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Talk:House of Windsor

Duke of Sussex's father
I don't know how to edit the pop ups on the family tree, but the one for Prince Harry currently states that he is the younger son of James Hewitt. Please can someone edit this asap?

Also, I guess, add in a box for Archie.

Updating photos of List of monarchs
I believe they should look like the ones on their articles. RicLightning (talk) 01:46, 8 October 2023 (UTC)
 * No consensus for such a massive alteration. --SergeWoodzing (talk) 13:55, 8 October 2023 (UTC)

The Queen, as of 2024
I do not agree with this edit. Googling old postcards of former British queens consort (in lieu of better sources right now) does not support it. It's a personal POV with nothing to back it. I am aware of, and can even respect the fact that many people take a more-or-less dim view of Camilla, ranging from just meek uncertainty or apprehensively positioned eyebrows to vehement, rabid, extreme, fanatic hatred. Anyone changing anything anywhere about her should ask h-elf what degree of that dimness of view might be swaying h to do so and how h motives might rightly be perceived. The woman has the exact same rank, title and style as previous British queens consort, and we all need to face that fact no later than now, no matter how it may hurt, somewhere, anatomically, with no sunshine. The king decides these things, not we Wikipedians. I will change this back unless someone can give us a good reason here not to. SergeWoodzing (talk) 19:17, 6 January 2024 (UTC)
 * As it stands now, Queen Camilla's entry on family tree matches those of Queen Mary (of Teck) and Queen Elizabeth (Queen Mum). Moons of Io (talk) 20:03, 6 January 2024 (UTC)
 * Current queens, whether consort or regnant, have always been called "The Queen". Those fine ladies are dead. --SergeWoodzing (talk) 20:14, 6 January 2024 (UTC)
 * Serg - it was you who brought them up when you were "googling old postcards" I don't understand this backtracking from you initial comment. 2A02:1406:1B:8F49:7589:F8D7:3489:F41B (talk) 23:34, 6 January 2024 (UTC)
 * Yes I did. They were called "The Queen" while their husbands were on the throne. No backtracking here. --SergeWoodzing (talk) 15:49, 7 January 2024 (UTC)
 * The royal family website refers to her as "The Queen", as does the coronation invitation . The use of the term queen mum was to distinguish from her daughter, who was also queen elizabeth. Both the queen mum and Mary of Teck were styled 'HM The Queen' during the reign of their husbands, as Camilla is known now. As she is the only Queen of the UK living, there is no need to distinguish her from anyone as was the case with the queen mum. EmilySarah99 (talk) 08:19, 10 January 2024 (UTC)
 * Thank you! Elizabeth II:s mother was known as "The Queen" during her husband's reign. Her daughter was (the only one) known as "The Queen" during hers. --SergeWoodzing (talk) 19:59, 10 January 2024 (UTC)

Charles III, Glücksburg or Windsor?
Children of female monarchs take the house of their fathers, but Charles III is listed as part of Windsor on his page and the current head of house Windsor on the House of Windsor page, but then on the Glücksburg page he is listed as a currently reigning monarchs part of House Glücksburg. By all reasonable definition Charles is part of house Glücksburg. Currently we are at an impasse with contradicting articles. If female monarchs could pass on their house then the house of Windsor wouldn't even exist, this logic is insane. Personally I believe it is worth adding Glücksburg to Charles's page alongside Windsor, and mentioning this on the Glücksburg page and the Windsor page. Zenryzap (talk) 02:55, 31 January 2024 (UTC)
 * "this logic is insane" No it is not? The United Kingdom has had several changes in its legislation concerning the reigning house and its succession since World War I. Dimadick (talk) 03:17, 31 January 2024 (UTC)
 * Britain has changed succession laws to be gender neutral, changed their branch of Saxe-Coburg-Gotha to Windsor, and changed the last name of the family to Mountenbatten-Windsor as far as I'm aware, what of that list would make Charles part of Windsor instead of Glücksburg? The best answer I've found says that he is indeed part of house glücksburg, but also windsor because Elizabeth II declared all monarchs descended from George V to be Windsor (is that really "legislation"), and one site said that this makes it a cadet branch, but i'm not entirely sure about that. Either way at least 1 article is wrong. I will admit calling it insane is harsh though. Zenryzap (talk) 04:36, 31 January 2024 (UTC)
 * The Royal.UK website directly addresses the royal house name, "Unless The Prince of Wales chooses to alter the present decisions when he becomes king, he will continue to be of the House of Windsor and his grandchildren will use the surname Mountbatten-Windsor." To my knowledge, no such change ever took place, so the official house is still House of Windsor. House name. Nford24 (PE121 Personnel Request Form) 05:58, 31 January 2024 (UTC)
 * Ok, on the Glücksburg page it mentions that charles III is only agnatically part of house glücksburg, and in a footnote it states that he reigns as house windsor, so does the windsor page, but Charles III's page doesn't mention Glücksburg at all. If both house pages are in agreement to mention charles's connection to the other house, then shouldn't charles's page include a section about his agnatic hertiage of glucksburg?  it should at least be mentioned. Zenryzap (talk) 19:25, 31 January 2024 (UTC)
 * If/until King Charles III decides otherwise, the British royal house is "Windsor". GoodDay (talk) 22:12, 31 January 2024 (UTC)
 * Then should he be removed from the glücksburg page? Zenryzap (talk) 00:04, 1 February 2024 (UTC)
 * You'll have to ask, over there. GoodDay (talk) 00:31, 1 February 2024 (UTC)
 * "Children of female monarchs take the house of their fathers" assumes that all houses operate on the same, i.e. agnatic principles. I think it's clear by George V's 1917 proclamation, Elizabeth II's 1960 proclamation, and current practice that the House of Windsor doesn't currently operate on such principles entirely. Seltaeb Eht (talk) 19:58, 2 February 2024 (UTC)

As long as there is genealogy as a recognized phenomenon, Charles will genealogically belong to the House of Oldenburg (Glücksburg branch). Officially Windsor. We'll have to wait till we hear from him re: any change in what the official dynasty is to be called now. I don't believe that has happened yet. --SergeWoodzing (talk) 13:23, 1 February 2024 (UTC)
 * As far as I know, there are no planned changes on the dynastic name. Charles' genealogy has no impact on any legislation on the matter. Dimadick (talk) 14:24, 1 February 2024 (UTC)
 * Legislation? Who mentioned legislation? --SergeWoodzing (talk) 16:07, 2 February 2024 (UTC)

title: Talk:House of Windsor


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Hessenberg matrix

In linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has zero entries below the first subdiagonal, and a lower Hessenberg matrix has zero entries above the first superdiagonal. They are named after Karl Hessenberg.

A Hessenberg decomposition is a matrix decomposition of a matrix $$A$$ into a unitary matrix $$P$$ and a Hessenberg matrix $$H$$ such that $$PHP^*=A$$ where $$P^*$$ denotes the conjugate transpose.

Upper Hessenberg matrix
A square $$n \times n$$ matrix $$A$$ is said to be in upper Hessenberg form or to be an upper Hessenberg matrix if $$a_{i,j}=0$$ for all $$i,j$$ with $$i > j+1$$.

An upper Hessenberg matrix is called unreduced if all subdiagonal entries are nonzero, i.e. if $$a_{i+1,i} \neq 0$$ for all $$i \in \{ 1,\ldots,n-1 \}$$.

Lower Hessenberg matrix
A square $$n \times n$$ matrix $$A$$ is said to be in lower Hessenberg form or to be a lower Hessenberg matrix if its transpose $$$$ is an upper Hessenberg matrix or equivalently if $$a_{i,j}=0$$ for all $$i,j$$ with $$j > i+1$$.

A lower Hessenberg matrix is called unreduced if all superdiagonal entries are nonzero, i.e. if $$a_{i,i+1} \neq 0$$ for all $$i \in \{ 1,\ldots,n-1 \}$$.

Examples
Consider the following matrices. $$A=\begin{bmatrix} 1 & 4 & 2 & 3 \\ 3 & 4 & 1 & 7 \\ 0 & 2 & 3 & 4 \\ 0 & 0 & 1 & 3 \\ \end{bmatrix}$$ $$B=\begin{bmatrix} 1 & 2 & 0 & 0 \\ 5 & 2 & 3 & 0 \\ 3 & 4 & 3 & 7 \\ 5 & 6 & 1 & 1 \\ \end{bmatrix}$$ $$C=\begin{bmatrix} 1 & 2 & 0 & 0 \\ 5 & 2 & 0 & 0 \\ 3 & 4 & 3 & 7 \\ 5 & 6 & 1 & 1 \\ \end{bmatrix}$$

The matrix $$A$$ is an upper unreduced Hessenberg matrix, $$B$$ is a lower unreduced Hessenberg matrix and $$C$$ is a lower Hessenberg matrix but is not unreduced.

Computer programming
Many linear algebra algorithms require significantly less computational effort when applied to triangular matrices, and this improvement often carries over to Hessenberg matrices as well. If the constraints of a linear algebra problem do not allow a general matrix to be conveniently reduced to a triangular one, reduction to Hessenberg form is often the next best thing. In fact, reduction of any matrix to a Hessenberg form can be achieved in a finite number of steps (for example, through Householder's transformation of unitary similarity transforms). Subsequent reduction of Hessenberg matrix to a triangular matrix can be achieved through iterative procedures, such as shifted QR-factorization. In eigenvalue algorithms, the Hessenberg matrix can be further reduced to a triangular matrix through Shifted QR-factorization combined with deflation steps. Reducing a general matrix to a Hessenberg matrix and then reducing further to a triangular matrix, instead of directly reducing a general matrix to a triangular matrix, often economizes the arithmetic involved in the QR algorithm for eigenvalue problems.

Householder transformations
Any $$n \times n$$ matrix can be transformed into a Hessenberg matrix by a similarity transformation using Householder transformations. The following procedure for such a transformation is adapted from A Second Course In Linear Algebra by Garcia & Roger.

Let $$A$$ be any real or complex $$n \times n$$ matrix, then let $$A^\prime$$ be the $$(n - 1) \times n$$ submatrix of $$A$$ constructed by removing the first row in $$A$$ and let $$\mathbf{a}^\prime_1$$ be the first column of $$A'$$. Construct the $$(n-1) \times (n-1)$$ householder matrix $$V_1 = I_{(n-1)} - 2\frac{ww^*}{\|w\|^2}$$ where $$ w = \begin{cases} \|\mathbf{a}^\prime_1\|_2\mathbf{e}_1 - \mathbf{a}^\prime_1 \;\;\;\;\;\;\;\;, \;\;\; a^\prime_{11} = 0 \\ \|\mathbf{a}^\prime_1\|_2\mathbf{e}_1 + \frac{\overline{a^\prime_{11}}}{|a^\prime_{11}|}\mathbf{a}^\prime_1 \;\;\;, \;\;\; a^\prime_{11} \neq 0 \\ \end{cases} $$

This householder matrix will map $$\mathbf{a}^\prime_1$$ to $$\|\mathbf{a}^\prime_1\| \mathbf{e}_1$$ and as such, the block matrix $$U_1 = \begin{bmatrix}1 & \mathbf{0} \\ \mathbf{0} & V_1 \end{bmatrix}$$ will map the matrix $$A$$ to the matrix $$U_1A$$ which has only zeros below the second entry of the first column. Now construct $$(n-2) \times (n-2)$$ householder matrix $$V_2$$ in a similar manner as $$V_1$$ such that $$V_2$$ maps the first column of $$A^{\prime\prime}$$ to $$\|\mathbf{a}^{\prime\prime}_1\| \mathbf{e}_1$$, where $$A^{\prime\prime}$$ is the submatrix of $$A^{\prime}$$ constructed by removing the first row and the first column of $$A^{\prime}$$, then let $$U_2 = \begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & V_2\end{bmatrix}$$ which maps $$U_1A$$ to the matrix $$U_2U_1A$$ which has only zeros below the first and second entry of the subdiagonal. Now construct $$V_3$$ and then $$U_3$$ in a similar manner, but for the matrix $$A^{\prime\prime\prime}$$ constructed by removing the first row and first column of $$A^{\prime\prime}$$ and proceed as in the previous steps. Continue like this for a total of $$n-2$$ steps.

By construction of $$U_k$$, the first $$k$$ columns of any $$n \times n$$ matrix are invariant under multiplication by $$U_k^*$$ from the right. Hence, any matrix can be transformed to an upper Hessenberg matrix by a similarity transformation of the form $$U_{(n-2)}( \dots (U_2(U_1 A U_1^*)U_2^*) \dots )U_{(n-2)}^* = U_{(n-2)} \dots U_2U_1A(U_{(n-2)} \dots U_2U_1)^* = UAU^*$$.

Jacobi (Givens) rotations
A Jacobi rotation (also called Givens rotation) is an orthogonal matrix transformation in the form

A\to A'=J(p,q,\theta)^TAJ(p,q,\theta) \;, $$ where $$J(p,q,\theta)$$, $$p< q$$, is the Jacobi rotation matrix with all matrix elements equal zero except for
 * $$\left\{\begin{align}

J(p,q,\theta)_{ii} &{}= 1 \; \forall i \ne p,q\\ J(p,q,\theta)_{pp} &{}= \cos(\theta) \\ J(p,q,\theta)_{qq} &{}= \cos(\theta) \\ J(p,q,\theta)_{pq} &{}= \sin(\theta) \\ J(p,q,\theta)_{qp} &{}= -\sin(\theta) \;. \end{align}\right.$$ One can zero the matrix element $$A'_{p-1,q}$$ by choosing the rotation angle $$\theta$$ to satisfy the equation

A_{p-1,p}\sin\theta+A_{p-1,q}\cos\theta=0 \;, $$ Now, the sequence of such Jacobi rotations with the following $$(p,q)$$

(p,q)=(2,3),(2,4),\dots,(2,n),(3,4),\dots,(3,n),\dots,(n-1,n) $$ reduces the matrix $$A$$ to the lower Hessenberg form.

Properties
For $$n \in \{1, 2\} $$, it is vacuously true that every $$ n \times n $$ matrix is both upper Hessenberg, and lower Hessenberg.

The product of a Hessenberg matrix with a triangular matrix is again Hessenberg. More precisely, if $$A$$ is upper Hessenberg and $$T$$ is upper triangular, then $$AT$$ and $$TA$$ are upper Hessenberg.

A matrix that is both upper Hessenberg and lower Hessenberg is a tridiagonal matrix, of which the Jacobi matrix is an important example. This includes the symmetric or Hermitian Hessenberg matrices. A Hermitian matrix can be reduced to tri-diagonal real symmetric matrices.

Hessenberg operator
The Hessenberg operator is an infinite dimensional Hessenberg matrix. It commonly occurs as the generalization of the Jacobi operator to a system of orthogonal polynomials for the space of square-integrable holomorphic functions over some domain—that is, a Bergman space. In this case, the Hessenberg operator is the right-shift operator $$S$$, given by $$[Sf](z) = z f(z).$$

The eigenvalues of each principal submatrix of the Hessenberg operator are given by the characteristic polynomial for that submatrix. These polynomials are called the Bergman polynomials, and provide an orthogonal polynomial basis for Bergman space.

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

title: Hessenberg matrix


text:
User:Milaiklainim~enwiki

Hello

title: User:Milaiklainim~enwiki


text:
Atkinson cycle

The Atkinson-cycle engine is a type of internal combustion engine invented by James Atkinson in 1882. The Atkinson cycle is designed to provide efficiency at the expense of power density.

A variation of this approach is used in some modern automobile engines. While originally seen exclusively in hybrid electric applications such as the earlier-generation Toyota Prius, later hybrids and some non-hybrid vehicles now feature engines with variable valve timing, which can run in the Atkinson cycle as a part-time operating regimen, giving good economy while running in Atkinson cycle, and conventional power density when running as a conventional, Otto cycle engine.

Design
Atkinson produced three different designs that had a short compression stroke and a longer expansion stroke. The first Atkinson-cycle engine, the differential engine, used opposed pistons. The second and best-known design was the cycle engine, which used an over-center arm to create four piston strokes in one crankshaft revolution. The reciprocating engine had the intake, compression, power, and exhaust strokes of the four-stroke cycle in a single turn of the crankshaft, and was designed to avoid infringing certain patents covering Otto-cycle engines. Atkinson's third and final engine, the utilite engine, operated much like any two-stroke engine.

The common thread throughout Atkinson's designs is that the engines have an expansion stroke that is longer than the compression stroke, and by this method the engine achieves greater thermal efficiency than a traditional piston engine. Atkinson's engines were produced by the British Gas Engine Company and also licensed to other overseas manufacturers.

Many modern engines now use unconventional valve timing to produce the effect of a shorter compression stroke/longer power stroke. Miller applied this technique to the four-stroke engine, so it is sometimes referred as the Atkinson/Miller cycle, US patent 2817322 dated Dec 24, 1957. In 1888, Charon filed a French patent and displayed an engine at the Paris Exhibition in 1889. The Charon gas engine (four-stroke) used a similar cycle to Miller, but without a supercharger. It is referred to as the "Charon cycle".

Hugo Güldner argued in his 1914 book that Körting was the first firm to build a gas engine with a short compression stroke and a longer expansion phase in 1891, based on a design first proposed by Otto Köhler in 1887. This engine also had an engine-load dependent valve train which increased the intake and compression stroke with increasing engine load. On the other hand, the compression was decreasing at low and medium loads, which ultimately reduced the efficiency.

Roy Fedden at Bristol tested an arrangement in the Bristol Jupiter IV engine in 1928, with variable retard timing allowing part of the charge to be blown back into the intake manifold, in order to have sustainable reduced operation pressures during takeoff.

Modern engine designers are realizing the potential fuel-efficiency improvements the Atkinson-type cycle can provide.

Atkinson "Differential Engine"
The first implementation of the Atkinson cycle was in 1882; unlike later versions, it was arranged as an opposed-piston engine, the Atkinson differential engine. In this, a single crankshaft was connected to two opposed pistons through a toggle-jointed linkage that had a nonlinearity; for half a revolution, one piston remained almost stationary while the other approached it and returned, and then for the next half revolution, the second-mentioned piston was almost stationary while the first approached and returned.

Thus, in each revolution, one piston provided a compression stroke and a power stroke, and then the other piston provided an exhaust stroke and a charging stroke. As the power piston remained withdrawn during exhaust and charging, it was practical to provide exhaust and charging using valves behind a port that was covered during the compression stroke and the power stroke, and so the valves did not need to resist high pressure and could be of the simpler sort used in many steam engines, or even reed valves.

Atkinson "Cycle Engine"
The next engine designed by Atkinson in 1887 was named the "Cycle Engine" This engine used poppet valves, a cam, and an over-center arm to produce four piston strokes for every revolution of the crankshaft. The intake and compression strokes were significantly shorter than the expansion and exhaust strokes.

The "Cycle" engines were produced and sold for several years by the British Engine Company. Atkinson also licensed production to other manufacturers. Sizes ranged from a few up to 100 horsepower.

Atkinson "Utilite Engine"

Atkinson's third design was named the "Utilite Engine". Atkinson's "Cycle" engine was efficient; however, its linkage was difficult to balance for high speed operation. Atkinson realized an improvement was needed to make his cycle more applicable as a higher-speed engine.

With this new design, Atkinson was able to eliminate the linkages and make a more conventional, well balanced engine capable of operating at speeds up to 600 rpm and capable of producing power every revolution, yet he preserved all of the efficiency of his "Cycle Engine" having a proportionally short compression stroke and a longer expansion stroke. The Utilite operates much like a standard two-stroke except that the exhaust port is located at about the middle of the stroke.

During the expansion/power stroke, a cam-operated valve (which remains closed until the piston nears the end of the stroke) prevents pressure from escaping as the piston moves past the exhaust port. The exhaust valve is opened near the bottom of the stroke; it remains open as the piston heads back toward compression, letting fresh air charge the cylinder and exhaust escape until the port is covered by the piston.

After the exhaust port is covered the piston begins to compress the remaining air in the cylinder. A small piston fuel pump injects liquid during compression. The ignition source was likely a hot tube as in Atkinson's other engines. This design resulted in a two-stroke engine with a short compression and longer expansion stroke.

The Utilite Engine tested as even more efficient than Atkinson's previous "differential" and "cycle" designs. Very few were produced, and none are known to survive. The British patent is from 1892, #2492. No US patent for the Utilite Engine is known.

Ideal thermodynamic cycle

The ideal Atkinson cycle consists of:
 * 1–2 Isentropic, or reversible, adiabatic compression
 * 2–3 Isochoric heating (Qp)
 * 3–4 Isobaric heating (Qp')
 * 4–5 Isentropic expansion
 * 5–6 Isochoric cooling (Qo)
 * 6–1 Isobaric cooling (Qo')

Modern Atkinson-cycle engines

In the late 20th century, the term "Atkinson cycle" began to be used to describe a modified Otto-cycle engine—in which the intake valve is held open longer than normal, allowing a reverse flow of intake air into the intake manifold. This "simulated" Atkinson cycle is most notably used in the Toyota 1NZ-FXE engine from the early Prius and the Toyota Dynamic Force engines.

The effective compression ratio is reduced—for the time the air is escaping the cylinder freely rather than being compressed—but the expansion ratio is unchanged (i.e., the compression ratio is smaller than the expansion ratio). The goal of the modern Atkinson cycle is to make the pressure in the combustion chamber at the end of the power stroke equal to atmospheric pressure. When this occurs, all available energy has been obtained from the combustion process. For any given portion of air, the greater expansion ratio converts more energy from heat to useful mechanical energy—meaning the engine is more efficient.

The disadvantage of the four-stroke Atkinson-cycle engine versus the more common Otto-cycle engine is reduced power density. Due to a smaller portion of the compression stroke being devoted to compressing the intake air, an Atkinson-cycle engine does not take in as much air as would a similarly designed and sized Otto-cycle engine. Four-stroke engines of this type that use the same type of intake valve motion but also utilize forced induction to make up for the loss of power density are known as Miller-cycle engines.

Rotary Atkinson-cycle engine

The Atkinson cycle can be used in a rotary engine. In this configuration, an increase in both power and efficiency can be achieved when compared to the Otto cycle. This type of engine retains the one power phase per revolution, together with the different compression and expansion volumes of the original Atkinson cycle.

Exhaust gases are expelled from the engine by compressed-air scavenging. This modification of the Atkinson cycle allows the use of alternative fuels such as diesel and hydrogen.

Disadvantages of this design include the requirement that rotor tips seal very tightly on the outer housing wall and the mechanical losses suffered through friction between rapidly oscillating parts of irregular shape. See external links below for more information.

The Sachs KC-27 Wankel engine in the Hercules W-2000 motorcycle used the Atkinson cycle. A depression capsule opens a secondary path for the incoming charge.

Vehicles using Atkinson-cycle engines

While a modified Otto-cycle piston engine using the Atkinson cycle provides good fuel efficiency, it is at the expense of a lower power-per-displacement as compared to a traditional four-stroke engine. If demand for more power is intermittent, the power of the engine can be supplemented by an electric motor during times when more power is needed. This forms the basis of an Atkinson cycle-based hybrid electric drivetrain. These electric motors can be used independently of, or in combination with, the Atkinson-cycle engine, to provide the most efficient means of producing the desired power. This drive-train first entered production in late 1997 in the first-generation Toyota Prius.

, many production hybrid vehicle drivetrains use Atkinson-cycle concepts—for example, in:

 * Chevrolet Volt
 * Chrysler Pacifica (front-wheel drive) plug-in hybrid model minivan
 * Ford C-Max (front-wheel drive / US market) hybrid and plug-in hybrid models
 * Ford Escape/Mercury Mariner/Mazda Tribute electric (front- and four-wheel drive) with a compression ratio of 12.4:1
 * Ford Fusion Hybrid/Mercury Milan Hybrid/Lincoln MKZ Hybrid electric (front-wheel drive) with a compression ratio of 12.3:1
 * Ford Maverick
 * Honda Accord Plug-in Hybrid
 * Honda Accord Hybrid (front-wheel drive)
 * Honda City (hybrid)
 * Honda Clarity Plug-In Hybrid
 * Honda CR-V (hybrid 2020–present)
 * Honda Insight (front-wheel drive)
 * Honda Fit (front-wheel drive) some of the 3rd generation engines switch between Atkinson and Otto cycles.
 * Hyundai Sonata Hybrid (front-wheel drive)
 * Hyundai Elantra Atkinson-cycle models
 * Hyundai Grandeur hybrid (front-wheel drive)
 * Hyundai Ioniq hybrid, plug-in hybrid (front-wheel drive)
 * Hyundai Palisade 3.8 L Lambda II V6 GDi
 * Infiniti M35h hybrid (rear-wheel drive)
 * Kia Forte 147 hp 2.0 petrol only (front-wheel drive)
 * Kia Niro hybrid, plug-in hybrid (front-wheel drive)
 * Kia Optima Hybrid Kia K5 hybrid 500h (front-wheel drive) with a compression ratio of 13:1
 * Kia Cadenza Hybrid Kia K7 hybrid 700h (front-wheel drive)
 * Kia Telluride 3.8 L Lambda II V6 GDi
 * Kia Seltos 2.0L (front-wheel drive)
 * Lexus CT 200h (front-wheel drive)
 * Lexus ES 300h (front-wheel drive)
 * Lexus GS 450h hybrid electric (rear-wheel drive) with a compression ratio of 13:1
 * Lexus RC F (rear-wheel drive)
 * Lexus GS F (rear-wheel drive)
 * Lexus HS 250h (front-wheel drive)
 * Lexus IS 200t (2016)
 * Lexus NX hybrid electric (four-wheel drive)
 * Lexus RX 450h hybrid electric (four-wheel drive)
 * Lexus UX hybrid electric (four-wheel drive)
 * Lexus LC (rear-wheel drive)
 * Mazda Mazda6 (2013 for the 2014 model year)
 * Mercedes ML450 Hybrid (four-wheel drive) electric
 * Mercedes S400 Blue Hybrid (rear-wheel drive) electric
 * Mitsubishi Outlander PHEV (2018 for the 2019 model year, plug-in hybrid four-wheel drive)
 * Subaru Crosstrek Hybrid (2018 for the 2019 model year, all-wheel drive)
 * Toyota Camry Hybrid electric (front-wheel drive) with a compression ratio of 12.5:1
 * Toyota Avalon Hybrid (front wheel drive)
 * Toyota Highlander Hybrid (2011 and newer)
 * Toyota Prius hybrid electric (front-wheel drive) with a (purely geometric) compression ratio of 13.0:1
 * Toyota Yaris Hybrid (front-wheel drive) with a compression ratio of 13.4:1
 * Toyota Auris Hybrid (front-wheel drive)
 * Toyota Tacoma V6 (beginning in 2015 for the 2016 model year)
 * Toyota RAV4 Hybrid (beginning in 2015 for the 2016 model year)
 * Toyota Sienna (2016 for the 2017 model year, hybrid beginning for 2021 model year)
 * Toyota Venza (hybrid beginning for 2021 model year)
 * Toyota C-HR Hybrid (2016–present)
 * Toyota Yaris Cross Hybrid (2021–present)
 * Toyota Innova Hybrid (2022–present)

Patents
The 1887 patent (US 367496) describes the mechanical linkages necessary to obtain all four strokes of the four-stroke cycle for a gas engine within one revolution of the crankshaft. There is also a reference to an 1886 Atkinson patent (US 336505), which describes an opposed-piston gas engine. The British patent for the "Utilite'" is from 1892 (#2492).

title: Atkinson cycle


text:
Talk:Moshe Greenberg

Untitled

 * author of The Hab/piru, New Haven, 1955 (American Oriental Series, vol. 39, ISBN 0-940490-39-0): Habiru/Sources;
 * translator of The Religion of Israel: From its Beginnings to the Babylonin Exile by Yehezkel Kaufman, Univ. of Chicago Press, 1960;
 * author of Biblical Prose Prayer as a Window to the Popular Religion of Ancient Israel;
 *

title: Talk:Moshe Greenberg


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Pak Tea House

Pak Tea House is an intellectual tea–café located in Lahore, Punjab, Pakistan known for its association with progressive academics and left-leaning South Asian intelligentsia.

Traditionally frequented by country's notably artistic, cultural and literary personalities, it was founded by a Sikh family in 1940 and quickly acquired its current name after it was leased to one of the locals in Lahore after the partition of India in 1947. Intervention of Lahore High Court had led to the re-opening of the Tea House in 2013. Noted for being the birthplace of influential literary movement, the Progressive Writers' Association, the place is described as a hub of Lahore's intellectual life for many years.

History
The café was set up in 1940 as the "India Tea House" by Boota Singh, a Sikh family in Lahore. In 1944, it was taken over by two Sikh brothers Surtej Singh Bhalla and Kaiser Singh Bhalla. It remained closed during the 1947 partition riots, and in 1948, it was allotted to Sirajuddin Ahmed. Ahmed who renamed it as "Pak Tea House" in 1950 and ran this restaurant successfully from 1948 to 1978. After his death, his son Zahid Hasan managed the cafe and restaurant, but due to reduction in customers, it was closed in 2000. During this period, its ownership was taken over by the Young Men's Christian.

After the independence of Pakistan in 1947, a local food supplier named Sirajuddin Ahmad rented the house from the YMCA administration and renamed it as "Pak Tea House" in 1947. This historic tea house was known as a meeting place and was traditionally frequented by the city's artistic, cultural and literary personalities especially until the 1990s. Attendees included were: Faiz Ahmed Faiz, Agha Shorish Kashmiri, Ibn-e-Insha, Ahmed Faraz, Saadat Hasan Manto, Josh Malihabadi, Sahir Ludhianvi, Amrita Pritam, Munshi Premchand, Majrooh Sultanpuri, M. D. Taseer, Krishan Chander, Ismat Chughtai, Ahmad Rahi, Muneer Niazi, Meeraji, Ahmed Nadeem Qasmi, Ahmed Faraz, Habib Jalib, Kaifi Azmi, Kamal Ahmed Rizvi, Nasir Kazmi, Professor Sayyid Sajjad Rizavi, Ustad Amanat Ali Khan, Dr. Muhammad Baqir, Intezar Hussain, Rajinder Singh Bedi, Firaq Gorakhpuri, Shaheer Ahmad Khan and Syed Qasim Mahmood.

Pak Tea House became a birthplace of the influential literary movement, the Progressive Writers' Association in Pakistan, which had been known for left-wing politics since its foundation in 1940. Many writers frequented it, and it was also a favorite gathering place of the section of Lahore youths with non-mainstream points of view. It maintained a reputation as a forum for people of diverse backgrounds to voice their opinions in a non-judgmental atmosphere.

In 1999, it was closed by its owner due to lack of business, a decision criticized by the intellectual community of Lahore. It remained closed for 13 years until 2 February 2012 when, on the orders of the Lahore commissioner, Pak Tea House was again put under the control of the YMCA. On 8 March 2013, Pak Tea House was reinaugurated by the Government of Punjab. Pak Tea House is located on the Mall Road, near Anarkali Bazaar and Neela Gumbad.

In 2014, Pak Tea House is said to be still popular amongst students who reportedly say that the food and snacks are reasonably priced and of good quality. This tea house walls are now decorated with pictures of many literary figures of the past.

Reopening
In June 2012, the government of Punjab announced its intention to reopen the Pak Tea House, where it would support itself. On Friday 8 March 2013, Lahore's iconic Pak Tea House reopened after 13 years of closure. Among the attendees was the Pakistani writer Ata ul Haq Qasmi. Pak Tea House remains a special place for those who remember Lahore's lively literary and cultural past.

title: Pak Tea House


text:
Quarth

Quarth (クォース), known as Block Hole outside Japan, is a hybrid puzzle/shoot 'em up game developed by Konami which was released in 1989 as an arcade game. Besides the arcade version, there were also ports of the game to the MSX2 (with a built-in SCC chip), Famicom, and Game Boy—home releases used the Quarth name worldwide (with the exception of the Game Boy Color release in Europe of Konami GB Collection Vol. 2, where the game was renamed to the generic title Block Game for unknown reasons).

Quarth was released on the Konami Net i-mode service as Block Quarth, with an updated Block Quarth DX in 2001. It was released without the "DX" suffix in 2005 and was made globally available through Konami Net licensing on many i-mode services offered by mobile operators. In Europe, for example, it was available from O2 UK, O2 Ireland, and Telefónica Spain.

In 2005, Konami also included the game in the Nintendo DS title Ganbare Goemon: Tōkaidōchū Ōedo Tengurikaeshi no Maki. An emulated version of the game was released in 2006 for PlayStation 2 in Japan as part of the Oretachi Geasen Zoku Sono series.

Gameplay
Quarth is a combination of Tetris-style gameplay and a fixed shooter in the Space Invaders tradition. The player's focus is on falling blocks, and the action is geometrical. Rather than arranging the blocks together to make a row of disappearing blocks, a spaceship positioned at the bottom of the screen shoots blocks upwards to make the falling block pattern into squares or rectangles. Once the blocks have been arranged properly, the shape is destroyed and the player is awarded points based on the shape's size. The blocks continue to drop from the top of the screen in various incomplete shapes. As each level progresses, the blocks drop at greater speed and frequency. There are also various power-ups which could be located to increase ship's speed, among other bonuses.

The game continues until the blocks reach the dotted line at the bottom of the screen, whereupon the player's ship is "player's ship is "quarthed", crushed flat.

Multiplayer
The Arcade, MSX2, and Famicom versions had two different 2-player modes: a split-screen mode with Player 1 on the left and Player 2 on the right, and a cooperative mode where both players shared the same screen.

For the Game Boy, multiplayer requires the Game Boy Link Cable with each player able to view only their fields on their own Game Boys.

Soundtrack

 * In addition, disc 14 of Konami Music Masterpiece Collection, which was released on October 1, 2004, is mostly devoted to Quarth.
 * The game soundtrack of Quarth Soundtracks (クォース) was released on May 30, 2014, by EGG MUSIC and Konami Kukeiha Club and composed by Norio Hanzawa, exclusively in Japan.

Manga

 * Quarth is one of the video games featured in the manga titled Rock'n Game Boy, by Shigeto Ikehara and published by Comic BomBom from October 1989 to December 1991.

Reception
In Japan, Game Machine listed Quarth on their December 1, 1989 issue as being the third most-successful table arcade unit of the month. Block Hole was a hit overseas in Europe, particularly the United Kingdom and Italy.

It has been generally acclaimed by many online reviewers, though Nintendo Life gave the Game Boy port on the 3DS Virtual Console a 6/10.

title: Quarth


text:
Magellanic subpolar forests

The Magellanic subpolar forests (Bosque Subpolar Magallánico) are a terrestrial ecoregion of southernmost South America, covering parts of southern Chile and Argentina, and are part of the Neotropical realm. It is a temperate broadleaf and mixed forests ecoregion, and contains the world's southernmost forests.

Setting
The Magellanic subpolar forests ecoregion lies to the west of the Andes Mountains, which run north-south for most of their length but curve eastward near the southern tip of South America, terminating at the archipelago of Tierra del Fuego. The Magellanic ecoregion was covered by glaciers during the last ice age, and the landscape is deeply dissected by fjords, with numerous islands, inlets, and channels, including the Strait of Magellan, which separates Tierra del Fuego from the South American mainland and is the route taken by Portuguese explorer Ferdinand Magellan from the South Atlantic to the South Pacific. North of roughly 48° south latitude lies the Valdivian temperate forests ecoregion, which shares many affinities with the Magellanic ecoregion in plant and animal life. To the east lie the drier temperate grasslands and shrublands ecoregions of Patagonia, which are in the rain shadow of the Andean and Fuegian mountains.

Climate
The Andean and Fuegan mountains intercept moisture-laden westerly winds, creating temperate rain forest conditions, while the cold oceanic Humboldt Current, which runs up the west coast of South America, and the cold Antarctic Circumpolar Current, which runs from west to east through the Southern Ocean, keep the Magellanic ecoregion cool and wet, and the strong oceanic influence moderates seasonal temperature extremes. Average annual temperatures vary from 6 °C in the north to 3 °C in the south and annual rainfall from 4000 mm in the west to 450 mm in the east. Snowfalls are very common in the west and can occur even in summer. Fog is very frequent. Very strong winds whip the region compelling trees to grow in twisted and bent shapes known as flag trees.

Flora
Like the Valdivian ecoregion, the Magellanic subpolar forests are a refuge for the Antarctic flora, and share many plant families with the temperate forest ecoregions of New Zealand, Tasmania, and Australia, especially the southern beech (Nothofagus). Species of Nothofagus, including N. betuloides, N. antarctica, and N. pumilio, are the characteristic trees of the Magellanic ecoregion. The Magellanic ecoregion does not have the same species richness as the milder Valdivian ecoregion, both on account of its colder climate and its recent glaciation. The advancing glaciers caused the forests to retreat far to the north, and the region was gradually reforested starting about 10,000 years ago when the climate warmed and the glaciers began retreating.

The Magellanic ecoregion has three main plant communities: the Magellanic moorland, the evergreen Magellanic rainforest, and the deciduous Magellanic forest.

The Magellanic moorland occurs on the western edge of the region where the oceanic influence is strongest. High rainfall of 5000 mm/a is typical of the moorland, as are cool temperatures, strong winds, bad drainage conditions, and rocky ground with generally thin soil. Most of the moorland consists of a mosaic of low-growing plants, including dwarf shrubs and wind-sheared trees, cushion plants, grasses, and mosses. These plants can form an underlayer of blanket peat and boggy areas. In more sheltered areas, small stands of evergreen forest can be found, which include Nothofagus betuloides, Drimys winteri, Lepidothamnus fonkii, and Pilgerodendron uviferum.

Farther from the ocean, in more moderate areas less exposed to the oceanic wind and rain, moorland yields to evergreen Magellanic rainforest. The Magellanic rainforest is mostly made up Nothofagus betuloides, together with other evergreen trees, most often Drimys winteri and Pilgerodendron uviferum, and occasionally Embothrium coccineum and Maytenus magellanica. In the better established forest stands, a species-rich shrub layer may develop. In exposed, rocky, and poorly drained areas, pockets of deciduous Nothofagus antarctica and the typical moorland species can be found.

As one moves further east, where rainfall decreases to 800-850 mm/a, Nothofagus betuloides becomes less dominant and mixes with deciduous Nothofagus pumilio in the transition to the deciduous forest community. The Magellanic deciduous forest is made up mostly of Nothofagus pumilio and Nothofagus antarctica. When one reaches the drier rain shadow east of the mountains, the forests disappear, transitioning to the grassland ecoregions of Patagonia.

In open spaces some succulent fruits can be found: Chilean strawberry (Fragaria chiloensis), and calafate (Berberis microphylla); they used to complement the nourishment of the (now almost nonexistent) native peoples.

These forests are peerless in their endurance of cold summers (averaging 9 °C at sea level) and violent subpolar winds. Due to these traits, Magellanic forests' tree species are exported to other parts of the world such as the Faroe Islands and neighboring archipelagos with similar conditions where trees from other biomes in the world cannot grow. The following species from Tierra del Fuego, Drimys winteri, Nothofagus antarctica, Nothofagus pumilio, and Nothofagus betuloides, have been successfully introduced to the Faroe Islands. As a general rule, Fueguian trees show better signs of acclimation than those from Continental Northern Europe to conditions in the Faroe Islands.

Fauna
The Magellanic subpolar forests are home to the southern pudú (Pudu puda), the world's smallest deer, which stands only 35–45 cm high at the shoulder. Other animal species include the cougar (Puma concolor) and the endangered southern river otter (Lontra provocax). Endemic rodents include the Patagonian mara, the long-clawed mole mouse, and the viscacha, a small rodent that looks almost like a rabbit with a long, bushy tail.

Native bird species include the Magellanic woodpecker (Campephilus magellanicus), Patagonian sierra-finch (Phrygilus patagonicus), Patagonian mockingbird (Mimus patagonicus), and Andean condor (Vultur gryphus).

The rich Magellanic coastal waters and numerous rocky islets host many seabirds, including albatrosses, auks, gulls, terns, and penguins.

Protected areas
A 2017 assessment found that 69,938 km², or 46%, of the ecoregion is in protected areas.

Argentina

 * Los Glaciares National Park
 * Tierra del Fuego National Park

Chile

 * Alberto de Agostini National Park
 * Bernardo O'Higgins National Park
 * Cabo de Hornos National Park
 * Katalalixar National Reserve
 * Kawésqar National Park
 * Patagonia National Park
 * Torres del Paine National Park

title: Magellanic subpolar forests


text:
Tridiagonal matrix

In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal (the first diagonal below this), and the supradiagonal/upper diagonal (the first diagonal above the main diagonal). For example, the following matrix is tridiagonal:
 * $$\begin{pmatrix}

1 & 4 & 0 & 0 \\ 3 & 4 & 1 & 0 \\ 0 & 2 & 3 & 4 \\ 0 & 0 & 1 & 3 \\ \end{pmatrix}.$$

The determinant of a tridiagonal matrix is given by the continuant of its elements.

An orthogonal transformation of a symmetric (or Hermitian) matrix to tridiagonal form can be done with the Lanczos algorithm.

Properties
A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. In particular, a tridiagonal matrix is a direct sum of p 1-by-1 and q 2-by-2 matrices such that p + q/2 = n — the dimension of the tridiagonal. Although a general tridiagonal matrix is not necessarily symmetric or Hermitian, many of those that arise when solving linear algebra problems have one of these properties. Furthermore, if a real tridiagonal matrix A satisfies ak,k+1 ak+1,k > 0 for all k, so that the signs of its entries are symmetric, then it is similar to a Hermitian matrix, by a diagonal change of basis matrix. Hence, its eigenvalues are real. If we replace the strict inequality by ak,k+1 ak+1,k ≥ 0, then by continuity, the eigenvalues are still guaranteed to be real, but the matrix need no longer be similar to a Hermitian matrix.

The set of all n × n tridiagonal matrices forms a 3n-2 dimensional vector space.

Many linear algebra algorithms require significantly less computational effort when applied to diagonal matrices, and this improvement often carries over to tridiagonal matrices as well.

Determinant
The determinant of a tridiagonal matrix A of order n can be computed from a three-term recurrence relation. Write f1 = |a1| = a1 (i.e., f1 is the determinant of the 1 by 1 matrix consisting only of a1), and let

 * $$f_n = \begin{vmatrix}

a_1 & b_1 \\ c_1 & a_2 & b_2 \\ & c_2 & \ddots & \ddots \\ & & \ddots & \ddots & b_{n-1} \\ & & & c_{n-1} & a_n \end{vmatrix}.$$

The sequence (fi) is called the continuant and satisfies the recurrence relation

 * $$f_n = a_n f_{n-1} - c_{n-1}b_{n-1}f_{n-2}$$

with initial values f0 = 1 and f−1 = 0. The cost of computing the determinant of a tridiagonal matrix using this formula is linear in n, while the cost is cubic for a general matrix.

Inversion
The inverse of a non-singular tridiagonal matrix T

 * $$T = \begin{pmatrix}

a_1 & b_1 \\ c_1 & a_2 & b_2 \\ & c_2 & \ddots & \ddots \\ & & \ddots & \ddots & b_{n-1} \\ & & & c_{n-1} & a_n \end{pmatrix}$$

is given by

 * $$(T^{-1})_{ij} = \begin{cases}

(-1)^{i+j}b_i \cdots b_{j-1} \theta_{i-1} \phi_{j+1}/\theta_n & \text{ if } i < j\\ \theta_{i-1} \phi_{j+1}/\theta_n & \text{ if } i = j\\ (-1)^{i+j}c_j \cdots c_{i-1} \theta_{j-1} \phi_{i+1}/\theta_n & \text{ if } i > j\\ \end{cases}$$

where the θi satisfy the recurrence relation

 * $$\theta_i = a_i \theta_{i-1} - b_{i-1}c_{i-1}\theta_{i-2} \qquad i=2,3,\ldots,n$$

with initial conditions θ0 = 1, θ1 = a1 and the ϕi satisfy

 * $$\phi_i = a_i \phi_{i+1} - b_i c_i \phi_{i+2} \qquad i=n-1,\ldots,1$$

with initial conditions ϕn+1 = 1 and ϕn = an.

Closed form solutions can be computed for special cases such as symmetric matrices with all diagonal and off-diagonal elements equal or Toeplitz matrices and for the general case as well.

In general, the inverse of a tridiagonal matrix is a semiseparable matrix and vice versa. The inverse of a symmetric tridiagonal matrix can be written as a single-pair matrix (a.k.a. generator-representable semiseparable matrix) of the form

$$\begin{pmatrix} \alpha_1 & -\beta_1 \\ -\beta_1 & \alpha_2 & -\beta_2 \\ & \ddots & \ddots & \ddots & \\ & & \ddots & \ddots & -\beta_{n-1} \\ & & & -\beta_{n-1} & \alpha_n \end{pmatrix}^{-1} = \begin{pmatrix} a_1 b_1 & a_1 b_2 & \cdots & a_1 b_n \\ a_1 b_2 & a_2 b_2 & \cdots & a_2 b_n \\ \vdots & \vdots & \ddots & \vdots \\ a_1 b_n & a_2 b_n & \cdots & a_n b_n \end{pmatrix} = \left( a_{\min(i,j)} b_{\max(i,j)} \right) $$

where $$\begin{cases} \displaystyle a_i = \frac{\beta_{i} \cdots \beta_{n-1}}{\delta_i \cdots \delta_n\,b_n} \\ \displaystyle b_i = \frac{\beta_1 \cdots \beta_{i-1}}{d_1 \cdots d_i}\end{cases}$$ with $$\begin{cases} d_n = \alpha_n,\quad d_{i-1} = \alpha_{i-1} - \frac{\beta_{i-1}^2}{d_{i}}, & i = n, n-1, \cdots, 2, \\       \delta_1 = \alpha_1, \quad \delta_{i+1} = \alpha_{i+1} - \frac{\beta_{i}^2}{\delta_{i}}, & i = 1, 2, \cdots, n-1. \end{cases} $$

Solution of linear system
A system of equations Ax = b for $$b\in \R^n$$ can be solved by an efficient form of Gaussian elimination when A is tridiagonal called tridiagonal matrix algorithm, requiring O(n) operations.

Eigenvalues
When a tridiagonal matrix is also Toeplitz, there is a simple closed-form solution for its eigenvalues, namely:

 * $$ a - 2 \sqrt{bc} \cos \left (\frac{k\pi}{n+1} \right ), \qquad k=1, \ldots, n. $$

A real symmetric tridiagonal matrix has real eigenvalues, and all the eigenvalues are distinct (simple) if all off-diagonal elements are nonzero. Numerous methods exist for the numerical computation of the eigenvalues of a real symmetric tridiagonal matrix to arbitrary finite precision, typically requiring $$O(n^2)$$ operations for a matrix of size $$n\times n$$, although fast algorithms exist which (without parallel computation) require only $$O(n\log n)$$.

As a side note, an unreduced symmetric tridiagonal matrix is a matrix containing non-zero off-diagonal elements of the tridiagonal, where the eigenvalues are distinct while the eigenvectors are unique up to a scale factor and are mutually orthogonal.

Similarity to symmetric tridiagonal matrix
For unsymmetric or nonsymmetric tridiagonal matrices one can compute the eigendecomposition using a similarity transformation. Given a real tridiagonal, nonsymmetric matrix

T = \begin{pmatrix} a_1 & b_1 \\ c_1 & a_2 & b_2 \\ & c_2 & \ddots & \ddots \\ & & \ddots & \ddots & b_{n-1} \\ & & & c_{n-1} & a_n \end{pmatrix} $$ where $$b_i \neq c_i $$. Assume that each product of off-diagonal entries is positive $$b_i c_i > 0 $$ and define a transformation matrix $$D$$ by

D := \operatorname{diag}(\delta_1, \dots, \delta_n) \quad \text{for} \quad \delta_i := \begin{cases} 1 &, \, i=1 \\ \sqrt{\frac{c_{i-1} \dots c_1}{b_{i-1} \dots b_1}} &, \, i=2,\dots,n \,. \end{cases} $$

The similarity transformation $$D^{-1} T D $$ yields a symmetric tridiagonal matrix $$J$$ by:

J:=D^{-1} T D = \begin{pmatrix} a_1 & \sgn b_1 \, \sqrt{b_1 c_1} \\ \sgn b_1 \, \sqrt{b_1 c_1} & a_2 & \sgn b_2 \, \sqrt{b_2 c_2} \\ & \sgn b_2 \, \sqrt{b_2 c_2} & \ddots & \ddots \\ & & \ddots & \ddots & \sgn b_{n-1} \, \sqrt{b_{n-1} c_{n-1}} \\ & & & \sgn b_{n-1} \, \sqrt{b_{n-1} c_{n-1}} & a_n \end{pmatrix} \,. $$ Note that $$T$$ and $$J$$ have the same eigenvalues.

Computer programming
A transformation that reduces a general matrix to Hessenberg form will reduce a Hermitian matrix to tridiagonal form. So, many eigenvalue algorithms, when applied to a Hermitian matrix, reduce the input Hermitian matrix to (symmetric real) tridiagonal form as a first step.

A tridiagonal matrix can also be stored more efficiently than a general matrix by using a special storage scheme. For instance, the LAPACK Fortran package stores an unsymmetric tridiagonal matrix of order n in three one-dimensional arrays, one of length n containing the diagonal elements, and two of length n − 1 containing the subdiagonal and superdiagonal elements.

Applications
The discretization in space of the one-dimensional diffusion or heat equation
 * $$\frac{\partial u(t,x)}{\partial t} = \alpha \frac{\partial^2 u(t,x)}{\partial x^2}$$

using second order central finite differences results in

\begin{pmatrix} \frac{\partial u_{1}(t)}{\partial t} \\ \frac{\partial u_{2}(t)}{\partial t} \\ \vdots \\ \frac{\partial u_{N}(t)}{\partial t} \end{pmatrix} = \frac{\alpha}{\Delta x^2} \begin{pmatrix} -2 & 1 & 0 & \ldots & 0 \\ 1 & -2 & 1 & \ddots & \vdots \\ 0 & \ddots & \ddots & \ddots & 0 \\ \vdots & & 1 & -2 & 1 \\ 0 & \ldots & 0 & 1 & -2 \end{pmatrix} \begin{pmatrix} u_{1}(t) \\ u_{2}(t) \\ \vdots \\ u_{N}(t) \\ \end{pmatrix} $$ with discretization constant $$\Delta x$$. The matrix is tridiagonal with $$a_{i}=-2$$ and $$b_{i}=c_{i}=1$$. Note: no boundary conditions are used here.

title: Tridiagonal matrix


text:
Prohibition of Mixed Marriages Act, 1949

The Prohibition of Mixed Marriages Act, Act No. 55 of 1949, was an apartheid-era law in South Africa that prohibited marriages between "whites" and "non-whites". It was among the first pieces of apartheid legislation to be passed following the National Party's rise to power in 1948. Subsequent legislation, especially the Population Registration and Immorality Acts of 1950, facilitated its implementation by requiring all individuals living in South Africa to register as a member of one of four officially defined racial groups and prohibiting extramarital sexual relationships between those classified as "white" on the one hand and those classified as "non-White" (Blacks, Coloureds, later also Asians) on the other. It did not criminalise sexual relationships between those classified as "non-Europeans".

Background
Mixed races relationships occurred in South Africa as far back as 1669, and often took place between Dutch colonisers and indigenous South African women.

While mixed marriages did not become completely taboo until the rise of the National Party in 1948, in the years immediately preceding the passing of this Act, mixed marriages accounted for just a small fraction of all marriages in South Africa, and occurred almost evenly between the four defined racial groups (Black, Coloured, White, and Asiatic).

Implementation
It was implemented in 1951. On July 1949,the Prohibition of Mixed Marriages Act, Act No 55 of 1949 that prohibited marriage or a sexual relationship between White people and people of other race groups in South Africa is passed. Enforcement of the act was left to the police, who often followed people to their homes to ensure they were not in violation and raided the homes of those believed to be in a mixed marriage. The act applied to all mixed marriages between South Africans, so even marriages which took place in another country were not recognised within South Africa. The punishment for people found to be in a mixed marriage involved arrest and a jail sentence. Anyone who knowingly officiated a marriage that violated the act was also subject to a punishment: a fine was imposed not exceeding 50 pounds. Anyone who was found to have lied to an officiant was also subject to the legal punishment for perjury.

Some of the social consequences of entering into a mixed-race marriage included being ostracised from or ridiculed by one's family and community. One example is a white South African sex worker named Ethal, who indicated that she felt more accepted by her peers when she was a sex worker than when she married a black African man.

Legislative history
The Prohibition of Mixed Marriages Amendment Act of 1968 updated the original legislation to invalidate interracial marriages involving a South African citizen that were contracted in other countries.

The Prohibition of Mixed Marriages Act was repealed by the Immorality and Prohibition of Mixed Marriages Amendment Act, 1985, which was passed during the presidency of P. W. Botha.


text:
Talk:Regular sequence

Moving (2004)
I think it's probably better to move this to regular sequence (algebra), now; and then redirect regular sequence to that.

Charles Matthews 08:17, 11 Mar 2004 (UTC)

That seems fine to me. I noticed yesterday that I wanted to put in some redirections as I've seen you do, but I don't know how to do it yet. Another related page is Koszul complex, which I'll put in part of today.

So that's done now. Redirect syntax is like

 * REDIRECT Whatever.

Charles Matthews 16:35, 11 Mar 2004 (UTC)

possible typo in the text
Hmm, the text says that the depth of R is the depth of the R-module R itself. A bit later it states that the dept of an R-module is at most the dimension of this R-module. This sentence seems to imply that the depth of R itself is at most 1? Or should one add the comment that the restriction to the depth only applies for free R-modules?

Melchior 146.186.134.176 (talk) 23:02, 18 January 2008 (UTC)

Move? (2011)

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

The result of the move request was: page moved.   A rbitrarily 0   ( talk ) 22:35, 31 December 2011 (UTC)

Regular sequence (algebra) → Regular sequence –
 * "Regular sequence" is a dab page which is no more needed because one of the two uses is rare and the disambiguation is resolved by a hatnote in "regular sequence (algebra)". Thus the precision "(algebra)" is also not needed D.Lazard (talk) 11:03, 25 December 2011 (UTC)
 * Support -- This is a good solution. Peterkingiron (talk) 19:02, 26 December 2011 (UTC)
 * Support Since there are only 2 items, and this seems to be the primary topic. --Enric Naval (talk) 23:28, 29 December 2011 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

"Some authors also require ..."?
I don't think it is correct to say that only some authors require that $$M/(r_1,\dots,r_d)M\neq 0$$. This requirement is critical to a correct definition. We can always add $$1$$ (or a unit) to the sequence otherwise. Perhaps this can be clarified. If we do not have the requirement $$1\in R$$, then we can also drop the requirement that this quotient is non-zero. kapil (talk) 05:53, 26 October 2017 (UTC)

title: Talk:Regular sequence


text:
MRP

MRP may refer to:

Business, economics and management

 * Manufacturing resource planning, (MRP II), derived from/a followup to MRP/Material requirements planning
 * Material requirements planning
 * Maximum retail price, in India and Bangladesh
 * Marginal revenue product, in the marginal revenue productivity theory of wages
 * Market risk premium, a risk premium

Politics

 * Papuan People's Assembly (Majelis Rakyat Papua), a cultural assembly for the indigenous people in Papua, Indonesia
 * Molotov–Ribbentrop Pact, a non-aggression pact between Nazi Germany and the Soviet Union
 * MRP-AEG, the Estonian Group on Publication of the Molotov–Ribbentrop Pact
 * Mouvement Républicain Populaire (Popular Republican Movement), a political party during the Fourth French Republic

Science and technology

 * Micronized rubber powder
 * Multidrug resistance protein
 * RNase MRP, a ribonucleoprotein
 * Multilevel regression with poststratification, used in opinion polling
 * Modified Rodrigues parameters, in rotation formalisms in three dimensions
 * Machine-readable passport

Computing

 * Media Redundancy Protocol, allowing fast Ethernet recovery
 * Metro Ring Protocol, proprietary networking protocol
 * Multiple Registration Protocol in IEEE 802.1
 * Managed Recovery Process in Oracle Data Guard

Other uses

 * Mega Rice Project of Kalimantan, Indonesia
 * Moorthorpe railway station (National Rail station code), England
 * Monolithic Rail Platform, a gun part manufactured by Lewis Machine and Tool Company
 * Master of Regional Planning, an urban planning qualification
 * Mr. Price, a South African retailer
 * Mike Pompeo (Michael Richard Pompeo), American politician
 * Mike Pence (Michael Richard Pence), American politician
 * MRP: Avi-Yonah, M., “Map of Roman Palestine” QDAP V, No. 4 (1936), 139-193. Egalement, Map of Roman Palestine, 2nd revised edition, Jerusalem, 1940. P.145
 * Mohammad Reza Pahlavi, the last Shah of Iran
 * Motion to revoke probation, a legal action

title: MRP


text:
John A. Burns

John Anthony Burns (March 30, 1909 – April 5, 1975) was an American politician. Burns was born in Montana and became a resident of Hawaii in 1913. He served as the second governor of Hawaii from 1962 to 1974.

Early life
John Burns was born in Fort Assinniboine, Montana, on March 30, 1909. He was the eldest son of Anne and Harry Burns. Christened Harry John Burns, as a teenager he changed his name to John Anthony Burns. Burns's father was in the army and was ordered to Fort Shafter in Hawaii, so in 1913 he and his family moved to Hawaii, and eventually to Kalihi. Harry Burns became overwhelmed with responsibility for four children and left the family in 1919. Burns's mother became a launderer for Tripler Army Medical Center. Burns took care of his siblings and attended Saint Louis School, while his mother worked. She joined the Postal Service, and with the help of her brother, became postmaster for Fort Shafter and a clerk at the Honolulu Post office. In 1925 Anne sent John to live with her brother in Kansas, where Jack Scally served as a father figure. In Kansas he attended Immaculata High School in Leavenworth, then transferred to St. Benedict High School (now Maur Hill – Mount Academy) in Atchison. In 1927 Burns dropped out of high school and joined the army, but did not like taking orders. He was honorably discharged after one year. Burns returned to Hawaii, waiting a semester to attend Saint Louis School and eventually graduate in 1930.

Political career
Burns's work as a police officer helped him build close ties with working class people from numerous ethnic groups, notably Japanese and native Hawaiians. While a police officer in Honolulu, his first political efforts arose from his work with the Police Benevolent Society. From 1948 he led the Hawaii Democratic Revolution of 1954, through various leadership positions in the territorial Democratic Party, culminating in being chair of the territorial party in 1952. He is credited with building a coalition for the Democratic Party that included the Communist Party, 442nd Regimental Combat Team veterans, ILWU, other organized labor groups, and Japanese Americans to strengthen the party. In 1956, he was elected a party delegate from Hawaii. As a delegate, Burns played a key role in lobbying for Hawaii statehood, a goal that was achieved on March 12, 1959, when the statehood bill was signed by President Dwight D. Eisenhower. He sought to become the first governor of the newly formed state, but lost the election to Territorial Governor William F. Quinn.

Governorship
Three years later in 1962, Burns won the election to become governor. Governor Burns played a leading role in stimulating the state economy and attracting foreign tourism and investment. His many achievements include the promotion of Hawaii as a center for oceanography, construction of the new State Capitol building, and expansion of the University of Hawaii, helping to transform it into a first-class university, attracting students and faculty from around the world and early planning for the construction of the Aloha Stadium to host university football and bowl games. Burns supported the construction of an expanded Honolulu International Airport with a new reef-runway and the construction of Interstate H-3.

Additionally, he supported planning for the future by establishing the Hawaii Commission on the Year 2000, which ultimately led to the development of the Quality Growth Policy for the State of Hawaii. Both the Commission on the Year 2000 and Hawaii's Quality Growth Policy were intended to supplement Hawaii's State Land-Use Plan. Finally, Governor Burns made Hawaii a leader in environmental management, establishing the Office of Environmental Quality Control, within the Governor's Office, to coordinate state environmental policy and to review environmental impact statements on all major state actions.

Burns was re-elected in 1966 and 1970, each time with a different lieutenant governor as his running mate. In 1966, he was elected governor with Lieutenant Governor Thomas Gill. During his term as lieutenant governor, Gill, considered outspoken and acerbic, developed differences with Burns, and was never shy about criticizing the incumbent, despite being part of his administration. In 1970, Gill challenged Burns in the Democratic primary. Gill ran as a reformer, campaigning against what he described as an entrenched, corrupt political machine. He narrowly lost, even though Burns significantly outspent him in a savvy campaign that included sophisticated use of expensive image-building television spots. Most in the state's large Japanese population remained loyal to Burns, who had spearheaded their rise to political power during the 1950s. Before Neil Abercrombie lost in 2014 this race stood as the closest anyone came to a primary defeat of an incumbent governor of Hawaii. Burns's running-mate in 1970, George Ariyoshi, ran to succeed Burns as governor in 1974, defeating Gill in the Democratic primary.

Later life and death
Burns became ill from cancer to the point of incapacity in October 1973. Burns's third elected lieutenant governor, George Ariyoshi, became acting governor through the end of Burns's third term. Ariyoshi was elected in his own right as governor for the term beginning in 1974. Burns died on April 5, 1975, in Honolulu.

Legacy
The John A. Burns School of Medicine, at the University of Hawaii at Manoa, is named for him. In 1997, Governor Ben Cayetano named the newly completed Interstate H-3 in his honor, and the road to the summit of Mauna Kea is also named after him. A Hawaii golf tournament, comprising the state's best amateurs and PGA professionals, was created in his honor. The Governor's Cup is a team event, and is played between the amateurs against the professionals. A special qualifier for the amateur team after the tournament will provide the medalist a chance to play in the Sony Open in Hawaii, a PGA Tour Event.

title: John A. Burns


text:
Talk:Drug withdrawal

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 28 January 2019 and 17 May 2019. Further details are available on the course page. Student editor(s): Annabeckmann727.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 19:52, 16 January 2022 (UTC)

Confusion
This page confuses physical dependence with addiction, which is a purely psychological phenomenon. Physical dependence on, e.g., an opioid used for pain control does *NOT* imply addiction, and conversely it is quite possible to become psychologically addicted to drugs (e.g., marijuana) that induce little or no physical dependence. If there is no objection I propose to rewrite this article to make this distinction clear.

User: karn

That would be great if you could do a rewrite. I would humbly suggest dividing the document into Psychological Withdrawal and Physical Withdrawal. You may want to coordinate this with the discussion on Talk:Addiction -- Tim 01:57, 2004 Oct 9 (UTC)

 * If someone could pin down the difference between physiological and psychological withdrawal I would be pleased and impressed, but, quit honestly, I don't think that there IS one. In both cases, your brain gets X chronically and re-wires in order to reach a new homeostasis; when X is removed that homeostasis is lost, resulting in nasty side-effects. —Preceding unsigned comment added by 142.68.239.5 (talk) 21:09, 1 July 2008 (UTC)
 * Actually, the difference is fairly clear from a purely biological standpoint depending on how much scientific research is behind the substance involved. If there is a detectable change in brain physiology caused by habituation to the substances' effects, which cause unpleasant symptoms upon sudden discontinuation of the substance after habituation, physical withdrawal is said to be present. Anything over and above what can be directly tied to the physiological changes brought on by the habituation is considered to be psychological dependency. (See physical dependency.) This of course leaves the grey area of substances whose effects on brain physiology (or even body physiology) remain unresearched or unresearched in humans. It also does nothing to tease apart the line between physiological and psychological withdrawal in substances such as alcohol, where the addictive syndrome (alcoholism) is known to have both physiological and psychological components.

 * You're correct in that there's theory saying synaptic connections in the brain could conceivably rewire themselves in the presence of substances, and the definition of physiological dependency may be expanded to include these neuronal rewirings. However, as I understand it, a withdrawal from a physical dependency and a withdrawal from a psychological dependency are two different things.

 * The vocabulary surrounding the whole topic is very precarious as well, since there's words that get used interchangeably that are not interchangeable. Habituation, addiction, dependency, withdrawal, etcetera all have synonyms which do not carry the full meaning of the original usage. I think that edits to clarify the lines between physiological vs psychological addiction (with psychological addiction defined as the syndrome combination of psychological disorders outlined in the DSM IV that makes up the rest of the spectrum.) Trying to expand on psychological withdrawal should probably cite the DSM IV categories on substance dependency and substance abuse.Wrin (talk) 08:12, 25 February 2009 (UTC)

 * My first time posting here in "Talk", so please forgive me for any protocol missteps. I was moved, however, to waste no time in expressing my serious objections to both the tone and substance of this article.  I agree with the comment by karn [], but I would state the matter more strongly:  this article is full of inappropriately judgmental and disparaging references toward those among us who may be unfortunate enough to experience true drug withdrawal.  The writer appears to suggest that drug tolerance and withdrawal are primarily a hazard for members of the drug underclass, people who "abuse" dangerous and illegal drugs for "recreational" purposes.

 * The legitimate use of opioids, for example, for treatment of chronic pain is mentioned only as an apparent afterthought, a minor exception to the implicit general rule: We're basically talking about bad things that happen to junkies and other drug fiends!

 * Why draw any such (moral) distinctions? The circumstances giving rise to dependence/withdrawal are tangential, at best, to the stated subject matter of the article.  I could parse the text line by line to demonstrate my point, but surely that isn't necessary. This article should be taken down, without delay, and replaced with a simple definition for a stub.  Let someone else take a crack at it.  Stuart Hammett  — Preceding unsigned comment added by 162.249.151.41 (talk) 16:02, 19 August 2014 (UTC)

Economics
I would like someone to explain the economic meaning of this word.
 * Simple! You cannot bear the withdrawal symptoms, buy a pack of fags and the tobacco industry rejoices! -- 194.89.2.109 16:57, 28 December 2005 (UTC)

DSM-IV
There are criteria for withdrawl established for different drugs in the DSM-IV TR. Those should also be considered part of this article. 70.48.159.12 16:43, 3 April 2007 (UTC)

All meanings of the word withdrawal?
Dear all, I am from Sweden and my mother tounge is therefore Swedish. My level of English is faily good. However, my fellow countymen here at work are mostly not that skilld. It very often ends up with direct translations that makes it more "Swinglings" than anything else... Mostly understandable, but clearly not correct. I just came across the word withdrawal in a form we use internally but regularly distribute to customers worldwide. I felt that this must be the wrong word, but couldn´t come up with the right word. Therefore I wanded to check what meanings Wikipedia (the English site) described. Perhaps I am wrong this time (most unlikely...). But can not withdrawal describe "pulling back from a market" or retreating troups for example.

I loved the comment on the economic meaning! (Of course it means "withdrawing money from the hole in the wall (ATM) to by the fags...?)) However I would appreciate some serious comments (Im I wrong or not to start with).

I am not suited to re-write the article, it should be done by someone with higher qualifications in the English language (British such preferably for me).

I will now find the answer I want elsewhere...

Inaccurate
The section on drug abuse withdrawal is highly inaccurate if not guess work. Can anything cite this? The statement that all drugs affect dopamine is ridiculous, along with the statement that says the brain will be eventually devoid of all pleasure. This seems like it was taken from unscientific low level propaganda. This needs a rewrite and a citation or two.

--Shplongl (talk) 03:15, 20 December 2008 (UTC)

Craving without withdrawal
I think this article misses the experience also called 'craving' that occurs during long-term abstinence. In this situation, the addict feels an extremely intense urge to use/drink. This may occur at any time during the abstinence (1 day to 20 yrs). It may or may not be accompanied by a trigger. It may or may not be preceded by a cognition justifying use ("I can stop after just one", "the consequences of my prior use weren't that bad"). Addressing cravings is a key part of 'relapse prevention,' during periods of abstinence. —Preceding unsigned comment added by 162.129.248.3 (talk) 16:45, 29 January 2009 (UTC)

Dopamine and neurobiology
Reward from any drug is mediated by dopamine at the level of communication between the Ventral Tegmentum (VT) and the Nucleus Accumbens (NA). Inputs to the VT can be mediated by any of a number of receptors (opiate, cannabanoid, acetyl choline (nicotine))

Lack of emotion in response to any particular drug occurs when the circuits connecting the limbic system and both the VT and NA are atrophied, as the result of ongoing use. This would more affect response to triggers, than to other stimuli. —Preceding unsigned comment added by 162.129.248.3 (talk) 16:51, 29 January 2009 (UTC)

Euphoria is not strongly related to addiction
This article attempts to strongly relate euphoric aspects of drugs with their addictive nature. While there may be some small degree of pleasure-centre connection, some of the most addictive substances (eg nicotine) are not strongly related to any euphoric effect, whearas some of the most euphoric (eg:extacy MDMA) are not addictive.

I'm tempted just to delete several paragraphs as lacking any citation or basis in reality. ??? --Jaymax (talk) 00:54, 2 June 2009 (UTC)

Benzodiazepine withdrawal syndrome
Does the coverage here of this topic exceed the suggestions in WP:SUMMARY ?Jim.henderson (talk) 11:17, 26 March 2013 (UTC)

RM

 * The following discussion is an archived discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: move to Drug withdrawal Martijn Hoekstra (talk) 18:21, 7 July 2013 (UTC)

Withdrawal → Withdrawal (drug dependency) – The word "withdrawal" has many different meanings, and most of the meanings of this word are unrelated to drug dependency. Withdrawal should redirect to Withdrawal (disambiguation) instead of only redirecting to one specific meaning of this term. Jarble (talk) 01:54, 29 June 2013 (UTC)

 * Support per nom. In ictu oculi (talk) 14:48, 29 June 2013 (UTC)
 * Neutral for now... page view statistics, Jarble? Red Slash 07:38, 30 June 2013 (UTC)
 * Support, as I agree it's unlikely this is the primary topic. But perhaps consider natural disambiguation: Drug withdrawal?  Powers T 15:19, 2 July 2013 (UTC)
 * Support Drug withdrawal LtPowers hit the nail on the head on this one. Drug withdrawal is a more appropriate and natural title.--Labattblueboy (talk) 00:43, 5 July 2013 (UTC)
 * The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.

Merger proposal
I propose to merge Cold turkey into this page, because it’s just a slang term for drug withdrawal. Brinerat (talk) 12:54, 28 December 2020 (UTC)
 * That's not true, though the topics are related. Cold turkey refers to a particular practice of stopping all use of a certain drug or habitual behaviour, or whatever, after being a heavy user, without any reduction in use before quitting. This method works for some individuals, but it can also make quitting much more difficult, and therefore less likely in others. For some substances (namely alcohol), quitting cold turkey after being a very heavy user can result in death.

 * Cold turkey is not a necessary condition for withdrawal effects to occur. Firejuggler86 (talk) 09:57, 6 February 2021 (UTC)
 * Closing; consensus not to merge on the grounds that the topics are distinct. Klbrain (talk) 07:25, 15 June 2021 (UTC)

Wiki Education assignment: Technical and Scientific Communication
— Assignment last updated by Vdanquah (talk) 15:59, 21 September 2022 (UTC)

miyadmukkood@gmail.com
miy 2402:3A80:1E10:A69F:0:49:73B0:C301 (talk) 20:50, 30 March 2023 (UTC)

Citations please!
What the hell is this trash. There are absolutely zero citations on a page dealing with such a complex issue. It is insane that such controversial claims are being made without use of citations.

Article needs complete review. Taifraser (talk) 09:56, 16 May 2023 (UTC)

Pharma
Side effect of Beta blocker Bradycardia Drug with drawal, sudden withdrawal may induce angina With ischemic heart disease 41.235.35.46 (talk) 01:39, 6 January 2024 (UTC)

title: Talk:Drug withdrawal


text:
Isetta

The Isetta is an Italian-designed microcar built under license in a number of different countries, including Argentina, Spain, Belgium, France, Brazil, Germany, and the United Kingdom. Because of its egg shape and bubble-like windows, it became known as a bubble car, a name also given to other similar vehicles.

In 1955, the BMW Isetta became the world's first mass-production car to achieve a fuel consumption of 3 l/100 km. It was the top-selling single-cylinder car in the world, with 161,728 units sold. Initially manufactured by the Italian firm Iso SpA, the name Isetta is the Italian diminutive form of Iso, meaning "little Iso".

Iso Isetta (Italy)
The car originated with the Italian firm of Iso SpA. In the early 1950s the company was building refrigerators, motor scooters and small three-wheeled trucks. Iso's owner, Renzo Rivolta, decided to build a small car for mass distribution. By 1952 the engineers Ermenegildo Preti and Pierluigi Raggi had designed a small car that used the motorcycle engine of the Iso Moto 200 and named it Isetta.

The Isetta caused a sensation when it was introduced to the motoring press in Turin in November 1953. It was unlike anything seen before. Small (only 2.29 m long by 1.37 m wide) and egg-shaped, with bubble-type windows, the entire front end of the car hinged outwards to allow entry. In the event of an accident, the driver and passenger were to exit through the canvas sunroof. The steering wheel and instrument panel swung out with the single door, simplifying access to the single bench seat. The seat provided reasonable comfort for two occupants, and perhaps a small child. Behind the seat was a large parcel shelf with a spare wheel located below. A heater was optional. Ventilation was provided by turning out the front triangle windows and/or opening the fabric sunroof.

Power came from a 236 cc, 9.5 hp-metric two-stroke split-single motorcycle engine. The engine was started by a combination generator-starter known as Dynastart. A manual gearbox provided four forward speeds and reverse. A chain drive connected the gearbox to a solid rear axle with a pair of closely spaced 250 mm rear wheels. The first prototypes had one wheel at the rear, but having a single rear wheel made the car prone to roll-overs, so the rear wheel layout was changed to two wheels set 480 mm apart from each other. This narrow track eliminated the need for a differential. The front axle was a modified version of a Dubonnet independent front suspension.

The Isetta took over 30 seconds to reach 50 km/h from rest. Top speed was about 75 km/h. The fuel tank held 13 l; the Isetta would get somewhere between 50 mpgimp and 70 mpgimp.

In 1954, Iso entered several Isettas in the legendary Mille Miglia where they took the top three spots in the economy classification. Over a distance of 1600 km, the drivers achieved an average speed of over 70 km/h.

After its initial success, the Isetta was beginning to slip in popularity at home, mainly due to renewed competition from Fiat with its 500C model.

Renzo Rivolta wanted to concentrate on his new Iso Rivolta sports car, and was interested in doing licensing deals. Plants in Spain and Belgium were already assembling Isettas and Autocarros using Italian-made Iso components. BMW began talking with Rivolta in mid-1954 and bought not just a license but also the complete Isetta body tooling. Rivolta also negotiated licensing deals with companies in France and Brazil.

After some 1,000 units, production of the Italian built cars ceased in 1955. Iso continued to build the Isetta in Spain until 1958.

Iso Autocarro

In addition to the Iso Isetta vettura described above, Iso also built the Autocarro, a commercial version with full-width rear axle. The Autocarro was offered in several body styles—a flatbed pickup, enclosed truck, a tilt-bed or even a fire engine—although some of these might not have been sold. The Autocarro was very popular in Italy, and many manufacturers produced some variant of the type.

Iso had previously produced a motorcycle-type Isocarro. The Iso Autocarro was larger than most, with its four-wheel layout, conventional rear axle with differential and leaf springs, and a large tubular, ladder-type frame. It could carry a 500 kg load. The name Isetta Autocarro was also used. It is thought that more than 4,000 Autocarros were built between 1954 and 1958. The Autocarro was also built in Spain.

VELAM Isetta (France)

In 1954, VELAM acquired a licence from Iso to manufacture a car based on the Isetta. Since Iso had sold the body making equipment to BMW, VELAM developed their own body but used the original Iso engine. The VELAM body was rounder and more egg-like than Iso's Isetta and was known by the French as the 'yogurt pot'. Instead of a chassis like the Italian and German versions, there was a sub-frame bolted to the body at the rear, which held the rear tires, engine, and transmission. The front suspension was bolted to the front of the body. The front door was opened by push button instead of a handle, and the speedometer was mounted in the center of the steering wheel.

VELAM started production of the car in June 1955 at the old Talbot factory at Suresnes, France, and the car was introduced at the 1955 Paris car show. All told, five versions of the car were built: the standard Isetta, a convertible version, a luxury version, a one-off "Sport" version, and a record car with a roadster body. The luxury model, called Écrin ("jewel box"), was presented in 1957 and built in 500 examples. In 1957, the streamlined roadster set seven world records for the sub-250 cc class at the Linas-Montlhéry autodrome. Due to competition from the Citroën 2CV and then the Renault Dauphine, production ceased in January 1958.

De Carlo - Isetta (Argentina)
The Metalmecánica Company in Buenos Aires commenced automotive manufacturing in 1959, when they started assembling a licensed version of the BMW Isetta. This received a light redesign, with a tiny, two-piece grille being installed on the door. 798 examples were made, but they soon changed over to the BMW 600, which was built in 1,413 examples from 1959 until 1962. Metalmecánica went on to built the BMW 700, which they later redesigned to look similar to the Simca 1000. In 1965, they changed over and began building Simca Arianes under license from the French company SIMCA.

Romi-Isetta (Brazil)
In 1955, Iso licensed the Isetta to Indústrias Romi S.A., a machine-tool manufacturer headquartered in the city of Santa Bárbara d'Oeste, in the state of São Paulo. The Isetta was chosen, because it was considered an ideal vehicle for use in the cities by virtue of its size and economy. Released on September 5, 1956, it was one of the first cars produced in Brazil, after Ford do Brasil and General Motors do Brasil. The car had received government approval as a part of a state-supported drive to establish an automotive industry in Brazil, but ended up being built without government backing.

Some 3,000 of the Romi-Isettas were manufactured from 1956 to 1961. They kept the Iso design and used Iso engines until 1958, in 1959 they switched to the BMW 300 cc engines.

BMW Isetta (West Germany)
The BMW Isetta differed widely from the Iso model. While the major elements of the Italian design remained intact, BMW re-engineered much of the car – so much so that none of the parts between a BMW Isetta Moto Coupe and an Iso Isetta are interchangeable. BMW changed the powerplant to a one-cylinder, four-stroke, 247 cc motorcycle engine of their own manufacture which generated 12 PS.

The first BMW Isetta appeared in April 1955. In May 1962, three years after launching the conventionally modern-looking BMW 700, BMW ceased production of Isettas. A total of 161,728 units had been built.

In the 1990s, the BMW Isetta had garnered a resurgence through the television show Family Matters, in which one of the main characters, Steve Urkel (Jaleel White), drives a 1960 BMW Isetta.

BMW Isetta 250
While it retained the "bubble window" styling, it differed from the Italian model in that its headlamps were fixed separately to the sides of the bodywork and it carried the BMW badge below the windscreen. The car was also redesigned to take a modified version of the 250 cc four-stroke engine from the BMW R25/3 motorcycle and the front suspension was changed. The single-cylinder generated 12 PS at 5800 rpm. The crankcase and cylinder were made of cast iron, the cylinder head of aluminium. The head was rotated by 180° compared with the motorcycle engine. The twin-bearing crankshaft was also different in the Isetta motor, being larger and featuring reinforced bearings. One of the reasons for this was the heavy Dynastart unit, a combined dynamo and starter-motor. The fuel mixture was provided by a Bing sliding throttle side draft motorcycle carburetor. In addition to further changes of detail, the BMW engineers enlarged the sump for installation in the car and cooled the engine by means of a radial fan and shrouded ducting.

The power train from the four-speed gearbox to the two rear wheels was also unusual: fixed to the gearbox output drive was something called a Hardy disc, which was a cardan joint made of rubber. On the other side of it was a cardan shaft, and finally a second Hardy disc, which in turn was located at the entrance to a chain case. A duplex chain running in an oil bath finally led to a rigid shaft, with the two rear wheels at each end. Thanks to this elaborate power transfer, the engine-gearbox-unit was free of tension in its linkage to the rear axle and well soundproofed.

In West Germany, the Isetta could be driven with a motorcycle license. The top speed of the Isetta 250 was rated as 85 km/h.

The first BMW Isetta rolled off the line in April 1955, and in the next eight months some 10,000 were produced.

BMW Isetta 300
In 1956, the government of the Federal Republic of Germany changed the regulations for motor vehicles. Class IV licences issued from that time onward could only be used to operate small motorcycles and could no longer be used to operate motor vehicles with a capacity of less than 250 cc. At the same time tax classes were restructured, with one category limit set at 300 cc. Class IV licences issued before the change in the regulations were grandfathered and allowed to be used as before. This change in regulations encouraged BMW to revise the Isetta: In February 1956 a 300cc engine was introduced. The engineers enlarged the single cylinder to a 72 mm bore and 73 mm stroke, which gave a displacement of exactly 298 cc; at the same time, they raised the compression ratio from 6.8 to 7.0:1. As a result, the engine power output rose to 13 PS at 5200 rpm, and the torque rose to 18.4 Nm at 4600 rpm. The maximum speed remained at 85 km/h, yet there was a marked increase in flexibility, chiefly noticeable on gradients.

In October 1956, the Isetta Moto Coupé DeLuxe (sliding-window Isetta) was introduced. The bubble windows were replaced by longer, sliding side windows.

BMW 600

The BMW 600 was intended as an enlarged Isetta with more power and a more conventional four-wheel configuration.

The front end of the 600 was virtually unchanged, but the 600's wheelbase was stretched to accommodate four seats. A conventional rear axle was added. BMW introduced the semi-trailing arm independent suspension on the 600. This suspension would be used on almost every new model for the next four decades. To deal with the increased size and weight, the 600 was fitted with the 582 cc boxer engine from the R67 motorcycle. Top speed was 103 km/h.

In the two years that the model was in production, 34,000 600s were made. In its price segment it was in competition with the entry-level VW Beetle. In the late 1950s, consumers wanted cars that looked like cars, and they had lost interest in economy models. Sales of the 600 were, however, aided by the energy crisis of 1956–1957.

BMW Isetta (United Kingdom)

In March 1957, Dunsfold Tools Ltd. signed a lease on part of the former Brighton railway works on the south coast of England with the intention of beginning production of the BMW Isetta under licence in May of that year. Shortly afterwards, Dunsfold Tools Ltd was renamed Isetta of Great Britain and the British Isetta was officially launched at the Dorchester hotel in April. The factory had no access by road, therefore components were delivered by rail and finished cars were shipped out the same way. The British cars had right-hand drive with the door hinged from the right hand side of the car and the steering column moved across to the right as well. Right-hand drive meant that both the driver and the engine were on the same side, so a 27 kg counterweight was added to the left side to compensate. Dunlop tyres were used, and Lucas electrics replaced the German Hella and Bosch components, with a different headlamp housing being used. Girling brake components replaced the ATE brake parts.

The Isetta was not popular in the UK until a three-wheeled version was introduced. Although three-wheeled vehicles offer a less stable ride, in the UK there was the advantage of being classed as three-wheeled motorcycles, which meant a lower tax class, and the requirement of only a motorcycle driving-licence. Isetta of Great Britain also continued to produce four-wheeled Isettas, but only for export to Canada, New Zealand, and Australia.

In 1962, Isetta of Great Britain stopped production of the cars. Isetta engines were produced until 1964.

Isetta replica kits
The now defunct British firm Tri-Tech, under the model name Zetta, sold a kit car or even an assembled complete BMW Isetta lookalike replica from modern parts, including Honda CN 250 cc single-cylinder water-cooled engines with automatic transmission (standard) or Kawasaki 500 GPS two-cylinder water-cooled motorcycle engines with optional manual transmission.

Some parts, new or used, were from donor vehicles. Front suspension and steering were from the Suzuki Super Carry/Bedford Rascal (later Vauxhall Rascal). Drum brakes and wheels were from Morris and the subsequent British Leyland Motor Corporation Mini. Prices ranged from c. £2650 for the kit up to c. £9450 for a complete version.

It could be legally registered for use under British laws. Tri-Tech also supplied some body parts which can be used for running non-exact restorations of BMW Isettas.

Possible BMW reintroduction
In 2009, Auto Express reported that BMW had partnered with the University of Bath in order to develop a series of three and four wheeled, rear engine, rear wheel drive city cars. This led to speculation that the Isetta badge would be returning as a competitor to small cars such as the Toyota iQ. Following this, during the development of the Megacity / BMW i brand, rumours and reports suggested that one of the upcoming cars would be named the 'iSetta', taking its name and inspiration from the classic BMW Isetta. No such car was produced, although the i brand was subsequently launched with the BMW i3 and BMW i8.

Durax D-Face
At the 2013 Tokyo Motor Show, Gifu based company D Art revealed the Durax D-Face, a front entry, rear engine bubble car taking inspiration from the Isetta. The microcar was powered by a 7 kW electric motor coupled with a 3kW petrol generator, giving a range of around 190 miles. A top speed of around 45 mph likely limited the car to city driving.

Microlino
At the 2016 Geneva Motor Show, Swiss entrepreneur Wim Ouboter of Micro Mobility Systems revealed the Microlino, a small electric microcar inspired by the Isetta. After being postponed, production of the vehicle commenced in 2022 with pre-orders for over 8,000 vehicles, costing EUR 12,000 each.

Suzhou Eagle EG6330K
In 2018, Chinese company Suzhou Eagle revealed the Eagle EG6330K, a low speed electric vehicle styled after the BMW Isetta and BMW 600. Primarily aimed at young people living in large cities, the car featured a 72 kWh lead acid battery giving a top speed of around 40 mph and a range of around 75 miles.

Artega Karo / Electric Brands Evetta

In 2019, German company Artega presented the Isetta-inspired Karo at the International Motor Show Germany. In 2022 Artega was acquired by German company Electric Brands. The Karo was renamed the Evetta, with plans to build commercial and non commercial versions, starting just under 20,000 EUR.

title: Isetta