OpenLLM-France/wikimedia huggingface dataset:
# 1997 World Weightlifting Championships – Men's 59 kg

The 1997 World Weightlifting Championships were held in Chiang Mai, Thailand from December 6 to December 14. The men's competition in the 59 kg division was staged on 7 December 1997.

## Medalists

| Event | Gold | Gold | Silver | Silver | Bronze | Bronze |
| Snatch | William Vargas (CUB) | 132.5 kg | Stefan Georgiev (BUL) | 130.0 kg | Le Maosheng (CHN) | 130.0 kg |
| Clean & Jerk | Stefan Georgiev (BUL) | 165.0 kg | Le Maosheng (CHN) | 165.0 kg | Sevdalin Minchev (BUL) | 162.5 kg |
| Total | Stefan Georgiev (BUL) | 295.0 kg | Le Maosheng (CHN) | 295.0 kg | Sevdalin Minchev (BUL) | 290.0 kg |

## Records

Prior to this competition, the existing world records were as follows.
| World Record | Snatch | Hafız Süleymanoğlu (TUR) | 140.0 kg | Warsaw, Poland | 3 May 1995 |
| World Record | Clean & Jerk | Nikolay Peshalov (BUL) | 170.0 kg | Warsaw, Poland | 3 May 1995 |
| World Record | Total | Tang Lingsheng (CHN) | 307.5 kg | Atlanta, United States | 21 July 1996 |

## Results

| Rank | Athlete | Body weight | Snatch (kg) | Snatch (kg) | Snatch (kg) | Snatch (kg) | Clean & Jerk (kg) | Clean & Jerk (kg) | Clean & Jerk (kg) | Clean & Jerk (kg) | Total |
| Rank | Athlete | Body weight | 1 | 2 | 3 | Rank | 1 | 2 | 3 | Rank | Total |
| | Stefan Georgiev (BUL) | 58.60 | 125.0 | 130.0 | 132.5 | | 157.5 | 162.5 | 165.0 | | 295.0 |
| | Le Maosheng (CHN) | 59.00 | 130.0 | 135.0 | 135.0 | | 165.0 | 165.0 | 167.5 | | 295.0 |
| | Sevdalin Minchev (BUL) | 58.60 | 127.5 | 132.5 | 132.5 | 4 | 157.5 | 162.5 | 170.0 | | 290.0 |
| 4 | William Vargas (CUB) | 58.70 | 127.5 | 130.0 | 132.5 | | 155.0 | 155.0 | 160.0 | 6 | 287.5 |
| 5 | Elkhan Suleymanov (AZE) | 58.55 | 120.0 | 125.0 | 130.0 | 5 | 150.0 | 157.5 | 160.0 | 5 | 282.5 |
| 6 | Yurik Sarkisyan (AUS) | 58.95 | 120.0 | 125.0 | 125.0 | 7 | 142.5 | 147.5 | — | 7 | 267.5 |
| 7 | Sedat Artuç (TUR) | 58.50 | 120.0 | 120.0 | 120.0 | 6 | 145.0 | 150.0 | 150.0 | 8 | 265.0 |
| 8 | Chom Singhnoi (THA) | 58.85 | 110.0 | 115.0 | 120.0 | 8 | 135.0 | 140.0 | 145.0 | 10 | 260.0 |
| 9 | Mohamed Osman (EGY) | 59.00 | 110.0 | 115.0 | 115.0 | 9 | 145.0 | 150.0 | 150.0 | 11 | 260.0 |
| 10 | Kenji Tominaga (JPN) | 58.55 | 112.5 | 117.5 | 117.5 | 11 | 145.0 | 147.5 | 147.5 | 9 | 257.5 |
| 11 | Liu Te-tsung (TPE) | 58.10 | 112.5 | 120.0 | 120.0 | 10 | 140.0 | 140.0 | 145.0 | 12 | 252.5 |
| 12 | Vassiliy Lim (KAZ) | 58.10 | 105.0 | 110.0 | 112.5 | 12 | 135.0 | 140.0 | 140.0 | 13 | 250.0 |
| 13 | Chen Po-pu (TPE) | 58.85 | 110.0 | 110.0 | 110.0 | 13 | 135.0 | 140.0 | 145.0 | 14 | 250.0 |
| 14 | Sinchai Ketsri (THA) | 58.95 | 110.0 | 110.0 | 110.0 | 14 | 135.0 | 140.0 | 145.0 | 15 | 250.0 |
| 15 | Johnny Hernández (VEN) | 58.95 | 105.0 | 110.0 | 110.0 | 15 | 140.0 | 140.0 | 145.0 | 16 | 245.0 |
| 16 | Tom Goegebuer (BEL) | 58.35 | 100.0 | 100.0 | 107.5 | 16 | 130.0 | 137.5 | 140.0 | 17 | 237.5 |
| — | Hiroshi Ikehata (JPN) | 58.65 | 125.0 | 125.0 | 125.0 | — | 152.5 | 160.0 | 165.0 | 4 | — |
| — | Jyrki Welling (FIN) | 58.85 | 110.0 | 110.0 | 110.0 | — | 152.5 | 137.5 | — | 18 | — |
| — | Traian Cihărean (ROM) | 58.95 | — | — | — | — | — | — | — | — | — |
# HUNT Biobank

HUNT Biobank is a biorepository, located in Levanger Municipality, Norway. It was established in conjunction with the cohort study Trøndelag Health Study (HUNT). The biobank is part of HUNT Research Centre, which is responsible for collecting and providing access to the data and samples from the health study, and the research centre is part of the Faculty of Medicine and Health Sciences at the Norwegian University of Science and Technology (NTNU).
The HUNT Study has, so far (2020), been carried out in four main surveys (HUNT1–HUNT4) of the population in the northern part of the county. Until 1 January, 2018, the northern and southern parts of Trøndelag were two separate counties: Nord-Trøndelag and Sør-Trøndelag. The first three HUNT surveys were carried out in Nord-Trøndelag. From 2019 the southern part of the county is included in the survey, in the first phase only by filling in questionnaires.
Comprehensive datasets covering health, disease, lifestyle and environmental factors are gathered by using questionnaires, collecting blood and urine samples and by clinical examination.
In connection with the HUNT3 survey (2006–2008), HUNT Biobank was established as a state-of-the-art biobank, with storage facilities that ensure availability of the biomaterial from the surveys for research decades ahead. Blood sampling follows a strict quality protocol, collecting serum, plasma, buffy coat, immortalized cells for cell line production, specialized tubes for trace metal/elements-analysis, RNA-tubes and urine. Comprehensive datasets covering health, disease, lifestyle and environmental factors are gathered using questionnaires and by clinical examination.
HUNT Biobank is, as part of the HUNT Research Centre, certified for its Management System in conformity with NS-EN ISO 9001:2015.

## Sample types

The table gives an overview of the sample types and numbers in The HUNT Study as a whole and how they are stored (2020).
| Participation/ material | HUNT1 | HUNT2 | HUNT3 | Young-HUNT3 | HUNT4 | Young-HUNT4 | Liquid nitrogen | -80 °C | Room temperature |
| Participation (1) | 77,721 | 65,237 | 50,807 | 8,200 (2) | 55,500 | 8,124 | | | |
| DNA | | 63,000 | 50,000/20,000 (3) | | | | | | |
| Buffy Coat | | | | | | 52,748 | | x | |
| ACD | 0 | 0 | 40,754 | 0 | | | x | | |
| NaHep | 0 | 0 | 25,420 | 0 | | | x | | |
| Plasma | 0 | 0 | 49,070 | 0 | | | x | | |
| Serum | 473 | 64,574 | 50,170 | 0 | | | x | x | |
| Tempus, RNA | 0 | 0 | 14,874 | 0 | | | | x | |
| Urine (spot urine) | 0 | 0 | 11,983 | 0 | | | | x | |
| Urine, MA | 0 | 0 | 5,759 | 0 | | | | x | |
| FTA card | 0 | 0 | 0 | 8,381 | | | | | x |
# Karimabad-e Jadval-e Now

Karimabad-e Jadval-e Now (Persian: كريم ابادجدول نو, also Romanized as Karīmābād-e Jadval-e Now; also known as Jadval-e Now and Qal‘eh-i-Nau) is a village in Derak Rural District, in the Central District of Shiraz County, Fars province, Iran. At the 2006 census, its population was 49, in 11 families.
# Dicing tape

Dicing tape is a backing tape used during wafer dicing or some other microelectronic substrate separation, the cutting apart of pieces of semiconductor or other material following wafer or module microfabrication. The tape holds the pieces of the substrate, in case of a wafer called as die, together during the cutting process, mounting them to a thin metal frame. The dies/substrate pieces are removed from the dicing tape later on in the electronics manufacturing process.

## Tape types

Dicing tape can be made of PVC, polyolefin, or polyethylene backing material with an adhesive to hold the wafer or substrate in place. In some cases dicing tape will have a release liner that will be removed prior to mounting the tape to the backside of the wafers, with a variety of adhesive strengths, designed for various wafer/substrate sizes and materials.
* UV tapes are dicing tapes in which the adhesive bond is broken by exposure to UV light after dicing, allowing the adhesive to be stronger during cutting while still allowing clean and easy removal. Semiconductor Tapes and Materials. UV equipment can range from low power (a few mW/cm2) to high power (more than 200 mW/cm2). Higher power results in a more complete cure, lower adhesion and reduced adhesive residue, while lower power is safer.
* Thermal release tapes (typically PET material) have been developed for specific cases when etching or material printing is needed after the tape is installed. These tapes can also handle heavy substrates such as ceramic substrates or printed circuit boards (PCBs/PWBs) if needed. Their adhesion disappears when heat (typically 90 to 170 °C (194 to 338 °F)) is applied.
# Arlan's

Arlan's was an American discount store chain.
Arlan's was founded in 1945 by William, Herbert, and Lester Palestine in New Bedford, Massachusetts.
In 1963, executives tried to start talks with King's of Newton, Massachusetts, regarding a merger. These plans were briefly revived in 1966.
Arlan's opened its 50th store in Cudahy, Wisconsin, in 1965. At this point, the chain had $174 million in revenue, and stores in 18 states from Maine to Colorado. It also owned 18 locations of a toy store called Play World. The chain peaked in size at 119 stores in 1970, by which time the company began experiencing heavy operating losses. The losses would later be attributed, in part, to an expansion strategy that was too geographically diverse for the chain's size, leading to inefficient distribution. In 1971, Arlan's explored the possibility of filing for bankruptcy, but it was concluded that such an action would be premature. That same year, Arlan's sold 16 stores to Target.
In May 1973, two years after the resignation of co-founder Herbert Palestine, Arlan's filed for Chapter 11 bankruptcy. By that time, the chain had contracted to 73 stores. An ambitious plan to revive sales during the Christmas 1973 season, called "Mission Impossible" by company insiders and executed without disclosure to, or approval of, the court, failed to turn the chain's fortunes around and an additional 38 stores closed by January 1974. The Securities and Exchange Commission successfully petitioned the court to have the bankruptcy converted to Chapter 10. The chain continued to shrink dramatically under bankruptcy as losses mounted and Arlan's liquidated its final ten stores in early 1975 by order of the bankruptcy court. Subsequent court rulings would document various unethical practices by Arlan's legal representatives, regarding fees and a lack of candor.
# Wildlife Park

Wildlife Park is a construction and management simulation game released in 2003. Like Zoo Tycoon and Zoo Empire, the game involves players in building a wildlife park or zoo. The game spawned two sequels.

## Reception

Aggregate score :
| Aggregator | Score |
| Metacritic | 62/100 |
The game received "mixed or average" reviews, according to video game review score aggregator Metacritic.
# Wilhelm Kobelt

Wilhelm Kobelt (20 February 1840 – 26 March 1916) was a German zoologist born in Alsfeld, Grand Duchy of Hesse. He specialized in the field of malacology.
Kobelt was born in Alsfeld to parish priest Wilhelm (1809–74) and Auguste (1815–97) née Kessler. He studied medicine at Gießen and received a doctorate in 1862. He practices as a physician in Biedenkopf where he began a natural history society, and in 1869 he went to Schwanheim near Frankfurt am Main. He became interested in molluscs and interacted with Emil Adolf Rossmäßler in Leipzig. He became a corresponding member of the Senckenberg nature research society and later became head of the mollusc section. He later worked as a curator of the Senckenberg Museum in Frankfurt am Main. He founded a journal for malacology.
Several species of mollusk contain his name, including Fusinus kobelti (Kobelt's spindle), Cymatium kobelti and Hyalinia kobelti. Kobeltia, a subgenus of Arion slugs, is named in honor of him.

## Selected publications

* Archiv für Molluskenkunde, 1868 - Archive of malacology.
* Jahrbücher der Deutschen Malakozoologischen Gesellschaft, 1874 - Yearbook of the German Malaco-zoology Society.
* Illustrirtes conchylienbuch, 1876 - Illustrated book of conchology.
* Reiseerinnerungen aus Algerien und Tunis, 1885 - Travel memoirs of Algeria and Tunis.
* Prodromus faunae molluscorum testaceorum maria europaea inhabitantium, 1886.
* Studien zur Zoogeographie, 1897 - Zoogeographical studies.
* Cyclophoridae, 1902 - Cyclophoridae.
* Die Verbreitung der Tierwelt : gemässigte Zone, 1902 - Distribution of wildlife; temperate zone.
* (in German) Kobelt W. (1909). "Die Gattung Paludina Lam. (Vivipara Montfort) (Neue Folge). In Abbildungen nach der Natur mit Beschreibungen". Systematisches Conchylien-Cabinet von Martini und Chemnitz, Nürnberg, 1(21a): pp. 97-430, plates 15–77.
# Cut the Rope: Time Travel

Cut the Rope: Time Travel is a physics-based puzzle video game developed by ZeptoLab for the iOS, Android and web browsers. The third entry in the Cut the Rope series, it follows Om Nom going through time.

## Gameplay

Time Travel shares the main idea with the previous games in the series, where the players must cut the ropes with swipes in order for Om Nom to get the candy. However, the game adds Om Nom's ancestors (or descendant in the future levels), which means there are now two candies for two creatures in each level. That leads to the puzzles where the players will have to plan to feed both creatures at the same time.
With each collected piece of candy, the players will gain stars that are equivalent to points; the more stars obtained in a certain level, the more bonus points are earned for other features like super powers, used as a help during the puzzles. By pressing the camera button, the players can view animated stories created by ZeptoLab, offering more info about Om Nom's ancestry.
Centered around time travel, the game consists of various time periods, from the Middle Ages to the Stone Age. Each one of them regularly add new obstacles and mechanisms to be used. Some of those are: the chains can hold up candies requiring to be cut by a blade, freeze button that stops any movement on the screen, bombs that will send everything in its radius up, and others.

## Reception

Aggregate score :
| Aggregator | Score |
| Metacritic | 84/100 |
Review scores :
| Publication | Score |
| Game Informer | 8.5/10 |
| Gamezebo | |
| Pocket Gamer | |
| TouchArcade | |
On its release, Cut the Rope: Time Travel was met with "generally favorable" reviews from critics, with an aggregate score of 84/100 on Metacritic.
# Karimeh

Karimeh (Persian: كريمه, also Romanized as Karīmeh) is a village in Jaydasht Rural District, in the Central District of Firuzabad County, Fars province, Iran. At the 2006 census, its population was 55, in 13 families.
# Cato Hansen

Cato Hansen (born 26 May 1988) is a Norwegian former professional footballer who played as a forward.

## Career

Hansen came to Brann from Bryne before the 2009 season. At Bryne, he played 45 times, scoring 10 goals in the Norwegian First Division.
On 7 August 2009, Hansen was loaned out to the first division club Løv-Ham for the remainder of the 2009 season.
On 29 March 2012, Hansen signed for Sandefjord.
Hansen has also played eight games for the Norway U21 national team.

## Personal life

He is the son of former Norway international footballer Hugo Hansen and his sister, Hege, plays as a striker for the Toppserien club Arna-Bjørnar, as well as being capped for Norway women's national football team, with youngest sister Tuva Hansen a Bayern Munich player.

## Career statistics

Appearances and goals by club, season and competition :
| Club | Season | League | League | League | Cup | Cup | Total | Total |
| Club | Season | Division | Apps | Goals | Apps | Goals | Apps | Goals |
| Bryne | 2006 | Norwegian First Division | 4 | 0 | 0 | 0 | 4 | 0 |
| Bryne | 2007 | Norwegian First Division | 14 | 5 | 1 | 1 | 15 | 6 |
| Bryne | 2008 | Norwegian First Division | 26 | 5 | 0 | 0 | 26 | 5 |
| Bryne | Total | Total | 44 | 10 | 1 | 1 | 45 | 11 |
| Brann | 2009 | Tippeligaen | 6 | 0 | 4 | 2 | 10 | 2 |
| Brann | 2010 | Tippeligaen | 17 | 0 | 2 | 1 | 19 | 1 |
| Brann | Total | Total | 23 | 0 | 6 | 3 | 29 | 3 |
| Løv-Ham (loan) | 2009 | Norwegian First Division | 9 | 6 | 0 | 0 | 9 | 6 |
| Sogndal | 2011 | Tippeligaen | 20 | 0 | 4 | 2 | 24 | 2 |
| Sandefjord | 2012 | Norwegian First Division | 29 | 8 | 2 | 0 | 31 | 8 |
| Sandefjord | 2013 | Norwegian First Division | 19 | 1 | 1 | 0 | 20 | 1 |
| Sandefjord | 2014 | 1. divisjon | 4 | 0 | 0 | 0 | 4 | 0 |
| Sandefjord | Total | Total | 42 | 9 | 3 | 0 | 45 | 9 |
| Egersund | 2015 | 2. divisjon | 23 | 8 | 1 | 0 | 23 | 8 |
| Career total | Career total | Career total | 171 | 33 | 15 | 6 | 186 | 39 |
# Bid Zard-e Olya

Bid Zard-e Olya (Persian: بيدزردعليا, also Romanized as Bīd Zard-e 'Olyā; also known as Bīd Zard-e Bālā) is a village in Bid Zard Rural District, in the Central District of Shiraz County, Fars province, Iran. At the 2006 census, its population was 1,206, in 295 families.
# Jovair Arantes

Jovair de Oliveira Arantes (born 4 June 1951) is a Brazilian politician.
Jovair Arantes is an advisor and has been leader of the Atlético Goianiense.
Jovair is known for being the rapporteur of the impeachment of Dilma Rousseff in the Chamber of Deputies. His report was, then, approved and proceeded to the Plenary to be voted by all of the 513 deputies.
On 7 July 2016, deputy Eduardo Cunha (PMDB-RJ) resigned of his office of Speaker of the Chamber. Acting Speaker Waldir Maranhão called in for new elections on the same day. Jovair Arantes wanted to run for Speaker, but gave up to support deputy Rogério Rosso (PSD-DF).
# Fleur de Lys centre commercial

Fleur de Lys centre commercial (formerly and still commonly called Place Fleur de Lys) is a shopping mall located in the Vanier borough of Quebec City, Quebec, Canada built in 1963. It is located across from L'Institut de réadaptation en déficience physique de Québec and close to the Videotron Centre. It is anchored by Walmart and Maxi. The mall is access by Quebec Autoroute 973 and Quebec Route 138 via boulevard Wilfrid-Hamel.

## History

Place Fleur de Lys opened on March 21, 1963, with anchors Simpsons-Sears (Sears), Steinberg and Zellers. Place Fleurs de Lys is notable for having the first ever Sears department store in the province of Quebec. This two level 140,000 square foot anchor space was the first French-speaking department store from the Toronto-based Simpsons-Sears Ltd.
On October 17, 1968, S.S. Kresge Co Ltée opened a Kmart store. As with Sears five years earlier, the Kmart at Place Fleurs de Lys was the first in the province.
In March 1980, Place Fleur de Lys expanded from 650 000 square feet to 850 000 to reach 170 stores including a new Pascal hardware store. After Pascal closed, its former space of 75 000 square feet was converted into another mall expansion of 145 000 square feet anchored by a single level The Bay store which opened on October 7, 1992.
Kmart closed on May 31, 1995, and the Zellers in the mall relocated in its space. Target acquired the lease of Zellers and opened a store at Fleur de Lys on October 18, 2013, as part of the retailer's second wave of openings in Quebec. On May 8, 2015, Walmart bought the lease of the former Target store.
Primaris REIT completed its acquisition of Fleurs de Lys on July 20, 2005. The mall was later managed by 20 VIC Management. On August 15, 2017, Cushman & Wakefield announced it would acquire 20 VIC Management and the transaction was completed the following month in September, bringing Fleurs de Lys to its portfolio.
Sears lasted until the end of the chain on January 14, 2018.
In July 2018, the Fleurs de Lys shopping mall was purchased by Trudel Alliance from KingSett Capital for $60 million. The acquisition happened in a time when the shopping mall had to deal with large vacant anchor spaces left by the departures of both Sears and Hudson's Bay. The new owners have since began the process of redeveloping the mall. The UQTR set up a campus for 6,000 students in the former Sears store. Hart also opened a store within the former Sears building. Hudson's Bay was replaced by Jysk, Dollarama and another local business. An entire section of the mall was razed between the Sports Experts store and the former Sears building in 2021–2022. Trudel has announced that it plans to build several residential towers on the site of the shopping mall, with one of the buildings already in construction as of 2023.
# Loch Iubhair

Loch Iubhair pronounced yoo-ar meaning yew loch, is a freshwater loch, located in Glen Dochart, and six kilometres (four miles) east of the village of Crianlarich. Loch Dochart is located immediately southeast, and the outflow of Loch Dochart, as the River Dochart flows into Loch Iubhair.
# Bunji Okada

Bunji Okada (Japanese: 岡田文次) (1874–1943) was Director of the Karafuto Agency (1914–1916). He was Governor of Tochigi Prefecture (1911–1914). He was a graduate of the University of Tokyo.
* This article about a Japanese politician is a stub. You can help Wikipedia by expanding it.
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* t
* e
# Karkuyeh

Karkuyeh (Persian: كركويه, also Romanized as Karkūyeh, Karakūyeh, and Karekūyeh; also known as Kareh Kūyeh) is a village in Efzar Rural District, Efzar District, Qir and Karzin County, Fars province, Iran. At the 2006 census, its population was 550, in 123 families.
# Linear stability

In mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form $dr/dt=Ar$, where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part. If all the eigenvalues have negative real part, then the solution is called linearly stable. Other names for linear stability include exponential stability or stability in terms of first approximation. If there exists an eigenvalue with zero real part then the question about stability cannot be solved on the basis of the first approximation and we approach the so-called "centre and focus problem".

## Examples
### Ordinary differential equation

The differential equation ${\frac {dx}{dt}}=x-x^{2}$ has two stationary (time-independent) solutions: x = 0 and x = 1. The linearization at x = 0 has the form ${\frac {dx}{dt}}=x$. The linearized operator is A$_0$ = 1. The only eigenvalue is $\lambda =1$. The solutions to this equation grow exponentially; the stationary point x = 0 is linearly unstable.
To derive the linearization at x = 1, one writes ${\frac {dr}{dt}}=(1+r)-(1+r)^{2}=-r-r^{2}$, where r = x − 1. The linearized equation is then ${\frac {dr}{dt}}=-r$; the linearized operator is A$_1$ = −1, the only eigenvalue is $\lambda =-1$, hence this stationary point is linearly stable.

### Nonlinear Schrödinger Equation

The nonlinear Schrödinger equation $i{\frac {\partial u}{\partial t}}=-{\frac {\partial ^{2}u}{\partial x^{2}}}-|u|^{2k}u,$ where u(x,t) ∈ C and k > 0, has solitary wave solutions of the form $\phi (x)e^{-i\omega t}$. To derive the linearization at a solitary wave, one considers the solution in the form $u(x,t)=(\phi (x)+r(x,t))e^{-i\omega t}$. The linearized equation on $r(x,t)$ is given by ${\frac {\partial }{\partial t}}{\begin{bmatrix}{\text{Re}}\,r\\{\text{Im}}\,r\end{bmatrix}}=A{\begin{bmatrix}{\text{Re}}\,r\\{\text{Im}}\,r\end{bmatrix}},$ where $A={\begin{bmatrix}0&L_{0}\\-L_{1}&0\end{bmatrix}},$ with $L_{0}=-{\frac {\partial }{\partial x^{2}}}-k\phi ^{2}-\omega$ and $L_{1}=-{\frac {\partial }{\partial x^{2}}}-(2k+1)\phi ^{2}-\omega$ the differential operators. According to Vakhitov–Kolokolov stability criterion, when k > 2, the spectrum of A has positive point eigenvalues, so that the linearized equation is linearly (exponentially) unstable; for 0 < k ≤ 2, the spectrum of A is purely imaginary, so that the corresponding solitary waves are linearly stable.
It should be mentioned that linear stability does not automatically imply stability; in particular, when k = 2, the solitary waves are unstable. On the other hand, for 0 < k < 2, the solitary waves are not only linearly stable but also orbitally stable.