partial x_{k}\,\partial x_{l}}}g_{km}g_{ml}.}
An Itô SDE as above also corresponds to a Stratonovich SDE which reads x ˙ k = h k + g k l ξ l − 1 2 ∂ g k l ∂ x m g m l . {\displaystyle {\dot {x}}_{k}=h_{k}+g_{kl}\xi _{l}-{\frac {1}{2}}{\frac {\partial g_{kl}}{\partial {x_{m}}}}g_{ml}.}
SDEs frequently occur in physics in Stratonovich form, as limits of stochastic differential equations driven by colored noise if the correlation time of the noise term approaches zero.
For a recent treatment of different interpretations of stochastic differential equations see for example ( Lau & Lubensky 2007 ). | https://en.wikipedia.org/wiki/Itô_calculus |
The Itô–Nisio theorem is a theorem from probability theory that characterizes convergence in Banach spaces . The theorem shows the equivalence of the different types of convergence for sums of independent and symmetric random variables in Banach spaces. The Itô–Nisio theorem leads to a generalization of Wiener's construction of the Brownian motion. [ 1 ] The symmetry of the distribution in the theorem is needed in infinite spaces.
The theorem was proven by Japanese mathematicians Kiyoshi Itô and Makiko Nisio [ d ] in 1968. [ 2 ]
Let ( E , ‖ ⋅ ‖ ) {\displaystyle (E,\|\cdot \|)} be a real separable Banach space with the norm induced topology, we use the Borel σ-algebra and denote the dual space as E ∗ {\displaystyle E^{*}} . Let ⟨ z , S ⟩ := E ∗ ⟨ z , S ⟩ E {\displaystyle \langle z,S\rangle :={}_{E^{*}}\langle z,S\rangle _{E}} be the dual pairing and i {\displaystyle i} is the imaginary unit . Let
The following is equivalent [ 2 ] : 40
Remarks: Since E {\displaystyle E} is separable point 3 {\displaystyle 3} (i.e. convergence in the Lévy–Prokhorov metric) is the same as convergence in distribution μ n ⟹ μ {\displaystyle \mu _{n}\implies \mu } . If we remove the symmetric distribution condition: | https://en.wikipedia.org/wiki/Itô–Nisio_theorem |
Ivan Cherednik (Иван Владимирович Чередник) is a Russian-American mathematician . He introduced double affine Hecke algebras , and used them to prove Macdonald's constant term conjecture in ( Cherednik 1995 ). He has also dealt with algebraic geometry , number theory and Soliton equations . His research interests include representation theory , mathematical physics , and algebraic combinatorics . He is currently the Austin M. Carr Distinguished Professor of mathematics at the University of North Carolina at Chapel Hill .
In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin. [ 1 ]
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This article about an American mathematician is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ivan_Cherednik |
The Ivanov reaction is the chemical reaction of the di anions (endiolates) of aryl acetic acids (Ivanov reagents) with electrophiles, primarily carbonyl compounds or isocyanates . [1] [2] [3] [4] The reaction was named after the Bulgarian organic chemist , Academician Dimitar Ivanov , who discovered it.
Ivanov reagents (dianions of aryl acetic acids) react with many electrophiles, including aldehydes , ketones , isocyanates , and alkyl halides . [5] The product does not usually spontaneously decarboxylate, but it is possible with some reagents. Use of the dianion of phenylacetic acid with formaldehyde gives tropic acid , an intermediate used in the synthesis of atropine and hyoscyamine . [6]
The Ivanov reaction is known to proceed through the Zimmerman-Traxler model transition state [7] . Toulec et al. have investigated the reaction rates and kinetics. [8] | https://en.wikipedia.org/wiki/Ivanov_reaction |
On April 20, 2021, it was reported that suspected Chinese-state backed hacker groups had breached multiple government agencies, defense companies and financial institutions in both the US and Europe after the hackers created and used a Zero-day exploit for Ivanti Pulse Connect Secure VPN devices. [ 1 ] [ 2 ] [ 3 ] A Cybersecurity and Infrastructure Security Agency alert reported that the attacks using the exploited started in June 2020 or earlier. [ 4 ] The attacks were believed to be the third major data breach against the U.S. in the previous year behind the 2020 United States federal government data breach and the 2021 Microsoft Exchange Server data breach. [ 5 ]
A Cybersecurity and Infrastructure Security Agency alert reported that the attacks affected "U.S. government agencies, critical infrastructure entities, and other private sector organizations." [ 6 ] A spokesperson for Ivanti said that only a "limited number" of customers had been compromised. [ 7 ] Mandiant's chief financial officer Charles Carmakal said that while the hack had only a small indication of having a large number of victims. He said the breach was significant because it had allowed unauthorized access to federal and corporate systems for months. [ 8 ]
A spokesperson for Ivanti said that while mitigations are in place a patch to fix the vulnerabilities was not expected until May. [ 9 ] With the patch finally being released on May 3, 2021. [ 10 ] The CISA issued an emergency directive requiring that federal agencies install product updates. [ 11 ] China has denied being behind the attack and accused the U.S. of being the "biggest empire of hacking and tapping." [ 12 ] | https://en.wikipedia.org/wiki/Ivanti_Pulse_Connect_Secure_data_breach |
Ivar Karl Ugi (9 September 1930 in Saaremaa , Estonia – 29 September 2005 in Munich ) was an Estonian -born German chemist who made major contributions to organic chemistry . He is known for the research on multicomponent reactions , yielding the Ugi reaction .
After he went to Germany from Estonia in 1941 he began his studies of chemistry in 1949 at the University of Tübingen until 1951. He became Dr. rer. nat. in 1954 at the Ludwig Maximilian University of Munich . He did his habilitation 1960 at the same university. After a short but very successful career in industry at Bayer from 1962 until 1968 when he joined the University of Southern California at Los Angeles.
From 1971 he worked at the Technical University of Munich , and was an emeritus from 1999 until his death in 2005.
The one pot reaction of a ketone or aldehyde , an amine , an isocyanide and a carboxylic acid to form a bis- amide is generally known as Ugi reaction .
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This article about a German academic is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Ivar_Karl_Ugi |
Ivars Knēts , (September 17, 1938, Riga, Latvia – March 1, 2019) was a rector and professor at Riga Technical University , as the Director of the Institute of Biomaterials and Biomechanics. [ 1 ] | https://en.wikipedia.org/wiki/Ivars_Knēts |
In mathematics, the Iwasawa algebra Λ( G ) of a profinite group G is a variation of the group ring of G with p -adic coefficients that take the topology of G into account. More precisely, Λ( G ) is the inverse limit of the group rings Z p ( G / H ) as H runs through the open normal subgroups of G . Commutative Iwasawa algebras were introduced by Iwasawa ( 1959 ) in his study of Z p extensions in Iwasawa theory , and non-commutative Iwasawa algebras of compact p -adic analytic groups were introduced by Lazard (1965) .
In the special case when the profinite group G is isomorphic to the additive group of the ring of p -adic integers Z p , the Iwasawa algebra Λ( G ) is isomorphic to the ring of the formal power series Z p [[ T ]] in one variable over Z p . The isomorphism is given by identifying 1 + T with a topological generator of G . This ring is a 2-dimensional complete Noetherian regular local ring , and in particular a unique factorization domain .
It follows from the Weierstrass preparation theorem for formal power series over a complete local ring that the prime ideals of this ring are as follows:
The rank of a finitely generated module is the number of times the module Z p [[ T ]] occurs in it. This is well-defined and is additive for short exact sequences of finitely-generated modules. The rank of a finitely generated module is zero if and only if the module is a torsion module, which happens if and only if the support has dimension at most 1.
Many of the modules over this algebra that occur in Iwasawa theory are finitely generated torsion modules. The structure of such modules can be described as follows. A quasi-isomorphism of modules is a homomorphism whose kernel and cokernel are both finite groups, in other words modules with support either empty or the height 2 prime ideal. For any finitely generated torsion module there is a quasi-isomorphism to a finite sum of modules of the form Z p [[ T ]]/( f n ) where f is a generator of a height 1 prime ideal. Moreover, the number of times any module Z p [[ T ]]/( f ) occurs in the module is well defined and independent of the composition series. The torsion module therefore has a characteristic power series , a formal power series given by the product of the power series f n , that is uniquely defined up to multiplication by a unit. The ideal generated by the characteristic power series is called the characteristic ideal of the Iwasawa module. More generally, any generator of the characteristic ideal is called a characteristic power series.
The μ-invariant of a finitely-generated torsion module is the number of times the module Z p [[ T ]]/( p ) occurs in it. This invariant is additive on short exact sequences of finitely generated torsion modules (though it is not additive on short exact sequences of finitely generated modules). It vanishes if and only if the finitely generated torsion module is finitely generated as a module over the subring Z p . The λ-invariant is the sum of the degrees of the distinguished polynomials that occur. In other words, if the module is pseudo-isomorphic to
where the f j are distinguished polynomials, then
and
In terms of the characteristic power series, the μ-invariant is the minimum of the ( p -adic) valuations of the coefficients and the λ-invariant is the power of T at which that minimum first occurs.
If the rank, the μ-invariant, and the λ-invariant of a finitely generated module all vanish, the module is finite (and conversely); in other words its underlying abelian group is a finite abelian p -group. These are the finitely generated modules whose support has dimension at most 0. Such modules are Artinian and have a well defined length, which is finite and additive on short exact sequences.
Write ν n for the element 1+γ+γ 2 +...+γ p n –1 where γ is a topological generator of Γ. Iwasawa ( 1959 ) showed that if X is a finitely generated torsion module over the Iwasawa algebra and X /ν n X has order p e n then
for n sufficiently large, where μ, λ, and c depend only on X and not on n . Iwasawa's original argument was ad hoc, and Serre (1958) pointed out that the Iwasawa's result could be deduced from standard results about the structure of modules over integrally closed Noetherian rings such as the Iwasawa algebra.
In particular this applies to the case when e n is the largest power of p dividing the order of the ideal class group of the cyclotomic field generated by the roots of unity of order p n +1 . The Ferrero–Washington theorem states that μ=0 in this case.
More general Iwasawa algebras are of the form
where G is a compact p -adic Lie group. The case above corresponds to G = Z p {\displaystyle G=\mathbf {Z} _{p}} . A classification of modules over Λ ( G ) {\displaystyle \Lambda (G)} up to pseudo-isomorphism is possible in case G = Z p n . {\displaystyle G=\mathbf {Z} _{p}^{n}.} [ 1 ]
For non-commutative G , Λ ( G ) {\displaystyle \Lambda (G)} -modules are classified up to so-called pseudo-null modules. [ 2 ] | https://en.wikipedia.org/wiki/Iwasawa_algebra |
In mathematics , in the field of differential geometry , an Iwasawa manifold is a compact quotient of a 3-dimensional complex Heisenberg group by a cocompact , discrete subgroup. An
Iwasawa manifold is a nilmanifold , of real dimension 6.
Iwasawa manifolds give examples where the first two terms E 1 and E 2 of the Frölicher spectral sequence are not isomorphic.
As a complex manifold , such an Iwasawa manifold is an important example of
a compact complex manifold which does not admit any Kähler metric . | https://en.wikipedia.org/wiki/Iwasawa_manifold |
The Izod impact strength test is an ASTM standard method of determining the impact resistance of materials. A pivoting arm is raised to a specific height (constant potential energy ) and then released. The arm swings down hitting a notched sample, breaking the specimen. The energy absorbed by the sample is calculated from the height the arm swings to after hitting the sample. A notched sample is generally used to determine impact energy and notch sensitivity.
The test is similar to the Charpy impact test but uses a different arrangement of the specimen under test. [ 1 ] The Izod impact test differs from the Charpy impact test in that the sample is held in a cantilevered beam configuration as opposed to a three-point bending configuration.
The test is named after the English engineer Edwin Gilbert Izod (1876–1946), who described it in his 1903 address to the British Association , subsequently published in Engineering . [ 2 ]
Impact , by definition, is a large force applied for a very short time, resulting in a sudden transfer of momentum and energy, and its effect is different when the same amount of energy is transferred more gradually. Everyday engineering structures are subjected to it and may develop cracks that, over time, propagate to a point where catastrophic failure would result.
Impact tests are used in comparing the shear fracture toughness of various materials under the same test conditions, or of one material versus temperature to determine its ductile -to- brittle transition temperature where a steep descent in impact strength with decreasing temperature is observed.
A material's toughness is a factor of its ability to absorb energy during relatively slow plastic deformation, though the rate at which strain occurs matters. Brittle materials have low toughness as a result of the small amount of plastic deformation they can endure at any rate. However, ductile materials may behave like brittle materials under high-energy impact, hence the need for this kind of test.
The test conditions are governed by many variables, most importantly:
The ASTM International standard for Izod Impact testing of plastics is ASTM D256. The results are expressed in energy lost per unit of thickness (such as ft·lb/in or J/cm) at the notch. Alternatively, the results may be reported as energy lost per unit cross-sectional area at the notch (J/m 2 or ft·lb/in 2 ). In Europe, ISO 180 methods are used and results are based only on the cross-sectional area at the notch (J/m 2 ). The dimensions of a standard specimen for ASTM D256 are 63.5 × 12.7 × 3.2 mm (2.5 × 0.5 × 0.125 in). The most common specimen thickness is 3.2 mm (0.13 in), but the width can vary between 3.0 and 12.7 mm (0.12 and 0.50 in). | https://en.wikipedia.org/wiki/Izod_impact_strength_test |
Izokibep is an investigational small protein therapeutic designed to selectively inhibit interleukin-17A (IL-17A), a pro-inflammatory cytokine implicated in various autoimmune and inflammatory diseases. [ 1 ] [ 2 ]
Developed initially by Affibody AB, a Swedish biotechnology company, izokibep has been evaluated for its potential in treating immune-mediated conditions such as psoriatic arthritis , hidradenitis suppurativa , uveitis , axial spondyloarthritis , and plaque psoriasis . Its small molecular size—approximately one-tenth that of a monoclonal antibody —enables high potency and enhanced tissue penetration, offering potential advantages over traditional antibody-based therapies. [ 1 ]
Izokibep is a small, 18.6 kDa fusion protein designed as a dimeric ligand trap, comprising two interleukin-17A (IL-17A)-specific Affibody domains flanking a central albumin-binding domain (ABD). [ 1 ] All three domains are smaller engineered derivatives of the 58-residue immunoglobulin (Ig)-binding Z-domain from Staphylococcal Protein A (SPA), with each Affibody domain forming a triple-helical structure that confers femtomolar affinity for IL-17A (K D = 0.32 pM). [ 1 ] The ABD, also based on a modified Z-domain scaffold, binds human serum albumin with high affinity (K D = 49 pM), thereby extending systemic circulation and enabling subcutaneous administration every two weeks. [ 1 ] With a chemical formula of C 824 H 1292 N 216 O 276 , izokibep’s compact size—approximately one-eighth that of a monoclonal antibody—enhances tissue penetration while maintaining serum stability for at least eight weeks at 37 °C. [ 1 ] The dimeric configuration increases inhibitory potency relative to monomeric forms and has demonstrated superior IL-17A blockade compared to monoclonal antibodies such as secukinumab in preclinical studies. [ 1 ]
Izokibep's pharmacokinetics are influenced by its small molecular size (18.6 kDa) and albumin-binding domain (ABD), which contribute to a long half-life and favorable tissue distribution, particularly to inflammatory sites. [ 3 ] The ABD enables sustained systemic exposure, allowing subcutaneous administration every 2 weeks while maintaining therapeutic efficacy. [ 3 ] Preclinical stability studies demonstrated izokibep remains stable in human serum at 37°C for ≥8 weeks and retains IL-17A binding capacity under various storage conditions. [ 1 ] Phase 1 trials showed rapid efficacy in psoriasis patients after single intravenous or subcutaneous doses, with pharmacokinetic profiles supporting further development of subcutaneous dosing regimens. [ 1 ]
Izokibep is a fusion protein that combines an IL-17A binding domain with albumin -binding technology to extend its half-life in the body. By selectively binding to IL-17A, izokibep prevents the cytokine from interacting with its receptor, thereby reducing inflammation and tissue damage associated with IL-17-driven diseases. Its small size, approximately 18.6 kDa, allows for high drug exposure via subcutaneous injection , potentially improving efficacy in tissues with limited accessibility to larger molecules like monoclonal antibodies. Preclinical studies have shown that izokibep inhibits IL-17A with 10 to 100 times greater potency than leading IL-17-inhibiting antibody drugs. [ 1 ]
Izokibep is administered via subcutaneous injection , with dosing regimens in trials ranging from weekly to every two weeks, typically at doses of 2 mg to 160 mg. Its small molecular size allows for high drug concentrations in inflamed tissues, potentially enhancing efficacy compared to larger biologics.
The most common adverse effects reported in clinical trials are injection site reactions, nasopharyngitis, and headaches. [ 3 ] [ 4 ] [ 2 ]
Izokibep was originally developed by Affibody AB, leveraging its proprietary Affibody® technology to create a novel IL-17A inhibitor.
In 2021, Acelyrin, Inc. , a California-based biopharmaceutical company, licensed global development and commercialization rights for izokibep (excluding certain Asian markets) for an upfront payment of $25 million, with potential milestone payments up to $280 million. [ 5 ] [ 6 ] Inmagene Biopharmaceuticals also held rights for development in select Asian markets, including China and South Korea. [ 7 ]
In August 2024, Acelyrin began scaling back its izokibep programs, discontinuing development for psoriatic arthritis and hidradenitis suppurativa despite earlier positive results. [ 8 ] This decision followed a Phase 2b/3 trial in uveitis that failed to meet its primary and secondary endpoints in late 2024. [ 9 ] [ 10 ] By February 2025, Acelyrin terminated its licensing agreement, returning full rights to Affibody. Concurrently, Inmagene Biopharmaceuticals ended its agreement covering Asian markets, leaving Affibody as the sole developer. [ 11 ]
The Phase 2b/3 trial, involving 351 patients, demonstrated significant improvements in joint and skin symptoms, with 40% and 43% of patients on weekly or biweekly 160 mg doses achieving ACR50 at 16 weeks, compared to 15% on placebo. The trial also met secondary endpoints, including ACR70 and PASI100, and showed a favorable safety profile. [ 12 ] A previous Phase 2 trial with 135 patients reported higher efficacy than standard treatments, with continued improvements through 46 weeks . Despite these results, Acelyrin discontinued development in August 2024, but Affibody plans a confirmatory Phase 3 trial. [ 2 ] [ 4 ]
A Phase 3 trial with approximately 250 patients was designed to evaluate HiSCR75 at 16 weeks, with topline data reported in the second half of 2024. [ 13 ] An earlier Phase 2b trial showed that one-third of patients in the open-label Part A achieved complete symptom reduction at 12 weeks. Part B did not meet its primary endpoint due to an unexpected placebo response, but post-hoc analyses indicated significant efficacy. A 32-week open-label extension confirmed further improvements and safety . Acelyrin halted development in 2024. [ 14 ] [ 8 ] [ 9 ]
A Phase 2b/3 trial for non-infectious uveitis failed to meet its primary and secondary endpoints in late 2024, prompting Acelyrin to reduce investment in this indication. [ 10 ] [ 15 ]
A Phase 3 program is planned to evaluate izokibep’s efficacy in reducing spinal inflammation and pain, building on earlier preclinical and clinical data. [ 1 ] [ 16 ] [ 13 ]
A Phase 2 trial with 108 patients demonstrated dose-dependent efficacy, with PASI 90 response rates at week 12 ranging from 0% for placebo to 71% for the 80 mg dose. The drug was well-tolerated, with mild injection site reactions as the primary adverse event. Efficacy was maintained at higher doses for up to three years, with no new safety signals. [ 3 ] Results were published in the British Journal of Dermatology in September 2023. [ 3 ]
As of early 2025, Affibody AB has regained full rights to izokibep following the termination of licensing agreements with Acelyrin and Inmagene. [ 17 ] [ 11 ]
Affibody is continuing development, with ongoing and planned trials in psoriatic arthritis, hidradenitis suppurativa, uveitis, and axial spondyloarthritis. The company is also exploring new indications and seeking partnerships to advance the drug. [ 11 ] | https://en.wikipedia.org/wiki/Izokibep |
The J-B Weld Company is an international company that produces epoxy products. The home office is based in Sulphur Springs, Texas . [ 1 ] J-B Weld (stylized as J-B WELD ) is the name of their flagship product: a specialized, high-temperature epoxy adhesive for use in bonding materials together. The company has run advertisements showing engine block repair with J-B Weld. [ citation needed ]
The J-B Weld Company, founded in 1969 by Sam Bonham in Sulphur Springs, Texas, specializes in epoxy products. Initially, the company sold to automotive shops in Texas, but now distributes its products across the United States and in 27 other countries through various retail channels. After being purchased by private investors in 2008, the company expanded its product line, which originally included J-B Weld, J-B Kwik, J-B Stik, and Waterweld.
J-B Weld epoxy is a two-part adhesive that can bond various surfaces and withstand high temperatures up to 500 °F (260 °C) constantly and 600 °F (316 °C) for short periods. It is water-resistant, petroleum/chemical-resistant, acid-resistant, and resists shock, vibration, and temperature fluctuations. The product consists of a resin and a hardener that need to be mixed before application. The mixture sets in 4-6 hours and fully cures in up to 15 hours. It can be used as an adhesive, laminate, plug, filler, sealant, or electrical insulator and can be drilled, ground, tapped, machined, sanded, and painted when cured.
J-B Kwik is a faster-curing two-part epoxy with medium-temperature resistance up to 300 °F (149 °C). Although not as strong or heat-resistant as J-B Weld, it has the same adhesion and does not shrink when hardening. J-B Kwik is waterproof, petroleum/chemical-resistant, acid-resistant, and resists shock, vibration, and extreme temperature fluctuations.
The company had its beginnings in 1969 [ 2 ] in Sulphur Springs, Texas . Sam Bonham, at the time running a machine shop, discovered a way to create what he called a "tougher than steel" epoxy. [ 2 ] In 1968, Sam's future wife Mary persuaded him to sell his invention and he founded the J-B Weld Company. After founding the company, Sam stated: "My life's dream is for J-B Weld to be all the way around the world, and for me to see an 18-wheeler load out of here with nothing but J-B Weld." [ 2 ] After Sam's death in 1989, Mary opened a European hub in London , internationalizing the J-B Weld Company and the distribution of the product. [ 2 ]
Initially, the company sold to automotive shops and jobbers in Texas . [ 2 ] Now, the J-B Weld Company distributes its products through multiple retail channels - including automotive chains, home improvement centers, hardware stores, and farm stores [ 1 ] - and does business in all states in the United States, as well as in 27 other countries. In 2008 the company was purchased by a group of private investors. Led by CEO Chip Hanson, they have expanded the product lines. [ 2 ]
The J-B Weld Company's original product line focused on a small number of products: J-B Weld (original 2-tube epoxy), J-B Kwik (4-hour epoxy), J-B Stik ( epoxy putty ), Waterweld (underwater adhesive/filler), and a few others. [ 3 ]
Since 2008, the company has broadened the product line to add J-B SteelStik, KwikWood, PlasticWeld, MarineWeld, Perm-O-Seal, WoodWeld and ClearWeld. [ 4 ] [ 5 ]
J-B Weld is a two-part epoxy adhesive (or filler) that can withstand high-temperature environments.
J-B Weld can be used to bond surfaces made from metal, porcelain , ceramic , glass, marble, PVC , ABS , concrete, fiberglass , wood, fabric, or paper. [ 6 ] [ 7 ] Alcohol should be avoided when cleaning surfaces, as it can degrade the bond. [ 8 ] J-B Weld is water-resistant, petroleum/chemical-resistant (when hardened), and acid-resistant. It also resists shock, vibration, and extreme temperature fluctuations. [ 7 ] J-B Weld can withstand a constant temperature of 500 °F (260 °C), and the maximum temperature threshold is approximately 600 °F (316 °C) for 10 minutes. [ 8 ] J-B Weld can also be used inside a microwave oven , exposed to microwave radiation instead of infrared radiation (heat). [ 6 ]
The product is contained in 2 separate tubes: the "steel" (black tube of resin) and the "hardener" (red tube). Equal amounts are squeezed from both tubes and mixed. [ 6 ] For the best bond, surfaces should be roughened (or scratched) with fine or coarse sandpaper.
When first mixed, J-B Weld is subject to sagging or running (slow dripping); even more so at warmer temperatures. [ 9 ] [ 6 ] After about 20 minutes the mixture begins to thicken into a putty that can be shaped with a putty knife or wooden spatula. [ 6 ] The mixture will set enough for the glued parts to be handled within 4–6 hours, [ 6 ] but requires up to 15 hours at cool temperatures to fully cure and harden. Temperatures above 50 °F (10 °C) shorten all these times. [ 6 ] After the initial setting period of a few hours, heat (e.g. from a heat lamp or incandescent light bulb placed near the bond) will speed the curing time. [ 9 ] [ 6 ]
J-B Weld can be used as an adhesive, laminate, plug, filler, sealant, or electrical insulator. [ 7 ] When fully cured, J-B Weld can be drilled, formed, ground, tapped, machined, sanded, and painted. [ 7 ]
While J-B Weld Original epoxy dries to a dark grey color, [ 10 ] J-B Weld's ClearWeld epoxy dries clear. [ 11 ] Although its bond is not quite as strong as the Original's (3900 psi vs. 5020 psi), [ 12 ] ClearWeld is often preferred when appearance is an important consideration. [ 13 ]
J-B Kwik (stylized as J-B KWIK ) is a two-part epoxy, intended as an adhesive or filler, that can withstand medium-temperature environments (up to 300 °F or 149 °C). [ 14 ]
J-B Kwik cures much more quickly, but it is not as strong or as heat-resistant as the original J-B Weld. [ 9 ] [ 14 ] However, J-B Kwik has the same adhesion (1,800 psi or 12 MPa) as J-B Weld, and also does not shrink when hardening. [ 14 ]
J-B Kwik can be used to bond surfaces made from any combination of iron, steel, copper, aluminum, brass, bronze, pewter, [ 14 ] plus porcelain , wood, ceramic , glass, marble, PVC , ABS , concrete, fiberglass, fabric, or paper. [ 7 ] [ 14 ] J-B Kwik is waterproof, petroleum/chemical-resistant (when cured), acid-resistant; plus resists shock, vibration, and extreme temperature fluctuations. [ 7 ] | https://en.wikipedia.org/wiki/J-B_Weld |
A J-aggregate is a type of dye with an absorption band that shifts to a longer wavelength ( bathochromic shift ) of increasing sharpness (higher absorption coefficient ) when it aggregates under the influence of a solvent or additive or concentration as a result of supramolecular self-organisation. [ 1 ] The dye can be characterized further by a small Stokes shift with a narrow band. The J in J-aggregate refers to E.E. Jelley who discovered the phenomenon in 1936. [ 2 ] [ 3 ] The dye is also called a Scheibe aggregate after G. Scheibe who also independently published on this topic in 1937. [ 4 ] [ 5 ]
Scheibe and Jelley independently observed that in ethanol the dye PIC chloride has two broad absorption maxima at around 19,000 cm −1 and 20,500 cm −1 (526 and 488 nm respectively) and that in water a third sharp absorption maximum appears at 17,500 cm −1 (571 nm). The intensity of this band further increases on increasing concentration and on adding sodium chloride . In the oldest aggregation model for PIC chloride the individual molecules are stacked like a roll of coins forming a supramolecular polymer but the true nature of this aggregation phenomenon is still under investigation. Analysis is complicated because PIC chloride is not a planar molecule. The molecular axis can tilt in the stack creating a helix pattern. In other models the dye molecules orient themselves in a brickwork, ladder, or staircase fashion. In various experiments the J-band was found to split as a function of temperature, liquid crystal phases were found with concentrated solutions and CryoTEM revealed aggregate rods 350 nm long and 2.3 nm in diameter.
J-aggregate dyes are found with polymethine dyes in general, with cyanines , merocyanines , squaraine and perylene bisimides . Certain π-conjugated macrocycles, reported by Swager and co-workers at MIT, were also found to form J-aggregates and exhibited exceptionally high photoluminescence quantum yields. [ 6 ] In 2020, a famous cyanine dye (TDBC) was reported with enhanced photoluminescence quantum yield (> 50%) in the solution at room-temperature. [ 7 ]
Molecular PIC aggregates exhibiting J-like properties have been shown to spontaneously template into sequence specific DNA duplex strands. These DNA based J-aggregates, known as J-bits, have been sought after as a bottom-up method of self-assembling PIC J-aggregates into large scale multi-functional DNA scaffolds. Critically, J-bits have been observed to engage in energy transfer when in proximity to quantum dots [ 8 ] as well as organic dyes such as Alexa Fluor dyes. [ 9 ] Prototypical DNA energy transfer arrays, which are based on the molecular photonic wire design, use FRET to transfer excitons step-wise down an energy gradient. Since the FRET efficiency between two Fluorophores decays by their separation distance to the 6th power, the spatial limitations of these systems are highly constrained. It is hypothesized that integrating J-bit relays between FRET nodes would allow some of this energy loss to be recouped. In theory, dense packing and rigid alignment of the PIC monomers enables superposition of the transition dipoles allowing excitons to propagate through the length of the aggregate with low loss. [ 10 ] | https://en.wikipedia.org/wiki/J-aggregate |
In nuclear chemistry and nuclear physics , J -couplings (also called spin-spin coupling or indirect dipole–dipole coupling ) are mediated through chemical bonds connecting two spins. It is an indirect interaction between two nuclear spins that arises from hyperfine interactions between the nuclei and local electrons. [ 1 ] In NMR spectroscopy , J -coupling contains information about relative bond distances and angles. Most importantly, J -coupling provides information on the connectivity of chemical bonds. It is responsible for the often complex splitting of resonance lines in the NMR spectra of fairly simple molecules.
J -coupling is a frequency difference that is not affected by the strength of the magnetic field, so is always stated in Hz.
The origin of J -coupling can be visualized by a vector model for a simple molecule such as hydrogen fluoride (HF). In HF, the two nuclei have spin 1 / 2 . Four states are possible, depending on the relative alignment of the H and F nuclear spins with the external magnetic field. The selection rules of NMR spectroscopy dictate that Δ I = 1, which means that a given photon (in the radio frequency range) can affect ("flip") only one of the two nuclear spins. J -coupling provides three parameters: the multiplicity (the "number of lines"), the magnitude of the coupling (strong, medium, weak), and the sign of the coupling.
The multiplicity provides information on the number of centers coupled to the signal of interest, and their nuclear spin. For simple systems, as in 1 H– 1 H coupling in NMR spectroscopy, the multiplicity is one more than the number of adjacent protons which are magnetically nonequivalent to the protons of interest. For ethanol, each methyl proton is coupled to the two methylene protons, so the methyl signal is a triplet, while each methylene proton is coupled to the three methyl protons, so the methylene signal is a quartet. [ 2 ]
Nuclei with spins greater than 1 / 2 , which are called quadrupolar, can give rise to greater splitting, although in many cases coupling to quadrupolar nuclei is not observed. Many elements consist of nuclei with nuclear spin and without. In these cases, the observed spectrum is the sum of spectra for each isotopomer . One of the great conveniences of NMR spectroscopy for organic molecules is that several important lighter spin 1 / 2 nuclei are either monoisotopic, e.g. 31 P and 19 F, or have very high natural abundance, e.g. 1 H. An additional convenience is that 12 C and 16 O have no nuclear spin so these nuclei, which are common in organic molecules, do not cause splitting patterns in NMR.
For 1 H– 1 H coupling, the magnitude of J decreases rapidly with the number of bonds between the coupled nuclei, especially in saturated molecules . [ 3 ] Generally speaking two-bond coupling (i.e. 1 H–C– 1 H) is stronger than three-bond coupling ( 1 H–C–C– 1 H). The magnitude of the coupling also provides information on the dihedral angles relating the coupling partners, as described by the Karplus equation for three-bond coupling constants.
For heteronuclear coupling, the magnitude of J is related to the nuclear magnetic moments of the coupling partners. 19 F, with a high nuclear magnetic moment, gives rise to large coupling to protons. 103 Rh, with a very small nuclear magnetic moment, gives only small couplings to 1 H. To correct for the effect of the nuclear magnetic moment (or equivalently the gyromagnetic ratio γ ), the "reduced coupling constant" K is often discussed, where
For coupling of a 13 C nucleus and a directly bonded proton, the dominant term in the coupling constant J C–H is the Fermi contact interaction , which is a measure of the s-character of the bond at the two nuclei. [ 4 ]
Where the external magnetic field is very low, e.g. as Earth's field NMR , J -coupling signals of the order of hertz usually dominate chemical shifts which are of the order of millihertz and are not normally resolvable.
The value of each coupling constant also has a sign, and coupling constants of comparable magnitude often have opposite signs. [ 5 ] If the coupling constant between two given spins is negative, the energy is lower when these two spins are parallel, and conversely if their coupling constant is positive. [ 6 ] For a molecule with a single J -coupling constant, the appearance of the NMR spectrum is unchanged if the sign of the coupling constant is reversed, although spectral lines at given positions may represent different transitions. [ 7 ] The simple NMR spectrum therefore does not indicate the sign of the coupling constant, which there is no simple way of predicting. [ 8 ]
However for some molecules with two distinct J -coupling constants, the relative signs of the two constants can be experimentally determined by a double resonance experiment. [ 9 ] For example in the diethylthallium ion (C 2 H 5 ) 2 Tl + , this method showed that the methyl-thallium (CH 3 -Tl) and methylene-thallium (CH 2 -Tl) coupling constants have opposite signs. [ 9 ]
The first experimental method to determine the absolute sign of a J -coupling constant was proposed in 1962 by Buckingham and Lovering, who suggested the use of a strong electric field to align the molecules of a polar liquid . The field produces a direct dipolar coupling of the two spins, which adds to the observed J -coupling if their signs are parallel and subtracts from the observed J -coupling if their signs are opposed. [ 10 ] [ 11 ] This method was first applied to 4-nitrotoluene , for which the J -coupling constant between two adjacent (or ortho ) ring protons was shown to be positive because the splitting of the two peaks for each proton decreases with the applied electric field. [ 10 ] [ 12 ]
Another way to align molecules for NMR spectroscopy is to dissolve them in a nematic liquid crystal solvent. This method has also been used to determine the absolute sign of J -coupling constants. [ 13 ] [ 14 ] [ 15 ]
The Hamiltonian of a molecular system may be taken as:
For a singlet molecular state and frequent molecular collisions, D 1 and D 3 are almost zero. The full form of the J -coupling interaction between spins ' I j and I k on the same molecule is:
where J jk is the J -coupling tensor, a real 3 × 3 matrix. It depends on molecular orientation, but in an isotropic liquid it reduces to a number, the so-called scalar coupling . In 1D NMR, the scalar coupling leads to oscillations in the free induction decay as well as splittings of lines in the spectrum.
By selective radio frequency irradiation, NMR spectra can be fully or partially decoupled , eliminating or selectively reducing the coupling effect. Carbon-13 NMR spectra are often recorded with proton decoupling.
In September 1951, H. S. Gutowsky , D. W. McCall, and C. P. Slichter reported experiments on HPF 6 {\displaystyle {\ce {HPF_6}}} , CH 3 OPF 2 {\displaystyle {\ce {CH_3OPF_2}}} , and POCl 2 F {\displaystyle {\ce {POCl_2F}}} , where they explained the presence of multiple resonance lines with an interaction of the form A μ 1 ⋅ μ 2 {\displaystyle A\mathbf {\mu } _{1}\cdot \mathbf {\mu } _{2}} . [ 16 ]
Independently, in October 1951, E. L. Hahn and D. E. Maxwell reported a spin echo experiment which indicates the existence of an interaction between two protons in dichloroacetaldehyde . In the echo experiment, two short, intense pulses of radiofrequency magnetic field are applied to the spin ensemble at the nuclear resonance condition and are separated by a time interval of τ . The echo appears with a given amplitude at time 2 τ . For each setting of τ , the maximum value of the echo signal is measured and plotted as a function of τ . If the spin ensemble consists of a magnetic moment , a monotonic decay in the echo envelope is obtained. In the Hahn–Maxwell experiment, the decay was modulated by two frequencies: one frequency corresponded with the difference in chemical shift between the two non-equivalent spins and a second frequency, J , that was smaller and independent of magnetic field strength ( J / 2π = 0.7 Hz). [ 17 ] Such interaction came as a great surprise. The direct interaction between two magnetic dipoles depends on the relative position of two nuclei in such a way that when averaged over all possible orientations of the molecule it equals to zero.
In November 1951, N. F. Ramsey and E. M. Purcell proposed a mechanism that explained the observation and gave rise to an interaction of the form I 1 · I 2 . The mechanism is the magnetic interaction between each nucleus and the electron spin of its own atom together with the exchange coupling of the electron spins with each other. [ 18 ]
In the 1990s, direct evidence was found for the presence of J -couplings between magnetically active nuclei on both sides of the hydrogen bond . [ 19 ] [ 20 ] Initially, it was surprising to observe such couplings across hydrogen bonds since J -couplings are usually associated with the presence of purely covalent bonds . However, it is now well established that the H-bond J -couplings follow the same electron-mediated polarization mechanism as their covalent counterparts. [ 21 ]
The spin–spin coupling between nonbonded atoms in close proximity has sometimes been observed between fluorine, nitrogen, carbon, silicon and phosphorus atoms. [ 22 ] [ 23 ] [ 24 ] | https://en.wikipedia.org/wiki/J-coupling |
The J-integral represents a way to calculate the strain energy release rate , or work ( energy ) per unit fracture surface area, in a material. [ 1 ] The theoretical concept of J-integral was developed in 1967 by G. P. Cherepanov [ 2 ] and independently in 1968 by James R. Rice , [ 3 ] who showed that an energetic contour path integral (called J ) was independent of the path around a crack .
Experimental methods were developed using the integral that allowed the measurement of critical fracture properties in sample sizes that are too small for Linear Elastic Fracture Mechanics (LEFM) to be valid. [ 4 ] These experiments allow the determination of fracture toughness from the critical value of fracture energy J Ic , which defines the point at which large-scale plastic yielding during propagation takes place under mode I loading. [ 1 ] [ 5 ]
The J-integral is equal to the strain energy release rate for a crack in a body subjected to monotonic loading. [ 6 ] This is generally true, under quasistatic conditions, only for linear elastic materials. For materials that experience small-scale yielding at the crack tip, J can be used to compute the energy release rate under special circumstances such as monotonic loading in mode III ( antiplane shear ). The strain energy release rate can also be computed from J for pure power-law hardening plastic materials that undergo small-scale yielding at the crack tip.
The quantity J is not path-independent for monotonic mode I and mode II loading of elastic-plastic materials, so only a contour very close to the crack tip gives the energy release rate. Also, Rice showed that J is path-independent in plastic materials when there is no non-proportional loading. Unloading is a special case of this, but non-proportional plastic loading also invalidates the path-independence. Such non-proportional loading is the reason for the path-dependence for the in-plane loading modes on elastic-plastic materials.
The two-dimensional J-integral was originally defined as [ 3 ] (see Figure 1 for an illustration)
where W ( x 1 , x 2 ) is the strain energy density, x 1 , x 2 are the coordinate directions, t = [ σ ] n is the surface traction vector, n is the normal to the curve Γ, [ σ ] is the Cauchy stress tensor , and u is the displacement vector . The strain energy density is given by
The J-integral around a crack tip is frequently expressed in a more general form [ 7 ] (and in index notation ) as
where J i {\displaystyle J_{i}} is the component of the J-integral for crack opening in the x i {\displaystyle x_{i}} direction and ε {\displaystyle \varepsilon } is a small region around the crack tip.
Using Green's theorem we can show that this integral is zero when the boundary Γ {\displaystyle \Gamma } is closed and encloses a region that contains no singularities and is simply connected . If the faces of the crack do not have any surface tractions on them then the J-integral is also path independent .
Rice also showed that the value of the J-integral represents the energy release rate for planar crack growth.
The J-integral was developed because of the difficulties involved in computing the stress close to a crack in a nonlinear elastic or elastic- plastic material. Rice showed that if monotonic loading was assumed (without any plastic unloading) then the J-integral could be used to compute the energy release rate of plastic materials too.
We can write this as
From Green's theorem (or the two-dimensional divergence theorem ) we have
Using this result we can express J 1 {\displaystyle J_{1}} as
where A {\displaystyle A} is the area enclosed by the contour Γ {\displaystyle \Gamma } . Now, if there are no body forces present, equilibrium (conservation of linear momentum) requires that
Also,
Therefore,
From the balance of angular momentum we have σ j k = σ k j {\displaystyle \sigma _{jk}=\sigma _{kj}} . Hence,
The J-integral may then be written as
Now, for an elastic material the stress can be derived from the stored energy function W {\displaystyle W} using
Then, if the elastic modulus tensor is homogeneous, using the chain rule of differentiation,
Therefore, we have J 1 = 0 {\displaystyle J_{1}=0} for a closed contour enclosing a simply connected region without any elastic inhomogeneity, such as voids and cracks.
Consider the contour Γ = Γ 1 + Γ + + Γ 2 + Γ − {\displaystyle \Gamma =\Gamma _{1}+\Gamma ^{+}+\Gamma _{2}+\Gamma ^{-}} . Since this contour is closed and encloses a simply connected region, the J-integral around the contour is zero, i.e.
assuming that counterclockwise integrals around the crack tip have positive sign. Now, since the crack surfaces are parallel to the x 1 {\displaystyle x_{1}} axis, the normal component n 1 = 0 {\displaystyle n_{1}=0} on these surfaces. Also, since the crack surfaces are traction free, t k = 0 {\displaystyle t_{k}=0} . Therefore,
Therefore,
and the J-integral is path independent.
For isotropic, perfectly brittle, linear elastic materials, the J-integral can be directly related to the fracture toughness if the crack extends straight ahead with respect to its original orientation. [ 6 ]
For plane strain, under Mode I loading conditions, this relation is
where G I c {\displaystyle G_{\rm {Ic}}} is the critical strain energy release rate, K I c {\displaystyle K_{\rm {Ic}}} is the fracture toughness in Mode I loading, ν {\displaystyle \nu } is the Poisson's ratio, and E is the Young's modulus of the material.
For Mode II loading, the relation between the J-integral and the mode II fracture toughness ( K I I c {\displaystyle K_{\rm {IIc}}} ) is
For Mode III loading, the relation is
Hutchinson, Rice and Rosengren [ 8 ] [ 9 ] subsequently showed that J characterizes the singular stress and strain fields at the tip of a crack in nonlinear (power law hardening) elastic-plastic materials where the size of the plastic zone is small compared with the crack length. Hutchinson used a material constitutive law of the form suggested by W. Ramberg and W. Osgood : [ 10 ]
where σ is the stress in uniaxial tension, σ y is a yield stress , ε is the strain , and ε y = σ y / E is the corresponding yield strain. The quantity E is the elastic Young's modulus of the material. The model is parametrized by α , a dimensionless constant characteristic of the material, and n , the coefficient of work hardening . This model is applicable only to situations where the stress increases monotonically, the stress components remain approximately in the same ratios as loading progresses (proportional loading), and there is no unloading .
If a far-field tensile stress σ far is applied to the body shown in the adjacent figure, the J-integral around the path Γ 1 (chosen to be completely inside the elastic zone) is given by
Since the total integral around the crack vanishes and the contributions along the surface of the crack are zero, we have
If the path Γ 2 is chosen such that it is inside the fully plastic domain, Hutchinson showed that
where K is a stress amplitude, ( r , θ ) is a polar coordinate system with origin at the crack tip, s is a constant determined from an asymptotic expansion of the stress field around the crack, and I is a dimensionless integral. The relation between the J-integrals around Γ 1 and Γ 2 leads to the constraint
and an expression for K in terms of the far-field stress
where β = 1 for plane stress and β = 1 − ν 2 for plane strain ( ν is the Poisson's ratio ).
The asymptotic expansion of the stress field and the above ideas can be used to determine the stress and strain fields in terms of the J-integral:
where σ ~ i j {\displaystyle {\tilde {\sigma }}_{ij}} and ε ~ i j {\displaystyle {\tilde {\varepsilon }}_{ij}} are dimensionless functions.
These expressions indicate that J can be interpreted as a plastic analog to the stress intensity factor ( K ) that is used in linear elastic fracture mechanics, i.e., we can use a criterion such as J > J Ic as a crack growth criterion. | https://en.wikipedia.org/wiki/J-integral |
The J. Lawrence Smith Medal is awarded every three years by the National Academy of Sciences for investigations of meteoric bodies. [ 1 ] The medal's namesake is the American chemist and meteoriticist J. Lawrence Smith .
List of recipients: [ 2 ] | https://en.wikipedia.org/wiki/J._Lawrence_Smith_Medal |
John Wilfred Jenkinson (1871–1915) was a pioneer in the field of comparative developmental biology (the forerunner of evolutionary developmental biology ) and one of the first to introduce experimental embryology to the UK at the start of the 20th century. [ 1 ] [ 2 ] He originally studied Classics as an undergraduate student at Oxford, before switching his attention to Zoology under the guidance of W. F. R. Weldon at University College London . [ 1 ] [ 2 ] He also travelled to Utrecht University in the Netherlands, to work with Ambrosius Hubrecht , and was exposed to new methods and approaches in embryology. In 1905, he was appointed the first lecturer in Embryology at the University of Oxford in England , and in 1909 published the first English textbook on experimental embryology [ 3 ] in which he summarized recent work in the emerging scientific discipline and criticized neo-vitalist theories of Hans Driesch . [ 2 ]
At the outbreak of war in 1914, Jenkinson joined the Oxford Volunteer Training Corps. [ 2 ] In January 1915 he was assigned to the 12th Battalion of the Worcestershire Regiment and was soon promoted to the rank of captain. [ 4 ] Jenkinson left England with his regiment in May, posted to the Dardanelles in Turkey. On 4 June 1915, just days after arriving on the Gallipoli peninsula, Jenkinson was killed. [ 2 ] After Jenkinson's death at Gallipoli in June 1915, the University of Oxford established the John Wilfred Jenkinson Lectureship in his memory. The original statutes required the lecturer or lecturers, appointed annually, to deliver “one or more lectures or lecture demonstrations on comparative or experimental embryology”. [ 5 ]
Each year, a Board of Electors selects one or two Jenkinson Lecturers who are invited to Oxford to present a lecture in the broad area of developmental biology. [ 5 ] The list of Jenkinson Lecturers includes many distinguished names, including Nobel Laureates (marked with *).
The lecturers are elected by an electoral board consisting of: the vice-chancellor of the University of Oxford ; the rector of Exeter College , Oxford; the Regius Professor of Medicine ; the Linacre Professor of Zoology ; the Waynflete Professor of Physiology ; Dr. Lee's Professor of Anatomy; and a member of the Mathematical, Physical and Life Sciences Board elected by that board. [ 5 ] | https://en.wikipedia.org/wiki/J._W._Jenkinson_Memorial_Lectureship |
J002E3 is an object in space which is thought to be the S-IVB third stage of the Apollo 12 Saturn V rocket. It was discovered on September 3, 2002, by amateur astronomer Bill Yeung . Initially thought to be an asteroid , it has since been tentatively identified as the third stage of Apollo 12 Saturn V based on spectrographic evidence consistent with the titanium dioxide in the paint used on the rockets. [ 1 ] [ 2 ] [ 3 ] The stage was intended to be injected into a permanent heliocentric orbit in November 1969, but is now believed instead to have gone into an unstable high Earth orbit which left Earth's proximity in 1971 and again in June 2003, with an approximately 40-year cycle between heliocentric and geocentric orbit . [ 4 ]
When it was first discovered, it was quickly found that the object was in an orbit around Earth . Astronomers were surprised at this, as the Moon is the only large object in orbit around the Earth, [ a ] and anything else would have been ejected long ago due to perturbations with the Earth, the Moon and the Sun .
Therefore, it probably entered into Earth orbit very recently, yet there was no recently launched spacecraft that matched the orbit of J002E3. One explanation could have been that it was a 30 meter-wide piece of rock, but University of Arizona astronomers found that spectral observations of the object indicated a strong correlation of absorption features with a combination of human-made materials including white paint, black paint, and aluminum, consistent with Saturn V rockets. [ 2 ] Back-tracing its orbit showed that the object had been orbiting the Sun for 31 years and had last been in the vicinity of the Earth in 1971. This seemed to suggest that it was a part of the Apollo 14 mission, but NASA knew the whereabouts of all hardware used for that mission; the third stage, for instance, was deliberately crashed into the Moon for seismic studies.
The most likely explanation appears to be the S-IVB third stage for Apollo 12 . [ 1 ] [ 2 ] Photometric observations of J002E3 made in February 2003 from the Air Force Maui Optical and Supercomputing Site (AMOS) matched an S-IVB light curve model consisting of a diffuse cylinder tumbling with a period of 63.46 seconds and a precession of 79 ± 10°. [ 5 ] NASA had originally planned to direct the S-IVB into a solar orbit, but an extra long burn of the ullage motors meant that venting the remaining propellant in the tank of the S-IVB did not give the rocket stage enough energy to escape the Earth–Moon system, and instead the stage ended up in a semi-stable orbit around the Earth after passing by the Moon on 18 November 1969.
It is thought that J002E3 left Earth orbit in June 2003, and that it may return to orbit the Earth in the mid-2040s. [ 1 ]
The object's Earth orbital paths occasionally take it within the radius of the Moon 's orbit, and could result in eventual entry into Earth's atmosphere, or collision with the Moon. The Apollo 12 empty S-IVB, Instrument Unit, and spacecraft adapter base, had a mass of about 14 tonnes; 15 short tons (30,000 lb). [ 6 ] This is less than one-fifth of the 77.1-tonne; 85.0-short-ton (169,900 lb) mass of the Skylab space station , which was constructed from a similar S-IVB and fell out of orbit on 11 July 1979. [ 7 ] Objects with a mass of about 10 tonnes (22,000 lb; 11 short tons) enter Earth's atmosphere approximately 10 times a year, [ 8 ] one of which impacts the Earth's surface approximately once every 10 years. [ 9 ]
Ten essentially similar empty S-IVB stages from Apollo, Skylab and Apollo-Soyuz Test Project missions [ b ] have re-entered the atmosphere from 1966 to 1975. In all cases (including the Skylab station), the objects burned in the atmosphere and broke into relatively small pieces, rather than striking the Earth as a single mass. On the other hand, these objects entered from low Earth orbit or a ballistic trajectory, with less energy than J002E3 might possibly have if it were to enter from solar orbit. | https://en.wikipedia.org/wiki/J002E3 |
In international diplomacy, JACKSNNZ (pronounced “Jacksons”) is the colloquial name of an informal grouping of the world's affluent non- EU countries, excluding the United States . The JACKSNNZ states are J apan , A ustralia , C anada , South K orea , S witzerland , N orway and N ew Z ealand .
The term originated in the proceedings to the Sixth Review Conference of the Biological and Toxins Weapons Convention held in Geneva in 2006. In the previous review conference talks broke down over American refusals to allow for a verification mechanism be established to monitor biological weapons programs in states parties. This was against the wishes of other WEOG (Western European and Others Group) states, which also include Canada , Turkey , Australasia and Western Europe . At the 2006 Review Conference the JACKSNNZ states remain supportive of a verification protocol (although are unlikely to push for it knowing that the current US government will not accede on this point). However, the JACKSNNZ also seeks balance within the WEOG, and to protect the interests of non-EU states.
Takeshi Aoki, director of the Bioweapons and Chemical Weapons Conventions Division of the Japanese Ministry of Foreign Affairs said that JACKSNNZ is "neither a binding instrument, nor an exclusive one." The JACKSNNZ states are yet to declare a common and exclusive position in other international fora under this name. | https://en.wikipedia.org/wiki/JACKSNNZ |
Jad (Java Decompiler) is, as of August 2011 [update] , an unmaintained decompiler for the Java programming language. [ 1 ] Jad provides a command-line user interface to extract source code from class files .
This programming-tool -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JAD_(software) |
The JAK-STAT signaling pathway is a chain of interactions between proteins in a cell, and is involved in processes such as immunity , cell division , cell death , and tumor formation . The pathway communicates information from chemical signals outside of a cell to the cell nucleus , resulting in the activation of genes through the process of transcription . There are three key parts of JAK-STAT signalling: Janus kinases (JAKs), signal transducer and activator of transcription proteins (STATs), and receptors (which bind the chemical signals). [ 1 ] Disrupted JAK-STAT signalling may lead to a variety of diseases, such as skin conditions, cancers , and disorders affecting the immune system. [ 1 ]
Main articles: JAKs and STATs
There are four JAK proteins: JAK1 , JAK2 , JAK3 and TYK2 . [ 1 ] JAKs contains a FERM domain (approximately 400 residues), an SH2-related domain (approximately 100 residues), a kinase domain (approximately 250 residues) and a pseudokinase domain (approximately 300 residues). [ 2 ] The kinase domain is vital for JAK activity, since it allows JAKs to phosphorylate (add phosphate groups to) proteins.
There are seven STAT proteins: STAT1 , STAT2 , STAT3 , STAT4 , STAT5A , STAT5B and STAT6 . [ 1 ] STAT proteins contain many different domains, each with a different function, of which the most conserved region is the SH2 domain . [ 2 ] The SH2 domain is formed of 2 α-helices and a β-sheet and is formed approximately from residues 575–680. [ 2 ] [ 3 ] STATs also have transcriptional activation domains (TAD), which are less conserved and are located at the C-terminus . [ 4 ] In addition, STATs also contain: tyrosine activation, amino-terminal, linker, coiled-coil and DNA-binding domains . [ 4 ]
The binding of various ligands , usually cytokines, such as interferons and interleukins , to cell-surface receptors, causes the receptors to dimerize, which brings the receptor-associated JAKs into close proximity. [ 6 ] The JAKs then phosphorylate each other on tyrosine residues located in regions called activation loops , through a process called transphosphorylation , which increases the activity of their kinase domains. [ 6 ] The activated JAKs then phosphorylate tyrosine residues on the receptor, creating binding sites for proteins possessing SH2 domains . [ 6 ] STATs then bind to the phosphorylated tyrosines on the receptor using their SH2 domains, and then they are tyrosine-phosphorylated by JAKs, causing the STATs to dissociate from the receptor. [ 2 ] At least STAT5 requires glycosylation at threonine 92 for strong STAT5 tyrosine phosphorylation. [ 7 ] These activated STATs form hetero- or homodimers , where the SH2 domain of each STAT binds the phosphorylated tyrosine of the opposite STAT, and the dimer then translocates to the cell nucleus to induce transcription of target genes. [ 2 ] STATs may also be tyrosine-phosphorylated directly by receptor tyrosine kinases - but since most receptors lack built-in kinase activity, JAKs are usually required for signalling. [ 1 ]
To move from the cytosol to the nucleus , STAT dimers have to pass through nuclear pore complexes (NPCs), which are protein complexes present along the nuclear envelope that control the flow of substances in and out of the nucleus. To enable STATs to move into the nucleus, an amino acid sequence on STATs, called the nuclear localization signal (NLS), is bound by proteins called importins . [ 4 ] Once the STAT dimer (bound to importins) enters the nucleus, a protein called Ran (associated with GTP) binds to the importins, releasing them from the STAT dimer. [ 8 ] The STAT dimer is then free in the nucleus.
Specific STATs appear to bind to specific importin proteins. For example, STAT3 proteins can enter the nucleus by binding to importin α3 and importin α6. [ 9 ] On the other hand, STAT1 and STAT2 bind to importin α5. [ 4 ] Studies indicate that STAT2 requires a protein called interferon regulatory factor 9 (IRF9) to enter the nucleus. [ 8 ] Not as much is known about nuclear entrance of other STATs, but it has been suggested that a sequence of amino acids in the DNA-binding domain of STAT4 might allow nuclear import; also, STAT5 and STAT6 can both bind to importin α3. [ 8 ] In addition, STAT3, STAT5 and STAT6 can enter the nucleus even if they are not phosphorylated at tyrosine residues. [ 8 ]
After STATs are made by protein biosynthesis , they have non-protein molecules attached to them, called post-translational modifications . One example of this is tyrosine phosphorylation (which is fundamental for JAK-STAT signalling), but STATs experience other modifications, which may affect STAT behaviour in JAK-STAT signalling. These modifications include: methylation , acetylation and serine phosphorylation.
Acetylation of STAT3 has been suggested to be important for its dimerization, DNA-binding and gene-transcribing ability, and IL-6 JAK-STAT pathways that use STAT3 require acetylation for transcription of IL-6 response genes. [ 12 ] STAT5 acetylation on lysines at positions 694 and 701 is important for effective STAT dimerization in prolactin signalling. [ 13 ] Adding acetyl groups to STAT6 is suggested to be essential for gene transcription in some forms of IL-4 signalling, but not all the amino acids which are acetylated on STAT6 are known. [ 12 ]
Like many other transcription factors, STATs are capable of recruiting co-activators such as CBP and p300 , and these co-activators increase the rate of transcription of target genes. [ 2 ] The coactivators are able to do this by making genes on DNA more accessible to STATs and by recruiting proteins needed for transcription of genes. The interaction between STATs and coactivators occurs through the transactivation domains (TADs) of STATs. [ 2 ] The TADs on STATs can also interact with histone acetyltransferases (HATs); [ 16 ] these HATs add acetyl groups to lysine residues on proteins associated with DNA called histones . Adding acetyl groups removes the positive charge on lysine residues, and as a result there are weaker interactions between histones and DNA, making DNA more accessible to STATs and enabling an increase in the transcription of target genes.
JAK-STAT signalling is able to interconnect with other cell-signalling pathways, such as the PI3K/AKT/mTOR pathway . [ 17 ] When JAKs are activated and phosphorylate tyrosine residues on receptors, proteins with SH2 domains (such as STATs) are able bind to the phosphotyrosines, and the proteins can carry out their function. Like STATs, the PI3K protein also has an SH2 domain, and therefore it is also able to bind to these phosphorylated receptors. [ 17 ] As a result, activating the JAK-STAT pathway can also activate PI3K/AKT/mTOR signalling.
JAK-STAT signalling can also integrate with the MAPK/ERK pathway . Firstly, a protein important for MAPK/ERK signalling, called Grb2 , has an SH2 domain, and therefore it can bind to receptors phosphorylated by JAKs (in a similar way to PI3K). [ 17 ] Grb2 then functions to allow the MAPK/ERK pathway to progress. Secondly, a protein activated by the MAPK/ERK pathway, called MAPK (mitogen-activated protein kinase), can phosphorylate STATs, which can increase gene transcription by STATs. [ 17 ] However, although MAPK can increase transcription induced by STATs, one study indicates that phosphorylation of STAT3 by MAPK can reduce STAT3 activity. [ 18 ]
One example of JAK-STAT signalling integrating with other pathways is Interleukin-2 (IL-2) receptor signaling in T cells . IL-2 receptors have γ (gamma) chains, which are associated with JAK3 , which then phosphorylates key tyrosines on the tail of the receptor. [ 19 ] Phosphorylation then recruits an adaptor protein called Shc , which activates the MAPK/ERK pathway, and this facilitates gene regulation by STAT5 . [ 19 ]
An alternative mechanism for JAK-STAT signalling has also been suggested. In this model, SH2 domain -containing kinases , can bind to phosphorylated tyrosines on receptors and directly phosphorylate STATs, resulting in STAT dimerization. [ 6 ] Therefore, unlike the traditional mechanism, STATs can be phosphorylated not just by JAKs, but by other receptor-bound kinases. So, if one of the kinases (either JAK or the alternative SH2-containing kinase) cannot function, signalling may still occur through activity of the other kinase. [ 6 ] This has been shown experimentally. [ 20 ]
Given that many JAKs are associated with cytokine receptors , the JAK-STAT signalling pathway plays a major role in cytokine receptor signalling. Since cytokines are substances produced by immune cells that can alter the activity of neighbouring cells, the effects of JAK-STAT signalling are often more highly seen in cells of the immune system. For example, JAK3 activation in response to IL-2 is vital for lymphocyte development and function. [ 21 ] Also, one study indicates that JAK1 is needed to carry out signalling for receptors of the cytokines IFNγ, IL-2, IL-4 and IL-10 . [ 22 ]
The JAK-STAT pathway in cytokine receptor signalling can activate STATs, which can bind to DNA and allow the transcription of genes involved in immune cell division, survival, activation and recruitment. For example, STAT1 can enable the transcription of genes which inhibit cell division and stimulate inflammation . [ 2 ] Also, STAT4 is able to activate NK cells (natural killer cells), and STAT5 can drive the formation of white blood cells . [ 2 ] [ 23 ] In response to cytokines, such as IL-4, JAK-STAT signalling is also able to stimulate STAT6 , which can promote B-cell proliferation, immune cell survival, and the production of an antibody called IgE . [ 2 ]
JAK-STAT signalling plays an important role in animal development. The pathway can promote blood cell division, as well as differentiation (the process of a cell becoming more specialised). [ 24 ] In some flies with faulty JAK genes, too much blood cell division can occur, potentially resulting in leukaemia . [ 25 ] JAK-STAT signalling has also been associated with excessive white blood cell division in humans and mice. [ 24 ]
The signalling pathway is also crucial for eye development in the fruit fly ( Drosophila melanogaster ). When mutations occur in genes coding for JAKs, some cells in the eye may be unable to divide, and other cells, such as photoreceptor cells , have been shown not to develop correctly. [ 24 ]
The entire removal of a JAK and a STAT in Drosophila causes death of Drosophila embryos, whilst mutations in the genes coding for JAKs and STATs can cause deformities in the body patterns of flies, particularly defects in forming body segments. [ 24 ] One theory as to how interfering with JAK-STAT signalling might cause these defects is that STATs may directly bind to DNA and promote the transcription of genes involved in forming body segments, and therefore by mutating JAKs or STATs, flies experience segmentation defects. [ 26 ] STAT binding sites have been identified on one of these genes, called even-skipped ( eve ), to support this theory. [ 27 ] Of all the segment stripes affected by JAK or STAT mutations, the fifth stripe is affected the most, the exact molecular reasons behind this are still unknown. [ 24 ]
Given the importance of the JAK-STAT signalling pathway, particularly in cytokine signalling, there are a variety of mechanisms that cells possess to regulate the amount of signalling that occurs. Three major groups of proteins that cells use to regulate this signalling pathway are protein inhibitors of activated STAT (PIAS), [ 28 ] protein tyrosine phosphatases (PTPs) [ 29 ] and suppressors of cytokine signalling (SOCS). [ 30 ] Computational models of JAK-STAT signaling based on the laws of chemical kinetics have elucidated the importance of these different regulatory mechanisms on JAK-STAT signaling dynamics. [ 31 ] [ 32 ] [ 33 ]
PIAS are a four-member protein family made of: PIAS1 , PIAS3 , PIASx , and PIASγ . [ 34 ] The proteins add a marker, called SUMO (small ubiquitin-like modifier), onto other proteins – such as JAKs and STATs, modifying their function. [ 34 ] The addition of a SUMO group onto STAT1 by PIAS1 has been shown to prevent activation of genes by STAT1. [ 35 ] Other studies have demonstrated that adding a SUMO group to STATs may block phosphorylation of tyrosines on STATs, preventing their dimerization and inhibiting JAK-STAT signalling. [ 36 ] PIASγ has also been shown to prevent STAT1 from functioning. [ 37 ] PIAS proteins may also function by preventing STATs from binding to DNA (and therefore preventing gene activation), and by recruiting proteins called histone deacetylases (HDACs), which lower the level of gene expression. [ 34 ]
Since adding phosphate groups on tyrosines is such an important part of how the JAK-STAT signalling pathway functions, removing these phosphate groups can inhibit signalling. PTPs are tyrosine phosphatases, so are able to remove these phosphates and prevent signalling. Three major PTPs are SHP-1 , SHP-2 and CD45 . [ 38 ]
One example of this is seen in the JAK-STAT signalling pathway mediated by the erythropoietin receptor (EpoR). Here, SHP-1 binds directly to a tyrosine residue (at position 429) on EpoR and removes phosphate groups from the receptor-associated JAK2. [ 41 ] The ability of SHP-1 to negatively regulate the JAK-STAT pathway has also been seen in experiments using mice lacking SHP-1. [ 42 ] These mice experience characteristics of autoimmune diseases and show high levels of cell proliferation, which are typical characteristics of an abnormally high level of JAK-STAT signalling. [ 42 ] Additionally, adding methyl groups to the SHP-1 gene (which reduces the amount of SHP-1 produced) has been linked to lymphoma (a type of blood cancer) . [ 43 ]
However, SHP-1 may also promote JAK-STAT signalling. A study in 1997 found that SHP-1 potentially allows higher amounts of STAT activation, as opposed to reducing STAT activity. [ 44 ] A detailed molecular understanding for how SHP-1 can both activate and inhibit the signalling pathway is still unknown. [ 38 ]
Negative regulation by SHP-2 has been reported in a number of experiments - one example has been when exploring JAK1 / STAT1 signalling, where SHP-2 is able to remove phosphate groups from proteins in the pathway, such as STAT1. [ 46 ] In a similar manner, SHP-2 has also been shown to reduce signalling involving STAT3 and STAT5 proteins, by removing phosphate groups. [ 47 ] [ 48 ]
Like SHP-1, SHP-2 is also believed to promote JAK-STAT signalling in some instances, as well as inhibit signalling. For example, one study indicates that SHP-2 may promote STAT5 activity instead of reducing it. [ 49 ] Also, other studies propose that SHP-2 may increase JAK2 activity, and promote JAK2/STAT5 signalling. [ 50 ] It is still unknown how SHP2 can both inhibit and promote JAK-STAT signalling in the JAK2/STAT5 pathway; one theory is that SHP-2 may promote activation of JAK2, but inhibit STAT5 by removing phosphate groups from it. [ 38 ]
There are eight protein members of the SOCS family: cytokine-inducible SH2 domain-containing protein (CISH), SOCS1 , SOCS2 , SOCS3 , SOCS4 , SOCS5 , SOCS6 , and SOCS7 , each protein has an SH2 domain and a 40-amino-acid region called the SOCS box. [ 53 ] The SOCS box can interact with a number of proteins to form a protein complex, and this complex can then cause the breakdown of JAKs and the receptors themselves, therefore inhibiting JAK-STAT signalling. [ 4 ] The protein complex does this by allowing a marker called ubiquitin to be added to proteins, in a process called ubiquitination , which signals for a protein to be broken down. [ 54 ] The proteins, such as JAKs and the receptors, are then transported to a compartment in the cell called the proteasome , which carries out protein breakdown. [ 54 ]
SOCS can also function by binding to proteins involved in JAK-STAT signalling and blocking their activity. For example, the SH2 domain of SOCS1 binds to a tyrosine in the activation loop of JAKs, which prevents JAKs from phosphorylating each other. [ 4 ] The SH2 domains of SOCS2, SOCS3 and CIS bind directly to receptors themselves. [ 54 ] Also, SOCS1 and SOCS3 can prevent JAK-STAT signalling by binding to JAKs, using segments called kinase inhibitory regions (KIRs) and stopping JAKs binding to other proteins. [ 55 ] The exact details of how other SOCS function is less understood. [ 4 ]
Since the JAK-STAT pathway plays a major role in many fundamental processes, such as apoptosis and inflammation , dysfunctional proteins in the pathway may lead to a number of diseases. For example, alterations in JAK-STAT signalling can result in cancer and diseases affecting the immune system, such as severe combined immunodeficiency disorder (SCID). [ 56 ]
JAK3 can be used for the signalling of IL-2 , IL-4 , IL-15 and IL-21 (as well as other cytokines); therefore patients with mutations in the JAK3 gene often experience issues affecting many aspects of the immune system. [ 57 ] [ 58 ] For example, non-functional JAK3 causes SCID, which results in patients having no NK cells , B cells or T cells , and this would make SCID individuals susceptible to infection. [ 58 ] Mutations of the STAT5 protein, which can signal with JAK3, has been shown to result in autoimmune disorders . [ 59 ]
It has been suggested that patients with mutations in STAT1 and STAT2 are often more likely to develop infections from bacteria and viruses. [ 60 ] Also, STAT4 mutations have been associated with rheumatoid arthritis , and STAT6 mutations are linked to asthma . [ 61 ] [ 62 ]
Patients with a faulty JAK-STAT signalling pathway may also experience skin disorders. For example, non-functional cytokine receptors, and overexpression of STAT3 have both been associated with psoriasis (an autoimmune disease associated with red, flaky skin). [ 58 ] STAT3 plays an important role in psoriasis, as STAT3 can control the production of IL-23 receptors , and IL-23 can help the development of Th17 cells , and Th17 cells can induce psoriasis. [ 63 ] Also, since many cytokines function through the STAT3 transcription factor, STAT3 plays a significant role in maintaining skin immunity . [ 58 ] In addition, because patients with JAK3 gene mutations have no functional T cells, B cells or NK cells, they would more likely to develop skin infections.
Cancer involves abnormal and uncontrollable cell growth in a part of the body. Therefore, since JAK-STAT signalling can allow the transcription of genes involved in cell division, one potential effect of excessive JAK-STAT signalling is cancer formation. High levels of STAT activation have been associated with cancer; in particular, high amounts of STAT3 and STAT5 activation is mostly linked to more dangerous tumours. [ 64 ] For example, too much STAT3 activity has been associated with increasing the likelihood of melanoma (skin cancer) returning after treatment and abnormally high levels of STAT5 activity have been linked to a greater probability of patient death from prostate cancer . [ 65 ] [ 64 ] Altered JAK-STAT signalling can also be involved in developing breast cancer . JAK-STAT signalling in mammary glands (located within breasts) can promote cell division and reduce cell apoptosis during pregnancy and puberty, and therefore if excessively activated, cancer can form. [ 66 ] High STAT3 activity plays a major role in this process, as it can allow the transcription of genes such as BCL2 and c-Myc , which are involved in cell division. [ 66 ]
Mutations in JAK2 can lead to leukaemia and lymphoma . [ 6 ] Specifically, mutations in exons 12, 13, 14 and 15 of the JAK2 gene are proposed to be a risk factor in developing lymphoma or leukemia. [ 6 ] Additionally, mutated STAT3 and STAT5 can increase JAK-STAT signalling in NK and T cells, which promotes very high proliferation of these cells, and increases the likelihood of developing leukaemia. [ 66 ] Also, a JAK-STAT signalling pathway mediated by erythropoietin (EPO), which usually allows the development of red blood cells, may be altered in patients with leukemia. [ 67 ]
The Janus kinase (JAK)/signal transducer and the activator of the transcription ( STAT ) pathway were at the centre of attention for driving hyperinflammation in COVID-19 , i.e., the SARS-CoV-2 infection triggers hyperinflammation through the JAK/STAT pathway, resulting in the recruitment of dendritic cells , macrophages , and natural killer (NK) cells, as well as differentiation of B cells and T cells progressing towards cytokine storm . [ 68 ]
Since excessive JAK-STAT signalling is responsible for some cancers and immune disorders, JAK inhibitors have been proposed as drugs for therapy. For instance, to treat some forms of leukaemia, targeting and inhibiting JAKs could eliminate the effects of EPO signalling and perhaps prevent the development of leukaemia. [ 67 ] One example of a JAK inhibitor drug is ruxolitinib , which is used as a JAK2 inhibitor. [ 64 ] STAT inhibitors are also being developed, and many of the inhibitors target STAT3. [ 66 ] It has been reported that therapies which target STAT3 can improve the survival of patients with cancer. [ 66 ] Another drug, called Tofacitinib , has been used for psoriasis and rheumatoid arthritis treatment, and has been approved for treatment of Crohn's disease and ulcerative colitis . [ 56 ] | https://en.wikipedia.org/wiki/JAK-STAT_signaling_pathway |
The JANNAF Interagency Propulsion Committee (JANNAF IPC, or simply JANNAF) is a joint-agency committee chartered by the USDOD and NASA . [ 3 ] JANNAF is composed of two committees: the Technical Committee and the Programmatic & Industrial Base (PIB) Committee. [ 4 ] The Technical Committee is itself divided into subcommittees focused on specific technology areas of mutual interest to the DoD and NASA. [ 5 ] The JANNAF PIB Committee is a forum for the discussion of strategic program planning and industrial base capabilities in the area of rocket propulsion and energetic systems and components for military and civil space, tactical and strategic missiles, and large gun systems. [ 6 ]
JANNAF was re-chartered on June 19th 2014 with the signatures of Frank Kendall III , Under Secretary of Defense for Acquisition, Technology, and Logistics (USD(AT&L)) and Robert Lightfoot Jr. , Associate Administrator of the National Aeronautics and Space Administration (NASA) . [ 3 ]
This United States government–related article is a stub . You can help Wikipedia by expanding it .
This United States military article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JANNAF |
JCAMP-DX are text-based file formats created by JCAMP for storing spectroscopic data. It started as a file format for Infrared spectroscopy . [ 1 ] It was later expanded to cover Nuclear magnetic resonance spectroscopy , [ 2 ] mass spectrometry , [ 3 ] electron magnetic resonance [ 4 ] and circular dichroism spectroscopy. [ 5 ] Later extensions for good laboratory practice were added to cover contract laboratories needs. [ 6 ] Despite all efforts to create an easy to comprehend standards, most vendor implementations differ slightly. [ 7 ] An open source implementation exists in Java . [ 8 ] | https://en.wikipedia.org/wiki/JCAMP-DX |
JChemPaint is computer software , a molecule editor and file viewer for chemical structures using 2D computer graphics . [ 1 ] It is free and open-source software , released under a GNU Lesser General Public License (LGPL). It is written in Java and so can run on the operating systems Windows , macOS , Linux , and Unix . There is a standalone application (editor), and two varieties of applet (editor and viewer) that can be integrated into web pages .
JChemPaint was initiated by Christoph Steinbeck and is currently being developed as part of The Chemistry Development Kit (CDK), and a Standard Widget Toolkit (SWT) based JChemPaint application is being developed, as part of Bioclipse . | https://en.wikipedia.org/wiki/JChemPaint |
The JEDEC memory standards are the specifications for semiconductor memory circuits and similar storage devices promulgated by the Joint Electron Device Engineering Council (JEDEC) Solid State Technology Association, a semiconductor trade and engineering standardization organization.
JEDEC Standard 100B.01 specifies common terms, units, and other definitions in use in the semiconductor industry. JESC21-C specifies semiconductor memories from the 256 bit static RAM to DDR4 SDRAM modules.
The Joint Electron Device Engineering Council characterizes its standardization efforts as follows: [ 1 ]
JEDEC standards and publications are designed to serve the public interest through eliminating misunderstandings between manufacturers and purchasers, facilitating interchangeability and improvement of products, and assisting the purchaser in selecting and obtaining with minimum delay the proper product for use by those other than JEDEC members, whether the standard is to be used either domestically or internationally.
The December 2002 JEDEC Standard 100B.01 is entitled Terms, Definitions, and Letter Symbols for Microcomputers, Microprocessors, and Memory Integrated Circuits . The purpose of the standard is to promote the uniform use of symbols, abbreviations, terms, and definitions throughout the semiconductor industry. [ 1 ]
The specification defines the two common units of information: [ 2 ]
The specification contains citations of the commonly used prefixes kilo , mega , and giga to prefix units of semiconductor storage capacity.
The specification cites three prefixes as follows, with the note that these prefixes are included in the document only to reflect common usage.
It refers to the IEEE/ASTM SI 10-1997 standard as stating that " this practice frequently leads to confusion and is deprecated ". The document further refers to the description of the IEC binary prefixes in Amendment 2 of IEC 60027-2, " Letter symbols to be used in electrical technology ", for an alternate system of prefixes [ note 1 ] and includes a table of the IEC prefixes in the note.
The document notes that these prefixes are used in their decimal sense for serial communication data rates measured in bits .
The JEDEC terms dictionary further includes, under the entry for mega , definitions for the binary prefixes kibi (Ki), mebi (Mi), gibi (Gi), and tebi (Ti) as powers of 2, and kilo, mega, giga, and tera as powers of 10. [ 6 ] For example,
The JEDEC DDR3 SDRAM standard JESD-79-3f uses Mb and Gb to specify binary memory capacity: [ 7 ] " The purpose of this Standard is to define the minimum set of requirements for JEDEC compliant 512 Mb through 8 Gb for x4, x8, and x16 DDR3 SDRAM devices. "
The standard JESD21-C: Configurations for Solid State Memories is maintained by JEDEC committee JC41. This committee consists of members from manufacturers of microprocessors, memory ICs, memory modules, and other components, as well as component integrators, such as video card and personal computer makers. Standard 21 is published in loose-leaf binder format to accommodate frequent updates.
The documentation of modern memory modules, such as the standards for the memory ICs [ 8 ] and a reference design of the module [ 9 ] requires over one hundred pages. The standards specify the physical and electrical characteristics of the modules, and include the data for computer simulations of the memory module operating in a system. [ 10 ]
Memory modules of the DDR2-SDRAM type are available for laptop, desktop, and server computers in a wide selection of capacities and access speeds. The standards specify memory module label formats for end-user markets. [ 11 ] For example:
1GB 2Rx4 PC2-3200P-333-11-D2 is a 1 GB DDR2 Registered DIMM, with address/command parity function, using 2 ranks of x4 SDRAMs operational to PC2-3200 performance with CAS Latency = 3, tRCD = 3, tRP = 3, using JEDEC SPD revision 1.1, raw card reference design file D revision 2 used for the assembly.
The definitions of kilo, giga, and mega based on powers of two are included only to reflect common usage. IEEE/ASTM SI 10-1997 states "This practice frequently leads to confusion and is deprecated." Further confusion results from the popular use of the megabyte representing 1 024 000 bytes to define the capacity of the 1.44-MB high-density diskette. An alternative system is found in Amendment 2 to IEC 60027-2: Letter symbols to be used in electrical technology – Part 2 . | https://en.wikipedia.org/wiki/JEDEC_memory_standards |
JEDMICS stands for "Joint Engineering Data Management Information and Control System”. It is a Department of Defense (DoD) initiative for the management and control of engineering drawings and related text in a standard repository . JEDMICS has been designed as an open, client-server architecture which provides the user with the ability to locate and obtain approved engineering drawings (and associated data). The system provides input services via electronic file transfer , quality assurance review of the drawings, selective retrieval of data using a relational database with built-in business rules, and digital output services.
In addition to providing the repository functions for engineering drawings and associated technical data , JEDMICS defines the indexing elements and data relationships needed to store and locate that data. JEDMICS also provides necessary interfacing to configuration management systems that control the version and applicability of that data. [ 1 ]
While JEDMICS can be used to create new engineering data, it is primarily intended to store data originally created by the various weapon system vendors. JEDMICS provides a centralized and secure publishing mechanism for access to this data by authorized personnel in their house and maintenance of the weapon systems as deployed within the DoD.
Drawings can be accessed from anywhere in the world through a web browser user interface. Requests for data may range from a single drawing to be used by a technician while making repairs, to thousands of drawings requested by an external configuration management system to be assembled into a bid set.
Additional Capabilities:
JEDMICS C4 and CALS are raster (bitmap) image formats developed by the US Department of Defense for military use. [ 2 ]
JEDMICS specifications and software downloads
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JEDMICS |
The Extreme Universe Space Observatory onboard Japanese Experiment Module ( JEM-EUSO ) is the first space mission concept devoted to the investigation of cosmic rays and neutrinos of extreme energy ( E > 5 × 10 19 eV ). Using the Earth's atmosphere as a giant detector, the detection is performed by looking at the streak of fluorescence produced when such a particle interacts with the Earth's atmosphere.
EUSO was a mission of the European Space Agency , designed to be hosted on the International Space Station as an external payload of the Columbus . EUSO successfully completed the "Phase A" study, however in 2004, ESA decided not to proceed with the mission because of programmatic and financial constraints. The mission was then re-oriented as a payload to be hosted on board the JEM module of the Japanese KIBO facility of the ISS. The mission was then renamed JEM-EUSO.
JEM-EUSO is currently (2013) studied by RIKEN and JAXA , in collaboration with 95 other institutions from 16 countries aiming for a flight after 2020. The proposed instrument consists of a set of three large Fresnel lenses of 2.65-metre diameter (with top and bottom cut off to reduce the minimum diameter to 1.9-metre so that they fit in the HTV resupply vehicle in which the instrument is to be launched) feeding a detector consisting of 137 modules each a 48 x 48 array of photomultipliers. The imaging takes place in the 300 nm-450 nm band (low-energy UV through deep-blue), and photons are time-tagged with 2.5-microsecond precision. [ 2 ]
In addition to its main, science mission, EUSO might also be used to detect orbiting space junk that could pose a threat to ISS, that is too small to be spotted by astronomers (1 to 10 cm). The ISS is shielded adequately against particles that are smaller than 1 cm. Particles in this range, or larger, can inflict serious damage, especially to other objects in orbit, since many of them are traveling at speeds of about 36,000 km/h. Nearly 3,000 tons of space debris resides in low Earth orbit ; more than 700,000 pieces of debris larger than 1 cm now orbit Earth. A laser might then be used to deflect dangerous particles. The project could be ready to implement after about 2017–2018, using better lasers. [ 3 ]
[ 4 ] [ 5 ] | https://en.wikipedia.org/wiki/JEM-EUSO |
JGB S.A. is a Colombian company that manufactures pharmaceutical products, multivitamin supplements, oral hygiene products and home care products, founded in 1875. [ 1 ] [ 2 ] [ 3 ] It is one of the oldest companies in Colombia. [ 1 ] [ 4 ]
In 1875, the doctor Enrique Garcés Velasco founded the Garcés drugstore, which he ran with his wife Joaquina Borrero de Garcés. [ 5 ] In 1899, Dr. Jorge Enrique Garcés died and his son Jorge Garcés Borrero, together with his mother, took over the management of the pharmacy. [ 5 ] In 1925 the company formally changed its name to Laboratorios JGB (initials of its name), specialising in the production of pharmaceutical products, especially one of its most marketed products, granulated glue "Tarrito Rojo". [ 6 ] [ 7 ] [ 8 ] [ 9 ]
The main plant is in the city of Cali and has two more in Cartagena and Cajicá . [ 10 ] Until 2014 it had 1,000 employees. [ 11 ] The company exports its products to several distributors located in the Región Andina and the Estados Unidos and maintains operations in Ecuador and Venezuela . [ 12 ] [ 13 ] [ 14 ] | https://en.wikipedia.org/wiki/JGB_(company) |
JIC fittings , defined by the SAE J514 and MIL-DTL-18866 standards, are a type of flare fitting machined with a 37-degree flare seating surface. JIC (Joint Industry Council) fittings are widely used in fuel delivery and fluid power applications, especially where high pressure (up to 10,000 pounds per square inch (690 bar)) is involved. The SAE J514 standard replaces the MS16142 US military specification , although some tooling is still listed under MS16142. JIC fittings are dimensionally identical to AN (Army-Navy) fittings, but are produced to less exacting tolerances and are generally less costly. [ 1 ] SAE 45-degree flare fittings are similar in appearance, but are not interchangeable, though dash sizes 2, 3, 4, 5, 8, and 10 share the same thread size. Some couplings may have dual machined seats for both 37-degree and 45-degree flare seats.
Komatsu and JIS (Japanese Industrial Standard) fittings have flare ends similar to JIC fittings. Komatsu and JIS both use a 30-degree flare seating surface. The only difference is Komatsu uses millimeter thread sizes while JIS use a BSP (British Standard Pipe) thread.
JIC fitting systems have three components that make a tubing assembly: fitting, flare nut, and sleeve. As with other flared connection systems, the seal is achieved through metal-to-metal contact between the finished surface of the fitting nose and the inside diameter of the flared tubing. The sleeve is used to evenly distribute the compressive forces of the flare nut to the flared end of the tube. Materials commonly used to fabricate JIC fittings include forged carbon steel , forged stainless steel , forged brass , machined brass, Monel and nickel-copper alloys.
JIC fittings are commonly used in the Fluid Power industry in a diagnostic and test-point setting. A three-way JIC coupling provides a port inline of circuit by which a user can connect a measurement or diagnostic device to take pressure readings and perform circuit and system diagnostics.
This article about a mechanical engineering topic is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JIC_fitting |
The JME Molecule Editor is a molecule editor Java applet with which users make and edit drawings of molecules and reactions (including generating substructure queries), and can display molecules within an HTML page. [ 1 ] The editor can generate Daylight simplified molecular-input line-entry system (SMILES) or MDL Molfiles of the created structures.
The JME Editor was written by Peter Ertl while at Comenius University in Bratislava, and then at Ciba-Geigy, later merged with Sandoz Laboratories, to form Novartis International AG, in Basel , Switzerland.
It is released as freeware for noncommercial use and has become a standard for molecular-structure input on the web. [1] [2]
JME has been ported to JavaScript using the Google Web Toolkit (GWT). In analogy to JME, the JavaScript version is named JSME. Its interface is almost identical to that of JME, [ 2 ] although some cosmetic options are available. [ 3 ] It is released as free and open-source software under a 3-clause BSD license in the form of minified JavaScript produced by GWT.
As of February 2017 [update] , JSME is capable of SMILES , MOL (original and V3000), InChI (and key), and SVG export. [ 3 ]
This computational chemistry -related article is a stub . You can help Wikipedia by expanding it .
This scientific software article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JME_Molecule_Editor |
JMODEM is a file transfer protocol developed by Richard Johnson in 1988. It is similar to the seminal XMODEM in most ways, but uses a variable-size packet in order to make better use of the available bandwidth on high-speed modems .
JMODEM uses variable-length records called blocks. These blocks start with 512 data-bytes and increase in length to a maximum of 8192 bytes per block. There is a 6-byte overhead associated with each block so the percentage of overhead starts at a fairly high 1.1 percent and decreases to a very low 0.07 percent as the transmission progresses. The block length will increase in 512-byte increments as long as there are no errors requiring retransmission. Should an error occur, the block-size is cut in half. This continues until the block-size is as short as 64 bytes.
JMODEM also included a basic RLE data compression system, which replaces strings of repeated characters with a counter. If a string of many similar characters are found, JMODEM sends a "sentinel byte" (hexadecimal 0xBB) followed by a two-byte number, followed by the byte to be repeated. JMODEM applied RLE on a block-by-block basis, as opposed to the file as a whole. Since many files were already compressed with systems like .zip , JMODEM only used RLE on blocks where it actually reduced the size of the block.
JMODEM is explained in some detail in the John Dvorak book Dvorak's Guide to PC Telecommunications . [ 1 ]
This article related to telecommunications is a stub . You can help Wikipedia by expanding it .
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JMODEM |
JOELib is computer software , a chemical expert system used mainly to interconvert chemical file formats . Because of its strong relationship to informatics , this program belongs more to the category cheminformatics than to molecular modelling . It is available for Windows , Unix and other operating systems supporting the programming language Java . It is free and open-source software distributed under the GNU General Public License (GPL) 2.0.
JOELib and OpenBabel were derived from the OELib Cheminformatics library.
The project logo is just the word JOELib in the Tengwar script of J. R. R. Tolkien . The letters are grouped as JO-E-Li-b. Vowels are usually grouped together with a consonant , but two following vowels must be separated by a helper construct. | https://en.wikipedia.org/wiki/JOELib |
JOM is a technical journal devoted to exploring the many aspects of materials, science and engineering published monthly by The Minerals, Metals & Materials Society (TMS) (a member-based professional society). [ 1 ] JOM reports scholarly work that explores the many aspects of materials science and engineering within the broad topical areas of light metals , structural materials , functional materials , extraction and processing, and materials processing and manufacturing. JOM strives to balance the interests of the laboratory and the marketplace by reporting academic , industrial , and government -sponsored work from around the world.
From 1949 through 1988, the journal was named Journal of Metals . With materials systems becoming commonplace and with the journal frequently covering composites , plastics , and other materials, its name was changed to JOM . It is published by TMS, which is headquartered in Pittsburgh, Pennsylvania . [ 2 ]
This science and technology magazine–related article is a stub . You can help Wikipedia by expanding it .
See tips for writing articles about magazines . Further suggestions might be found on the article's talk page . | https://en.wikipedia.org/wiki/JOM_(journal) |
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jOrgan is a Java -based MIDI processor. It is free software for complex transmitting and dynamical modifying of MIDI messages on their way between MIDI encoders and MIDI decoders, through an own MIDI Programming Language MPL. It can be used as Virtual Pipe Organ (virtual organ console). Runs on Microsoft Windows , Linux and macOS operating systems. [ 1 ] [ 2 ]
Sources: [ 1 ] [ 2 ] | https://en.wikipedia.org/wiki/JOrgan |
JP-10 (Jet Propellant 10) is a synthetic jet fuel , specified and used mainly as fuel in missiles . Being designed for military purposes, it is not a kerosene based fuel.
Developed to be a gas turbine fuel for cruise missiles , [ 1 ] it contains mainly exo-tetrahydrodicyclopentadiene (exo-THDCPD) with some endo-isomer impurity. [ 2 ] About 100 ppm of alkylphenol -based antioxidant is added to prevent gumming. Optionally, 0.10–0.15% of fuel system icing inhibitor may be added. [ 3 ] Exo-THDCPD is produced by catalytic hydrogenation of dicyclopentadiene and then isomerization. [ 4 ]
It superseded JP-9 , which is a mixture of norbornadiene -based RJ-5 fuel, tetrahydrodicyclopentadiene and methylcyclohexane , because of a lower temperature service limit and about four times lower price. [ 5 ] Since the lack of volatile methylcyclohexane makes its ignition difficult, a separate priming fluid PF-1 with about 10-12% of this additive is required for the engine start-up. [ 5 ] Its main use is in the Tomahawk missiles. [ 6 ]
The Russian equivalent is called detsilin [ ru ] .
JP-10 absorbs heat energy, so is endothermic with a relatively high density of 940 kg/m 3 . It has a low freezing point of less than −110 °C (−166 °F) and the flash point is 130 °F (54 °C). The high energy density of 39.6 MJ/L makes it ideal for military aerospace applications - its primary use. The ignition and burn chemistry has been extensively studied. [ 8 ] [ 9 ] [ 10 ] The exo isomer also has a low freezing point. [ 11 ] [ 12 ] Its other properties have also been studied extensively. [ 13 ] [ 14 ] [ 15 ] [ 16 ] [ 17 ]
Even though its uses are mainly for the military, the relatively high cost has meant research has been undertaken to find lower costs routes including the use of cellulosic materials . [ 18 ]
Current and past areas of research focus on:
This aviation -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JP-10_(fuel) |
JSBML [ 1 ] [ 2 ] (Java Systems Biology Markup Language) is an open-source Java (API) for the SBML (Systems Biology Markup Language [ 3 ] [ 4 ] [ 5 ] ) format. Its API strives to attain a strong similarity to the Java binding of the corresponding library libSBML , but is entirely implemented in Java and therefore platform independent . JSBML provides an elaborated abstract type hierarchy, whose data types implement or extend many interfaces and abstract classes from the standard Java library. In this way, JSBML integrates smoothly into existing Java projects, and provides methods to read, write, evaluate, and manipulate the content of SBML documents.
In May 2009 the SBML team conducted a community survey for requests of potential further software development. It turned out that, even though the library libSBML provides a generated binding for the programming language Java , its internal C code makes it difficult to implement platform independent or Web Start applications.
Around that time, several groups from multiple institutes had already implemented small Java versions of libSBML , each being a customized library covering the needs of the particular research project. In order to avoid unnecessary duplications of work and to unify existing development, the international community project JSBML was launched in September 2009, mainly by groups from EBI , Caltech , and a team of students at the University of Tübingen led by Andreas Dräger .
Since JSBML has been implemented considerably later than the first version of libSBML , it could therefore benefit from the existence of the specifications of SBML in the Levels 1–3. Hence, JSBML has not just been developed by porting existing C code from the libSBML project into a new Java . Instead, the developers used this as a chance to completely redesign the class and API structure. This is why JSBML provides a much richer abstract type hierarchy compared to libSBML . Furthermore, the development of JSBML enabled making design decisions that are not possible in libSBML because no backward compatibility had to be considered at this time.
The first stable release version 0.8 of JSBML was made publicly available for download in February 2011. Since then, support for multiple SBML extension packages is being implemented and will be included with the release of JSBML 1.0.
The development of JSBML is driven by three aims:
The following example assumes that a JAR file of JSBML has been included into the class path and that a local installation of a Java Virtual Machine is available on the platform where the code is executed.
The following coding example shows how an SBML file can be parsed and its content can be displayed in form of a tree in a window.
The result can look, e.g., as the image on the right. It can be seen that the actual parsing of SBML is done in a single line, by calling a static method in the class SBMLReader. The creation of the tree for the display is also trivial, because the entire data structure in JSBML is organized as a tree . | https://en.wikipedia.org/wiki/JSBML |
JSFiddle is an online IDE service and online community for testing and showcasing user-created and collaborational HTML , CSS and JavaScript code snippets, known as 'fiddles'. It allows for simulated AJAX calls. In 2019, JSFiddle was ranked the second most popular online IDE by the PopularitY of Programming Language (PYPL) index based on the number of times it was searched, directly behind Cloud9 IDE , worldwide [ 1 ] and in the USA. [ 2 ]
JSFiddle is an online IDE which is designed to allow users to edit and run HTML, JavaScript, and CSS code on a single page. [ 3 ] Its interface is minimalist and split into four main frames, which correspond to editable HTML, JavaScript and CSS fields and a result field which displays the user's project after it is run. [ 3 ] Since early on, JSFiddle adopted smart source-code editor with programming features .
As of 2020, JSFiddle uses CodeMirror to support its editable fields, providing multicursors , syntax highlighting , syntax verification (linter), brace matching , auto indentation , autocompletion , code/text folding , Search and Replace to assist web developers in their actions. [ 4 ] On the left, a sidebar allows users to integrate external resources such as external CSS stylesheets and external JavaScript libraries. The most popular JavaScript frameworks and CSS frameworks are suggested to users and available via a click.
JSFiddle allows users to publicly save their code an uncapped number of times for free. [ 3 ] Each version is saved online at the application's website with an incremental numbered suffix . [ citation needed ] This allows users to re-access their saved code. [ 3 ] Code saved on JSFiddle may also be edited into new versions, shared with other parties, and forked into a new line. [ 3 ]
JSFiddle is widely used among web developers to share simple tests and demonstrations. JSFiddle is also widely used on Stack Overflow , the dominant question-answer online forum for the web industry.
In 2009, JSFiddle's predecessor, MooShell, was created by Piotr Zalewa as a website application which was exclusive to the MooTools community. [ 5 ] In 2010, Oskar Krawczyk joined the project as a developer, and the platform was made freely available under the name of JSFiddle. [ 5 ]
In 2016, JSFiddle underwent a full platform overhaul and became ad-sponsored. [ 5 ] In 2017, Michał Laskowski and Andrzej Kała joined the company. [ citation needed ]
This computing article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JSFiddle |
JT (Jupiter Tessellation) is an openly-published ISO-standardized 3D CAD data exchange format used for product visualization , collaboration , digital mockups , and other purposes. [ 1 ] It was developed by Siemens . [ 1 ]
It can contain any combination of approximate (faceted) data, boundary representation surfaces ( NURBS ), Product and Manufacturing Information (PMI), and Metadata (textual attributes) either exported from the native CAD system or inserted by a product data management (PDM) system.
The JT format contains a scene graph representation of an assembly, nested sub-assemblies of parts with CAD specific node and attributes data. [ 2 ] : 17 Facet information (triangles) is stored by using geometry compression techniques. Visual attributes of 3D scene and model like lights, textures, and/or materials are supported. Product and Manufacturing Information (PMI), Precise Part definitions (BRep), additional metadata, and a variety of representation configurations are supported. The JT format is designed to be streamable . [ 2 ] : 17
JT files are used in product lifecycle management (PLM) software programs and their respective CAD systems, by engineers and other professionals that need to analyze the geometry of complex products. The format and associated software is structured so that extremely large numbers of components can be quickly loaded, shaded and manipulated in real-time. Because all major 3D CAD formats are supported, a JT assembly can contain a mixture of any combination which has led to the term "multi-CAD". As JT is typically implemented as an integral part of a PLM solution, the resulting multi-CAD assembly is managed such that changes to the original CAD product definition files can be automatically synchronized with their associated JT files resulting in a multi-CAD assembly that is always up-to-date.
Because JT files are inherently "lightweight" (~1-10% of the size of a CAD file) they are ideal for internet collaboration. With the growing trend toward globalization, more companies are leveraging resources wherever they are available in the world. Collaboration using JT allows companies to send 3D visualization data to suppliers and partners much more easily than sending the associated "heavy" CAD files. In addition, real-time, on-line collaboration is easier because the amount of information sent back-and-forth across the internet is reduced. Finally, JT provides an inherent security feature such that intellectual property does not have to be shared with inappropriate parties. As indicated above, JT can contain any combination of data such that the right amount of information can be shared without exposing the underlying proprietary design definition information.
JT is often used for Digital mock-up (DMU) work, which allows engineers to validate that a product can be assembled without interferences long before a physical prototype could be produced. This "spatial validation" is enabled by precise measurements and cross-sectioning as well as sophisticated clearance/interference detection. Leveraging JT for digital mock-up allows users to reduce or eliminate costly physical prototypes and enables decision-making to occur much earlier in the development process.
Finally, JT is used as a CAD interoperability format for exchanging design data for Collaborative Product Development , where JT files are created by translating data from CAD systems such as NX (Unigraphics) , Creo Elements/Pro , FORAN , I-DEAS , Solid Edge , Catia , Microstation or Autodesk Inventor .
JT was created to support the interactive display of very large assemblies (i.e. those containing tens of thousands of components). The JT file format is capable of storing an arbitrary number of faceted representations with varying levels of detail (LODs). When the whole product is displayed on the computer screen the hosting application displays only a simple, coarse, model. However, as the user zooms into a particular area, progressively finer representations are loaded and displayed. Over time, unused representations are unloaded to save memory.
JT was originally developed by Engineering Animation, Inc. and Hewlett-Packard as the DirectModel toolkit (initially Jupiter). JT is the abbreviation for Jupiter Tesselation. When EAI was purchased by UGS Corp. , JT became a part of UGS's suite of products. Early in 2007 UGS announced the publication of the JT data format easing the adoption of JT as a master 3D format. Also in 2007, UGS was acquired by Siemens AG and became Siemens Digital Industries Software . JT is the common interoperability format in use across all of Siemens Digital Industries Software and has been adopted as the long term data archival format across all of Siemens.
On September 18, 2009, the ISO stated officially that the JT specification has been accepted for publication as an ISO Publicly Available Specification (PAS). End of August 2010 the Ballot for the New Work Item (NWI) proposal for JT as ISO International Standard was started by ProSTEP iViP . ProSTEP iViP thereby aimed on the one hand to publish the JT file format specification as ISO Standard and, on the other hand, to harmonize this undertaking with the new STEP AP 242 development, so that JT and STEP (especially STEP AP 242 XML) can be used together to assure major benefits within industrial data exchange scenarios.
In 2012 December, JT has been officially published as ISO 14306:2012 (ISO JT V1) [ 3 ] as a 3D visualization format, based on version 9.5 of JT specifications released by Siemens Digital Industries Software. Through this publication via ISO, for the first time a completely neutral and royalty-free specification of JT was available. [ 4 ]
Beginning of 2013, in ISO the specification of ISO JT V2 was started. The ISO/DIS 14306 V2 [ 5 ] was accepted by ISO in November 2016. The final International Standard was published in November 2017. [ 2 ] Main difference between V1 and V2 is the incorporation of a STEP B-rep as an additional B-rep segment.
For providing additional functionalities and innovations required by industry, ProSTEP iViP and VDA decided mid of 2015 to specify a so-called JT Industrial Application Package (JTIAP), [ 6 ] which is a JT file format specification completely compatible to ISO 14306 (V1 as well as the future V2) and currently existing JT-Open-based implementations. Thereby, JTIAP provide a more comprehensive compression algorithm ( LZMA ), specifies XT B-rep as recommended representation of exact geometry and allows the neutral and royalty-free implementation of JT.
The JT data model is capable of representing a wide range of engineering data. This data can be very lightweight, holding little more than facet data or it can be quite rich, containing complete NURBS geometry representations along with product structure, attributes, meta data and PMI . It also supports multiple tessellations and level-of-detail (LOD) generation. [ 2 ] : 17
The relationship of product structure hierarchy to exported JT file structure is arbitrary. Any node in the hierarchy may be specified as the start of a new JT file. Thus, product structure may be represented in a variety of JT file configurations.
JT supports common product structure-to-file structure mappings. These include:
Client applications may use these mappings, or choose to define their own custom mapping.
To help shrink the storage and transmission bandwidth requirements of 3D models, JT files may take advantage of compression. Use of compression is transparent to the user of the JT data, and a given model may be composed of JT files using different compression settings (including none).
To date, the JT file format has evolved through two forms of compression, exposed in JT Open Toolkit as standard and advanced compression. These differ in that the former employs a simple, lossless compression algorithm, while the latter employs a more sophisticated, domain-specific compression scheme supporting lossy geometry compression. Client applications are encouraged to take advantage of advanced compression over standard compression, as attainable compression ratios are much greater. Support for standard compression is maintained only in the interest of backward compatibility with legacy JT file viewing applications.
The compression form used by a JT file is related to the JT file format version in which it was written. This version is readily viewable by opening a JT file in a text editor and looking at its ASCII header information. | https://en.wikipedia.org/wiki/JT_(visualization_format) |
JUICE is a non-commercial software package for editing and analysing phytosociological data.
It was developed at the Masaryk University in Brno , Czech Republic in 1998, and is fully described in English manual. It makes use of the previously-developed TURBOVEG software for entering and storing such data) and performs vegetation data analysis, including: | https://en.wikipedia.org/wiki/JUICE_(software) |
JULES (Joint UK Land Environment Simulator) is a land-surface parameterisation model scheme describing soil-vegetation-atmosphere interactions. [ 1 ] JULES is a community led [ citation needed ] project which evolved from MOSES, the United Kingdom Meteorological Office (Met Office) Surface Exchange Scheme. [ 2 ] It can be used as a stand-alone model or as the land surface part of the Met Office Unified Model. [ 2 ] JULES has been used to help decide what tactics would be effective to help meet the goals of the Paris Agreement . [ 3 ] As well as use by the Met Office climate modelling group [ 4 ] a number of studies have cited JULES and used it as a tool to assess the effects of climate change , and to simulate environmental factors from groundwater to carbon in the atmosphere . [ 5 ] [ 6 ] [ 7 ] [ 8 ] [ 9 ]
JULES has been described as the most accurate global carbon budget model of net ecosystem productivity, because it has more years of data than other models. [ 10 ]
This article about atmospheric science is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/JULES |
JUNQ and IPOD are types of cytosolic protein inclusion bodies in eukaryotes .
Neurodegenerative diseases , such as Parkinson's , Alzheimer's , and Huntington's , are associated and correlated with protein aggregation and accumulation of misfolded proteins in inclusion bodies . For many years, protein aggregation was considered a random process by which misfolded proteins stick to each other to form inclusions [ 1 ] (imagine a bundle of hairs haphazardly piling up in a corner of a room). Moreover, protein aggregates were thought to be toxic agents and the cause for neuronal dysfunction and death. However, recent studies, using advanced methods (i.e. fluorescence microscopy ), show that protein aggregation may actually be a tightly regulated, organized process, by which the cell protects itself from toxic proteins by sequestration to inclusion bodies. [ 2 ] In 2008, Daniel Kaganovich working in the Frydman lab showed that eukaryotic cells sort misfolded proteins into two distinct inclusion bodies in a well-managed cellular process: [ 3 ]
JUNQ and IPOD are evolutionarily conserved , and are found in specific and defined cellular sites. Delivery of misfolded, aggregated proteins to JUNQ and IPOD require an intact cytoskeleton and specific cellular quality control components, such as Heat Shock Proteins (HSPs) . [ 4 ] The partition into the two distinct inclusion bodies is due to the different handling and processing of different kinds of misfolded proteins (e.g. ubiquitinated vs. non-ubiquitinated proteins). Segregation of toxic protein aggregates into JUNQ and IPOD inclusion bodies is a means by which mammalian cells can be rejuvenated through asymmetric division. [ 5 ]
Thus, the discovery of JUNQ and IPOD provided a new striking perspective of how cells manage misfolded aggregated proteins and gave convincing proof that protein aggregation is a non-random, well regulated and controlled cellular process. Furthermore, the discovery of JUNQ and IPOD suggested that in addition to temporal quality control (i.e. time dependent administration of damaged proteins) cells exploit homeostasis spatially: [ 6 ] If degradation is unavailable, protection of the cellular environment from a misfolded protein is accomplished by its sequestration to an aggregate inclusion. [ citation needed ]
To function properly, most proteins must preserve a low-energy, three-dimensional structure known as the native state . The stability of a protein is tightly regulated through all its life stages: from cradle, as it is synthesized at the ribosome , through folding or assembly , till grave – when the protein is degraded and cleared from the cellular environment. [ 7 ] Protein homeostasis (proteostasis), [ 8 ] results from the coordinated action of the different arms of the cellular quality control system: molecular chaperones , proteases and other regulatory factors. Hence, cellular viability depends on timely and efficient management of misfolded proteins. Such management, by the quality control machinery, includes recognition of the misfolded protein by chaperones and E3 ligases , ubiquitination and degradation . [ citation needed ]
Proteostasis collapse, due to damage, stress, mutations , and aging , has been implicated as a basis for a large number of common human disorders, such as neurodegenerative diseases . [ 9 ] Although caused by different kinds of mutated proteins (e.g. in Huntington's disease – the protein Huntingtin ) and disruptive to distinct tissues (e.g. in Huntington's disease – the striatum ), such diseases share a common feature: accumulation of misfolded proteins in inclusion bodies . Thus, it was thought that the inclusion bodies are the cause of such diseases. However, the nature and characteristics of those intra-cellular inclusion bodies stayed elusive. Different kinds of proteins (e.g. prions , ERAD substrates ) were reported to form different kinds of inclusion bodies (e.g. aggresomes , amyloids ), yet it remained obscure if those observations combine into one and relate to the same sub-cellular site. Moreover, the pathways leading to inclusion formation and the involvement of the cellular protein quality control machinery were undefined and unknown. Thus, a systematic study providing a comprehensive understanding of protein aggregation and inclusion bodies was required. The discovery of JUNQ and IPOD [ 3 ] suggested new insights of how the cell manages different kinds of misfolded proteins and offered a novel framework for putting together the great puzzle of protein aggregation . [ 2 ]
The fate of misfolded proteins and the process leading to the formation of aggregate inclusions, were initially studied using biochemical methods (e.g. western blotting ). [ citation needed ]
Deeper insights into the biological process of protein quality control and aggregation was made possible by a novel approach to looking at this problem, termed "Live Cell Imaging". [ 10 ]
Live cell imaging enables in vivo tracking of proteins in space and time, in their natural endogenous environment. Thus, such a method provides more information about the dynamics and stages of biological events and processes. The method takes advantage of the easily detectable fluorescent proteins fused to a protein of interest, which can then be followed inside a cell using a fluorescence microscope . The cell may then be treated by a perturbation of interest (e.g. a drug, expression of a misfolded protein ), and various properties of the fluorescently tagged protein can be assayed using time-lapse microscopy :
In order to monitor the fate of cytosolic misfolded proteins in vivo , a plasmid carrying a GFP tagged folding reporter was cloned . The folding reporter, a model protein for aggregation, was a Ubc9 (SUMO-conjugating enzyme) mutant (UBC9ts), harboring a missense mutation ( Y68L ) with a temperature- sensitive (ts) phenotype. [ 12 ] [ 13 ] The marginally stable Ubc9ts is fully functional under physiological permissive conditions (25 °C) due to active cellular chaperones . The GFP–Ubc9ts was transformed into yeast and visualized using a fluorescence microscope . [ citation needed ]
Monitoring the folding sensor GFP–Ubc9ts was thought to indicate the cellular proteostasis, and to assay the ability of the cellular protein quality control system to deal with various kinds of stress. It was then observed that under normal conditions, GFP–Ubc9ts is diffused in the nucleus and in the cytosol . However, upon heat shock , GFP–Ubc9ts formed cytosolic punctate structures. Strikingly, when the proteasome was impaired and clearance of the misfolded protein by degradation was blocked, two distinct cytosolic inclusions were observed to be formed. Standard and conservative biochemical methods, such as cell fractionation and western blotting would not have revealed the partition into the two types of cytosolic aggregates. [ citation needed ]
The two detected inclusions were shown to be evolutionarily conserved quality control compartments, with different characteristics and distinct functions. They were named JUNQ (JUxta Nuclear Quality control compartment) and IPOD (Insoluble Protein Deposit), [ 3 ] and represent two cellular pathways for the sequestration and management of aggregation prone, potentially toxic proteins. [ citation needed ]
Partition of quality control substrates (i.e. misfolded proteins ) to either compartment depends on their ubiquitination status and aggregation state (i.e. solubility): [ citation needed ]
Proteins that are ubiquitinated are delivered to the JUNQ, where they are processed for degradation by the proteasome . Misfolded proteins that are not ubiquitinated and terminally aggregated are sequestered to the IPOD.
Thus, the sub-cellular location of a misfolded protein (i.e. in the JUNQ or in the IPOD) provides information about its interaction with the cellular protein quality control machinery (e.g. its E3 ligase ).
JUNQ is the JU xta N uclear Q uality control compartment.
To maintain cellular homeostasis, the cellular quality control system must distinguish between folded and misfolded proteins. A misfolded protein will be recognized and tightly taken care of by either refolding or ubiquitination and proteasomal degradation.
However, cellular increase of misfolded protein loads, due to various kinds of stresses (e.g. heat shock ), may saturate and exhaust the quality control machinery. In such cases, degradation of misfolded proteins is unavailable, and a second line of active cellular defense mechanism must be executed: directing misfolded proteins to specific cellular sites. [ 2 ]
The JUNQ serves as such a sequestration site. It was shown [ 3 ] that when the proteasome is impaired (e.g. by low expression levels of the proteasome subunit RPN11), ubiquitinated misfolded proteins are sorted into the JUNQ. Upon recovery from stress conditions (e.g. recovery from heat shock at a permissive temperature), misfolded proteins that accumulate in the JUNQ may be either refolded by the cellular chaperone machinery, or degraded by the 26S proteasome . Thus, the sequestration of a protein to the JUNQ is reversible. [ citation needed ]
The JUNQ is a non- membrane bound cellular site located in a margin of the nucleus, in close proximity to the endoplasmic reticulum . FRAP and FLIP assays revealed that proteins in the JUNQ are soluble and exchange with the cytosol , suggesting that the JUNQ has a dynamic structure.
Delivery to the JUNQ depends on molecular chaperones and co-chaperones and on the actin cytoskeleton . [ 4 ] Misfolded proteins must be ubiquitinated to be sorted to the JUNQ. If ubiquitination is blocked, a misfolded protein will be directed to the IPOD inclusion. Misfolded protein accumulation recruits 26S proteasomes to the JUNQ.
IPOD is the I nsoluble P rotein D eposit compartment.
It is becoming more evident that the cellular capacity to maintain proteostasis [ 8 ] declines with age, [ 9 ] thereby causing the late onset of neurodegenerative diseases. In such diseases (e.g. Huntington's disease ), a mutated protein misfolds and becomes toxic to the cellular environment by various ways such as denaturating cytosolic proteins. [ 14 ] Incompetent of degrading those toxic species, the cell must isolate them to avoid their hazardous interaction with the cellular proteome . The IPOD was shown [ 3 ] to be the sub-cellular site to which toxic amyloidogenic proteins are sequestered to, hereby serving as a protective quality control compartment.
In addition, it was suggested by the Lindquist group , that the IPOD is the site where yeast prions undergo a maturation process. [ 15 ] Thus, the IPOD may serve not only as a sequestration site, but also as a functional compartment. [ 15 ]
The IPOD is a non- membrane bound cellular site, which in yeast is located by the vacuole . FRAP and FLIP assays revealed that proteins in the IPOD are tightly packed, in-soluble and do not exchange with the cytosol . Amyloidogenic proteins, such as the Huntingtin protein, are the IPOD's substrates. [ citation needed ]
Misfolded proteins must be non- ubiquitinated to be sorted to the IPOD. Ubiquitination of an otherwise IPOD substrate, such as the RNQ1 fungal prion , will result in its sequestration in the JUNQ inclusion. [ citation needed ]
Upon accumulation of misfolded proteins , the disaggregase chaperone , AAA protein HSP104, localizes to the IPOD. It is yet to be determined if HSP104 functions in the IPOD or is simply sequestered there being hooked to a substrate.
The pre-autophagosomal structure (PAS) is localized by the IPOD. [ 16 ] However, it was not shown that IPOD substrates are delivered to the vacuole, and so the link between the IPOD and autophagy is yet to be determined. [ 3 ] | https://en.wikipedia.org/wiki/JUNQ_and_IPOD |
The JVC HR-3300 VIDSTAR is the world's first VHS -based VCR to be released to the market, introduced by the president of JVC at the Okura Hotel on September 9, 1976. [ 1 ] [ 2 ] Sales started in Japan under the name Victor HR-3300 on 31 October 1976. Foreign sales followed in 1977 with the HR-3300U in the United States, and HR-3300EK in the United Kingdom.
In 2008, the HR-3300 became the first VCR to be registered with the National Museum of Nature and Science , based in Tokyo, Japan . [ 3 ] It was noted as one of the 85 most disruptive ideas by Business Week in 2014. [ 4 ]
The first video recording system sold directly to home users was the 1963 1 ⁄ 4 -inch open reel Telcan from the UK, but this was not a commercial success. Sony 's CV-2000 was a complete system based on commercial 1 ⁄ 2 -inch tape on open reels, requiring the user to thread the tape around the helical scan heads. In order to conserve tape, the system recorded every other field of the television signal, producing half-resolution output. Similar models from Ampex and RCA followed that year. The number of video tape recorders continued to increase during the late 1960s, leading to the EIAJ-1 standard for 1 ⁄ 2 -inch tape on a 7 inch reel. The follow-up EIAJ-2 built the take-up reel into the recorder body.
In September 1971, Sony introduced the U-matic format, aimed at professional users, which replaced the open reels with a cassette. The next year Philips introduced the Video Cassette Recording format specifically for home users. Over the next five years, a number of companies introduced similar cassette-based home formats, all of which were incompatible. Among the better known examples are Sanyo 's V-Cord from 1974, Sony's Betamax from 1975, and Panasonic 's VX from 1975.
JVC engineers Yuma Shiraishi and Shizuo Takano led the effort in developing the VHS tape format starting in 1971. [ 5 ] The project started off by designing guidelines for VHS, creating a matrix on a blackboard called the VHS Development Matrix. Included in the matrix was a list of objectives in building a home video recording unit. [ 6 ] The HR-3300 is a result of these objectives.
Soon after the matrix was produced, the commercial video recording industry in Japan took a financial hit. As a result, JVC cut its budgets and restructured its video division - even going as far as shelving the VHS project. However, despite the lack of funding for the VHS project, Takano and Shiraishi continued to work on the project in secrecy within the video division. By 1973, the two engineers successfully produced a functional prototype of the HR-3300. [ 6 ]
The first HR-3300 was released in 1976. These early units used two large rotary knobs for tuning television signals for recording, one for VHF and another for UHF. Separate antenna inputs and pass-throughs were provided for both frequencies, as well composite video in and out via RCA jacks . An electronic timer with four seven-segment displays was located in the lower left of the front panel allowed the user to automatically record programs, one event up to 24 hours in the future. It also included a mechanical three-digit counter, similar to those on audio cassette recorders.
For the US and UK release the next year, the system was updated by replacing the mechanical tuning dials with a push-button system with eight pre-selected channels. A panel in the top flipped up to access small mechanical tuning dials for each of the eight channels. Push-button tuning was relatively rare at this time. The UK model was also released under the Ferguson brand name.
In December 1974, Sony attempted to standardize their Betamax format by inviting Matsushita (Panasonic) and JVC to license the system. [ 7 ] Apparently to their surprise, both companies refused. At the time, Matsushita not only sold through its own Panasonic brand, but was the majority shareholder in JVC as well. Through 1976 Sony was unrivalled in the VCR market, selling 30,000 units in the US alone.
The HR-3300 was introduced late in 1976 with one crucial feature, the ability to hold two hours of video on a single cassette. This made the format able to record an entire movie. JVC licensed the VHS format as an open standard , and in January 1977 there were VHS products from four other Japanese companies on the market.
In February Sony once again started to look for licensors for the Betamax format, and joined forces with US-based Zenith Electronics . Matsushita then started looking for US partners as well, and formed an alliance with RCA . RCA was interested, but stated that the format should be extended to allow recordings of five to six hours. JVC refused to compromise on picture quality by slowing down the tape speed, but Matsushita produced a prototype of such a system, and RCA announced they were going with VHS in March 1977. Simply re-badging units made by Matsushita in Japan, by 1978, RCA held 36% of the VCR market, and VHS was on its way to becoming a de facto standard.
Being the very first VHS-based VCR, the HR-3300 is the result of the VHS Development Matrix in terms of ease of servicing. Almost every component of this VCR can be purchased at any electronic surplus store. | https://en.wikipedia.org/wiki/JVC_HR-3300 |
In molecular spectroscopy , a Jablonski diagram is a diagram that illustrates the electronic states and often the vibrational levels of a molecule , and also the transitions between them. The states are arranged vertically by energy and grouped horizontally by spin multiplicity . [ 1 ] Nonradiative transitions are indicated by squiggly arrows and radiative transitions by straight arrows. The vibrational ground states of each electronic state are indicated with thick lines, the higher vibrational states with thinner lines. [ 2 ] The diagram is named after the Polish physicist Aleksander Jabłoński who first proposed it in 1933. [ 3 ]
When a molecule absorbs a photon , the photon energy is converted and increases the molecule's internal energy level. Likewise, when an excited molecule releases energy, it can do so in the form of a photon. Depending on the energy of the photon, this could correspond to a change in vibrational, electronic, or rotational energy levels . The changes between these levels are called "transitions" and are plotted on the Jablonski diagram.
Radiative transitions involve either the absorption or emission of a photon. As mentioned above, these transitions are denoted with solid arrows with their tails at the initial energy level and their tips at the final energy level.
Nonradiative transitions arise through several different mechanisms, all differently labeled in the diagram. Relaxation of the excited state to its lowest vibrational level is called vibrational relaxation (VR). This process involves the dissipation of energy from the molecule to its surroundings, and thus it cannot occur for isolated molecules.
A second type of nonradiative transition is internal conversion (IC), which occurs when a vibrational state of an electronically excited state can couple to a vibrational state of a lower electronic state. The molecule could then subsequently relax further through vibrational relaxation. [ 4 ]
A third type is intersystem crossing (ISC); this is a transition to a state with a different spin multiplicity. In molecules with large spin-orbit coupling , intersystem crossing is much more important than in molecules that exhibit only small spin-orbit coupling. ISC can be followed by phosphorescence .
This molecular physics –related article is a stub . You can help Wikipedia by expanding it .
This spectroscopy -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jablonski_diagram |
JackBe Corporation was a privately held vendor of enterprise mashup software for real-time intelligence applications. [ 1 ] In August 2013 JackBe was acquired by Software AG . [ 2 ] [ 3 ]
JackBe's flagship product is an enterprise mashup platform called Presto, which is used for enterprise mashups, business management dashboards, and real-time intelligence applications. [ 4 ]
JackBe’s main product, Presto, is an enterprise mashup platform. Presto provides real-time intelligence through functionality for self-service, on-demand data integration, and business dashboards . [ 5 ]
JackBe launched a cloud computing -based version of its Presto product in March 2010. [ 6 ] It is hosted on Amazon EC2 . Jackbe launched Mashup Sites for SharePoint (MSS) in July 2010 [ 7 ] Jackbe announced an Enterprise App Depot in 2010, as a platform for creating internal application directories. [ 8 ] The Enterprise App Depot is aimed at non-developers (business users), allowing them to create new business applications and then share the applications with other users. [ 9 ] Industry analyst Joe McKendrick described the Enterprise App Store, as a "cool idea" on ZDNet . [ 10 ] | https://en.wikipedia.org/wiki/JackBe |
John Wilfrid Linnett (3 August 1913 – 7 November 1975) was Vice-Chancellor at the University of Cambridge from 1973 to 1975. [ 1 ] [ 2 ] [ 3 ] He was for many years a Fellow of the Queen's College, Oxford , and a demonstrator in Inorganic Chemistry at the University of Oxford .
He was born on 3 August 1913 in Coventry in England and educated at King Henry VIII School and St John's College , University of Oxford , and was later a Junior Fellow there.
He was appointed Professor of Physical Chemistry at Cambridge University in 1965. He was Master of Sidney Sussex College, Cambridge , on the Council of the Royal Society , and was President of the Faraday Society .
Throughout his career as a chemist, he was noted for his wide interests, making substantial contributions in theoretical chemistry , mass spectrometry , explosion limits, atom recombination reactions, combustion, and several other areas.
In 1960, Linnett originated a modification to the octet rule , originally proposed by Lewis , concerning valence electrons . He proposed that the octet should be considered as a double quartet of electrons rather than as four pairs, and hence the theory became known as " Linnett double-quartet theory ". Using this method, he was able to explain the stability of 'odd electron' molecules such as nitric oxide and oxygen. This theory was set out in a book "The Electronic Structure of Molecules: A New Approach", published by Methuen & Co Ltd, London, 1964. [ 4 ] His general book "Wave Mechanics and Valency" also published by Methuen & Co Ltd, London, appeared in 1960. [ 5 ]
He died of a heart attack in the Athenaeum Club, London , on 7 November 1975, only five weeks after ceasing to be Vice-Chancellor of the University of Cambridge.
The John Wilfrid Linnett Visiting Professor of Chemistry was established in his memory in 1993 at the University of Cambridge. [ 6 ] | https://en.wikipedia.org/wiki/Jack_Linnett |
Arie Jacobus Johannes "Jack" Ooms (1925 - 6 September 1999, Spain ) was a Dutch chemist, diplomat and chemical weapons researcher. As head of Dutch chemical defence research, Ooms worked for 23 years for the eradication of chemical warfare , which he believed could best be achieved by a combination of effective chemical protection and international chemical arms control and a permanent, multilateral ban on chemical weapons, as implementation of the Chemical Weapons Convention . [ 1 ]
In 1942, during the German occupation of the Netherlands , Ooms entered the University of Utrecht to study chemistry. The following year, he refused to sign the Nazi loyalty declaration and became an Engelandvaarder by escaping to the United Kingdom through Spain and Portugal , much of it on foot. He joined the United States Army and in August 1944 returned to mainland Europe with the Allies in southern France. After the war, in 1948, he finished his MSc and was subsequently conscripted into the Netherlands Army for his three years of required national service. His doctoral dissertation, which he successfully defended in 1961 at the University of Leiden , was called "Reactivity of Organic Phosphorus Compounds towards Certain Esterases." [ 1 ]
While carrying out his national service, Ooms joined the National Defence Research Organization's (RVO-TNO) new Chemical Laboratory. He was appointed director in 1965 and retained this position in 1978 when the lab merged with the organisation's Technological Laboratory. It was renamed the TNO Prins Maurits Laboratory. He remained in his role until his retirement in 1988. [ 1 ] In 1990, he was a founding member of the advisory board of the Harvard Sussex Program on Chemical and Biological Weapons. [ 2 ] [ 1 ]
Ooms’ active participation in the negotiation of a permanent, multilateral ban on chemical weapons, began in 1969 when he joined the Netherlands' delegation to the Eighteen Nation Committee on Disarmament (ENCD) in Geneva as a technical adviser. The ENCD (1962-1969) was one of several predecessors to the Conference on Disarmament (CD). Ooms became the only CD delegate that continuously participated over the full 20 years of negotiations, which culminated in the adoption of the Chemical Weapons Convention by the United Nations General Assembly in 1992. He attended the 1980 International School of Disarmament and Research on Conflicts [ 3 ] and later served on the Dutch delegation to the preparatory commission that founded the Organisation for the Prohibition of Chemical Weapons with its headquarters in The Hague . In 1991, Ooms was appointed to the United Nations Special Commission , at that time forming to oversee Iraq's renunciation of weapons of mass destruction . This work continued to engage him in the months immediately prior to his death in 1999. [ 1 ] [ 4 ]
Ooms died on 6 September 1999 at his home in Spain and was survived by his wife Marjan. [ 1 ]
One of the main conference rooms used by the Organisation for the Prohibition of Chemical Weapons in The Hague is called the Ooms Room to commemorate his efforts. On 27 April 2006, Prime Minister Jan-Peter Balkenende unveiled a photograph of Ooms during his visit on the first observance of the Day of Remembrance for All Victims of Chemical Warfare . [ 5 ] | https://en.wikipedia.org/wiki/Jack_Ooms |
Jack Richard Norton (born May 5, 1945) is an American organometallic chemist and Professor at Columbia University . His research has focused on the studying the reactivity and properties of transition metal hydrides . He coauthored the textbook "Principles and Applications of Organotransition Metal Chemistry." [ 1 ]
Norton was born in Dallas, Texas in 1945. He received his B.A. from Harvard University in 1967 and was awarded his Ph.D. at Stanford in 1972 under the mentorship of James P. Collman . After a postdoctoral appointment with Jack Lewis , he was appointed assistant professor at Princeton University . He moved to Colorado State University in 1979, and again to Columbia University in 1997, where he remains Professor of Chemistry. From 1992-2003 he was an associate editor of Journal of the American Chemical Society
His laboratory demonstrated the possibility of dinuclear reductive elimination from transition metal alkyls and hydrides by comparing the mechanisms of reductive elimination from (H) 2 Os(CO) 4 , (H)(CH 3 )Os(CO) 4 , and (CH 3 ) 2 Os(CO) 4 . His group later reported some of the first detailed pK a measurements of metal hydrides and demonstrated that the rates of protonation at transition metals can be quite slow. [ 2 ] His group has also reported on the use of metal-hydride bonds as radical initiators of cyclization reactions. [ 3 ]
In 2005 he received the ACS Award for Organometallic Chemistry [ 4 ] and in 2013 the Cope Scholar Award [ 5 ] | https://en.wikipedia.org/wiki/Jack_R._Norton |
Jack Rudloe is a writer, naturalist, and environmental activist from Panacea, Florida , United States, who co-founded Gulf Specimen Marine Laboratory .
Jack Rudloe was born in Brooklyn, New York on February 17, 1943. At age 14, he moved to Carrabelle , Florida. His first work, "Experiments With Sensitive Plants, Cassia Nictitans ", was published in Scientific American while he was attending Tallahassee's Leon High School. He later enrolled in Florida State University , but left after only two months. [ 1 ] [ 2 ] According to Rudloe's first book, The Sea Brings Forth , he was asked to leave FSU by the dean, who had decided Rudloe was not college material and advised that he should consider a trade instead. [ 3 ] In spite of his premature departure from FSU, Rudloe was hired by marine biologist Dexter M. Easton of Harvard University to collect striped burrfish and bat fish. This launched his independent career as a writer and specimen collector. [ 4 ] He was mentored in the early days by John Steinbeck . [ 5 ] [ 6 ] He founded Gulf Specimen Marine Company in 1963. In 1971, Rudloe married marine biologist Anne Rudloe , and together they founded Gulf Specimen Marine Laboratory in 1980. He has two sons, Sky and Cypress and a grandson Kai. He lives in Panacea, Florida and is semi-retired but still assists at GSML and he continues to write. [ 7 ] He is the author/coauthor of nine books, both fiction and nonfiction.
Rudloe has multiple acknowledgements from scientists about his personal contributions to and support of their research efforts in the marine science literature. Rudloe has also written numerous scientific articles, and technical publications himself. [ 8 ] [ 9 ] Rudloe was involved in early efforts to establish the now successful jellyfish export industry on the East Coast of the US. [ 10 ] [ 11 ] [ 12 ] [ 13 ] [ 14 ] [ 15 ] In 1968 he provided the first specimens of the bryozoan Bugula neritina used by the National Cancer Institute (NCI) to develop the bryostatin family of drugs used for treatment of cancer, HIV, Alzheimer's disease and strokes. [ 16 ] [ 17 ] [ 18 ] He continues to work to find natural medicines from other sea organisms. [ 19 ] Rudloe provides marine specimens to scientists worldwide, including some that were the first specimen known to science, such as Chiropsella rudloei . [ 20 ] [ 21 ] [ 22 ] [ 23 ] Rudloe has developed live culture techniques for food for captive animals otherwise considered difficult to raise in captivity including sea horses [ 24 ] and the lesser electric ray ( Narcine brasiliensis ) [ 25 ]
Rudloe is noted for two particular areas of effort in environmentalism. He was a strong proponent and advocate of turtle exclusion devices and his work is widely cited in efforts to introduce and later to enforce their use [ 26 ] and his interest in general sea turtle welfare which were the subject of two of his books. [ 27 ] Whenever a sea turtle rehabilitated at GSML is released back to the wild he is well known for arriving in sea blue suit which he wears into the water for the release. [ 28 ] Working with his wife, he has also been credited with directly saving 35,000 acres of wetlands in the Florida Panhandle and the Florida Big Bend region through government lobbying [ 29 ] appearances at public meetings and on television and radio broadcasts, about marine wetlands. [ 30 ] [ 31 ] [ 32 ] [ 33 ] [ 34 ] He also wrote about shrimp and their contributions to the economy and to the environment. [ 35 ] During the Deepwater Horizon oil spill Rudloe began a project to try to protect ocean invertebrates from contamination. [ 36 ] He published numerous popular articles on environmental topics including several in Sports Illustrated, National Geographic and Audubon. [ 37 ] Rudloe opposed Florida's commercial net fishing ban because he was concerned about the impact on small town fisheries and fishermen placing him at odds with many large environmental groups. [ 1 ] He has been raising awareness of the issue of plastic and waste dumping into the ocean since at least 1992. [ 38 ]
Rudloe began his career as an environmental activist at age 8 by biting the leg of a camp counsellor who was about to kill a turtle with a sledge hammer. [ 39 ] His style of "high drama" and "lampooning" [ 40 ] to promote environmental causes has not always endeared him to either the environmental movement or politicians. [ 41 ] In 1972 Rudloe sued financier Edward Ball to try to force him to remove a fence across the Wakulla River , lost and was almost bankrupted by the resulting legal costs. A Wakulla News editorial called him "a nut" and "an extremist" in 1978. [ 39 ] An owner of a local business has also called him "a nut". [ 36 ] In 1988 he sued the Wakulla County Commissioner over alleged environmental damage caused by the building of a marina approved by the county and being built by the commissioner's brother. The county then resurrected a previously dropped legal battle from 1975 over his aquarium's water intake pipeline. While at a meeting over the marina, his boat was sunk and Rudloe was sued for slander when he claimed there was a connection. He was also arrested for cruelty to animals in the same period, a charge which was dismissed. [ 39 ] In 1988 Rudloe organized a campaign to have people return their Exxon credit cards in a sealed bag of used motor oil to protest the Exxon Valdez 's Prince William Sound oil spill. [ 42 ]
There has been tension between members of the Florida State University Coastal and Marine Laboratory and Rudloe. Dr. Robert Livingstone of FSU publicly stated in 1988 that he takes care not to associate with Rudloe's fights. [ 39 ] This tension reached a crescendo in 2002 with the publication of Alumni Notes by David M. Karl which included an account of persistent rumours at FSU that Rudloe had stolen a "priceless Neopilina specimen" which later appeared for sale in a Gulf Specimen Marine Laboratory catalogue and that this was the reason for Rudloe's departure from FSU in his first semester in 1962. Rudloe sued both Karl and FSU for slander. The case was initially dismissed by a local judge on the basis FSU had no liability but Rudloe appealed. After winning on appeal to The District Court of Appeal, State of Florida, the matter was later settled out of court. [ 37 ] [ 43 ] [ 44 ] In 2015 FSU Coastal and Marine Lab donated giant sea roaches and hagfish to a "very grateful" Gulf Specimen Marine Lab to use in their aquarium for educating the public indicating the tension is resolved. [ 45 ]
Rudloe submitted an article to Sports Illustrated describing how an alligator attacked and ate his dog in 1981. The editor sent a copy to Dr. F Wayne King, Professor and curator of the University of Florida's Florida Museum of Natural History in Gainesville who returned a marked up copy of the article [ 37 ] with numerous objections taking particular exception to three items. Rudloe described the alligator as rearing to an upright position with front arms apart and fingers spread, he described vapour from the alligator's nostrils and how the alligator puffed up when Rudloe leaped on it and wrestled it in a vain attempt to save the dog. [ 37 ] Based on the review, the editor excoriated Rudloe as a fraud and Rudloe did not write for Sports Illustrated again. Alligators have been observed to rise up and balance on their hind legs as part of a forward or upward lunge. [ 46 ] [ 47 ] [ 48 ] King himself later published that it is possible to observe vapour from an alligator's nostrils and for them to puff up (although in the context of bellowing). [ 49 ] There are also observations of alligators puffing up when aggressive. [ 50 ] Rudloe eventually published the account in Audubon (1982) and Reader's Digest (1983). [ 37 ] [ 51 ] [ 52 ]
In August 2016, Rudloe was removed by security for refusing to yield the microphone in a meeting of the Wakulla County, Florida Commissioners when they voted to adjourn instead of voting on a resolution opposing the permit for Foley Cellulose Mill's effluent pipeline extension project. [ 53 ] | https://en.wikipedia.org/wiki/Jack_Rudloe |
In mathematics , the Jack function is a generalization of the Jack polynomial , introduced by Henry Jack . The Jack polynomial is a homogeneous , symmetric polynomial which generalizes the Schur and zonal polynomials, and is in turn generalized by the Heckman–Opdam polynomials and Macdonald polynomials .
The Jack function J κ ( α ) ( x 1 , x 2 , … , x m ) {\displaystyle J_{\kappa }^{(\alpha )}(x_{1},x_{2},\ldots ,x_{m})} of an integer partition κ {\displaystyle \kappa } , parameter α {\displaystyle \alpha } , and arguments x 1 , x 2 , … , x m {\displaystyle x_{1},x_{2},\ldots ,x_{m}} can be recursively defined as
follows:
where the summation is over all partitions μ {\displaystyle \mu } such that the skew partition κ / μ {\displaystyle \kappa /\mu } is a horizontal strip , namely
where B κ μ ν ( i , j ) {\displaystyle B_{\kappa \mu }^{\nu }(i,j)} equals κ j ′ − i + α ( κ i − j + 1 ) {\displaystyle \kappa _{j}'-i+\alpha (\kappa _{i}-j+1)} if κ j ′ = μ j ′ {\displaystyle \kappa _{j}'=\mu _{j}'} and κ j ′ − i + 1 + α ( κ i − j ) {\displaystyle \kappa _{j}'-i+1+\alpha (\kappa _{i}-j)} otherwise. The expressions κ ′ {\displaystyle \kappa '} and μ ′ {\displaystyle \mu '} refer to the conjugate partitions of κ {\displaystyle \kappa } and μ {\displaystyle \mu } , respectively. The notation ( i , j ) ∈ κ {\displaystyle (i,j)\in \kappa } means that the product is taken over all coordinates ( i , j ) {\displaystyle (i,j)} of boxes in the Young diagram of the partition κ {\displaystyle \kappa } .
In 1997, F. Knop and S. Sahi [ 1 ] gave a purely combinatorial formula for the Jack polynomials J μ ( α ) {\displaystyle J_{\mu }^{(\alpha )}} in n variables:
The sum is taken over all admissible tableaux of shape λ , {\displaystyle \lambda ,} and
with
An admissible tableau of shape λ {\displaystyle \lambda } is a filling of the Young diagram λ {\displaystyle \lambda } with numbers 1,2,…, n such that for any box ( i , j ) in the tableau,
A box s = ( i , j ) ∈ λ {\displaystyle s=(i,j)\in \lambda } is critical for the tableau T if j > 1 {\displaystyle j>1} and T ( i , j ) = T ( i , j − 1 ) . {\displaystyle T(i,j)=T(i,j-1).}
This result can be seen as a special case of the more general combinatorial formula for Macdonald polynomials .
The Jack functions form an orthogonal basis in a space of symmetric polynomials, with inner product:
This orthogonality property is unaffected by normalization. The normalization defined above is typically referred to as the J normalization. The C normalization is defined as
where
For α = 2 , C κ ( 2 ) ( x 1 , … , x n ) {\displaystyle \alpha =2,C_{\kappa }^{(2)}(x_{1},\ldots ,x_{n})} is often denoted by C κ ( x 1 , … , x n ) {\displaystyle C_{\kappa }(x_{1},\ldots ,x_{n})} and called the Zonal polynomial .
The P normalization is given by the identity J λ = H λ ′ P λ {\displaystyle J_{\lambda }=H'_{\lambda }P_{\lambda }} , where
where a λ {\displaystyle a_{\lambda }} and l λ {\displaystyle l_{\lambda }} denotes the arm and leg length respectively. Therefore, for α = 1 , P λ {\displaystyle \alpha =1,P_{\lambda }} is the usual Schur function.
Similar to Schur polynomials, P λ {\displaystyle P_{\lambda }} can be expressed as a sum over Young tableaux. However, one need to add an extra weight to each tableau that depends on the parameter α {\displaystyle \alpha } .
Thus, a formula [ 2 ] for the Jack function P λ {\displaystyle P_{\lambda }} is given by
where the sum is taken over all tableaux of shape λ {\displaystyle \lambda } , and T ( s ) {\displaystyle T(s)} denotes the entry in box s of T .
The weight ψ T ( α ) {\displaystyle \psi _{T}(\alpha )} can be defined in the following fashion: Each tableau T of shape λ {\displaystyle \lambda } can be interpreted as a sequence of partitions
where ν i + 1 / ν i {\displaystyle \nu _{i+1}/\nu _{i}} defines the skew shape with content i in T . Then
where
and the product is taken only over all boxes s in λ {\displaystyle \lambda } such that s has a box from λ / μ {\displaystyle \lambda /\mu } in the same row, but not in the same column.
When α = 1 {\displaystyle \alpha =1} the Jack function is a scalar multiple of the Schur polynomial
where
is the product of all hook lengths of κ {\displaystyle \kappa } .
If the partition has more parts than the number of variables, then the Jack function is 0:
In some texts, especially in random matrix theory, authors have found it more convenient to use a matrix argument in the Jack function. The connection is simple. If X {\displaystyle X} is a matrix with eigenvalues x 1 , x 2 , … , x m {\displaystyle x_{1},x_{2},\ldots ,x_{m}} , then | https://en.wikipedia.org/wiki/Jack_function |
In chemical engineering , a jacketed vessel is a container that is designed for controlling temperature of its contents, by using a cooling or heating "jacket" around the vessel through which a cooling or heating fluid is circulated.
A jacket is a cavity external to the vessel that permits the uniform exchange of heat between the fluid circulating in it and the walls of the vessel. There are several types of jackets, depending on the design: [ 1 ]
Jackets can be applied to the entire surface of a vessel or just a portion of it. For a vertical vessel, the top head is typically left unjacketed. Jackets can be divided into zones, to divide the flow of the heating or cooling medium. Advantages include: ability to direct flow to certain portions of the jacket, such as only the bottom head when minimal heating or cooling is needed and the entire jacket when maximum heating or cooling is required; ability to provide a higher volume of flow overall (zones are piped in parallel) because the pressure drop through a zone is lower than if the entire jacket is a single zone.
Jacketed vessels can be employed as chemical reactors (to remove the elevated heat of reaction ) or to reduce the viscosity of high viscous fluids (such as tar ).
Agitation can be also used in jacketed vessels to improve the homogeneity of the fluid properties (such as temperature or concentration ). | https://en.wikipedia.org/wiki/Jacketed_vessel |
Jackie King (1945 – January 2025) was a South African water scientist. She was an internationally recognized aquatic ecosystems researcher and advocate for maintaining environmental flows in rivers that were being considered for development. Her work influenced water resource management policies worldwide, among others stimulating inclusion of environmental flows for river maintenance in South Africa's 1998 National Water Act, [ 1 ] recognition of the need to compensate downstream communities for deterioration of river health in the Lesotho Highlands Water Project, [ 2 ] and awareness of environmental flows in the work of the Mekong River Commission. [ 3 ]
Jackie King began her academic career as a young mother in Cape Town. In 1973 she earned a BSc in Zoology and Chemistry at the University of Cape Town and studied macoinvertebrate fauna in the Eerste River in Stellenbosch for fieldwork to support a University of Cape Town PhD that she was awarded in 1983. [ 4 ]
King was instrumental in formation of the University of Cape Town 's Freshwater Research Unit, where she was a researcher, lecturer, and supervisor of postgraduates from 1975 to 2008. She formed a consulting firm, Water Matters, focused on the science of integrated flow management in 2000. In 2012 she was appointed Extraordinary Professor at the University of the Western Cape 's Institute for Water Studies, continuing to work as a consulting expert in China, Laos, Cambodia, Pakistan, Vietnam, South America and throughout southern Africa, where she provided formative advice to the region's growing family of transboundary river basin organizations. [ 5 ] In later years she frequently collaborated with Cate Brown of Southern Waters Ecological Research and Consulting. [ 6 ]
In 2016 King received the Gold Medal of the Southern African Society of Aquatic Scientists and was the 2016 recipient of WWF-SA’s Living Planet Award. In 2018 King was elected an international member of the American Academy of Arts and Sciences . She was winner of the 2020 Stockholm Water Prize for her contributions to global river management. [ 7 ]
Throughout her career, she contributed her knowledge and experience to building capacity [ 8 ] and published science. [ 9 ] [ 10 ] [ 11 ]
She served on the Board of Directors of the Worldwide Fund for Nature South Africa, [ 12 ] the Research Advisory Panel of South Africa’s Council for Scientific and Industrial Research and as a Senior Scientific Advisor to the International Crane Foundation .
King was, in her semi-retirement, an active community volunteer, becoming a SANParks Honorary Ranger, patrolling the trails that she also visited regularly while walking with her dogs. She died in January 2025. [ 13 ] | https://en.wikipedia.org/wiki/Jackie_King |
Jackiw–Teitelboim gravity , also known as the R = T model , [ 1 ] or simply JT gravity (after physicists Roman Jackiw and Claudio Teitelboim ), is a theory of gravity with dilaton coupling in one spatial and one time dimension. It should not be confused [ 2 ] [ 3 ] with the CGHS model or Liouville gravity . The action is given by
The metric in this case is more amenable to analytical solutions than the general 3+1D case though a canonical reduction for the latter has recently been obtained. [ 4 ] For example, in 1+1D, the metric for the case of two mutually interacting bodies can be solved exactly in terms of the Lambert W function , even with an additional electromagnetic field.
Varying with respect to Φ yields R = Λ {\displaystyle R=\Lambda } on shell, which means the metric is either Anti-de Sitter space or De Sitter space , depending upon the sign of Λ.
Dilaton § The dilaton in quantum gravity
This relativity -related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jackiw–Teitelboim_gravity |
In approximation theory , Jackson's inequality is an inequality bounding the value of function's best approximation by algebraic or trigonometric polynomials in terms of the modulus of continuity or modulus of smoothness of the function or of its derivatives. [ 1 ] Informally speaking, the smoother the function is, the better it can be approximated by polynomials.
For trigonometric polynomials, the following was proved by Dunham Jackson :
The Akhiezer – Krein – Favard theorem gives the sharp value of C ( r ) {\displaystyle C(r)} (called the Akhiezer–Krein–Favard constant ):
Jackson also proved the following generalisation of Theorem 1:
An even more general result of four authors can be formulated as the following Jackson theorem.
For k = 1 {\displaystyle k=1} this result was proved by Dunham Jackson. Antoni Zygmund proved the inequality in the case when k = 2 , ω 2 ( t , f ) ≤ c t , t > 0 {\displaystyle k=2,\omega _{2}(t,f)\leq ct,t>0} in 1945. Naum Akhiezer proved the theorem in the case k = 2 {\displaystyle k=2} in 1956. For k > 2 {\displaystyle k>2} this result was established by Sergey Stechkin in 1967.
Generalisations and extensions are called Jackson-type theorems. A converse to Jackson's inequality is given by Bernstein's theorem . See also constructive function theory .
This mathematical analysis –related article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jackson's_inequality |
Jackson Oswalt (born 19 January 2005) holds the Guinness World Record for the youngest person to achieve nuclear fusion , at the age of 12 years. [ 1 ] Oswalt created a Fusor in a home laboratory in Memphis, Tennessee , using his parents' financial help to purchase the needed equipment from EBay . [ 2 ]
This United States biographical article is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jackson_Oswalt |
The term Jacob's staff is used to refer to several things, also known as cross-staff , a ballastella , a fore-staff , a ballestilla , or a balestilha . In its most basic form, a Jacob's staff is a stick or pole with length markings; most staffs are much more complicated than that, and usually contain a number of measurement and stabilization features. The two most frequent uses are:
The simplest use of a Jacob's staff is to make qualitative judgements of the height and angle of an object relative to the user of the staff.
In navigation the instrument is also called a cross-staff and was used to determine angles, for instance the angle between the horizon and Polaris or the sun to determine a vessel's latitude , or the angle between the top and bottom of an object to determine the distance to said object if its height is known, or the height of the object if its distance is known, or the horizontal angle between two visible locations to determine one's point on a map.
The Jacob's staff, when used for astronomical observations, was also referred to as a radius astronomicus . With the demise of the cross-staff, in the modern era the name "Jacob's staff" is applied primarily to the device used to provide support for surveyor's instruments.
The origin of the name of the instrument is not certain. Some refer to the Biblical patriarch Jacob , [ 1 ] specifically in the Book of Genesis ( Gen 32:11 ). [ 1 ] It may also take its name after its resemblance to Orion , referred to by the name of Jacob on some medieval star charts . [ 2 ] [ 3 ] Another possible source is the Pilgrim's staff, the symbol of St James (Jacobus in Latin). The name cross staff simply comes from its cruciform shape.
The original Jacob's staff was developed as a single pole device, in the 14th century, that was used in making astronomical measurements. It was first described by the French-Jewish mathematician Levi ben Gerson [ 4 ] [ 5 ] of Provence , in his "Book of the Wars of the Lord" (translated in Latin as well as Hebrew). [ 6 ] He used a Hebrew name for the staff that translates to "Revealer of Profundities", while the term "Jacob's staff" was used by his Christian contemporaries. [ 7 ] Its invention was likely due to fellow French-Jewish astronomer Jacob ben Makir , who also lived in Provence in the same period. [ 8 ] Attribution to 15th century Austrian astronomer Georg Purbach [ 9 ] is less likely, because Purbach was not born until 1423. (Such attributions may refer to a different instrument with the same name.) Its origins may [ 10 ] be traced to the Chaldeans around 400 BCE.
Although it has become quite accepted that ben Gerson first described Jacob's staff, the British Sinologist Joseph Needham theorizes that the Song dynasty Chinese scientist Shen Kuo (1031–1095), in his Dream Pool Essays of 1088, described a Jacob's staff. [ 11 ] Shen was an antiquarian interested in ancient objects; after he unearthed an ancient crossbow-like device from a home's garden in Jiangsu , he realized it had a sight with a graduated scale that could be used to measure the heights of distant mountains, likening it to how mathematicians measure heights by using right-angle triangles. [ 11 ] He wrote that when one viewed the whole breadth of a mountain with it, the distance on the instrument was long; when viewing a small part of the mountainside, the distance was short; this, he wrote, was due to the cross piece that had to be pushed further away from the eye, while the graduation started from the further end. Needham does not mention any practical application of this observation. [ 11 ]
During the medieval European Renaissance , the Dutch mathematician and surveyor Adriaan Metius developed his own Jacob's staff; Dutch mathematician Gemma Frisius made improvements to this instrument. In the 15th century, the German mathematician Johannes Müller (called Regiomontanus ) made the instrument popular in geodesic and astronomical measurements. [ 12 ]
In the original form of the cross-staff, the pole or main staff was marked with graduations for length. The cross-piece ( BC in the drawing to the right), also called the transom or transversal , slides up and down on the main staff. On older instruments, the ends of the transom were cut straight across. Newer instruments had brass fittings on the ends, with holes in the brass for observation. (In marine archaeology , these fittings are often the only components of a cross-staff that survive.) [ 13 ]
It was common to provide several transoms, each with a different range of angles it would measure; three transoms were common. In later instruments, separate transoms were switched in favour of just one with pegs to indicate the ends. These pegs were mounted in one of several pairs of holes symmetrically located on either side of the transom. This provided the same capability with fewer parts. [ 10 ] The transom on Frisius ' version had a sliding vane on the transom as an end point. [ 10 ]
The user places one end of the main staff against their cheek, just below the eye. By sighting the horizon at the end of the lower part of the transom (or through the hole in the brass fitting) [ B ], then adjusting the cross arm on the main arm until the sun is at the other end of the transom [ C ], the altitude can be determined by reading the position of the cross arm on the scale on the main staff. This value was converted to an angular measurement by looking up the value in a table.
The original version was not reported to be used at sea, until the Age of Discoveries . Its use was reported by João de Lisboa in his Treatise on the Nautical Needle of 1514. [ 14 ] Johannes Werner suggested the cross-staff be used at sea in 1514 [ 10 ] and improved instruments were introduced for use in navigation. John Dee introduced it to England in the 1550s. [ 1 ] In the improved versions, the rod was graduated directly in degrees. This variant of the instrument is not correctly termed a Jacob's staff but is a cross-staff. [ 8 ]
The cross-staff was difficult to use. In order to get consistent results, the observer had to position the end of the pole precisely against his cheek. He had to observe the horizon and a star in two different directions while not moving the instrument when he shifted his gaze from one to the other. In addition, observations of the sun required the navigator to look directly at the sun. This could be a uncomfortable exercise and made it difficult to obtain an accurate altitude for the sun. Mariners took to mounting smoked-glass to the ends of the transoms to reduce the glare of the sun. [ 10 ] [ 15 ]
As a navigational tool, this instrument was eventually replaced, first by the backstaff or quadrant , neither of which required the user to stare directly into the sun, and later by the octant and the sextant . Perhaps influenced by the backstaff, some navigators modified the cross-staff to operate more like the former. Vanes were added to the ends of the longest cross-piece and another to the end of the main staff. The instrument was reversed so that the shadow of the upper vane on the cross piece fell on the vane at the end of the staff. The navigator held the instrument so that he would view the horizon lined up with the lower vane and the vane at the end of the staff. By aligning the horizon with the shadow of the sun on the vane at the end of the staff, the elevation of the sun could be determined. [ 16 ] This actually increased the accuracy of the instrument, as the navigator no longer had to position the end of the staff precisely on his cheek.
Another variant of the cross-staff was a spiegelboog , invented in 1660 by the Dutchman, Joost van Breen.
Ultimately, the cross-staff could not compete with the backstaff in many countries. In terms of handling, the backstaff was found to be more easy to use. [ 17 ] However, it has been proven by several authors that in terms of accuracy, the cross-staff was superior to the backstaff. [ 18 ] Backstaves were no longer allowed on board Dutch East India Company vessels as per 1731, with octants not permitted until 1748. [ 18 ]
In surveying , the term jacob staff refers to a monopod , a single straight rod or staff made of nonferrous material, pointed and metal-clad at the bottom for penetrating the ground. [ 19 ] It also has a screw base and occasionally a ball joint on the mount, and is used for supporting a compass , transit, or other instrument. [ 20 ]
The term cross-staff may also have a different meaning in the history of surveying. While the astronomical cross-staff was used in surveying for measuring angles, two other devices referred to as a cross-staff were also employed. [ 21 ]
In the past, many surveyor's instruments were used on a Jacob's staff. These include:
Some devices, such as the modern optical targets for laser-based surveying, are still in common use on a Jacob's staff.
In geology, the Jacob's staff is mainly used to measure stratigraphic thicknesses in the field, especially when bedding is not visible or unclear (e.g., covered outcrop) and when due to the configuration of an outcrop , the apparent and real thicknesses of beds diverge therefore making the use of a tape measure difficult. There is a certain level of error to be expected when using this tool, due to the lack of an exact reference mean for measuring stratigraphic thickness. High-precision designs include a laser able to slide vertically along the staff and to rotate on a plane parallel to bedding. [ 23 ] | https://en.wikipedia.org/wiki/Jacob's_staff |
Jacob Nissim Israelachvili , FRS (19 August 1944 – 20 September 2018) was an Israeli physicist who was a professor at the University of California, Santa Barbara (UCSB). [ 1 ] He made contributions in understanding the behavior of matter at small length scales.
He was born in Tel Aviv, Israel and sent to an English boarding school at the age of 7. After completing his secondary education he returned to Israel to carry out his military service before moving back to England to study the Natural Sciences Tripos at the University of Cambridge . He received his Ph.D. in Physics from Christ's College, Cambridge in 1972 under the supervision of David Tabor . He then became a Research Fellow at the Biophysics Institute, Stockholm University and at the Karolinska Institute , Sweden until 1974.
He moved to Australia to take a post as fellow in the Research School of Physical Science and the Research School of Biological Sciences at the Institute of Advanced Studies, Australian National University in Canberra from 1974 to 1977. He was then appointed senior fellow in the Department of Applied Mathematics and Department of Neurobiology at the Institute of Advanced Studies, Australian National University in Canberra.
He relocated to California to join UCSB in 1986, where he worked till his death on the 20th of September 2018. [ 2 ]
His research has involved study of molecular and interfacial forces. His work is applicable to a wide range of industrial and fundamental science problems. In particular, he has contributed significantly to the understanding of colloidal dispersions , biological systems, and polymer engineering applications. He has studied interfacial phenomena, the physics of thin films, and fundamental questions in rheology and tribology of surfaces. [ 3 ] [ 4 ] [ 5 ]
Israelachvili has developed numerous techniques for the static and dynamic measurement of material and molecular properties of vapors, liquids, and surfaces. In particular, he pioneered a sensitive interfacial force-sensing technique known as the surface forces apparatus (SFA). This instrument involves carefully approaching two surfaces (usually immersed in a solvent , such as water ), and measuring the force of attraction and repulsion between them. Using piezoelectric positional movement and optical interferometry for position sensing, this instrument can resolve distances to within 0.1 nanometer , and forces at the 10 −8 N level. This technique is similar to measuring the force of interaction between an atomic force microscope (AFM) and a sample surface, except that the specialized SFA can measure much longer-range forces and is intended for surface-surface interaction measurements (as opposed to tip-surface or molecule-surface measurements). The results of SFA experiments can be used to characterize the nature of intermolecular potentials and other molecular properties.
Israelachvili is also well known as the author of the textbook "Intermolecular and Surface Forces," published by Academic Press . This authoritative book describes the fundamental concepts and equations applicable to all intermolecular and interfacial science disciplines.
Israelachvili was also founder of SurForce, LLC. The company specializes in researching surface force interactions and producing SFA systems. [1] | https://en.wikipedia.org/wiki/Jacob_Israelachvili |
Jacob Klein (March 3, 1899 – July 16, 1978) was a Russian-American philosopher and interpreter of Plato , who worked extensively on the nature and historical origin of modern symbolic mathematics.
Klein was born in Libava , Russian Empire . He studied at Berlin and Marburg , where he received his Ph.D. in 1922. A student of Nicolai Hartmann , Martin Heidegger , and Edmund Husserl , he later taught at St. John's College in Annapolis, Maryland from 1938 until his death. He served as dean from 1949 to 1958.
Klein was affectionately known as Jasha (pronounced "Yasha"). He was one of the world's preeminent interpreters of Plato and the Platonic tradition. As one of many Jewish scholars who were no longer safe in Europe, he fled the Nazis. [ 1 ] He was a friend of fellow émigré and German-American philosopher Leo Strauss . Of Klein's first book Greek Mathematical Thought and the Origin of Algebra , Strauss said:
The work is much more than a historical study. But even if we take it as a purely historical work, there is not, in my opinion, a contemporary work in the history of philosophy or science or in "the history of ideas" generally speaking which in intrinsic worth comes within hailing distance of it. [ 2 ]
Russian born French philosopher Alexandre Kojève counted Klein as one of the two people (along with Strauss) from whom he could learn anything. [ 3 ]
The central thesis of his work Greek Mathematical Thought and the Origin of Algebra is that the modern concept of mathematics is based on the symbolic interpretation of the Greek concept of number ( arithmos ).
Klein died in 1978 in Annapolis, Maryland .
This biography of a German philosopher is a stub . You can help Wikipedia by expanding it . | https://en.wikipedia.org/wiki/Jacob_Klein_(philosopher) |
In matrix calculus , Jacobi's formula expresses the derivative of the determinant of a matrix A in terms of the adjugate of A and the derivative of A . [ 1 ]
If A is a differentiable map from the real numbers to n × n matrices, then
where tr( X ) is the trace of the matrix X and adj ( X ) {\displaystyle \operatorname {adj} (X)} is its adjugate matrix . (The latter equality only holds if A ( t ) is invertible .)
As a special case,
Equivalently, if dA stands for the differential of A , the general formula is
The formula is named after the mathematician Carl Jacobi .
Theorem. (Jacobi's formula) For any differentiable map A from the real numbers to n × n matrices,
Proof. Laplace's formula for the determinant of a matrix A can be stated as
Notice that the summation is performed over some arbitrary row i of the matrix.
The determinant of A can be considered to be a function of the elements of A :
so that, by the chain rule , its differential is
This summation is performed over all n × n elements of the matrix.
To find ∂ F /∂ A ij consider that on the right hand side of Laplace's formula, the index i can be chosen at will. (In order to optimize calculations: Any other choice would eventually yield the same result, but it could be much harder). In particular, it can be chosen to match the first index of ∂ / ∂ A ij :
Thus, by the product rule,
Now, if an element of a matrix A ij and a cofactor adj T ( A ) ik of element A ik lie on the same row (or column), then the cofactor will not be a function of A ij , because the cofactor of A ik is expressed in terms of elements not in its own row (nor column). Thus,
so
All the elements of A are independent of each other, i.e.
where δ is the Kronecker delta , so
Therefore,
Lemma 1. det ′ ( I ) = t r {\displaystyle \det '(I)=\mathrm {tr} } , where det ′ {\displaystyle \det '} is the differential of det {\displaystyle \det } .
This equation means that the differential of det {\displaystyle \det } , evaluated at the identity matrix, is equal to the trace. The differential det ′ ( I ) {\displaystyle \det '(I)} is a linear operator that maps an n × n matrix to a real number.
Proof. Using the definition of a directional derivative together with one of its basic properties for differentiable functions, we have
det ( I + ε T ) {\displaystyle \det(I+\varepsilon T)} is a polynomial in ε {\displaystyle \varepsilon } of order n . It is closely related to the characteristic polynomial of T {\displaystyle T} . The constant term in that polynomial (the term with ε = 0 {\displaystyle \varepsilon =0} ) is 1, while the linear term in ε {\displaystyle \varepsilon } is t r T {\displaystyle \mathrm {tr} \ T} .
Lemma 2. For an invertible matrix A , we have: det ′ ( A ) ( T ) = det A t r ( A − 1 T ) {\displaystyle \det '(A)(T)=\det A\;\mathrm {tr} (A^{-1}T)} .
Proof. Consider the following function of X :
We calculate the differential of det X {\displaystyle \det X} and evaluate it at X = A {\displaystyle X=A} using Lemma 1, the equation above, and the chain rule:
Theorem. (Jacobi's formula) d d t det A = t r ( a d j A d A d t ) {\displaystyle {\frac {d}{dt}}\det A=\mathrm {tr} \left(\mathrm {adj} \ A{\frac {dA}{dt}}\right)}
Proof. If A {\displaystyle A} is invertible, by Lemma 2, with T = d A / d t {\displaystyle T=dA/dt}
using the equation relating the adjugate of A {\displaystyle A} to A − 1 {\displaystyle A^{-1}} . Now, the formula holds for all matrices, since the set of invertible linear matrices is dense in the space of matrices.
Both sides of the Jacobi formula are polynomials in the matrix
coefficients of A and A' . It is therefore
sufficient to verify the polynomial identity on the dense subset
where the eigenvalues of A are distinct and nonzero.
If A factors differentiably as A = B C {\displaystyle A=BC} , then
In particular, if L is invertible, then I = L − 1 L {\displaystyle I=L^{-1}L} and
Since A has distinct eigenvalues,
there exists a differentiable complex invertible matrix L such that A = L − 1 D L {\displaystyle A=L^{-1}DL} and D is diagonal.
Then
Let λ i {\displaystyle \lambda _{i}} , i = 1 , … , n {\displaystyle i=1,\ldots ,n} be the eigenvalues of A .
Then
which is the Jacobi formula for matrices A with distinct nonzero
eigenvalues.
The following is a useful relation connecting the trace to the determinant of the associated matrix exponential :
det e B = e tr ( B ) {\displaystyle \det e^{B}=e^{\operatorname {tr} \left(B\right)}}
This statement is clear for diagonal matrices, and a proof of the general claim follows.
For any invertible matrix A ( t ) {\displaystyle A(t)} , in the previous section "Via Chain Rule" , we showed that
Considering A ( t ) = exp ( t B ) {\displaystyle A(t)=\exp(tB)} in this equation yields:
The desired result follows as the solution to this ordinary differential equation.
Several forms of the formula underlie the Faddeev–LeVerrier algorithm for computing the characteristic polynomial , and explicit applications of the Cayley–Hamilton theorem . For example, starting from the following equation, which was proved above:
and using A ( t ) = t I − B {\displaystyle A(t)=tI-B} , we get:
where adj denotes the adjugate matrix . | https://en.wikipedia.org/wiki/Jacobi's_formula |
In number theory , Jacobi's four-square theorem gives a formula for the number of ways that a given positive integer n can be represented as the sum of four squares (of integers ).
The theorem was proved in 1834 by Carl Gustav Jakob Jacobi .
Two representations are considered different if their terms are in different order or if the integer being squared (not just the square) is different; to illustrate, these are three of the eight different ways to represent 1:
1 2 + 0 2 + 0 2 + 0 2 0 2 + 1 2 + 0 2 + 0 2 ( − 1 ) 2 + 0 2 + 0 2 + 0 2 . {\displaystyle {\begin{aligned}1^{2}&+0^{2}+0^{2}+0^{2}\\0^{2}&+1^{2}+0^{2}+0^{2}\\(-1)^{2}&+0^{2}+0^{2}+0^{2}.\end{aligned}}}
The number of ways to represent n as the sum of four squares is eight times the sum of the divisors of n if n is odd and 24 times the sum of the odd divisors of n if n is even (see divisor function ), i.e.
r 4 ( n ) = { 8 ∑ m | n m if n is odd , 24 ∑ m | n m odd m if n is even . {\displaystyle r_{4}(n)={\begin{cases}\displaystyle 8\sum _{m|n}m&{\text{if }}n{\text{ is odd}},\\[12pt]\displaystyle 24\sum _{{m|n} \atop {m{\text{ odd}}}}m&{\text{if }}n{\text{ is even}}.\end{cases}}}
Equivalently, it is eight times the sum of all its divisors which are not divisible by 4, i.e.
r 4 ( n ) = 8 ∑ m ∣ n , 4 ∤ m m . {\displaystyle r_{4}(n)=8\sum _{{m\mid n,} \atop {4\nmid m}}m.}
An immediate consequence is r 4 ( 2 n ) = r 4 ( 8 n ) {\displaystyle r_{4}(2n)=r_{4}(8n)} ; for odd n {\displaystyle n} , r 4 ( 2 ⋅ 4 a n ) = r 4 ( 2 n ) {\displaystyle r_{4}(2\cdot 4^{a}n)=r_{4}(2n)} . [ 1 ]
We may also write this as
r 4 ( n ) = 8 σ ( n ) − 32 σ ( n / 4 ) {\displaystyle r_{4}(n)=8\,\sigma (n)-32\,\sigma (n/4)}
where the second term is to be taken as zero if n is not divisible by 4. In particular, for a prime number p we have the explicit formula r 4 ( p ) = 8( p + 1) . [ 2 ]
Some values of r 4 ( n ) occur infinitely often as r 4 ( n ) = r 4 (2 m n ) whenever n is even. The values of r 4 ( n ) can be arbitrarily large: indeed, r 4 ( n ) is infinitely often larger than 8 log n . {\displaystyle 8{\sqrt {\log n}}.} [ 2 ]
The theorem can be proved by elementary means starting with the Jacobi triple product . [ 3 ]
The proof shows that the Theta series for the lattice Z 4 is a modular form of a certain level, and hence equals a linear combination of Eisenstein series . | https://en.wikipedia.org/wiki/Jacobi's_four-square_theorem |
In the theory of many-particle systems, Jacobi coordinates often are used to simplify the mathematical formulation. These coordinates are particularly common in treating polyatomic molecules and chemical reactions , [ 3 ] and in celestial mechanics . [ 4 ] An algorithm for generating the Jacobi coordinates for N bodies may be based upon binary trees . [ 5 ] In words, the algorithm is described as follows: [ 5 ]
Let m j and m k be the masses of two bodies that are replaced by a new body of virtual mass M = m j + m k . The position coordinates x j and x k are replaced by their relative position r jk = x j − x k and by the vector to their center of mass R jk = ( m j q j + m k q k )/( m j + m k ). The node in the binary tree corresponding to the virtual body has m j as its right child and m k as its left child. The order of children indicates the relative coordinate points from x k to x j . Repeat the above step for N − 1 bodies, that is, the N − 2 original bodies plus the new virtual body.
For the N -body problem the result is: [ 2 ]
with
The vector r N {\displaystyle {\boldsymbol {r}}_{N}} is the center of mass of all the bodies and r 1 {\displaystyle {\boldsymbol {r}}_{1}} is the relative coordinate between the particles 1 and 2:
The result one is left with is thus a system of N -1 translationally invariant coordinates r 1 , … , r N − 1 {\displaystyle {\boldsymbol {r}}_{1},\dots ,{\boldsymbol {r}}_{N-1}} and a center of mass coordinate r N {\displaystyle {\boldsymbol {r}}_{N}} , from iteratively reducing two-body systems within the many-body system.
This change of coordinates has associated Jacobian equal to 1 {\displaystyle 1} .
If one is interested in evaluating a free energy operator in these coordinates, one obtains
In the calculations can be useful the following identity | https://en.wikipedia.org/wiki/Jacobi_coordinates |
A Jacobi ellipsoid is a triaxial (i.e. scalene) ellipsoid under hydrostatic equilibrium which arises when a self-gravitating , fluid body of uniform density rotates with a constant angular velocity . It is named after the German mathematician Carl Gustav Jacob Jacobi . [ 1 ]
Before Jacobi, the Maclaurin spheroid , which was formulated in 1742, was considered to be the only type of ellipsoid which can be in equilibrium. [ 2 ] [ 3 ] Lagrange in 1811 [ 4 ] considered the possibility of a tri-axial ellipsoid being in equilibrium, but concluded that the two equatorial axes of the ellipsoid must be equal, leading back to the solution of Maclaurin spheroid. But Jacobi realized that Lagrange 's demonstration is a sufficiency condition, but not necessary. He remarked: [ 5 ]
"One would make a grave mistake if one supposed that the spheroids of revolution are the only admissible figures of equilibrium even under the restrictive assumption of second-degree surfaces" (...) "In fact a simple consideration shows that ellipsoids with three unequal axes can very well be figures of equilibrium; and that one can assume an ellipse of arbitrary shape for the equatorial section and determine the third axis (which is also the least of the three axes) and the angular velocity of rotation such that the ellipsoid is a figure of equilibrium."
For an ellipsoid with equatorial semi-principal axes a , b {\displaystyle a,\ b} and polar semi-principal axis c {\displaystyle c} , the angular velocity Ω {\displaystyle \Omega } about c {\displaystyle c} is given by
where ρ {\displaystyle \rho } is the density and G {\displaystyle G} is the gravitational constant , subject to the condition
For fixed values of a {\displaystyle a} and b {\displaystyle b} , the above condition has solution for c {\displaystyle c} such that
The integrals can be expressed in terms of incomplete elliptic integrals . [ 6 ] In terms of the Carlson symmetric form elliptic integral R J {\displaystyle R_{J}} , the formula for the angular velocity becomes
and the condition on the relative size of the semi-principal axes a , b , c {\displaystyle a,\ b,\ c} is
The angular momentum L {\displaystyle L} of the Jacobi ellipsoid is given by
where M {\displaystyle M} is the mass of the ellipsoid and r {\displaystyle r} is the mean radius , the radius of a sphere of the same volume as the ellipsoid.
The Jacobi and Dedekind ellipsoids are both equilibrium figures for a body of rotating homogeneous self-gravitating fluid. However, while the Jacobi ellipsoid spins bodily, with no internal flow of the fluid in the rotating frame, the Dedekind ellipsoid maintains a fixed orientation, with the constituent fluid circulating within it. This is a direct consequence of Dedekind's theorem .
For any given Jacobi ellipsoid, there exists a Dedekind ellipsoid with the same semi-principal axes a , b , c {\displaystyle a,\ b,\ c} and same mass and with a flow velocity field of [ 7 ]
where x , y , z {\displaystyle x,\ y,\ z} are Cartesian coordinates on axes x ^ , y ^ , z ^ {\displaystyle {\hat {x}},\ {\hat {y}},\ {\hat {z}}} aligned respectively with the a , b , c {\displaystyle a,\ b,\ c} axes of the ellipsoid. Here ζ {\displaystyle \zeta } is the vorticity , which is uniform throughout the spheroid ( ∇ × u = ζ z ^ {\displaystyle \nabla \times \mathbf {u} =\zeta \mathbf {\hat {z}} } ). The angular velocity Ω {\displaystyle \Omega } of the Jacobi ellipsoid and vorticity of the corresponding Dedekind ellipsoid are related by [ 7 ]
That is, each particle of the fluid of the Dedekind ellipsoid describes a similar elliptical circuit in the same period in which the Jacobi spheroid performs one rotation.
In the special case of a = b {\displaystyle a=b} , the Jacobi and Dedekind ellipsoids (and the Maclaurin spheroid) become one and the same; bodily rotation and circular flow amount to the same thing. In this case ζ = 2 Ω {\displaystyle \zeta =2\Omega } , as is always true for a rigidly rotating body.
In the general case, the Jacobi and Dedekind ellipsoids have the same energy, [ 8 ] but the angular momentum of the Jacobi spheroid is the greater by a factor of [ 8 ] | https://en.wikipedia.org/wiki/Jacobi_ellipsoid |
In Riemannian geometry , a Jacobi field is a vector field along a geodesic γ {\displaystyle \gamma } in a Riemannian manifold describing the difference between the geodesic and an "infinitesimally close" geodesic. In other words, the Jacobi fields along a geodesic form the tangent space to the geodesic in the space of all geodesics. They are named after Carl Jacobi .
Jacobi fields can be obtained in the following way: Take a smooth one parameter family of geodesics γ τ {\displaystyle \gamma _{\tau }} with γ 0 = γ {\displaystyle \gamma _{0}=\gamma } , then
is a Jacobi field, and describes the behavior of the geodesics in an infinitesimal neighborhood of a
given geodesic γ {\displaystyle \gamma } .
A vector field J along a geodesic γ {\displaystyle \gamma } is said to be a Jacobi field if it satisfies the Jacobi equation :
where D denotes the covariant derivative with respect to the Levi-Civita connection , R the Riemann curvature tensor , γ ˙ ( t ) = d γ ( t ) / d t {\displaystyle {\dot {\gamma }}(t)=d\gamma (t)/dt} the tangent vector field, and t is the parameter of the geodesic.
On a complete Riemannian manifold, for any Jacobi field there is a family of geodesics γ τ {\displaystyle \gamma _{\tau }} describing the field (as in the preceding paragraph).
The Jacobi equation is a linear , second order ordinary differential equation ;
in particular, values of J {\displaystyle J} and D d t J {\displaystyle {\frac {D}{dt}}J} at one point of γ {\displaystyle \gamma } uniquely determine the Jacobi field. Furthermore, the set of Jacobi fields along a given geodesic forms a real vector space of dimension twice the dimension of the manifold.
As trivial examples of Jacobi fields one can consider γ ˙ ( t ) {\displaystyle {\dot {\gamma }}(t)} and t γ ˙ ( t ) {\displaystyle t{\dot {\gamma }}(t)} . These correspond respectively to the following families of reparametrizations: γ τ ( t ) = γ ( τ + t ) {\displaystyle \gamma _{\tau }(t)=\gamma (\tau +t)} and γ τ ( t ) = γ ( ( 1 + τ ) t ) {\displaystyle \gamma _{\tau }(t)=\gamma ((1+\tau )t)} .
Any Jacobi field J {\displaystyle J} can be represented in a unique way as a sum T + I {\displaystyle T+I} , where T = a γ ˙ ( t ) + b t γ ˙ ( t ) {\displaystyle T=a{\dot {\gamma }}(t)+bt{\dot {\gamma }}(t)} is a linear combination of trivial Jacobi fields and I ( t ) {\displaystyle I(t)} is orthogonal to γ ˙ ( t ) {\displaystyle {\dot {\gamma }}(t)} , for all t {\displaystyle t} .
The field I {\displaystyle I} then corresponds to the same variation of geodesics as J {\displaystyle J} , only with changed parametrizations.
On a unit sphere , the geodesics through the North pole are great circles . Consider two such geodesics γ 0 {\displaystyle \gamma _{0}} and γ τ {\displaystyle \gamma _{\tau }} with natural parameter, t ∈ [ 0 , π ] {\displaystyle t\in [0,\pi ]} , separated by an angle τ {\displaystyle \tau } . The geodesic distance
is
Computing this requires knowing the geodesics. The most interesting information is just that
Instead, we can consider the derivative with respect to τ {\displaystyle \tau } at τ = 0 {\displaystyle \tau =0} :
Notice that we still detect the intersection of the geodesics at t = π {\displaystyle t=\pi } . Notice further that to calculate this derivative we do not actually need to know
rather, all we need do is solve the equation
for some given initial data.
Jacobi fields give a natural generalization of this phenomenon to arbitrary Riemannian manifolds .
Let e 1 ( 0 ) = γ ˙ ( 0 ) / | γ ˙ ( 0 ) | {\displaystyle e_{1}(0)={\dot {\gamma }}(0)/|{\dot {\gamma }}(0)|} and complete this to get an orthonormal basis { e i ( 0 ) } {\displaystyle {\big \{}e_{i}(0){\big \}}} at T γ ( 0 ) M {\displaystyle T_{\gamma (0)}M} . Parallel transport it to get a basis { e i ( t ) } {\displaystyle \{e_{i}(t)\}} all along γ {\displaystyle \gamma } .
This gives an orthonormal basis with e 1 ( t ) = γ ˙ ( t ) / | γ ˙ ( t ) | {\displaystyle e_{1}(t)={\dot {\gamma }}(t)/|{\dot {\gamma }}(t)|} . The Jacobi field can be written in co-ordinates in terms of this basis as J ( t ) = y k ( t ) e k ( t ) {\displaystyle J(t)=y^{k}(t)e_{k}(t)} and thus
and the Jacobi equation can be rewritten as a system
for each k {\displaystyle k} . This way we get a linear ordinary differential equation (ODE).
Since this ODE has smooth coefficients we have that solutions exist for all t {\displaystyle t} and are unique, given y k ( 0 ) {\displaystyle y^{k}(0)} and y k ′ ( 0 ) {\displaystyle {y^{k}}'(0)} , for all k {\displaystyle k} .
Consider a geodesic γ ( t ) {\displaystyle \gamma (t)} with parallel orthonormal frame e i ( t ) {\displaystyle e_{i}(t)} , e 1 ( t ) = γ ˙ ( t ) / | γ ˙ | {\displaystyle e_{1}(t)={\dot {\gamma }}(t)/|{\dot {\gamma }}|} , constructed as above. | https://en.wikipedia.org/wiki/Jacobi_field |
In mathematics , the Jacobi identity is a property of a binary operation that describes how the order of evaluation, the placement of parentheses in a multiple product, affects the result of the operation. By contrast, for operations with the associative property , any order of evaluation gives the same result (parentheses in a multiple product are not needed). The identity is named after the German mathematician Carl Gustav Jacob Jacobi . He derived the Jacobi identity for Poisson brackets in his 1862 paper on differential equations. [ 1 ] [ 2 ]
The cross product a × b {\displaystyle a\times b} and the Lie bracket operation [ a , b ] {\displaystyle [a,b]} both satisfy the Jacobi identity. [ 3 ] In analytical mechanics , the Jacobi identity is satisfied by the Poisson brackets . In quantum mechanics , it is satisfied by operator commutators on a Hilbert space and equivalently in the phase space formulation of quantum mechanics by the Moyal bracket .
Let + {\displaystyle +} and × {\displaystyle \times } be two binary operations , and let 0 {\displaystyle 0} be the neutral element for + {\displaystyle +} . The Jacobi identity is
Notice the pattern in the variables on the left side of this identity. In each subsequent expression of the form a × ( b × c ) {\displaystyle a\times (b\times c)} , the variables x {\displaystyle x} , y {\displaystyle y} and z {\displaystyle z} are permuted according to the cycle x ↦ y ↦ z ↦ x {\displaystyle x\mapsto y\mapsto z\mapsto x} . Alternatively, we may observe that the ordered triples ( x , y , z ) {\displaystyle (x,y,z)} , ( y , z , x ) {\displaystyle (y,z,x)} and ( z , x , y ) {\displaystyle (z,x,y)} , are the even permutations of the ordered triple ( x , y , z ) {\displaystyle (x,y,z)} .
The simplest informative example of a Lie algebra is constructed from the (associative) ring of n × n {\displaystyle n\times n} matrices, which may be thought of as infinitesimal motions of an n -dimensional vector space. The × operation is the commutator , which measures the failure of commutativity in matrix multiplication. Instead of X × Y {\displaystyle X\times Y} , the Lie bracket notation is used:
In that notation, the Jacobi identity is:
That is easily checked by computation.
More generally, if A is an associative algebra and V is a subspace of A that is closed under the bracket operation: [ X , Y ] = X Y − Y X {\displaystyle [X,Y]=XY-YX} belongs to V for all X , Y ∈ V {\displaystyle X,Y\in V} , the Jacobi identity continues to hold on V . [ 4 ] Thus, if a binary operation [ X , Y ] {\displaystyle [X,Y]} satisfies the Jacobi identity, it may be said that it behaves as if it were given by X Y − Y X {\displaystyle XY-YX} in some associative algebra even if it is not actually defined that way.
Using the antisymmetry property [ X , Y ] = − [ Y , X ] {\displaystyle [X,Y]=-[Y,X]} , the Jacobi identity may be rewritten as a modification of the associative property :
If [ X , Z ] {\displaystyle [X,Z]} is the action of the infinitesimal motion X on Z , that can be stated as:
The action of Y followed by X (operator [ X , [ Y , ⋅ ] ] {\displaystyle [X,[Y,\cdot \ ]]} ), minus the action of X followed by Y (operator ( [ Y , [ X , ⋅ ] ] {\displaystyle ([Y,[X,\cdot \ ]]} ), is equal to the action of [ X , Y ] {\displaystyle [X,Y]} , (operator [ [ X , Y ] , ⋅ ] {\displaystyle [[X,Y],\cdot \ ]} ).
There is also a plethora of graded Jacobi identities involving anticommutators { X , Y } {\displaystyle \{X,Y\}} , such as:
Most common examples of the Jacobi identity come from the bracket multiplication [ x , y ] {\displaystyle [x,y]} on Lie algebras and Lie rings . The Jacobi identity is written as:
Because the bracket multiplication is antisymmetric , the Jacobi identity admits two equivalent reformulations. Defining the adjoint operator ad x : y ↦ [ x , y ] {\displaystyle \operatorname {ad} _{x}:y\mapsto [x,y]} , the identity becomes:
Thus, the Jacobi identity for Lie algebras states that the action of any element on the algebra is a derivation . That form of the Jacobi identity is also used to define the notion of Leibniz algebra .
Another rearrangement shows that the Jacobi identity is equivalent to the following identity between the operators of the adjoint representation:
There, the bracket on the left side is the operation of the original algebra, the bracket on the right is the commutator of the composition of operators, and the identity states that the a d {\displaystyle \mathrm {ad} } map sending each element to its adjoint action is a Lie algebra homomorphism . | https://en.wikipedia.org/wiki/Jacobi_identity |
In mathematics , the Jacobi triple product is the identity:
for complex numbers x and y , with | x | < 1 and y ≠ 0. It was introduced by Jacobi ( 1829 ) in his work Fundamenta Nova Theoriae Functionum Ellipticarum .
The Jacobi triple product identity is the Macdonald identity for the affine root system of type A 1 , and is the Weyl denominator formula for the corresponding affine Kac–Moody algebra .
Jacobi's proof relies on Euler's pentagonal number theorem , which is itself a specific case of the Jacobi triple product identity.
Let x = q q {\displaystyle x=q{\sqrt {q}}} and y 2 = − q {\displaystyle y^{2}=-{\sqrt {q}}} . Then we have
The Rogers–Ramanujan identities follow with x = q 2 q {\displaystyle x=q^{2}{\sqrt {q}}} , y 2 = − q {\displaystyle y^{2}=-{\sqrt {q}}} and x = q 2 q {\displaystyle x=q^{2}{\sqrt {q}}} , y 2 = − q q {\displaystyle y^{2}=-q{\sqrt {q}}} .
The Jacobi Triple Product also allows the Jacobi theta function to be written as an infinite product as follows:
Let x = e i π τ {\displaystyle x=e^{i\pi \tau }} and y = e i π z . {\displaystyle y=e^{i\pi z}.}
Then the Jacobi theta function
can be written in the form
Using the Jacobi triple product identity, the theta function can be written as the product
There are many different notations used to express the Jacobi triple product. It takes on a concise form when expressed in terms of q -Pochhammer symbols :
where ( a ; q ) ∞ {\displaystyle (a;q)_{\infty }} is the infinite q -Pochhammer symbol.
It enjoys a particularly elegant form when expressed in terms of the Ramanujan theta function . For | a b | < 1 {\displaystyle |ab|<1} it can be written as
Let f x ( y ) = ∏ m = 1 ∞ ( 1 − x 2 m ) ( 1 + x 2 m − 1 y 2 ) ( 1 + x 2 m − 1 y − 2 ) {\displaystyle f_{x}(y)=\prod _{m=1}^{\infty }\left(1-x^{2m}\right)\left(1+x^{2m-1}y^{2}\right)\left(1+x^{2m-1}y^{-2}\right)}
Substituting xy for y and multiplying the new terms out gives
Since f x {\displaystyle f_{x}} is meromorphic for | y | > 0 {\displaystyle |y|>0} , it has a Laurent series
which satisfies
so that
and hence
To show that c 0 ( x ) = 1 {\displaystyle c_{0}(x)=1} , use the fact that the infinite expansion
has the following infinite polynomial coefficient at y 0 {\displaystyle y^{0}}
which is the Durfee square generating function with x 2 {\displaystyle x^{2}} instead of x {\displaystyle x} .
Therefore at y 0 {\displaystyle y^{0}} we have f x ( y ) = 1 {\displaystyle f_{x}(y)=1} , and so c 0 ( x ) = 1 {\displaystyle c_{0}(x)=1} .
A different proof is given by G. E. Andrews based on two identities of Euler. [ 1 ]
For the analytic case, see Apostol. [ 2 ] | https://en.wikipedia.org/wiki/Jacobi_triple_product |
In mathematics, a Jacobian , named for Carl Gustav Jacob Jacobi , may refer to: | https://en.wikipedia.org/wiki/Jacobian |
In mathematics , the Jacobian conjecture is a famous unsolved problem concerning polynomials in several variables . It states that if a polynomial function from an n -dimensional space to itself has Jacobian determinant which is a non-zero constant, then the function has a polynomial inverse. It was first conjectured in 1939 by Ott-Heinrich Keller , [ 1 ] and widely publicized by Shreeram Abhyankar , as an example of a difficult question in algebraic geometry that can be understood using little beyond a knowledge of calculus .
The Jacobian conjecture is notorious for the large number of attempted proofs that turned out to contain subtle errors. As of 2018, there are no plausible claims to have proved it. Even the two-variable case has resisted all efforts. There are currently no known compelling reasons for believing the conjecture to be true, and according to van den Essen [ 2 ] there are some suspicions that the conjecture is in fact false for large numbers of variables (indeed, there is equally also no compelling evidence to support these suspicions). The Jacobian conjecture is number 16 in Stephen Smale's 1998 list of Mathematical Problems for the Next Century .
Let N > 1 be a fixed integer and consider polynomials f 1 , ..., f N in variables X 1 , ..., X N with coefficients in a field k . Then we define a vector-valued function F : k N → k N by setting:
Any map F : k N → k N arising in this way is called a polynomial mapping .
The Jacobian determinant of F , denoted by J F , is defined as the determinant of the N × N Jacobian matrix consisting of the partial derivatives of f i with respect to X j :
then J F is itself a polynomial function of the N variables X 1 , ..., X N .
It follows from the multivariable chain rule that if F has a polynomial inverse function G : k N → k N , then J F has a polynomial reciprocal, so is a nonzero constant. The Jacobian conjecture is the following partial converse:
Jacobian conjecture: Let k have characteristic 0. If J F is a non-zero constant, then F has an inverse function G : k N → k N which is regular , meaning its components are polynomials.
According to van den Essen, [ 2 ] the problem was first conjectured by Keller in 1939 for the limited case of two variables and integer coefficients.
The obvious analogue of the Jacobian conjecture fails if k has characteristic p > 0 even for one variable. The characteristic of a field, if it is not zero, must be prime, so at least 2. The polynomial x − x p has derivative 1 − p x p −1 which is 1 (because px is 0) but it has no inverse function. However, Kossivi Adjamagbo [ ht ] suggested extending the Jacobian conjecture to characteristic p > 0 by adding the hypothesis that p does not divide the degree of the field extension k ( X ) / k ( F ) . [ 3 ]
The existence of a polynomial inverse is obvious if F is simply a set of functions linear in the variables, because then the inverse will also be a set of linear functions. A simple non-linear example is given by
so that the Jacobian determinant is
In this case the inverse exists as the polynomials
But if we modify F slightly, to
then the determinant is
which is not constant, and the Jacobian conjecture does not apply.
The function still has an inverse:
but the expression for x is not a polynomial.
The condition J F ≠ 0 is related to the inverse function theorem in multivariable calculus . In fact for smooth functions (and so in particular for polynomials) a smooth local inverse function to F exists at every point where J F is non-zero. For example, the map x → x + x 3 has a smooth global inverse, but the inverse is not polynomial.
Stuart Sui-Sheng Wang proved the Jacobian conjecture for polynomials of degree 2. [ 4 ] Hyman Bass, Edwin Connell, and David Wright showed that the general case follows from the special case where the polynomials are of degree 3, or even more specifically, of cubic homogeneous type, meaning of the form F = ( X 1 + H 1 , ..., X n + H n ), where each H i is either zero or a homogeneous cubic. [ 5 ] Ludwik Drużkowski showed that one may further assume that the map is of cubic linear type, meaning that the nonzero H i are cubes of homogeneous linear polynomials. [ 6 ] It seems that Drużkowski's reduction is one most promising way to go forward. These reductions introduce additional variables and so are not available for fixed N .
Edwin Connell and Lou van den Dries proved that if the Jacobian conjecture is false, then it has a counterexample with integer coefficients and Jacobian determinant 1. [ 7 ] In consequence, the Jacobian conjecture is true either for all fields of characteristic 0 or for none. For fixed dimension N , it is true if it holds for at least one algebraically closed field of characteristic 0.
Let k [ X ] denote the polynomial ring k [ X 1 , ..., X n ] and k [ F ] denote the k -subalgebra generated by f 1 , ..., f n . For a given F , the Jacobian conjecture is true if, and only if, k [ X ] = k [ F ] . Keller (1939) proved the birational case, that is, where the two fields k ( X ) and k ( F ) are equal. The case where k ( X ) is a Galois extension of k ( F ) was proved by Andrew Campbell for complex maps [ 8 ] and in general by Michael Razar [ 9 ] and, independently, by David Wright. [ 10 ] Tzuong-Tsieng Moh checked the conjecture for polynomials of degree at most 100 in two variables. [ 11 ] [ 12 ]
Michiel de Bondt and Arno van den Essen [ 13 ] [ 14 ] and Ludwik Drużkowski [ 15 ] independently showed that it is enough to prove the Jacobian Conjecture for complex maps of cubic homogeneous type with a symmetric Jacobian matrix, and further showed that the conjecture holds for maps of cubic linear type with a symmetric Jacobian matrix, over any field of characteristic 0.
The strong real Jacobian conjecture was that a real polynomial map with a nowhere vanishing Jacobian determinant has a smooth global inverse. That is equivalent to asking whether such a map is topologically a proper map , in which case it is a covering map of a simply connected manifold , hence invertible. Sergey Pinchuk constructed two variable counterexamples of total degree 35 and higher. [ 16 ]
It is well known that the Dixmier conjecture implies the Jacobian conjecture. [ 5 ] Conversely, it is shown by Yoshifumi Tsuchimoto [ 17 ] and independently by Alexei Belov-Kanel and Maxim Kontsevich [ 18 ] that the Jacobian conjecture for 2N variables implies the Dixmier conjecture in N dimensions. A self-contained and purely algebraic proof of the last implication is also given by Kossivi Adjamagbo and Arno van den Essen [ 19 ] who also proved in the same paper that these two conjectures are equivalent to the Poisson conjecture. [ clarification needed ] | https://en.wikipedia.org/wiki/Jacobian_conjecture |
In vector calculus , the Jacobian matrix ( / dʒ ə ˈ k oʊ b i ə n / , [ 1 ] [ 2 ] [ 3 ] / dʒ ɪ -, j ɪ -/ ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives . If this matrix is square , that is, if the number of variables equals the number of components of function values, then its determinant is called the Jacobian determinant . Both the matrix and (if applicable) the determinant are often referred to simply as the Jacobian . [ 4 ] They are named after Carl Gustav Jacob Jacobi .
The Jacobian matrix is the natural generalization to vector valued functions of several variables of the derivative and the differential of a usual function. This generalization includes generalizations of the inverse function theorem and the implicit function theorem , where the non-nullity of the derivative is replaced by the non-nullity of the Jacobian determinant, and the multiplicative inverse of the derivative is replaced by the inverse of the Jacobian matrix.
The Jacobian determinant is fundamentally used for changes of variables in multiple integrals .
Let f : R n → R m be a function such that each of its first-order partial derivatives exists on R n . This function takes a point x = ( x 1 , … , x n ) ∈ R n {\displaystyle \mathbf {x} =(x_{1},\ldots ,x_{n})\in \mathbf {R} ^{n}} as input and produces the vector f ( x ) = ( f 1 ( x ) , … , f m ( x ) ) ∈ R m {\displaystyle \mathbf {f} (\mathbf {x} )=(f_{1}(\mathbf {x} ),\ldots ,f_{m}(\mathbf {x} ))\in \mathbf {R} ^{m}} as output. Then the Jacobian matrix of f , denoted J f , is the m × n {\displaystyle m\times n} matrix whose ( i , j ) entry is ∂ f i ∂ x j ; {\textstyle {\frac {\partial f_{i}}{\partial x_{j}}};} explicitly J f = [ ∂ f ∂ x 1 ⋯ ∂ f ∂ x n ] = [ ∇ T f 1 ⋮ ∇ T f m ] = [ ∂ f 1 ∂ x 1 ⋯ ∂ f 1 ∂ x n ⋮ ⋱ ⋮ ∂ f m ∂ x 1 ⋯ ∂ f m ∂ x n ] {\displaystyle \mathbf {J_{f}} ={\begin{bmatrix}{\dfrac {\partial \mathbf {f} }{\partial x_{1}}}&\cdots &{\dfrac {\partial \mathbf {f} }{\partial x_{n}}}\end{bmatrix}}={\begin{bmatrix}\nabla ^{\mathsf {T}}f_{1}\\\vdots \\\nabla ^{\mathsf {T}}f_{m}\end{bmatrix}}={\begin{bmatrix}{\dfrac {\partial f_{1}}{\partial x_{1}}}&\cdots &{\dfrac {\partial f_{1}}{\partial x_{n}}}\\\vdots &\ddots &\vdots \\{\dfrac {\partial f_{m}}{\partial x_{1}}}&\cdots &{\dfrac {\partial f_{m}}{\partial x_{n}}}\end{bmatrix}}} where ∇ T f i {\displaystyle \nabla ^{\mathsf {T}}f_{i}} is the transpose (row vector) of the gradient of the i {\displaystyle i} -th component.
The Jacobian matrix, whose entries are functions of x , is denoted in various ways; other common notations include D f , ∇ f {\displaystyle \nabla \mathbf {f} } , and ∂ ( f 1 , … , f m ) ∂ ( x 1 , … , x n ) {\textstyle {\frac {\partial (f_{1},\ldots ,f_{m})}{\partial (x_{1},\ldots ,x_{n})}}} . [ 5 ] [ 6 ] Some authors define the Jacobian as the transpose of the form given above.
The Jacobian matrix represents the differential of f at every point where f is differentiable. In detail, if h is a displacement vector represented by a column matrix , the matrix product J ( x ) ⋅ h is another displacement vector, that is the best linear approximation of the change of f in a neighborhood of x , if f ( x ) is differentiable at x . [ a ] This means that the function that maps y to f ( x ) + J ( x ) ⋅ ( y – x ) is the best linear approximation of f ( y ) for all points y close to x . The linear map h → J ( x ) ⋅ h is known as the derivative or the differential of f at x .
When m = n , the Jacobian matrix is square, so its determinant is a well-defined function of x , known as the Jacobian determinant of f . It carries important information about the local behavior of f . In particular, the function f has a differentiable inverse function in a neighborhood of a point x if and only if the Jacobian determinant is nonzero at x (see inverse function theorem for an explanation of this and Jacobian conjecture for a related problem of global invertibility). The Jacobian determinant also appears when changing the variables in multiple integrals (see substitution rule for multiple variables ).
When m = 1 , that is when f : R n → R is a scalar-valued function , the Jacobian matrix reduces to the row vector ∇ T f {\displaystyle \nabla ^{\mathsf {T}}f} ; this row vector of all first-order partial derivatives of f is the transpose of the gradient of f , i.e. J f = ∇ T f {\displaystyle \mathbf {J} _{f}=\nabla ^{\mathsf {T}}f} . Specializing further, when m = n = 1 , that is when f : R → R is a scalar-valued function of a single variable, the Jacobian matrix has a single entry; this entry is the derivative of the function f .
These concepts are named after the mathematician Carl Gustav Jacob Jacobi (1804–1851).
The Jacobian of a vector-valued function in several variables generalizes the gradient of a scalar -valued function in several variables, which in turn generalizes the derivative of a scalar-valued function of a single variable. In other words, the Jacobian matrix of a scalar-valued function of several variables is (the transpose of) its gradient and the gradient of a scalar-valued function of a single variable is its derivative.
At each point where a function is differentiable, its Jacobian matrix can also be thought of as describing the amount of "stretching", "rotating" or "transforming" that the function imposes locally near that point. For example, if ( x ′, y ′) = f ( x , y ) is used to smoothly transform an image, the Jacobian matrix J f ( x , y ) , describes how the image in the neighborhood of ( x , y ) is transformed.
If a function is differentiable at a point, its differential is given in coordinates by the Jacobian matrix. However, a function does not need to be differentiable for its Jacobian matrix to be defined, since only its first-order partial derivatives are required to exist.
If f is differentiable at a point p in R n , then its differential is represented by J f ( p ) . In this case, the linear transformation represented by J f ( p ) is the best linear approximation of f near the point p , in the sense that
f ( x ) − f ( p ) = J f ( p ) ( x − p ) + o ( ‖ x − p ‖ ) ( as x → p ) , {\displaystyle \mathbf {f} (\mathbf {x} )-\mathbf {f} (\mathbf {p} )=\mathbf {J} _{\mathbf {f} }(\mathbf {p} )(\mathbf {x} -\mathbf {p} )+o(\|\mathbf {x} -\mathbf {p} \|)\quad ({\text{as }}\mathbf {x} \to \mathbf {p} ),}
where o (‖ x − p ‖) is a quantity that approaches zero much faster than the distance between x and p does as x approaches p . This approximation specializes to the approximation of a scalar function of a single variable by its Taylor polynomial of degree one, namely
f ( x ) − f ( p ) = f ′ ( p ) ( x − p ) + o ( x − p ) ( as x → p ) . {\displaystyle f(x)-f(p)=f'(p)(x-p)+o(x-p)\quad ({\text{as }}x\to p).}
In this sense, the Jacobian may be regarded as a kind of " first-order derivative " of a vector-valued function of several variables. In particular, this means that the gradient of a scalar-valued function of several variables may too be regarded as its "first-order derivative".
Composable differentiable functions f : R n → R m and g : R m → R k satisfy the chain rule , namely J g ∘ f ( x ) = J g ( f ( x ) ) J f ( x ) {\displaystyle \mathbf {J} _{\mathbf {g} \circ \mathbf {f} }(\mathbf {x} )=\mathbf {J} _{\mathbf {g} }(\mathbf {f} (\mathbf {x} ))\mathbf {J} _{\mathbf {f} }(\mathbf {x} )} for x in R n .
The Jacobian of the gradient of a scalar function of several variables has a special name: the Hessian matrix , which in a sense is the " second derivative " of the function in question.
If m = n , then f is a function from R n to itself and the Jacobian matrix is a square matrix . We can then form its determinant , known as the Jacobian determinant . The Jacobian determinant is sometimes simply referred to as "the Jacobian".
The Jacobian determinant at a given point gives important information about the behavior of f near that point. For instance, the continuously differentiable function f is invertible near a point p ∈ R n if the Jacobian determinant at p is non-zero. This is the inverse function theorem . Furthermore, if the Jacobian determinant at p is positive , then f preserves orientation near p ; if it is negative , f reverses orientation. The absolute value of the Jacobian determinant at p gives us the factor by which the function f expands or shrinks volumes near p ; this is why it occurs in the general substitution rule .
The Jacobian determinant is used when making a change of variables when evaluating a multiple integral of a function over a region within its domain. To accommodate for the change of coordinates the magnitude of the Jacobian determinant arises as a multiplicative factor within the integral. This is because the n -dimensional dV element is in general a parallelepiped in the new coordinate system, and the n -volume of a parallelepiped is the determinant of its edge vectors.
The Jacobian can also be used to determine the stability of equilibria for systems of differential equations by approximating behavior near an equilibrium point.
According to the inverse function theorem , the matrix inverse of the Jacobian matrix of an invertible function f : R n → R n is the Jacobian matrix of the inverse function. That is, the Jacobian matrix of the inverse function at a point p is
J f − 1 ( p ) = J f − 1 ( f − 1 ( p ) ) , {\displaystyle \mathbf {J} _{\mathbf {f} ^{-1}}(\mathbf {p} )={\mathbf {J} _{\mathbf {f} }^{-1}(\mathbf {f} ^{-1}(\mathbf {p} ))},}
and the Jacobian determinant is
det ( J f − 1 ( p ) ) = 1 det ( J f ( f − 1 ( p ) ) ) . {\displaystyle \det(\mathbf {J} _{\mathbf {f} ^{-1}}(\mathbf {p} ))={\frac {1}{\det(\mathbf {J} _{\mathbf {f} }(\mathbf {f} ^{-1}(\mathbf {p} )))}}.}
If the Jacobian is continuous and nonsingular at the point p in R n , then f is invertible when restricted to some neighbourhood of p . In other words, if the Jacobian determinant is not zero at a point, then the function is locally invertible near this point.
The (unproved) Jacobian conjecture is related to global invertibility in the case of a polynomial function, that is a function defined by n polynomials in n variables. It asserts that, if the Jacobian determinant is a non-zero constant (or, equivalently, that it does not have any complex zero), then the function is invertible and its inverse is a polynomial function.
If f : R n → R m is a differentiable function , a critical point of f is a point where the rank of the Jacobian matrix is not maximal. This means that the rank at the critical point is lower than the rank at some neighbour point. In other words, let k be the maximal dimension of the open balls contained in the image of f ; then a point is critical if all minors of rank k of f are zero.
In the case where m = n = k , a point is critical if the Jacobian determinant is zero.
Consider a function f : R 2 → R 2 , with ( x , y ) ↦ ( f 1 ( x , y ), f 2 ( x , y )), given by
f ( [ x y ] ) = [ f 1 ( x , y ) f 2 ( x , y ) ] = [ x 2 y 5 x + sin y ] . {\displaystyle \mathbf {f} \left({\begin{bmatrix}x\\y\end{bmatrix}}\right)={\begin{bmatrix}f_{1}(x,y)\\f_{2}(x,y)\end{bmatrix}}={\begin{bmatrix}x^{2}y\\5x+\sin y\end{bmatrix}}.}
Then we have
f 1 ( x , y ) = x 2 y {\displaystyle f_{1}(x,y)=x^{2}y}
and
f 2 ( x , y ) = 5 x + sin y . {\displaystyle f_{2}(x,y)=5x+\sin y.}
The Jacobian matrix of f is
J f ( x , y ) = [ ∂ f 1 ∂ x ∂ f 1 ∂ y ∂ f 2 ∂ x ∂ f 2 ∂ y ] = [ 2 x y x 2 5 cos y ] {\displaystyle \mathbf {J} _{\mathbf {f} }(x,y)={\begin{bmatrix}{\dfrac {\partial f_{1}}{\partial x}}&{\dfrac {\partial f_{1}}{\partial y}}\\[1em]{\dfrac {\partial f_{2}}{\partial x}}&{\dfrac {\partial f_{2}}{\partial y}}\end{bmatrix}}={\begin{bmatrix}2xy&x^{2}\\5&\cos y\end{bmatrix}}}
and the Jacobian determinant is
det ( J f ( x , y ) ) = 2 x y cos y − 5 x 2 . {\displaystyle \det(\mathbf {J} _{\mathbf {f} }(x,y))=2xy\cos y-5x^{2}.}
The transformation from polar coordinates ( r , φ ) to Cartesian coordinates ( x , y ), is given by the function F : R + × [0, 2 π ) → R 2 with components
x = r cos φ ; y = r sin φ . {\displaystyle {\begin{aligned}x&=r\cos \varphi ;\\y&=r\sin \varphi .\end{aligned}}}
J F ( r , φ ) = [ ∂ x ∂ r ∂ x ∂ φ ∂ y ∂ r ∂ y ∂ φ ] = [ cos φ − r sin φ sin φ r cos φ ] {\displaystyle \mathbf {J} _{\mathbf {F} }(r,\varphi )={\begin{bmatrix}{\frac {\partial x}{\partial r}}&{\frac {\partial x}{\partial \varphi }}\\[0.5ex]{\frac {\partial y}{\partial r}}&{\frac {\partial y}{\partial \varphi }}\end{bmatrix}}={\begin{bmatrix}\cos \varphi &-r\sin \varphi \\\sin \varphi &r\cos \varphi \end{bmatrix}}}
The Jacobian determinant is equal to r . This can be used to transform integrals between the two coordinate systems:
∬ F ( A ) f ( x , y ) d x d y = ∬ A f ( r cos φ , r sin φ ) r d r d φ . {\displaystyle \iint _{\mathbf {F} (A)}f(x,y)\,dx\,dy=\iint _{A}f(r\cos \varphi ,r\sin \varphi )\,r\,dr\,d\varphi .}
The transformation from spherical coordinates ( ρ , φ , θ ) [ 7 ] to Cartesian coordinates ( x , y , z ), is given by the function F : R + × [0, π ) × [0, 2 π ) → R 3 with components
x = ρ sin φ cos θ ; y = ρ sin φ sin θ ; z = ρ cos φ . {\displaystyle {\begin{aligned}x&=\rho \sin \varphi \cos \theta ;\\y&=\rho \sin \varphi \sin \theta ;\\z&=\rho \cos \varphi .\end{aligned}}}
The Jacobian matrix for this coordinate change is
J F ( ρ , φ , θ ) = [ ∂ x ∂ ρ ∂ x ∂ φ ∂ x ∂ θ ∂ y ∂ ρ ∂ y ∂ φ ∂ y ∂ θ ∂ z ∂ ρ ∂ z ∂ φ ∂ z ∂ θ ] = [ sin φ cos θ ρ cos φ cos θ − ρ sin φ sin θ sin φ sin θ ρ cos φ sin θ ρ sin φ cos θ cos φ − ρ sin φ 0 ] . {\displaystyle \mathbf {J} _{\mathbf {F} }(\rho ,\varphi ,\theta )={\begin{bmatrix}{\dfrac {\partial x}{\partial \rho }}&{\dfrac {\partial x}{\partial \varphi }}&{\dfrac {\partial x}{\partial \theta }}\\[1em]{\dfrac {\partial y}{\partial \rho }}&{\dfrac {\partial y}{\partial \varphi }}&{\dfrac {\partial y}{\partial \theta }}\\[1em]{\dfrac {\partial z}{\partial \rho }}&{\dfrac {\partial z}{\partial \varphi }}&{\dfrac {\partial z}{\partial \theta }}\end{bmatrix}}={\begin{bmatrix}\sin \varphi \cos \theta &\rho \cos \varphi \cos \theta &-\rho \sin \varphi \sin \theta \\\sin \varphi \sin \theta &\rho \cos \varphi \sin \theta &\rho \sin \varphi \cos \theta \\\cos \varphi &-\rho \sin \varphi &0\end{bmatrix}}.}
The determinant is ρ 2 sin φ . Since dV = dx dy dz is the volume for a rectangular differential volume element (because the volume of a rectangular prism is the product of its sides), we can interpret dV = ρ 2 sin φ dρ dφ dθ as the volume of the spherical differential volume element . Unlike rectangular differential volume element's volume, this differential volume element's volume is not a constant, and varies with coordinates ( ρ and φ ). It can be used to transform integrals between the two coordinate systems:
∭ F ( U ) f ( x , y , z ) d x d y d z = ∭ U f ( ρ sin φ cos θ , ρ sin φ sin θ , ρ cos φ ) ρ 2 sin φ d ρ d φ d θ . {\displaystyle \iiint _{\mathbf {F} (U)}f(x,y,z)\,dx\,dy\,dz=\iiint _{U}f(\rho \sin \varphi \cos \theta ,\rho \sin \varphi \sin \theta ,\rho \cos \varphi )\,\rho ^{2}\sin \varphi \,d\rho \,d\varphi \,d\theta .}
The Jacobian matrix of the function F : R 3 → R 4 with components
y 1 = x 1 y 2 = 5 x 3 y 3 = 4 x 2 2 − 2 x 3 y 4 = x 3 sin x 1 {\displaystyle {\begin{aligned}y_{1}&=x_{1}\\y_{2}&=5x_{3}\\y_{3}&=4x_{2}^{2}-2x_{3}\\y_{4}&=x_{3}\sin x_{1}\end{aligned}}}
is
J F ( x 1 , x 2 , x 3 ) = [ ∂ y 1 ∂ x 1 ∂ y 1 ∂ x 2 ∂ y 1 ∂ x 3 ∂ y 2 ∂ x 1 ∂ y 2 ∂ x 2 ∂ y 2 ∂ x 3 ∂ y 3 ∂ x 1 ∂ y 3 ∂ x 2 ∂ y 3 ∂ x 3 ∂ y 4 ∂ x 1 ∂ y 4 ∂ x 2 ∂ y 4 ∂ x 3 ] = [ 1 0 0 0 0 5 0 8 x 2 − 2 x 3 cos x 1 0 sin x 1 ] . {\displaystyle \mathbf {J} _{\mathbf {F} }(x_{1},x_{2},x_{3})={\begin{bmatrix}{\dfrac {\partial y_{1}}{\partial x_{1}}}&{\dfrac {\partial y_{1}}{\partial x_{2}}}&{\dfrac {\partial y_{1}}{\partial x_{3}}}\\[1em]{\dfrac {\partial y_{2}}{\partial x_{1}}}&{\dfrac {\partial y_{2}}{\partial x_{2}}}&{\dfrac {\partial y_{2}}{\partial x_{3}}}\\[1em]{\dfrac {\partial y_{3}}{\partial x_{1}}}&{\dfrac {\partial y_{3}}{\partial x_{2}}}&{\dfrac {\partial y_{3}}{\partial x_{3}}}\\[1em]{\dfrac {\partial y_{4}}{\partial x_{1}}}&{\dfrac {\partial y_{4}}{\partial x_{2}}}&{\dfrac {\partial y_{4}}{\partial x_{3}}}\end{bmatrix}}={\begin{bmatrix}1&0&0\\0&0&5\\0&8x_{2}&-2\\x_{3}\cos x_{1}&0&\sin x_{1}\end{bmatrix}}.}
This example shows that the Jacobian matrix need not be a square matrix.
The Jacobian determinant of the function F : R 3 → R 3 with components
y 1 = 5 x 2 y 2 = 4 x 1 2 − 2 sin ( x 2 x 3 ) y 3 = x 2 x 3 {\displaystyle {\begin{aligned}y_{1}&=5x_{2}\\y_{2}&=4x_{1}^{2}-2\sin(x_{2}x_{3})\\y_{3}&=x_{2}x_{3}\end{aligned}}}
is
| 0 5 0 8 x 1 − 2 x 3 cos ( x 2 x 3 ) − 2 x 2 cos ( x 2 x 3 ) 0 x 3 x 2 | = − 8 x 1 | 5 0 x 3 x 2 | = − 40 x 1 x 2 . {\displaystyle {\begin{vmatrix}0&5&0\\8x_{1}&-2x_{3}\cos(x_{2}x_{3})&-2x_{2}\cos(x_{2}x_{3})\\0&x_{3}&x_{2}\end{vmatrix}}=-8x_{1}{\begin{vmatrix}5&0\\x_{3}&x_{2}\end{vmatrix}}=-40x_{1}x_{2}.}
From this we see that F reverses orientation near those points where x 1 and x 2 have the same sign; the function is locally invertible everywhere except near points where x 1 = 0 or x 2 = 0 . Intuitively, if one starts with a tiny object around the point (1, 2, 3) and apply F to that object, one will get a resulting object with approximately 40 × 1 × 2 = 80 times the volume of the original one, with orientation reversed.
Consider a dynamical system of the form x ˙ = F ( x ) {\displaystyle {\dot {\mathbf {x} }}=F(\mathbf {x} )} , where x ˙ {\displaystyle {\dot {\mathbf {x} }}} is the (component-wise) derivative of x {\displaystyle \mathbf {x} } with respect to the evolution parameter t {\displaystyle t} (time), and F : R n → R n {\displaystyle F\colon \mathbb {R} ^{n}\to \mathbb {R} ^{n}} is differentiable. If F ( x 0 ) = 0 {\displaystyle F(\mathbf {x} _{0})=0} , then x 0 {\displaystyle \mathbf {x} _{0}} is a stationary point (also called a steady state ). By the Hartman–Grobman theorem , the behavior of the system near a stationary point is related to the eigenvalues of J F ( x 0 ) {\displaystyle \mathbf {J} _{F}\left(\mathbf {x} _{0}\right)} , the Jacobian of F {\displaystyle F} at the stationary point. [ 8 ] Specifically, if the eigenvalues all have real parts that are negative, then the system is stable near the stationary point. If any eigenvalue has a real part that is positive, then the point is unstable. If the largest real part of the eigenvalues is zero, the Jacobian matrix does not allow for an evaluation of the stability. [ 9 ]
A square system of coupled nonlinear equations can be solved iteratively by Newton's method . This method uses the Jacobian matrix of the system of equations.
The Jacobian serves as a linearized design matrix in statistical regression and curve fitting ; see non-linear least squares . The Jacobian is also used in random matrices, moments, local sensitivity and statistical diagnostics. [ 10 ] [ 11 ] | https://en.wikipedia.org/wiki/Jacobian_matrix_and_determinant |
In mathematics , the Jacobi–Anger expansion (or Jacobi–Anger identity ) is an expansion of exponentials of trigonometric functions in the basis of their harmonics. It is useful in physics (for example, to convert between plane waves and cylindrical waves ), and in signal processing (to describe FM signals). This identity is named after the 19th-century mathematicians Carl Jacobi and Carl Theodor Anger .
The most general identity is given by: [ 1 ] [ 2 ]
where J n ( z ) {\displaystyle J_{n}(z)} is the n {\displaystyle n} -th Bessel function of the first kind and i {\displaystyle i} is the imaginary unit , i 2 = − 1. {\textstyle i^{2}=-1.} Substituting θ {\textstyle \theta } by θ − π 2 {\textstyle \theta -{\frac {\pi }{2}}} , we also get:
Using the relation J − n ( z ) = ( − 1 ) n J n ( z ) , {\displaystyle J_{-n}(z)=(-1)^{n}\,J_{n}(z),} valid for integer n {\displaystyle n} , the expansion becomes: [ 1 ] [ 2 ]
The following real-valued variations are often useful as well: [ 3 ] | https://en.wikipedia.org/wiki/Jacobi–Anger_expansion |
The Jacobi–Madden equation is the Diophantine equation
proposed by the physicist Lee W. Jacobi and the mathematician Daniel J. Madden in 2008. [ 1 ] [ 2 ] The variables a , b , c , and d can be any integers , positive, negative or 0. [ a ] Jacobi and Madden showed that there are an infinitude of solutions of this equation with all variables non-zero.
The Jacobi–Madden equation represents a particular case of the equation
first proposed in 1772 by Leonhard Euler who conjectured that four is the minimum number (greater than one) of fourth powers of non-zero integers that can sum up to another fourth power. This conjecture, now known as Euler's sum of powers conjecture , was a natural generalization of the Fermat's Last Theorem , the latter having been proved for the fourth power by Pierre de Fermat himself.
Noam Elkies was first to find an infinite series of solutions to Euler's equation with exactly one variable equal to zero, thus disproving Euler's sum of powers conjecture for the fourth power. [ 3 ]
However, until Jacobi and Madden's publication, it was not known whether there exist infinitely many solutions to Euler's equation with all variables non-zero. Only a finite number of such solutions was known. [ 4 ] [ 5 ] One of these solutions, discovered by Simcha Brudno in 1964, [ 6 ] yielded a solution to the Jacobi–Madden equation:
Jacobi and Madden started with,
and the identity,
Adding ( a + b ) 4 + ( c + d ) 4 {\displaystyle (a+b)^{4}+(c+d)^{4}} to both sides of the equation,
it can be seen it is a special Pythagorean triple ,
They then used Brudno's solution and a certain elliptic curve to construct an infinite series of solutions to the Jacobi–Madden equation.
Jacobi and Madden noticed that a different starting value, such as
found by Jaroslaw Wroblewski, [ 5 ] would result in a different infinite series of solutions. [ 7 ]
In August 2015, Seiji Tomita announced two new small solutions to the Jacobi–Madden equation: [ 8 ]
which lead to two new series of solutions constructed by the Jacobi and Madden method. | https://en.wikipedia.org/wiki/Jacobi–Madden_equation |
Jacobsen's catalyst is the common name for N,N'-bis(3,5-di-tert-butylsalicylidene)-1,2-cyclohexanediaminomanganese(III) chloride, a coordination compound of manganese and a salen-type ligand . It is used as an asymmetric catalyst in the Jacobsen epoxidation , which is renowned for its ability to enantioselectively transform prochiral alkenes into epoxides. [ 1 ] [ 2 ] Before its development, catalysts for the asymmetric epoxidation of alkenes required the substrate to have a directing functional group, such as an alcohol as seen in the Sharpless epoxidation . [ 3 ] This compound has two enantiomers, which give the appropriate epoxide product from the alkene starting material.
Enantiomerically pure epoxides are desirable as building blocks for complex molecules with specific chirality. Biologically active compounds can exhibit radically different activity based on differences in chirality and therefore the ability to obtain desired stereocenters in a molecule is of great importance to the pharmaceutical industry. [ 4 ] Jacobsen's catalyst and other asymmetric catalysts are particularly useful in this field; for example, Jacobsen's catalyst was used to synthesize phenylisoserine, a side chain to the famous anti-cancer drug Taxol , in a four-step synthesis as early as 1992. [ 5 ]
Jacobsen's catalyst consists of a salen ligand , tetradentate, meaning it binds to the central manganese metal through four bonds, one to each oxygen and nitrogen atom of the salen backbone. Its chirality is conferred from the diamine-derived backbone . [ 3 ] The aryl groups are decorated with tert-butyl substituents, which amplify the asymmetry around the Mn center. [ 4 ]
Both enantiomers of Jacobsen's catalyst are commercially available. Jacobsen's catalyst can be prepared by separating 1,2-diaminocyclohexane into its component enantiomers and then reacting the appropriate tartrate with 3,5-di-tert-butyl-2-hydroxybenzaldehyde to form a Schiff base (see intermediate formed in the reaction scheme below). Reaction with manganese(II) acetate in the presence of air gives the manganese(III) complex, which may be isolated as the chloro derivative after the addition of lithium chloride . Shown below is the preparation of the (R,R)-enantiomer. [ 6 ] The synthesis has been adapted for undergraduate level chemistry courses in order to stress the importance of enantiomerically pure compounds. [ 7 ]
In general, two mechanisms have been suggested. [ 8 ] Because Jacobsen's catalyst epoxidizes conjugated alkenes (i.e. those in which there are multiple double bonds on alternating carbons) most effectively, the generally accepted mechanism is based on a radical intermediate which is stabilized due to the conjugated nature of the substrate. For non-conjugated alkenes, the substrate is far less able to stabilize a radical, making a radical intermediate more unlikely. In this case, a concerted mechanism in which the bond to the oxygen is simultaneously broken with metal-center while it is formed with the substrate is probable. However, more recent studies have indicated a radical intermediate is possible, challenging the assumption that non-conjugated alkenes undergo concerted mechanisms. [ 8 ]
In the original catalytic reaction, iodosylarenes (PhIO) were used as the stoichiometric oxidant , but soon after it was found that chlorine bleach (NaClO), a cheaper alternative, works as well. While other oxidants subsequently have been used, bleach continues to be the most common. [ 8 ]
After the addition of the oxidant to the system, O=Mn(V) is generally accepted to be the active oxidant species formed (step A). The substrate is thought to approach the metal- oxo bond from the side at a perpendicular orientation in relation to the catalyst in order to allow favorable orbital overlap. This mechanism, which was originally proposed by John Groves to explain porphyrin-catalyzed epoxidation reactions, [ 9 ] is commonly referred to as a "side-on perpendicular approach". The approach is over the diamine bridge, where the steric bulk of the tert-butyl groups on the periphery of the ligand do not interfere with the alkene's approach (see below). [ 2 ] However, as is the case with the overall mechanism, the pathway of alkene approach is also debated. [ 8 ]
The ease with which Jacobsen's catalyst selectively epoxidizes cis-alkenes has been difficult to replicate with terminal and trans-alkenes. [ 2 ] Structural changes to the ligand and adaptations to the protocol for the epoxidation reaction, however, have led to some successes in these areas. [ 8 ] For example, derivatives of Jacobsen's catalyst with small structural changes to the salen backbone have been used in conjunction with low temperatures and the oxidant m-chloroperbenzoic acid (m-CPBA) to epoxidize the terminal alkene styrene . [ 10 ] The low temperature of the reaction favors only one pathway, the cis pathway, while m-CPBA is used because of water's high freezing point. Little success has occurred with the epoxidation of trans alkenes by manganese compounds but other salen coordination compounds, such as oxochromium complexes, can be used. [ 8 ] [ 11 ]
The ligand structure of Jacobsen's catalyst is easily modified for use over a wide range of reactions, such as epoxide-ring openings, Diels-Alder reactions , and conjugate additions. [ 12 ] [ 13 ] For example, an analogous catalyst with an aluminum center has been used for the carbonylation of epoxides in order to obtain beta- lactones . [ 14 ] | https://en.wikipedia.org/wiki/Jacobsen's_catalyst |
The Jacobsen epoxidation , sometimes also referred to as Jacobsen-Katsuki epoxidation is a chemical reaction which allows enantioselective epoxidation of unfunctionalized alkyl- and aryl- substituted alkenes. [ 1 ] [ 2 ] [ 3 ] It is complementary to the Sharpless epoxidation (used to form epoxides from the double bond in allylic alcohols ). The Jacobsen epoxidation gains its stereoselectivity from a C 2 symmetric manganese(III) salen-like ligand , which is used in catalytic amounts. The manganese atom transfers an oxygen atom from chlorine bleach or similar oxidant. The reaction takes its name from its inventor, Eric Jacobsen , with Tsutomu Katsuki sometimes being included. Chiral-directing catalysts are useful to organic chemists trying to control the stereochemistry of biologically active compounds and develop enantiopure drugs .
Several improved procedures have been developed. [ 4 ] [ 5 ] [ 6 ]
A general reaction scheme follows: [ 7 ]
In the early 1990s, Jacobsen and Katsuki independently released their initial findings about their catalysts for the enantioselective epoxidation of isolated alkenes. [ 1 ] [ 3 ] In 1991, Jacobsen published work where he attempted to perfect the catalyst. He was able to obtain ee values above 90% for a variety of ligands. Also, the amount of catalyst used was no more than 15% of the amount of alkene used in the reaction. [ 2 ]
The degree of enantioselectivity depends on numerous factors, namely the structure of the alkene, the nature of the axial donor ligand on the active oxomanganese species and the reaction temperature. Cyclic and acyclic cis -1,2-disubstituted alkenes are epoxidized with almost 100% enantioselectivity whereas trans -1,2-disubstituted alkenes are poor substrates for Jacobsen's catalysts but yet give higher enantioselectivities when Katsuki's catalysts are used. Furthermore, the enantioselective epoxidation of conjugated dienes is much higher than that of the nonconjugated dienes. [ 8 ]
The enantioselectivity is explained by either a "top-on" approach (Jacobsen) or by a "side-on" approach (Katsuki) of the alkene.
The mechanism of the Jacobsen–Katsuki epoxidation is not fully understood, but most likely a manganese(V)-species (similar to the ferryl intermediate of Cytochrome P450 ) is the reactive intermediate which is formed upon the oxidation of the Mn(III)- salen complex . There are three major pathways. The concerted pathway, the metalla oxetane pathway and the radical pathway. The most accepted mechanism is the concerted pathway mechanism. After the formation of the Mn(V) complex, the catalyst is activated and therefore can form epoxides with alkenes. The alkene comes in from the "top-on" approach (above the plane of the catalyst) and the oxygen atom now is bonded to the two carbon atoms (previously C=C bond) and is still bonded to the manganese metal. Then, the Mn–O bond breaks and the epoxide is formed. The Mn(III)-salen complex is regenerated, which can then be oxidized again to form the Mn(V) complex. [ 2 ] [ 3 ]
The radical intermediate accounts for the formation of mixed epoxides when conjugated dienes are used as substrates. [ 8 ]
Dimethyldioxirane can be used as a source of O atoms. DMD of a chiral metal catalyst followed by epoxidation, or (2) epoxidation by chiral dioxiranes, which are generated in situ from a catalytic amount of ketone and a stoichiometric amount of a terminal oxidant). [ 9 ] Mn- salen complexes have been used with success to accomplish the first strategy. [ 10 ] | https://en.wikipedia.org/wiki/Jacobsen_epoxidation |
The Jacobsen rearrangement is a chemical reaction , commonly described as the migration of an alkyl group in a sulfonic acid derived from a polyalkyl- or polyhalobenzene:
The exact reaction mechanism is not completely clear, but evidence indicates that the rearrangement occurs intermolecularly and that the migrating group is transferred to a polyalkylbenzene, not to the sulfonic acid ( sulfonation only takes place after migration). The intermolecular mechanism is partially illustrated by the side products found in the following example:
Furthermore, the reaction is limited to benzene rings with at least four substituents (alkyl and/or halogen groups). The sulfo group is easily removed, so the Jacobsen rearrangement can also be considered as a rearrangement of polyalkylbenzenes. It was Herzig who described this type of rearrangement for the first time in 1881 using polyhalogenated benzenesulfonic acids, but the reaction took the name of the German chemist Oscar Jacobsen [ de ] , who described the rearrangement of polyalkylbenzene derivatives in 1886. | https://en.wikipedia.org/wiki/Jacobsen_rearrangement |
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