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Patagonian toothfish

The Patagonian toothfish (Dissostichus eleginoides), also known as Chilean sea bass, mero, icefish, and Antarctic cod, is a species of notothen found in cold waters (1 - 4 C) between depths of 45 and 3850 m in the southern Atlantic, Pacific, and Indian Oceans and Southern Ocean on seamounts and continental shelves around most Subantarctic islands.

The average weight of a commercially caught Patagonian toothfish is 7 - 10 kg, depending on the fishery, with large adults occasionally exceeding 100 kg. They are thought to live up to 50 years and to reach a length up to 2.3 m. Several commercial fisheries exist for Patagonian toothfish, which are detailed below.

A close relative, the Antarctic toothfish ( Dissostichus mawsoni ), is found farther south around the edges of the Antarctic shelf, and a Marine Stewardship Council-certified fishery is active in the Ross Sea; it is also sometimes marketed as Chilean sea bass.

Taxonomy
The Patagonian toothfish was first formally described in 1898 by the Swedish zoologist Fredrik Adam Smitt with the type locality given as Puerto Toro at 55°24'S, 68°17'W on the Chilean part of Tierra del Fuego. Smitt also described the new genus Dissostichus for this new species, meaning that the Patagonian toothfish is the type species of this genus by monotypy. The specific name eleginoides means having the form of, i.e. having a similar shape to, Eleginops.

Description
The Patagonian toothfish has a streamlined, fusiform body that has a depth that fits into its standard length 5 to 6.4 times. It has a flattened head with a wide, flat area between the eyes. The snout is longer than the diameter of the eyes. The mouth is large, extending past the middle of the eye. There are two rows of teeth in the upper jaw, the teeth in the outer row being the larger and canine-like. The lower jaw has a row of spaced canine-like teeth. Additional canine-like teeth are found outside the teeth rows at the joint of the upper and lower jaws. There are two lateral lines; both made up of tubed scales, an upper one and another along the mid flanks. The upper lateral line has 88-104 scales while the lower line has 61-77 scales. The first dorsal fin has 8 to 10 spines; the second dorsal fin has 28 to 30 soft rays, while the anal fin also has 28-30 soft rays. The caudal fin is emarginate. The pectoral fins are large and shaped like fans. The head and body are covered in ctenoid scales except for the front of the head. This species attains a maximum total length of 215 cm although 70 cm is more typical, and a maximum published weight of 200 kg. The overall colour is brownish-grey with darker blotches.

Distribution and habitat
The Patagonian toothfish is found in the southeastern Pacific and southwestern Atlantic Oceans. It occurs in southern Chile around the coast of Patagonia, in Argentina, and the Falkland Islands. It has also been recorded at Macquarie Island in the southwestern Pacific Ocean and the Southern Ocean at South Georgia and from the sub-Antarctic islands and seamounts of the Indian Sector. There is a single record of a vagrant from the Davis Strait in the northwestern Atlantic Ocean off Greenland, it is thought that this individual migrated over 10000 km and that it transited across the tropical areas in deep, cold regions of the Ocean. The juveniles are semi-pelagic becoming demersal at depths between 150 and 400 m. Adults move to deeper habitats, being found at depths in excess of 1,000 m.

Biology
Patagonian toothfish spawn in deep water (around 1,000 m) during the austral winter, producing pelagic eggs and larvae. Larvae switch to a demersal habitat at around 100 m (1 year old) and inhabit relatively shallow water (<300 m) until 6–7 years of age when they begin a gradual migration into deeper water. As juveniles in shallow water, toothfish are primarily piscivorous, consuming the most abundant, suitably sized local prey. With increasing size and habitat depth, the diet diversifies and includes more scavenging of squid, fish, and crustaceans. In turn, toothfish constitute a small part of the diets of sperm whales, southern elephant seals, and colossal squid.

As most toothfish fisheries are managed in accordance with Commission for the Conservation of Antarctic Marine Living Resources (CCAMLR) regulations and conservation measures, CCAMLR adopts an “ecosystem approach”, which requires that all other living resources of the Southern Ocean are treated as an integrated system where effects on predator, prey, and related species are considered, and decisions on sustainable harvesting levels are made based on sound, internationally peer-reviewed scientific advice.

Commercial name

The Patagonian and the Antarctic toothfishes are sometimes sold under the culinary name "Chilean sea bass" in the United States and Canada.

The name "Chilean seabass" was invented by a fish wholesaler named Lee Lantz in 1977. He was looking for a name to make it attractive to the American market. He considered "Pacific sea bass" and "South American sea bass" before settling on "Chilean sea bass". In 1994, the U.S. Food and Drug Administration accepted "Chilean seabass" as an "alternative market name" for Patagonian toothfish, and in 2013 for Antarctic toothfish.

In the UK, the approved commercial designations for D. eleginoides and D. mawsoni are "icefish" and "toothfish". This has created some confusion, as a genuine "icefish" (Champsocephalus gunnari) caught in subantarctic waters does not resemble toothfish in any way.

In Singapore, the Patagonian toothfish is marketed as a type of cod fish.

Management
Commercial fishing of toothfish is managed by the CCAMLR inside the CCAMLR Convention Area, which spans the Antarctic continent and waters between the 45th and 60th parallels south. Some fisheries inside territorial waters within the convention area (e.g. Crozet, Prince Edward, and Marion Islands) are managed separately by countries with territorial waters taking CCAMLR management practices into account. Toothfish fisheries outside the CCAMLR Convention Area in the coastal waters of Argentina, Chile, and Uruguay are managed by the relevant coastal state. However, these fisheries are still subject to the CCAMLR Catch Documentation Scheme, which tracks the trade of toothfish from the point of unloading to the point of final consumption.

In the legal toothfish fisheries managed by CCAMLR and countries with territorial waters, the most common method is fishing by longlines (where a long "mainline" is set in the water, with many baited hooks coming off that line). A small quantity of toothfish is caught by trawling (where a net is towed behind the boat for short periods). For all methods of legal fishing for toothfish, the interactions with, and risks to, seabirds are minimal. This is a result of requirements for legal operators to use mitigation devices or approaches, such as:
 * Seasonal fishery closures during the summer due to increases in seabird abundance for chick rearing
 * No setting of hooks during the daytime
 * No fishing without having a bird-scaring line trailing out the back of the boat to keep birds away from the hooks
 * Bird exclusion devices or "Brickle curtains" to be used on 100% of hauls
 * Boats must use weighted longlines so that the baits and hooks sink before the birds can grab them;
 * Limitations on release of offal overboard at the same time as the setting or hauling of lines (to avoid attracting seabirds when they may otherwise be vulnerable to the baits and hooks)

In 2011, the CCAMLR Scientific Committee Chair, David Agnew, was quoted as saying, “levels of seabird mortality are negligible in most areas”, with the one region yet to achieve these "near zero" results, having reduced seabird interactions by over 98% from their peak levels, and have continued to improve each year. Nevertheless, interactions between the fishery and marine mammals such as sperm whales, orca, fur seals, and elephant seals are not uncommon and can be fatal.

Trawling generally catches toothfish in the smaller size range, which requires calculations to be made at the annual stock assessment meetings of CCAMLR to take these catches of smaller-sized fish into account, and lowers the overall available catch of toothfish by trawl. CCAMLR has prohibited all trawl fishing in high seas waters and exploratory fisheries.

Compliance
To minimize the risk of long-term adverse effects on target species, bycatch species, and marine ecosystems, CCAMLR uses several compliance systems to monitor fishing activities in the convention area. These include:
 * Vessel licensing
 * Monitoring of transhipments
 * Vessel and port inspection systems
 * Automated satellite-linked vessel-monitoring systems
 * Catch document scheme (CDS): The scheme for Patagonian toothfish (Dissostichus eleginoides) and Antarctic toothfish (Dissostichus mawsoni) was one measure that ensured reductions in illegal fishing for toothfish and reduced the scope for trade in illegally caught fish. The CDS is an innovative online catch document information system (Dissostichus Catch Document) developed to identify legal toothfish harvested, which tracks toothfish from the point of landing throughout the trade cycle to the point of sale. The CDS requires verification and authorization by national authorities at regular intervals in the trade cycle. Identification of the origin of toothfish entering the ports and markets of CDS parties is essential.

Legal fishing
The Coalition of Legal Toothfish Operators, Inc. (COLTO) is a toothfish fishing industry group whose members represent around 80% of the legal toothfish catch worldwide. Seven of the fisheries that COLTO members fish are now independently certified by the Marine Stewardship Council (MSC) as sustainable and well-managed fisheries. Commercial fishing of Patagonian and Antarctic toothfish is managed by CCAMLR around most of the Subantarctic and Antarctic regions, but a fishery that lies within a nation's exclusive economic zone (EEZ) is managed by that nation, taking into account management recommendations and approaches by CCAMLR.

In 2004, the South Georgia toothfish fishery (CCAMLR Statistical Division 48.3) was the first toothfish fishery to be MSC-certified and was recertified in 2009 and 2014, as all MSC-certified fisheries must be audited annually and fully reassessed every five years. The South Georgia fishery is managed by the UK overseas territory of South Georgia and the South Sandwich Islands.

The Ross Sea fishery (CCAMLR Statistical Division 88.1 and 88.2) was the second toothfish fishery to be independently evaluated and certified by the MSC as sustainable and well-managed in 2010 and recertified in 2015. This fishery catches mainly Antarctic toothfish, a close relative of the Patagonian toothfish.

The Heard Island and McDonald Islands fishery (CCAMLR Statistical Division 58.5.2) was certified as a sustainable and well-managed fishery by the MSC in March 2012 (and recertified in 2017) and is operated under Australian jurisdiction in a manner consistent with CCAMLR regulations. Two Australian companies operate four vessels - Austral Fisheries and Australian Longline.

The Macquarie Island toothfish fishery is within the Australian EEZ and is situated outside the CCAMLR Convention Area within FAO Statistical Area 81, though it is managed in a complementary way with the conservation measures adopted by CCAMLR. In May 2012, this was the fourth toothfish fishery to gain MSC certification (and recertified in 2017). Two Australian companies are allocated quota in this fishery.

France regulates Patagonian toothfish in the waters surrounding the French islands in the South Indian Ocean, with scientific oversight from the National Museum of Natural History. These fisheries are located around the Kerguelen Islands (CCAMLR Statistical Division 58.5.1) and the Crozet Islands (CCAMLR Statistical Division 58.6). Six fishing companies based out of Reunion Island have been granted authorisations. The Kerguelen Island fishery was certified by the MSC in September 2013 (recertified in 2018) and the Crozet Islands fishery was certified by the MSC in 2017.

The Falkland Islands, a self-governing British Overseas Territory, also has a toothfish fishery and was awarded MSC certification in 2014. The Falklands do not fall in the CCAMLR Convention area, though regulations on fishing methods, science, and management mirror CCAMLR requirements. The Total Allowable Catch (TAC) is caught by a sole longline vessel.

Combined, over 50% of all legally harvested toothfish is independently assessed and certified by the MSC as being from sustainable and well-managed fisheries.

The Chilean toothfish fishery is separated into two separate fleets. The "artisanal fleet" of small boats operates in the region north of 47°S inside the Chilean EEZ, and six vessels from the "industrial fleet" operate south of 47°S inside the Chilean EEZ, as well as on the high seas both within and outside CCAMLR waters. The TAC for the industrial fleet is determined each year by the Chilean government based on biological studies carried out by both public and private, scientific bodies. Since 2006, artisanal fleet catches have fluctuated between 2,091t and 1,558t per annum.

The Argentine Federal Fisheries Council manages Argentina's toothfish fishery off its coastline under recommendations from the National Fisheries Research Institute. The Argentine TAC is caught by five vessels.

The Prince Edward and Marion Islands toothfish fishery is managed and regulated by Branch Fisheries, part of the South African Minister of Agriculture, Forestry, and Fisheries. The South African Marine Resource Authorities fully supports and follows all CCAMLR conservation measures. The TAC is fished by two vessels belonging to two fishing companies/cooperatives, with catches having been restricted significantly following excessive illegal, unreported, and unregulated (IUU) fishing in those waters in the late 1990s. TACs from this fishery have slowly started to increase as the stock begins to recover.

The global toothfish catch is around 30,000 tonnes, with around 80% of this coming from COLTO members and around half being independently certified as coming from sustainable and well-managed fisheries by the Marine Stewardship Council.

Illegal fishing
In the late 1990s to early 2000s, illegal, unreported and unregulated (IUU) fishing for toothfish nearly collapsed some fisheries in the Southern Ocean. However, since 2005, because of CCAMLR member nations, government patrol vessels, NGOs, media exposure, and trade and port state measures, IUU fishing has been all but eliminated from within countries' EEZs, and until 2015, a relatively small portion of IUU fishing still occurred in high seas areas. In 2014 and 2015, several major campaigns tried to eliminate IUU fishing for toothfish. This included the Sea Shepherd campaign, "Operation Icefish", which pursued one of the vessels, the Thunder, for 110 days before it was scuttled. Operations by the Royal New Zealand Navy, the Royal Australian Navy, Interpol, and governments of Spain, Thailand, Malaysia, and Indonesia all combined to successfully apprehend, arrest and prosecute all of the remaining 6 IUU vessels fishing illegally for toothfish on the high seas.

At the peak of IUU fishing, illegal catches were estimated to be 32,000 tonnes in 1997, with about 55 vessels believed to be active. By 2010, IUU catches had fallen to an estimated 1,615 tonnes, all taken in high-seas areas, with just four IUU fishing vessels reported to be active. This decreased IUU fishing by over 95% since the mid-1990s. CCAMLR estimated in 2012 that 90% of IUU catches at the time were of Antarctic toothfish, not Patagonian toothfish.

CCAMLR annually reviews information on IUU fishing activities in the convention area and has established a contracting party and a noncontracting party IUU vessel list (CCAMLR Conservation Measure 10-06 and Conservation Measure 10–07). Vessels included on the IUU lists have engaged in IUU activities in the convention area and undermined the effectiveness of conservation measures, thereby threatening toothfish stocks, marine habitats, and bycatch species. Vessels are included on the IUU vessel lists after a consensus decision based on set criteria from the commission. This measure, combined with additional surveillance by member nations' catch documentation schemes, has played a significant part in the reduction of IUU fishing for toothfish.

In the past, France sold some fishing rights to Japanese and other foreign fisheries, but because of IUU fishing, rights are now reserved for French fishers based at Réunion Island. Because of the previous poaching, the French Navy and Australian Customs vessels still work in concert, patrolling both French and Australian EEZs, having made numerous arrests and seizures in the late 1990s to early 2000s. An Australian Customs vessel, the Southern Supporter, was involved in the renowned chase and apprehension of an IUU vessel in the 2003 Viarsa incident that stretched over 7,200 km.

TACs for legal operators in CCAMLR are set, taking into account the estimated IUU catches from past years and any IUU activity that may be occurring in the different fisheries. In some fisheries, this has meant a considerable reduction in legal catches – an example of this is the Australian Heard Island and McDonald Islands fishery, where the legal TAC was 3,800 t in 1996/97. This was dropped to a minimum of 2,427 t by 2006/07, with a substantial portion of that decline attributed to the IUU catches taken from the fishery between 1996 and 2002. Since then, no IUU fishing has occurred in that fishery, and the legal TAC has steadily increased.

In addition to the catch documentation system mentioned above, USA regulations do not allow toothfish imports without valid Dissostichus catch documents; dealer permits and preapproval certificates must be issued in advance by NOAA. In addition, toothfish must be caught from vessels equipped with satellite-linked automated VMSs that track vessel movements from port to port to ensure compliance with set quotas and boundaries. All vessel VMS data must be reported to the centralized CCAMLR system, with confirmation to USA required that it has occurred, for any products from those boats to be imported into the United States.

As revealed by the "black spider memos", Charles, Prince of Wales, was worried about the future for the species. An open reply noted that sea birds had been protected in toothfish fisheries globally and that IUU fishing was virtually eliminated.

The EU has also imposed requirements against IUU fishing that include:
 * Only marine fisheries products validated as legal by the relevant flag state or exporting state can be imported or exported from the EU.
 * A European blacklist covers IUU vessels and states that turn a blind eye to illegal fishing activities.
 * EU operators who fish illegally anywhere in the world, under any flag, face substantial penalties proportionate to the economic value of their catch, which deprive them of any profit.

Seafood chooser organizations
Patagonian toothfish is listed by the Monterey Bay Aquarium on its Seafood Watch list and pocket guides. In April 2013, Seafood Watch produced an updated report, indicating new ratings for some fisheries, which allocates about 78% of toothfish caught worldwide, which are:
 * Best Choice – Heard Island and McDonald Islands Fishery (Australia), Macquarie Island Fishery (Australia), Falkland Islands Fishery
 * Good Alternative – South Georgia Fishery, Kerguelen Islands Fishery (France), Ross Sea Antarctic toothfish Fishery
 * Avoid – Prince Edward & Marion Island Fishery (South Africa), Chile, Crozet Islands Fishery (France)
 * Not Rated – Argentina

In 2010, Greenpeace International added the Patagonian toothfish to its seafood red list. "The Greenpeace International seafood red list is a list of fish that are commonly sold in supermarkets around the world, and which have a very high risk of being sourced from unsustainable fisheries." Greenpeace have not updated their rating of toothfish since the 2013 Monterey Bay Aquarium review.

title: Patagonian toothfish


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Talk:Galois connection

Galois Insertions
Need to add the definition (and properties?) of Galois insertions, that is Galois connections with a composition of adjoins being the identity function. VictorPorton (talk) 22:45, 17 December 2012 (UTC)

Definition
There was some confusion about the definition (whether it is "F(a) <= b if and only if a ≤ G(b)" or "F(a) <= b if and only if G(b) ≤ a"). I changed it back to the former version (sorry Axel), since it is more common in the order-theory literature I know of. This definition is also the only one that is currently cited in other articles (see adjoint functors, heyting algebra and order theory glossary). However, to make it still possible to use the historical definition, I include this one too. It should be called antitone Galois connection in Wikipedia.

At least the following authors use the current definition of Galois connection in a book published after 1990: Abramski, Borceux, Davey, Gierz, Hofmann, Jung, Keimel, Lawson, Mislove, Priestley, Scott. Especially [Davey & Priestley] is probably the introductory text-book in this field.

--Markus Krötzsch 20:53, 3 Feb 2004 (UTC)

 * That's fine, we should definitely use the modern definition. When I found the discrepancy, I went back to the original papers and copied their antitone definition, not realizing that conventions had changed in the meantime. AxelBoldt 15:56, 14 Feb 2004 (UTC)

 * I don't think that conventions changed completely. Where it is convenient (in some applications, such as formal concept analysis) the antitone definition is used as well. So it might be good to mention "monotone" or "antitone" in articles that use Galois connections. --Markus Krötzsch 18:55, 29 Mar 2004 (UTC)

The definition is lacking in a few ways. First, "monotone" is not the opposite of "antitone". "Monotone increasing" is the opposite, and the word for that is "isotone". Second, it is invalid to claim that "Galois connection" should mean isotone mappings; that is one perspective but not fully representative of the literature. I will edit the article to say "isotone Galois connection" and "antitone Galois connection" to reflect the range of usage. It's too bad if other articles assume a "Galois connection" is isotone; this article should be correct. The others can be fixed. Zaslav (talk) 19:49, 21 February 2022 (UTC)

Uniqueness of adjoints
In the Definition section is said As detailed below, each part of a Galois connection uniquely determines the other mapping.

But below there are no proof nor any details nor any reference about each part of a Galois connection uniquely determining the other.

The proof needs to be added. —Preceding unsigned comment added by Porton (talk • contribs) 12:15, 13 June 2009 (UTC)

porton (talk) 12:16, 13 June 2009 (UTC)

Applications in programming
It would be nice if somebody could amplify about applications, including the application cited to programming. My vague understanding is that it has something to do with programming semantics, perhaps denotational semantics where data objects form a complete partial order and operations on them are partial functions. I seem to recall that Galois connections are used in relation to formal methods, perhaps to ensure that program refinements preserve some correctness properties (liveness and safety) from the unrefined to the refined domain, but I don't know the details. I heard this from somebody who audited a course in program semantics at Oxford U, which used Galois connections as a unifying concept.

Fred Kintanar

Cebu City

 * I'm afraid we have to wait until someone shows up who has audited that course at Oxford U. Can't you give a call to your friend? :-) AxelBoldt 15:53, 14 Feb 2004 (UTC)

As part of the whole Tony Hoare tradition, there are 'weakest preconditions' for something to happen with a program, and so on. This leads very quickly (if somewhat superficially) to the use of Galois connections. I don't see anything substantive about this on WP, currently.

Charles Matthews 09:16, 5 Apr 2004 (UTC)

Definitions, again
About the definitions (again):

We currently have F(a) <= b if and only if G(b) ≤ a for antitone Galois connections. In contrast, a book on my desk (Ganter & Wille) says it should be b <= F(a) if and only if a ≤ G(b). This is not the same, since orders may be partial ("not ≤" is not the same as "≥"). Is the definition in the article also used somewhere (it certainly affects the results, since one gets no closure operators in this case, but obtains their duals -- kernel operators -- instead)? If not, it's an error and needs to be corrected. --Markus Krötzsch 23:39, 19 Feb 2005 (UTC)

Is it possible to change ≤ and <= to ≤a and ≤b to make it clear that there are 2 different orders that are related to the sets A and B.

Like this: (A,≤a) and (B,≤b) F(a) ≤b b if and only if a ≤a G(b).

The red lettered text denoting a yet-to-be-written-article appearing in this article reads: adjoint functor theorem for order theory. The one-sentence description of its application here is vaguely reminiscent of the Freyd Adjoint Functor Theorem described in the article on Adjoint functors. Are these theorems one and the same? I'm seeking concurrence before making this change. Vonkje 00:24, 2 August 2005 (UTC)

Another resource, a better notation
Hi. There is a document about Galois connections, written by Roland Backhouse, which uses a different (better, IMO) notation. The link is: http://www.cs.nott.ac.uk/~rcb/G53PAL/FPandGC.pdf

 * The notation in this article is a mess, but not much more so than what other authors use. For starters, the *-notation is only used in Erné, but not in Davey and Priestley or in Gierz et al. What's worse, is that the notation in this article places the asterisk in the opposite way than Erné. On the bright side, the terms "upper" and "lower" are from Gierz, and they make way more mnemonic sense compared with those the Davey and Pristely (left/right) or Erné (adjoint/coadjoint). Pcap ping  22:13, 5 August 2009 (UTC)

Merge proposal
Per this discussion it has been proposed that this article be merged with Residuated mapping. However the topic hasn't been discussed for the past two months in the respective talk-pages. I suggest to either continue the discussion here (untill some kind of consensus is reached) or remove the tag from the article. --Omnipaedista (talk) 06:26, 29 October 2009 (UTC)

Power set example
The power set example doesn't seem right -- I think the names of things are changed mid-explanation and it makes no sense. Could someone less confused than me take a look and try to fix it? 128.193.60.168 (talk) 02:43, 10 November 2009 (UTC)

Definition by composition of relations?
Am I right that that galois connections could be defined using composition of relations? I.e.:

Let $$(A, \leq_1), (B, \leq_2)$$ be two Posets.

$$(f : A \to B, g : B \to A)$$ is a galois connection iff $$\forall a \in A: \forall b \in B: f(a) \leq_2 b \Leftrightarrow a \leq_1 g(b)$$.

$$f(a) \leq_2 b$$ iff $$\exists y: (a,y) \in G_f \land (y,b) \in G_{\leq_2}$$ iff $$(\mathord{\leq}_2 \circ f)(a,b)$$

and

$$a \leq_1 g(b)$$ iff $$\exists z: (a, z) \in G_{\leq_1} \land (z,b) \in G_g$$ iff $$(g \circ \mathord{\leq}_1)(b,a)$$

I.e. $$(f,g)$$ is a galois connection iff $$\mathord{\leq}_2 \circ f = (g \circ \mathord{\leq}_1)^{-1}$$?

One might even write iff $$\mathord{\leq}_2 \circ f = \mathord{\geq}_1 \circ g^{-1}$$.

Is there any such definition in literature?

-- 188.192.84.97 (talk) 14:26, 9 December 2011 (UTC)

 * Perhaps this one: Jacques Riguet (1948) "Relations binaires, fermetures, correspondances de Galois", Bulletin de la Société Mathématique de France 76: 114–55. — Rgdboer (talk) 21:44, 27 April 2018 (UTC)

Suggest to cite "own" article in section "Applications in the theory of programming"
In section Galois connection, I added two references to the original papers of Cousot and Cousot, and one to a tech. report correcting a false theorem of their 1977 paper. Following an advice of User:Deltahedron on my talk page, I deleted the tech. report reference where I was a co-author. Below follows the text before deletion; I'd like to restore it if there are no objections. - Jochen Burghardt (talk) 21:09, 1 February 2014 (UTC)

 Galois connections may be used to describe many forms of abstraction in the theory of abstract interpretation of programming languages.

F or G invertible implies each is the inverse of the other
The article states "if F or G is invertible, then each is the inverse of the other, i.e. F = G–1", this being stated as a consequence of the formulas $$F(a) = \min\{b \in B \mid a \leq G(b)\}$$ and $$G(b) = \max\{a \in A \mid F(a) \leq b\}$$. My issue is that the word "invertible" was linked to the article Bijection, but the fact is only clear to me if F or G is invertible with a monotone inverse (the inverse function of a monotone bijection is not in general monotone), since then we have
 * $$F \text{ invertible with monotone inverse} \implies Gb = \max\{a \in A \mid F(a) \leq b\} = \max\{a \in A \mid a \leq F^{-1}(b)\} = F^{-1}(b) \implies G = F^{-1},$$ and similarly
 * $$G \text{ invertible with monotone inverse} \implies Fa = \min\{b \in B \mid a \leq G(b)\} = \min\{b \in B \mid G^{-1}(a) \leq b\} = G^{-1}(a) \implies F = G^{-1}.$$

Maybe I am missing something and one can make a different argument to conclude that if F or G is invertible just as a function (i.e. is a bijection) then F and G are each other's inverses (I haven't tried to look for a counterexample). Could somebody in the know please fill me in, and also update the article to clarify (and then remove the "Clarify" tag that I added). Thanks. Joel Brennan (talk) 21:06, 7 December 2021 (UTC)

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

title: Talk:Galois connection


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Meritaten

Meritaten, also spelled Merytaten, Meritaton or Meryetaten (mrii.t-itn) (14th century BC), was an ancient Egyptian royal woman of the Eighteenth Dynasty of Egypt. Her name means "She who is beloved of Aten"; Aten being the sun-deity whom her father, Pharaoh Akhenaten, worshipped. She held several titles, performing official roles for her father and becoming the Great Royal Wife to Pharaoh Smenkhkare, who may have been a brother or son of Akhenaten. Meritaten also may have served as pharaoh in her own right under the name Ankhkheperure Neferneferuaten.

Family
Meritaten was the first of six daughters born to Pharaoh Akhenaten and his Great Royal Wife, Nefertiti. Her sisters are Meketaten, Ankhesenpaaten, Neferneferuaten Tasherit, Neferneferure, and Setepenre. Meritaten is mentioned in diplomatic letters, by the name Mayati. She is mentioned in a letter from Abimilki of Tyre. The reference usually is thought to date to the period when Meritaten's position at court became more important, during the latter part of the reign of Akhenaten. It is possible, however, that the letter refers to the birth of Meritaten.

She was married to Akhenaten's successor, the Pharaoh Smenkhkare.

Inscriptions mention a young princess named Meritaten Tasherit, who may be the daughter of Meritaten and Smenkhkare. Inscriptions from Ashmunein suggest that Meritaten-tasherit is the daughter of Meritaten. The scene dates to the reign of Akhenaten, and this means the father of the young princess could be Akhenaten. If so, this means Akhenaten took his own daughters as wives. Another princess named Ankhesenpaaten Tasherit had been suggested as an additional daughter of Meritaten, but it is more likely that she is a daughter of Ankhesenpaaten.

Early years in Thebes
Meritaten most likely was born in Thebes, early in her father's marriage to Nefertiti, perhaps before he assumed the throne, as she is shown officiating during year five of his reign. The royal family first lived in Thebes and the royal palace may have been part of the Temple Complex of Akhenaten at Karnak. The exact use of the buildings in Karnak is not known, but the scenes decorating the Teni-menu suggest it may have served as a residence. Meritaten is depicted beside her mother Nefertiti in reliefs carved into the Hut-Benben. The Hut-Benben was a structure associated with Nefertiti, who is the main officiant in the scenes, the great royal wife being the highest priestess. Meritaten appears behind her mother shaking a sistrum. Her younger sisters Meketaten and Ankhesenpaaten also appear in some of the scenes, but not so often as Meritaten.

Amarna princess
In year five of her father Akhenaten's reign, Meritaten appears on the boundary stelae designating the boundaries of the new capital to which her father moved the royal family and his administrators. During Akhenaten's reign, she was the most frequently depicted and mentioned of the six daughters. Her figure appears on paintings in temples, tombs, and private chapels. Not only is she shown among images showing the family life of the pharaoh, which were typical of the Amarna Period, but on those depicting official ceremonies, as well.

The two structures most associated with Meritaten at Amarna are the Northern Palace and the Maru-Aten. The Maru-Aten was located to the south of the city limits of Amarna. The structure consisted of two enclosures containing pools or lakes and pavilions set in an area planted with trees. An artificial island contained a pillared construction that held a painted pavement showing scenes from nature.

Meritaten's name seems to replace that of another royal lady in several places, among them in the Northern Palace and in the Maru-Aten. This had been misinterpreted as evidence of Nefertiti's disgrace and banishment from the royal court but, more recently, the erased inscriptions turned out to be the name of Kiya, one of Akhenaten's secondary wives, disproving that interpretation.

Great Royal Wife
At some point, Meritaten married Smenkhkare and became his Great Royal Wife. She is depicted with him in the tomb of Meryre II, bestowing honors and gifts upon Meryre. The chronology of the final years of the Amarna Period is unclear, however Smenkhkare is believed to have served as a co-regent to Akhenaten. Meritaten was the Great Royal Wife to Smenkhkare, while Nefertiti continued as the Great Royal Wife of Akhenaten. Nefertiti still held the Great Royal Wife title in year 16, hence Smenkhkare must have been a co-regent at that time, or otherwise ruled with his wife Meritaten sometime after year 16 of Akhenaten.

Meritaten is mentioned on gold daisies that decorated a garment found in Tutankhamen's tomb. She also is mentioned on a wooden box meant to contain linen garments. The box mentions two kings: Neferkheperure-Waenre (Akhenaten) and Ankhkheperure-mr-waenre, Neferneferuaten-mr-waenre and the Great Royal Wife Meritaten.

According to some scholars, such as J.P. Allen, Ankhkheperure Smenkhkare ruled together with Meritaten, but in the year following Akhenaten's death, Smenkhkare died. The theory is, that Meritaten was the 'king's daughter' Akenkeres who is recorded in Manetho's Epitome to have assumed the throne next, in her own right as king and bearing the name Neferneferuaten. Neferneferuaten is assigned a reign of two years and one month and is placed in Manetho's account as the immediate predecessor of the king, Rathothis, who is believed to be Tutankhamun, her half-brother by another, unnamed wife of Akhenaten.

Archaeologist Alain Zivie asserts that Meritaten also became a foster mother to Tutankhamun, referred to as Maia in some ancient records. Zivie noted that Thutmose, the sculptor appointed vizier by Akhenaten and who was found to be the creator of the famous bust of Nefertiti also created one of Maïa (Bubasteion I.20), the foster mother of Tutankhamun and who, in fact, was "Merytaten, the elder daughter of Akhenaten", "who sat briefly on the throne".

Death and burial
The texts of its boundary stele mention that Meritaten was meant to be buried at Akhet-Aten (modern Amarna). "Let a tomb be made for me in the eastern mountain of Akhetaten. Let my burial be made in it, in the millions of jubilees which the Aten, my father, has decreed for me. Let the burial of the Great King's Wife, Nefertiti, be made in it, in the millions of years which the Aten, my father, decreed for her. Let the burial of the King's Daughter, Meritaten, [be made] in it, in these millions of years."

The royal tomb in Amarna was used for the burial of Meketaten, Tiye, and Akhenaten, and likely was closed after the death and burial of Akhenaten. After that, Meritaten's burial may have been planned for one of the other royal tombs in Amarna.

title: Meritaten


text:
User talk:Rniba

Welcome to the Wikipedia. I thought I should mention that .doc Files won't work here, the software doesn't understand them. Here's a link to the FAQ if you're interested, there's quite a bit of good info linked from there. - Hephaestos 16:50, 16 Dec 2003 (UTC)

title: User talk:Rniba


text:
Talk:Bruce Andrews

Untitled
This article is part of WikiProject Poetry. See that page for guidelines.

General comment & info.. He's about as liberal as one can get. He makes a point of asking students not to tape record his lectures because he does not want someone to be able to play portions of them out of context (he might be pretending to be pro-cannibalism and engage students in a debate about it, in an effort to force students to give arguments based on reason rather than things like "Ew! That's gross!" He said that his office is in room 666, and that he picked it because 1) he finds it hilarious 2) and he believes that it discourages unnecessary visits to his office (under the assumption that most Catholic students would not want to visit an office with that number on the door. A notion which I think is pretty far-fetched and unlikely, but thats just me.)

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title: Talk:Bruce Andrews


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Alexius Meinong

Alexius Meinong Ritter von Handschuchsheim (17 July 1853 – 27 November 1920) was an Austrian philosopher, a realist known for his unique ontology and theory of objects. He also made contributions to philosophy of mind and theory of value.

Life
Alexius Meinong's father was officer Anton von Meinong (1799–1870), who was granted the hereditary title of Ritter in 1851 and reached the rank of Major General in 1858 before retiring in 1859.

From 1868 to 1870, Meinong studied at the Akademisches Gymnasium, Vienna. In 1870, he entered the University of Vienna law school where he was drawn to Carl Menger's lectures on economics. In summer 1874, he earned a doctorate in history by writing a thesis on Arnold of Brescia. It was during the winter term (1874–1875) that he began to focus on history and philosophy. Meinong became a pupil of Franz Brentano, who was then a recent addition to the philosophical faculty. Meinong would later claim that his mentor did not directly influence his shift into philosophy, though he did acknowledge that during that time Brentano may have helped him improve his progress in philosophy. Meinong studied under Brentano with Edmund Husserl, who would also become a notable and influential philosopher. Both their works exhibited parallel developments, particularly from 1891 to 1904. Both are recognized for their respective contribution to philosophical research.

In 1882, Meinong became a professor at the University of Graz and was later promoted as chair of its philosophy department. During his tenure, he founded the Graz Psychological Institute (Grazer Psychologische Institut; founded in 1894) and the Graz School of experimental psychology. Meinong supervised the doctorates of Christian von Ehrenfels (founder of Gestalt psychology) and Adalbert Meingast, as well as the habilitation of Alois Höfler and Anton Oelzelt-Newin.

Ontology
Meinong wrote two early essays on David Hume, the first dealing with his theory of abstraction, the second with his theory of relations, and was relatively strongly influenced by British empiricism. He is most noted, however, for his edited book Theory of Objects (full title: Investigations in Theory of Objects and Psychology, Untersuchungen zur Gegenstandstheorie und Psychologie, 1904), which grew out of his work on intentionality and his belief in the possibility of intending nonexistent objects. Whatever can be the target of a mental act, Meinong calls an "object."

His theory of objects, now known as "Meinongian object theory," is based around the purported empirical observation that it is possible to think about something, such as a golden mountain, even though that object does not exist. Since we can refer to such things, they must have some sort of being. Meinong thus distinguishes the "being" of a thing, in virtue of which it may be an object of thought, from a thing's "existence", which is the substantive ontological status ascribed to—for example—horses but not to unicorns. Meinong called such nonexistent objects "homeless"; others have nicknamed their place of residence "Meinong's jungle" because of their great number and exotic nature.

Historically, Meinong has been treated, especially by Gilbert Ryle, as an eccentric whose theory of objects was allegedly dealt a severe blow in Bertrand Russell's essay "On Denoting" (1905) (see Russellian view). However, Russell himself thought highly of the vast majority of Meinong's work and, until formulating his theory of descriptions, held similar views about nonexistent objects. Further, recent Meinongians such as Terence Parsons and Roderick Chisholm have established the consistency of a Meinongian theory of objects, while others (e.g., Karel Lambert) have defended the uselessness of such a theory.

Meinong is also seen to be controversial in the field of philosophy of language for holding the view that "existence" is merely a property of an object, just as color or mass might be a property. Closer readers of his work, however, accept that Meinong held the view that objects are "indifferent to being" and that they stand "beyond being and non-being". On this view Meinong is expressly denying that existence is a property of an object. For Meinong, what an object is, its real essence, depends on the properties of the object. These properties are genuinely possessed whether the object exists or not, and so existence cannot be a mere property of an object.

Types of objects
Meinong holds that objects can be divided into three categories on the basis of their ontological status. Objects may have one of the following three modalities of being and non-being:
 * Existence (Existenz, verb: existieren), or actual reality (Wirklichkeit), which denotes the material and temporal being of an object
 * Subsistence (Bestand, verb: bestehen), which denotes the being of an object in a non-temporal sense.
 * Absistence or being-given (Gegebenheit, as in the German use es gibt, i.e. "there are", "it is given"), which denotes being an object but not having being.

Certain objects can exist (mountains, birds, etc.); others cannot in principle ever exist, such as the objects of mathematics (numbers, theorems, etc.): such objects simply subsist. Finally, a third class of objects cannot even subsist, such as impossible objects (e.g. square circle, wooden iron, etc.). Being-given is not a minimal mode of being, because it is not a mode of being at all. Rather, to be "given" is just to be an object. Being-given, termed "absistence" by J. N. Findlay, is better thought of as a mode of non-being than as a mode of being. Absistence, unlike existence and subsistence, does not have a negation; everything absists. (Note that all objects absist, while some subset of these subsist, of which a yet-smaller subset exist.) The result that everything absists allows Meinong to deal with our ability to affirm the non-being (Nichtsein) of an object. Its absistence is evidenced by our act of intending it, which is logically prior to our denying that it has being.

Object and subject
Meinong distinguishes four classes of "objects":
 * Object (Objekt), which can be real (like horses) or ideal (like the concepts of difference, identity, etc.)
 * Objective (Objectiv), e.g. the affirmation of the being (Sein) or non-being (Nichtsein), of a being-such (Sosein), or a being-with (Mitsein), of an object—parallel to existential, categorical and hypothetical judgements. Objectives are close to what contemporary philosophers call states of affairs (where these may be actual—may "obtain"—or not)
 * Dignitative, e.g. the true, the good, the beautiful
 * Desiderative, e.g. duties, ends, etc.

To these four classes of objects correspond four classes of psychological acts:
 * (Re)presentation (das Vorstellen), for objects
 * Thought (das Denken), for the objectives
 * Feeling (das Fühlen), for dignitatives
 * Desire (das Begehren), for the desideratives

Books

 * Meinong, A. (1885). Über philosophische Wissenschaft und ihre Propädeutik.
 * Meinong, A. (1894). Psychologisch-ethische Untersuchungen zur Werttheorie.
 * Meinong, A. (1902). Über Annahmen, 1st ed.
 * Meinong, A., ed. (1904). Untersuchungen zur Gegenstandstheorie und Psychologie (Investigations in Theory of Objects and Psychology), Leipzig: Barth (contains Alexius Meinong, "Über Gegenstandstheorie", pp. 1–51).
 * Meinong, A. (1910). Über Annahmen, 2nd ed.
 * Meinong, A. (1915). Über Möglichkeit und Wahrscheinlichkeit.
 * Meinong, A. (1917). Über emotionale Präsentation.

Articles

 * Meinong, A. (1877). "Hume Studien I. Zur Geschichte und Kritik des modernen Nominalismus", in Sitzungsbereiche der phil.-hist. Classe der kais. Akademie der Wissenschaften, 78:185–260.
 * Meinong, A. (1882). "Hume Studien II. Zur Relationstheorie", in Sitzungsbereiche der phil.-hist. Classe der kais. Akademie der Wissenschaften, 101:573–752.
 * Meinong, A. (1891). "Zur psychologie der Komplexionen und Relationen", in Zeitschrift für Psychologie und Physiologie der Sinnesorgane, II:245–265.
 * Meinong, A. (1899). "Über Gegenstände höherer Ordnung und deren Verhältniss zur inneren Wahrnehmung", in Zeitschrift für Psychologie und Physiologie der Sinnesorgane, 21, pp. 187–272.

Books together with other authors

 * Höfler, A., & Meinong, A. (1890). Philosophische Propädeutik. Erster Theil: Logik. F. Tempsky / G. Freytag, Vienna.

Posthumously edited works

 * Haller, R., Kindinger, R., and Chisholm, R., editors (1968–78). Gesamtausgabe, 7 vols., Akademische Druck- und Verlagsanstalt, Graz.
 * Meinong, A. (1965). Philosophenbriefe, ed. Kindinger, R., Akademische Druck- und Verlagsanstalt, Graz.

English translations

 * On Assumptions (Über Annahmen), trans. James Heanue. Berkeley: University of California Press, 1983.
 * On Emotional Presentation (Über emotionale Präsentation), trans. M.-L. Schubert Kalsi. Evanston, Ill: Northwestern University Press, 1972.
 * "The Theory of Objects" ("Über Gegenstandstheorie"), trans. I. Levi, D. B. Terrell, and R. Chisholm. In Realism and the Background of Phenomenology, ed. Roderick Chisholm. Atascadero, CA: Ridgeview, 1981, pp. 76–117.

Books

 * Albertazzi, L., Jacquette, D., and Poli, R., editors (2001). The School of Alexius Meinong. Aldershot: Ashgate. ISBN 978-1-84014-374-4
 * Bergmann, G. Realism: A Critique of Brentano and Meinong. Madison, Wisconsin: University of Wisconsin Press, 1967.
 * Chisholm, R. Brentano and Meinong Studies. Amsterdam: Rodopi,  1982.
 * Dölling, E. Wahrheit Suchen und Wahrheit Bekennen. Alexius Meinong: Skizze seines Lebens.  Amsterdam: Rodopi, 1999. ISBN 978-90-420-0774-1
 * Findlay, J. N. Meinong's Theory of Objects and Values, 2nd ed. Oxford: Clarendon Press, 1963.
 * Grossman, R. Meinong. London and Boston: Routledge & Kegan Paul,  1974. ISBN 978-0-7100-7831-5
 * Haller, R., editor. Jenseits von Sein und Nichtsein. Graz: Akademische Druck- und Verlagsanstalt,  1972.
 * Lindenfeld, D. F. The Transformation of Positivism: Alexius Meinong and European Thought, 1880–1920. Berkeley: University of California Press, 1980. ISBN 978-0-520-03994-0
 * Rollinger, R. D. Meinong and Husserl on Abstraction and Universals. Number XX in Studien zur Österreichischen Philosophie. Amsterdam and Atlanta: Rodopi, 1993. ISBN 978-90-5183-573-1
 * Rollinger, Robin D. Austrian Phenomenology: Brentano, Husserl, Meinong, and Others on Mind and Object. Frankfurt am Main: Ontos, 2008. ISBN 978-3-86838-005-7
 * Routley, R. (1982). Exploring Meinong's Jungle and Beyond. Ridgeview Pub Co. ISBN 978-0-685-05636-3. (Also published by the Research School of Social Sciences, Australian National University, Canberra, 1979.)
 * Schubert Kalsi, Marie-Luise. Alexius Meinong: On Objects of Higher Order and Husserl's Phenomenology. Martinus Nijhoff, The Hague, Netherlands. ISBN 978-90-247-2033-0
 * Smith, Barry. Austrian Philosophy: The Legacy of Franz Brentano. Chicago: Open Court, 1996. ISBN 978-0-8126-9307-2

Articles

 * Chrudzimski, A. (2005). "Abstraktion und Relationen beim jungen Meinong" in [Schramm, 2005], pages 7–62.
 * Dölling, E. (2005). "Eine semiotische Sicht auf Meinongs Annahmenlehre" in [Schramm, 2005], pages 129–158.
 * Kenneth, B. (1970). "Meinong’s Hume Studies. Part I: Meinong’s Nominalism" in Philosophy and Phenomenological Research, 30:550–567.
 * Kenneth, B. (1971). "Meinong’s Hume Studies. Part II: Meinong’s Analysis of Relations" in PPR, 31:564–584.
 * Rollinger, R. D. (2005). "Meinong and Brentano". In [Schramm, 2005], pages 159–197.
 * Routley, R. and Valerie Routley. "Rehabilitating Meinong's Theory of Objects". Review Internationale de Philosophie 104–105 (1973).
 * Russell, Bertrand. "Meinong's Theory of Complexes and Assumptions" in Essays in Analysis, ed. Douglas Lackey. New York: George Braziller, 1973.
 * Ryle, Gilbert. "Intentionality-Theory and the Nature of Thinking." Review Internationale de Philosophie 104–105 (1973).
 * Schermann, H. (1972). "Husserls II. Logische Untersuchung und Meinongs Hume-Studien I" in [Haller, 1972], pages 103–116.
 * Vendrell-Ferran, I. (2009): "Meinongs Philosophie der Gefühle und ihr Einfluss auf die Grazer Schule" in Meinong Studien III Graz

Journals

 * Schramm, A., editor. Meinong Studies – Meinong Studien, Volume 1 (2005). Ontos Verlag.

Podcasts

 * The philosopher A. C. Grayling discusses Meinong in a podcast about Bertrand Russell's theory of descriptions on Philosophy Bites.

title: Alexius Meinong


text:
Indestructible (Rancid album)

Indestructible is the sixth studio album by the American punk rock band Rancid. It was produced by Brett Gurewitz (Bad Religion) and released by Hellcat Records with distribution through Warner Bros. Records on August 19, 2003. Despite critical acclaim, the band was criticized by some of its fans for Indestructible's "poppier" sound on some of its tracks. It debuted at number 15 on the charts, selling 51,000 copies in its first week. It was Rancid's highest debut at the time, which was surpassed six years later with their 2009 album, Let the Dominoes Fall. Indestructible marks the last recording by drummer Brett Reed, who left the band in 2006 and was replaced by current drummer Branden Steineckert (formerly of The Used). Additionally, it is the only album that features songwriting contributions from Reed.

Writing and production
Production of the album began with following a US tour with NOFX in April and concluded in November 2002. Indestructible was described as the band's most personal album, covering personal issues including Tim Armstrong's divorce from ex-wife Brody Dalle on songs such as "Fall Back Down", "Ghost Band" and "Tropical London". The album's final track, "Otherside", was written by Lars Frederiksen and dedicated to his brother Robert, who died in 2001. The album was also dedicated two of band's mentors and influences: Joe Strummer and Joey Ramone, who both died during the making of the album. Strummer is mentioned in the album's title track.

Post production of the album consisted of cutting the record down from 25 tracks to 19 tracks. The six tracks left off of the final album were "Killing Zone", "Stranded", "Trouble", "Road to Hell", "Warfare", and "Squatter House"." Killing Zone" and "Stranded" were used as b-sides and bonus tracks for the record. "Trouble" was reworked and released as a single on Pink's third album Try This. That version of the song won Tim Armstrong and Pink a Grammy. "Road to Hell" was re-recorded and a Japanese bonus track on the 2nd Lars Frederiksen And The Bastards album Viking. "Warfare" and "Squatter House" remain unreleased.

Release
On June 6, 2003, the album's track listing was posted online. From June to August 2003, the group went on the 2003 edition of Warped Tour. On July 24, "Indestructible", "Back Against the Wall", and "Red Hot Moon" were posted on the band's website. "Fall Back Down" was released to radio on July 22, 2003. A music video for the song was posted on Yahoo! Launch on August 4, 2003.

The album was delayed a number of times before its official release. It was first scheduled for release in summer/fall 2002 beforing being delayed to early 2003, mid, and finally August 19, 2003. Chief among the reasons for the album's delay were band members' other commitments. Singer/guitarist Tim Armstrong released an album with his then-new side project Transplants and second guitarist Lars Frederiksen released an album with Lars Frederiksen and the Bastards. Warner Bros. Records released the CD version while LP was released by Epitaph. In August and September, the band toured Europe, a few shows of which were as part of the Reconstruction Festival. On September 30, they appeared on Late Night with Conan O'Brien. They then embarked on a headlining US tour in November, with Tiger Army; Nekromantix, the Frisk, and Roger Miret and the Disasters appeared on select dates. In February 2003, Rancid toured across Japan. "Red Hot Moon" was released to radio on October 28, 2003; a music video for the song was released to days later, and was filmed at CBGBs in New York City. In December, the band went on the Hellcat Tour with Tiger Army and F-Minus. Tim Shaw of Ensign sang Skinhead Rob's section of "Red Hot Moon" during the tour. Later in the month, the band performed at the KROQ Almost Acoustic Christmas festival. "Tropical London" was released as a promotional single to radio on April 27, 2004. A music video was released for "Spirit of '87" however it was not released as a single.

Following the release of the album, the group went on hiatus while each of the members toured and recorded albums with other bands.

Reception
Prior to the album's release the band signed a special distribution deal with Warner Bros. Records, which was met with major backlash from many of the band's fans for abandoning their independent roots. To ease tension among the fans, the album was released with no mention of Warner Bros. on the album packaging. According to a label spokesman "It's a unique deal that doesn't play by the traditional record biz rules. It's Rancid putting out an album on Hellcat, with the possibility of additional support from [Warner Bros.]." In a statement, Lars Frederiksen discussed the Warner Bros. deal by saying "We have absolutely no complaints with Hellcat. Yes, we are considering additional support that Warner Bros. might be able to provide, but whatever happens, we're sticking with Brett Gurewitz. All I care about and all I have is my music, my bandmates and my band. We are going to do whatever we need to do to survive."

The album was with mostly positive critical reviews, reaching #15 on the charts and making it the band's biggest debut at the time. However, some fans criticized the album for its stylistic departure from earlier work, claiming that a major label had influenced the band's music to appeal to mainstream listeners (despite the album being written prior to the band's agreement with the label). Still others felt the album to be a mixture of ...And Out Come the Wolves and Life Won't Wait. The album's first single "Fall Back Down", a song written about Armstrong's divorce and reliance on his close friends, was also met with some backlash from fans for featuring members of Good Charlotte and Kelly Osbourne in its music video.

Brody Dalle has never listened to the album. "I had no desire to listen to [Tim's] record [at the time it came out]. Someone said there was a song called "Tropic London", which was maybe about me and Melbourne. I still haven't heard it."

Album notes

 * "Out of Control" was used for the video game Need For Speed: Underground.
 * "Fall Back Down", was used on Tony Hawk's Underground 2 soundtrack, the EA Sports video game NASCAR Thunder 2004 and the Forza Horizon 3 soundtrack.
 * The average score on Metacritic for the album was a positive 84%
 * The LP bonus track "Killing Zone" is also available on the Give 'Em the Boot IV compilation.
 * "Killing Zone" was also the last song Rancid recorded with Brett Reed in the band.
 * "Fall Back Down" was also featured in the movie Agent Cody Banks 2

Personnel
Adapted from the album liner notes.

Rancid Additional personnel
 * Tim Armstrong – vocals, guitar, mixing (18), cover photo
 * Lars Frederiksen - vocals, guitar
 * Matt Freeman - vocals, bass
 * Brett Reed - drums
 * Luis Conte - percussion
 * Vic Ruggiero - keyboards
 * Skinhead Rob - vocals (3)
 * Siedah Garrett - vocals
 * Brett Gurewitz - vocals, producer, additional engineer, mixing (6, 10, 12, 13, 14, 19)
 * Nick Raskulinecz - engineer, editing
 * Andrew Alekel - additional engineer
 * John "Silas" Cranfield - assistant engineer
 * Pete Martinez - assistant engineer
 * Citris Reynolos - assistant engineer
 * Dave Carlock - editing
 * Seth McLain - editing
 * Edmond Monsef - editing
 * Doug Boehm - mixing (1, 3, 4, 7-9, 11, 15-17)
 * Rob Schnapf - mixing (1, 3, 4, 7-9, 11, 15-17)
 * Kevin Dran - mixing assistant (1, 3, 4, 7-9, 11, 15-17)
 * Joe Barresi - mixing (2, 5)
 * Brian Gardner - mastering
 * Nick Pritchard - design

title: Indestructible (Rancid album)


text:
Battles of Narvik

The Battles of Narvik were fought from 9 April to 8 June 1940, as a naval battle in Ofotfjord and as a land battle in the mountains surrounding the north Norwegian town of Narvik, as part of the Norwegian Campaign of the Second World War.

The two naval battles in Ofotfjord on 10 April and 13 April were fought between the British Royal Navy and the German Kriegsmarine, while the two-month land campaign was fought by Norwegian, French, British, and Polish troops against German mountain troops, shipwrecked Kriegsmarine sailors, and German paratroopers (Fallschirmjäger) from the 7th Air Division. Although defeated at sea off Narvik, losing control of the town of Narvik and being pushed back towards the Swedish border, the Germans eventually prevailed because of the Allied evacuation from Norway in June 1940 following the Battle of France.

Narvik provided an ice-free harbour in the North Atlantic for iron ore transported by rail from Kiruna in Sweden. Both sides in the war had an interest in securing this iron supply for themselves and denying it to the enemy, thereby setting the stage for one of the biggest battles since the Invasion of Poland.

Prior to the German invasion, British forces had considered Narvik as a possible landing point for an expedition to help Finland in the Winter War. Such an expedition also had the potential of taking control of the Swedish mines and opening up the Baltic for the Allies.

German invasion
On 1 March 1940, Adolf Hitler ordered the invasion of Norway, codenamed Operation Weserübung as a preventive manoeuvre against a planned, and openly discussed, Franco-British occupation of Norway. This operation would involve most of the Kriegsmarine. Participating units were divided into five groups, which were to occupy six of the main Norwegian ports.

Group I departed Bremerhaven on 6 April. It consisted of 10 German destroyers of the 1934A and 1936 classes Georg Thiele, Wolfgang Zenker, Bernd von Arnim, Erich Giese, Erich Koellner, Diether von Roeder, Hans Lüdemann, Hermann Künne, Wilhelm Heidkamp (flagship) and Anton Schmitt, commanded by Kommodore Friedrich Bonte. Each of the warships carried around 200 soldiers (a total of 1,900 mountain troops (Gebirgsjäger) from the 139th Mountain Regiment (Gebirgsjägerregiment) of the 3rd Mountain Division commanded by General Eduard Dietl). The troop-carrying destroyers were escorted most of the way by the battlecruisers GERMAN BATTLESHIP Scharnhorst and GERMAN BATTLESHIP Gneisenau.

In the early morning of 9 April, the destroyers of Group I passed the Vestfjorden and arrived at the Ofotfjorden leading to Narvik, in fog and heavy snow. In Ofotfjord, they captured three Norwegian patrol boats (Senja, Michael Sars and Kelt). Before capture Kelt managed to send a message to the coastal defence ship HNoMS Norge, alerting the local Norwegian naval commander of the incoming vessels. The German ships Wolfgang Zenker, Erich Koellner and Hermann Künne landed their soldiers in Herjangsfjord (a northern branch of Ofotfjorden) in order to capture a Norwegian regimental supply base at Elvegårdsmoen. Hans Ludemann and Hermann Künne also landed their troops in order to engage the nearby Norwegian forts (which turned out to be non-existent). Diether von Roeder remained in Ofotfjord in order to ensure German control of the sea. Erich Giese was delayed by engine trouble and did not join the main force for some time.

The main defence of Narvik were the old coastal defence ships Eidsvold and her sister ship Norge. Having been alerted by Kelt, both Norwegian ships prepared for combat: the guns were loaded and life preservers issued to the crew. Around 04:15, the Germans spotted Eidsvold, and Eidsvold immediately signalled the leading German destroyer with an aldis lamp. When the Germans failed to respond to the signal, a warning shot was fired across their bow.

The Germans had orders to occupy Norway peacefully if at all possible, so the German flagship Wilhelm Heidkamp stopped and signalled that it would send an officer to negotiate. A small launch ferried Korvettenkapitän Gerlach over to Eidsvold. Gerlach was taken to the bridge to speak to Captain Odd Isaachsen Willoch.

Gerlach tried to convince Willoch that the Germans had arrived as friends, but that the Norwegians had to hand over their warships to the German armed forces. Captain Willoch asked for time to consult his commander, Captain Per Askim, the commander of Norge. This request was refused by the Germans, but while Willoch had been talking to the German officer, the radio officer on board Eidsvold had communicated the events to Askim. Askim's response to the German demands and order to Willoch came immediately; Willoch and Eidsvold was to open fire. Willoch responded to Askim; "I am attacking." While this was going on, the German destroyer Wilhelm Heidkamp had positioned herself 700 m off the port side of Eidsvold and trained her torpedo launchers on the Norwegian ship.

Gerlach tried once again to convince Willoch to surrender, but Willoch refused. As Gerlach left Eidsvold, he fired a red flare, indicating that the Norwegians intended to fight. At this point, Captain Willoch shouted: "På plass ved kanonene. Nå skal vi slåss, gutter!" ("Man the guns. We're going to fight, boys!"). Eidsvold turned towards the closest destroyer and accelerated, closing the distance to Wilhelm Heidkamp to 300 m while the battery commander ordered the port battery (three 15 cm guns) to open fire.

The Germans, afraid that Eidsvold might ram the destroyer, fired four torpedoes from Wilhelm Heidkamp at the old ship. Two of the torpedoes hit before the port guns could fire. The Norwegian ammunition magazine was ignited and Eidsvold was blown in two. The forward part of the ship sank in seconds, the stern followed in minutes, propellers still turning. At around 04:37, she was gone. 175 Norwegian sailors died in the freezing water, including Captain Willoch, with just eight surviving.

Deeper inside the fjord, the explosions were heard aboard Norge, but nothing could be seen until two German destroyers suddenly appeared out of the darkness and Captain Per Askim of Norge gave orders to open fire at 04:45. Four rounds were fired from the 21 cm guns (one from the fore gun and three from the aft) as well as seven or eight rounds from the starboard 15 cm guns, against the German destroyer Bernd von Arnim, at a range of about 800 m. Due to the difficult weather conditions, the guns' optical sights were ineffective: the first salvo fell short of the target and the next ones overshot it.

The German destroyers waited until they were alongside the pier before returning fire. Bernd von Armin opened fire with her 12.7 cm guns as well as with machine guns, but the weather gave the Germans problems as well. The destroyer also fired three salvoes of two torpedoes each. The first two salvoes missed, but the last struck Norge midships and she sank in less than one minute. Ninety of the crew were rescued, but 101 perished in the battle which had lasted less than 20 minutes. The destruction of Norge signalled the end of Norwegian resistance in the port.

Much of the Norwegian garrison at Narvik awoke to the sound of gunfire and were unprepared to face the Germans. Many were surrounded and disarmed as they scrambled to occupy defensive positions. The commander-in-chief of the Narvik area, Colonel Konrad Sundlo, is often cited as the reason for the quick capitulation. Described by Kriegsmarine Admiral Erich Raeder as "an officer with reportedly pro-German feelings", he quickly withdrew from the area following the naval engagement and began negotiations with the Germans. After the initial loss of Narvik, Norwegian general Carl Gustav Fleischer sent out a communiqué, part of which read:

"Colonel Sundlo initiated immediate negotiations for a cease-fire and withdrew the troops to Framnes. The Germans occupied the city and the Norwegian troops were surrounded between the Germans and the sea. The division commander, who was in East Finnmark, was notified about the situation by telephone and he ordered Colonel Sundlo's second in command, Major Omdal, to arrest Colonel Sundlo"

Sundlo was charged with treason for the surrender of Narvik after the war, but these charges were dismissed. Instead he was found guilty of negligence for failing to adequately prepare for Narvik's defence, and on charges of cooperating with the Germans during the occupation.

The morning of the German attack four Norwegian steamers were anchored in Narvik; the Cate B, the  Eldrid, the  Haalegg and the  Saphir. In addition to the Norwegian vessels, four foreign, neutral ships were present; the Dutch steamer Bernisse, and the three Swedish steamships Boden, Oxelösund  and Strassa. As well as neutral ships, the warring parties had vessels at Narvik, riding anchor in the same port. The British had five steamers in the harbour; the Blythmoor, the  Mersington Court, the  North Cornwall, the  Riverton, and the  Romanby. As the German flotilla seized Narvik, there were 11 German merchant steamers at the port town; the Aachen, the  Altona, the  Bockenheim, the  Hein Hoyer, the  Martha Henrich Fisser, the  Neuenfels, the  Odin, the  Lippe, the  Frielinghaus, the  Planet, and the  replenishment oiler/maintenance ship SS Jan Wellem (1935). Jan Wellem, a converted former whale factory ship, awaited the arrival of the German warships, which she was tasked to refuel. Working in the harbour were the Swedish tugs Diana  and Styrbjörn. As the German destroyers entered the harbour, the captain of Bockenheim, who assumed that the intruding warships were British, beached and scuttled his vessel. In total, 25 ore ships had been riding at anchor in Narvik at the outset of the fighting, 10 of which were German.

The German destroyers were now short of fuel and had only one fuel tanker in support, the ex-whale factory ship Jan Wellem that had been despatched to Narvik, according to some sources from the secret German naval base Basis Nord at Zapadnaya Litsa in the Soviet Union, where she had been based since 4 February 1940. Another source indicates that she departed Murmansk in the evening of the 6 April and that Basis Nord was never even established. She had arrived off Narvik from the north on 8 April, and had been stopped by the Norwegian patrol boat Kvitøy. Jan Wellem was allowed entry to Narvik by the regional Norwegian naval command, where she was inspected. Her captain claimed that she was carrying 8500 ST of fuel oil and 8,098 crates of food provisions and that she was on her way to Germany. A second tanker, the Kattegat which had sailed to Norway from Wilhelmshaven, had been sunk in the Glomfjord in the evening of 9 April. Kattegat had been stopped by the Norwegian fishery protection ship HNoMS Nordkapp, the Norwegian ship first trying to take the tanker as a prize, but due to the large German crew could not control it all the way to Bodø, in the end sinking Kattegat by firing four 47 mm rounds into the tanker's water line.

Kattegat had been delayed from reaching Narvik in time by the British 8 April mining operations off Norway (Operation Wilfred). A third tanker—Skagerrak—had also been despatched to Norway, in support of the German landings at Trondheim, but she was intercepted by the British cruiser HMS Suffolk (55), on 14 April, after she had been redirected by German naval command to a waiting position at sea. When the British warship tried to board Skagerrak her crew scuttled her at 68.25°N, 2°W. Both Kattegat and Skagerrak, which were sister ships, were inspected at Kopervik by the Norwegian torpedo boat HNOMS Stegg (1921), on 5 and 7 April respectively. The captain of Kattegat told the Norwegians that he was headed to Narvik for further orders, and the captain of Skagerrak claimed Murmansk as their destination, and inspections revealed that both tankers had a full load of fuel oil. Skagerrak also carried 165 ST of food provisions, which was claimed as supplies for German merchant ships. The food crates were labelled "Wehrmacht". According to the German plan the destroyers were supposed to have been refuelled by two tankers, Kattegat and Jan Wellem, each receiving some 600 ST of fuel oil.

The flotilla was then to be on its way back to Germany by the evening of 9 April. The plan failed because only Jan Wellem made it to Narvik. Refuelling with just one tanker was difficult; only two destroyers could be refuelled simultaneously, taking seven or eight hours. At arrival in Narvik, the destroyers were almost out of fuel. Making the refuelling more challenging was the fact that Jan Wellem had only improvised refuelling arrangements and inferior pumping equipment. While two destroyers were being refuelled at a time, a third was on guard in fjord, the remaining seven being spread around in the nearby area. By 04:00 on 10 April, Jan Wellem had managed to fully refuel three of the German destroyers, and was in the process of refuelling two more.

In the meantime, British forces had tried to engage the Kriegsmarine, but for the most part, unsuccessfully. On 8 April, the British G-class destroyer HMS Glowworm (H92) engaged the heavy cruiser GERMAN CRUISER Admiral Hipper and two destroyers, and was lost, ramming and damaging Hipper in the battle. On the 9 April morning, the British battlecruiser HMS Renown (1916) exchanged artillery salvos with the German battleships Scharnhorst and Gneisenau, which were screening the destroyers. During the battle one of the artillery shells from Renown damaged the fire control system on Gneisenau, the British battlecruiser was also hit two times and slightly damaged. After that the German battleships withdrew from the battle at high speed. The destroyers' main mission had been completed, however, as they had succeeded in landing the invasion force.

First naval Battle of Narvik
The day after the German invasion, the Royal Navy took an opportunity to defeat the Kriegsmarine. The 2nd Destroyer Flotilla—under Commodore Bernard Warburton-Lee and comprising five H-class destroyers (HMS Hardy (H87) (flagship), HMS Hotspur (H01), HMS Havock (H43), HMS Hunter (H35) and HMS Hostile (H55)—moved up the fjord in the early morning. The German destroyers Hermann Künne and Hans Lüdemann were anchored alongside the tanker Jan Wellem and refuelling when the British destroyer attack began at 04:30. The German picket ship (Diether von Roeder) had left its post to refuel, and as the British flotilla approached Narvik, they surprised and engaged a German force at the entrance to the harbour and sank the two destroyers Wilhelm Heidkamp (killing Commodore Bonte) and Anton Schmitt, heavily damaged Diether von Roeder and inflicted lesser damage on two others. They also exchanged fire with German invasion troops ashore but did not have a landing force aboard and therefore turned to leave. Before the destroyers left the scene, Hostile fired her torpedoes at the merchant ships in the harbour. In total, eleven merchant ships (six German, one British, two Swedish and two Norwegian) were sunk during the British sortie into the harbour.

The British flotilla was then engaged by three more German destroyers (Wolfgang Zenker, Erich Koellner and Erich Giese) emerging from the Herjangsfjord, led by Commander Erich Bey and then two more (Georg Thiele and Bernd von Arnim) coming from Ballangen Bay, under Commander Fritz Berger. In the ensuing battle, two British destroyers were lost: the flotilla leader HMS Hardy, which was beached in flames and HMS Hunter, which was torpedoed and sunk. A third—HMS Hotspur—was also damaged badly by a torpedo. Hotspur and the remaining British destroyers left the battlefield, damaging Georg Thiele as they did so. The German destroyers—now short of fuel and ammunition—did not pursue and the British ships were able to sink the ammunition supply ship SS Rauenfels (1928) which they encountered on their way out of the fjord. Soon, the German naval forces were blocked in by British reinforcements, including the cruiser HMS Penelope (97). During the night of 11–12 April, while manoeuvring in Narvik harbour, Erich Koellner and Wolfgang Zenker ran aground. Wolfgang Zenker damaged her propellers and was restricted to a speed of 20 kn. Erich Koellner was much more badly damaged, so the Germans planned—when she was repaired enough to move—to moor her at Tårstad in the same capacity as Diether von Roeder, as an immobile defence battery.

As the British destroyers left the Vestfjorden outside Narvik, two German submarines—GS U-25 (1936) and GS U-51 (1938)—fired torpedoes at them but German torpedoes at the time had severe problems with their magnetic detonator systems—possibly due to the high northern latitude: all of them failed and either did not detonate at all or detonated well before reaching their targets.

Both the German naval commander—Kommodore Friedrich Bonte (on Wilhelm Heidkamp)—and the British commander—Captain Bernard Warburton-Lee (on Hardy)—were killed in the battle. Warburton-Lee was posthumously awarded the Victoria Cross, Bonte the Knight's Cross of the Iron Cross.

Second naval Battle of Narvik
The Royal Navy considered it imperative, for morale and strategic purposes, to defeat the Germans in Narvik, so Vice Admiral William Whitworth was sent with the battleship HMS Warspite (03) and nine destroyers; four Tribal-class (HMS Bedouin (F67), HMS Cossack (F03), Punjabi, and HMS Eskimo (F75)) and five others (HMS Kimberley, HMS Hero (H99), HMS Icarus (D03), Forester and Foxhound), accompanied by aircraft from the aircraft carrier HMS Furious (47). These forces arrived in the Ofotfjord on 13 April to find that the eight remaining German destroyers—now under the command of Fregattenkapitän Erich Bey—were virtually stranded due to lack of fuel and were short of ammunition.

Before the battle, Warspite launched its catapult plane (a float-equipped Fairey Swordfish, L 9767), with the crew ordered to search for German ships and to bomb any targets of opportunity. After spotting and reporting several of the German destroyers, the crew spotted the U-boat GS U-64 (1939), anchored just 50 yards off-shore in the Herjangsfjord near Bjerkvik. The Swordfish attacked and dropped two 100 lb anti-submarine bombs: one was a near-miss, but one hit and sank the submarine. Most of the crew survived and were rescued by German mountain troops. This was the first U-boat sunk by an aircraft during the war and the only instance of an aircraft launched from a battleship sinking a U-boat. In the ensuing battle, three of the German destroyers were sunk by Warspite and her escorts and the other five were scuttled by their crews when they ran out of fuel and ammunition. The first lost was Erich Koellner, which tried to ambush the Allied forces but was spotted by Warspite's Swordfish and subsequently torpedoed and shelled by the destroyers and battleship. The destroyer's commander, Alfred Schulze-Hinrichs, and the surviving members of his crew, were captured by Norwegian forces. Then Wolfgang Zenker, Bernd von Arnim, Hans Ludemann and Hermann Künne engaged the British forces but only managed to lightly damage HMS Bedouin and Wolfgang Zenker tried to torpedo Warspite.

The British launched a force of ten Swordfish from Furious to attack the German destroyers with 250lb bombs. They scored no hits and two aircraft were shot-down; the crew of one were lost, the crew of the other were picked up by Punjabi after making a forced-landing on the shore.

Finally, when the German destroyers were low on ammunition, they retreated, except for Hermann Künne, which had not received the order. Hermann Künne was fired upon by the pursuing HMS Eskimo, but she took no hits. Out of ammunition but undamaged, Hermann Künne was scuttled by her crew in Trollvika in the Herjangsfjord. After scuttling the ship, the crew placed demolition depth charges on the ship, attempting to sink her in Trollvika's shallow waters. Eskimo, still in hot pursuit, launched a torpedo which hit Hermann Künne, setting her on fire. Whether the German ship's own depth charges or the torpedo from Eskimo was the source of the explosion is unclear. Eskimo was in turn ambushed by Georg Thiele and Hans Ludemann, losing her bow but surviving. Diether von Roeder and Erich Giese, both suffering engine problems, fired upon the British forces while still docked, damaging Punjabi and Cossack but they were both sunk before they could cause further damage. That was the last German counter-attack.

Shore batteries and installations were also very badly damaged by Warspite's guns. On the Allied side, the damage to HMS Eskimo kept her in Norway until 31 May 1940. German submarines again suffered torpedo failures, when GS U-46 (1938) and GS U-48 (1939) fired at the departing Warspite on 14 April.

The remaining German destroyers (Wolfgang Zenker, Georg Thiele, Bernd von Arnim and Hans Lüdemann) retreated into Rombaksfjord and were scuttled soon after. The only German ship which survived within the port area was the submarine U-51.

The Germans lost over 1,000 men, a U-boat, and eight destroyers. With the losses from the previous battle this constituted 50% of the Kriegsmarine's destroyer strength.

It was reported by the Germans that shipwrecked Germans from Erich Giese were fired upon by British artillery and machine guns during the engagement.

About 2,600 survivors were organised into an improvised marine infantry unit, the Gebirgsmarine and fought with the 139. Gebirgsjägerregiment in the subsequent land battle. Although unsuited for combat in the mountainous terrain around Narvik, the shipwrecked sailors manned the two 10.5 cm FlaK guns and the 11 light anti-aircraft guns salvaged from the ships sunk during the naval battles and conducted defensive operations. The sailors were armed from the stocks captured at the Norwegian army base Elvegårdsmoen, more than 8,000 Krag-Jørgensen rifles and 315 machine guns intended for the mobilisation of Norwegian army units in the Narvik area.

Later naval operations
After the naval battles of Narvik, the port and its surroundings remained in German hands, as no Allied forces were available to be landed there. Naval operations were limited at this stage to shore bombardment, as Narvik was not a primary Allied objective.

Among others, the Polish destroyers Grom, Burza and Błyskawica took part in these operations, during which Grom was sunk by German aircraft on 4 May 1940, with the loss of 59 sailors.

Land battle

During the Norwegian Campaign, Narvik and its surrounding area saw significant fighting, initially from 9 April between German and Norwegian forces, subsequently between Allied and German forces, conducted by the Norwegian 6th Division of the Norwegian Army as well as by an Allied expeditionary corps until 9 June 1940. Unlike the campaign in southern Norway, the Allied troops in Narvik would eventually outnumber the Norwegian troops. Five nations participated in the fighting. From 5–10 May, the fighting in the Narvik area was the only active theatre of land war in the Second World War.

At the outset, the position of the German commander—Dietl—was not good: his 2,000 troops were outnumbered. After the German destroyers had been sunk, however, about 2,600 German sailors joined in the land battle. Another 290 German specialists travelled via Sweden posing as health care workers. During the last three to four weeks, the Germans were also reinforced by about 1,000 men air dropped over Bjørnfjell, thus bringing the total number of Germans to around 5,600. Their position and outlook changed from good to dire several times. On occasions, the entire operation was controlled directly from the German High Command in Berlin; Hitler's mood was reportedly swinging heavily and he repeatedly contemplated withdrawal. Intelligence agents captured later in the war also stated that Dietl himself had been considering crossing the Swedish frontier with his troops to be interned, until the German agent Marina Lee infiltrated Auchinleck's headquarters at Tromsø and obtained the British battle plan; however, the accuracy of this allegation has been questioned. The Norwegian force—under General Carl Gustav Fleischer—eventually reached 8,000–10,000 men after a few weeks. The total number of Allied troops in the campaign—in and around Narvik—reached 24,500 men.

The early phase of the invasion was marked by the German advantage of surprise. Norwegian troops in northern Norway had been called out on a three-month neutrality watch during the winter of 1939/1940, and so they had trained together. From 9–25 April, the Norwegian forces suffered three catastrophes. First, the forces protecting Narvik were unable to resist the Germans due to the commanding officer—the later NS Hird commander Colonel Konrad Sundlo—refusing to fight the invaders; second, around 200 soldiers from the Narvik garrison who had escaped capture and were blocking the railway to Sweden were caught by surprise while resting at Bjørnfjell, most of the men being captured; third, I/IR12 (1st battalion of Infantry Regiment 12) sent to hold Gratangsbotn was attacked by surprise while in camp, suffering casualties that ruined its spirit and effectively knocked it out of the remainder of the campaign.

From Denmark, a battalion-sized detachment of the Luftwaffe's Regiment General Göring, commanded by Hauptmann Kluge was sent by sea to Oslo, in April, being engaged alongside the Army first in the advance to Trondheim, then north up into the Arctic Circle to take the port of Bodø and relieve the pressure on the beleaguered élite Gebirgsjäger further north at Narvik.

Due to mounting Norwegian pressure and difficulties with bringing up supplies to the forward lying troops, the Germans abandoned Gratangsbotn and withdrew from the hill Lapphaugen and the valley Gratangsdalen, following the Battle of Gratangen. In the beginning of May, the Norwegians started an advance southwards towards Narvik. Once it became clear that the Allies would mount the main invasion of Narvik itself in mid-May, the Norwegian direction altered towards Bjørnfjell. The British arrived first and set up headquarters in Harstad on 14 April. In the following days, three battalions were deployed mainly at Sjøvegan, Skånland (where a naval base was established) and at Bogen. Later, they were deployed south of Ofotfjord, at Ballangen and Håkvik. The initial British detachment was reinforced on 28 April by a French expeditionary force (Corps expéditionnaire français en Scandinavie, CEFS), led by General Antoine Béthouart and composed of mountain troops. Three battalions of Alpine troops and two battalions of 13th Demi-Brigade of the Foreign Legion were deployed both north and south of the Ofotfjord, but later, the north would be the main French area of operation. Four Polish battalions arrived on 9 May. They were first deployed north of the Ofotfjord, but later redeployed to the area south of the fjord. In early June they were formed into the Polish Podhale Independent Highland Brigade under General Zygmunt Bohusz-Szyszko and part of CEFS. In addition, the Allies had difficulty in deciding how best to retake Narvik and the iron ore railway. There was no unified command for the troops facing the Germans at Narvik: the Norwegians and the Allies retained separate commanders and cooperation between them was not always smooth. Even within the British forces, the Army and Navy commanders—Major-General Pierse J. Mackesy and Admiral of the Fleet William Boyle, Lord Cork—had difficulty cooperating: Cork advocated a swift and direct attack from the sea while Mackesy advocated a cautious approach from both sides of the Ofotfjord. Consequent to this, on 21 April, Lord Cork was given supreme command of all Allied forces.

In the second week of May, the Norwegian advances against the Germans east of Gratangseidet were the most significant movements on the Narvik front. In addition, on the Norwegians' right flank French alpine troops advanced up the Laberg valley, supported by a company of Norwegian ski troops. In the south, the Allies did not have much success, and in the north of the Ofotfjord, they were not making any progress. The Norwegians continued their successful mountain campaign, and in mid-May the Allies took the initiative and achieved significant victories. Both Paris and London had been growing impatient with the slow progress in Narvik, and the French commander—Béthouart—had pressed for more action.

The cautious approach on land was abandoned and an amphibious attack was launched at around midnight on 12 May. This was directed at Bjerkvik and was preceded by a naval bombardment from British warships in Herjangsfjord. Then landing craft put ashore French Foreign Legionnaires, supported by five French Hotchkiss H39 light tanks of the 342e CACC (Compagnie Autonome de Chars de Combat/ Independent Tank Company), which successfully attacked Bjerkvik, the Elvegårdsmoen army camp and advanced northeast to where the Germans were withdrawing and south along the east side of Herjangsfjord. The plan also required Polish troops to advance toward Bjerkvik from land on the west side of the fjord, but heavy terrain delayed them and they did not arrive before Bjerkvik was taken. It had also been part of the plan for French and Norwegian troops to advance from the north in order to box the Germans in, but cooperation problems between the Norwegian and French commanders left a gap through which the Germans escaped. Despite this, the Allies had a clear path north of Narvik and planned to attack over Rombaksfjord.

It had been anticipated in London that as the buildup of troops in Narvik slowly continued, a corps headquarters would be needed to exercise effective control. On 11 May, Lieutenant-General Claude Auchinleck arrived in Narvik, and on 13 May assumed leadership of the Allied land and air forces (under Lord Cork's overall command), which at this time was designated the North-Western Expeditionary Force. It was clear to the Allies that once Narvik was captured, its long-term retention would depend on permanently holding the town of Bodø to the south in Nordland which was on the route of the German advance from Trondheim. Consequently, Auchinleck redeployed all British troops to concentrate on this southern enterprise, and appointed French Brigadier-General Béthouart—an expert in both mountain and winter warfare—to command the French and Polish troops, which would be responsible for operations in the Narvik area in conjunction with Norwegian forces.

Again, the attack was stalled while the Allies waited for air support to be fully established from Bardufoss. At 23:40 on 27 May, a naval bombardment commenced from the north. Two French and one Norwegian battalions would be transported across the Rombaksfjord and advance on Narvik from the north. In the south, the Polish battalions would advance toward Ankenes and inner Beisfjord. The maximum capacity of the landing barges was 290 men, and these troops could not be reinforced for 45 minutes. These first troops were able to get a foothold on Ornes by the time the rest of the French and the Norwegians were landed. The French moved west toward the city and east along the railway. The Norwegians moved toward Taraldsvik mountain, circled around and moved down toward the city. The German commander decided to evacuate before 07:00 and retired along Beisfjord. This was the first major Allied victory on land.

Operation Alphabet

It seemed now that it was only a matter of time before the Germans would have to surrender. They were pushed from the north by the Norwegians, from the west by the French and from the southwest by the Poles. It appeared that Bjørnfjell would be the Germans' last stand, but events elsewhere in Europe came to their rescue. London had already secretly decided to evacuate on 24 May and that became apparent in the following days. On the night of 24/25 May, Lord Cork received orders to retreat, but under cover so the Germans would be prevented from interfering. The Allied commanders agreed that an attack on Narvik would disguise the retreat and allow the destruction of the iron ore harbour.

The Norwegian government and commanders were first told in early June and the news was met with disbelief and bitterness. The Norwegians still hoped to defeat the Germans alone and, as late as 5 June, one of the two Norwegian brigades was ordered to attack. The Norwegian government also explored the possibility of creating a neutral, but free Northern Norway. This plan proved futile, and on 7 June the King and government were evacuated to Britain. All Allied troops were evacuated from Narvik between 4 and 8 June.

Three Polish passenger ships, MS Sobieski, Batory and Chrobry, took part in the evacuation operation. Chrobry was sunk on 14–15 May by German bombers. On 8 June, General Dietl retook Narvik, and on 10 June the last Norwegian forces in Norway surrendered.

Operation Juno
On 7 June, the British aircraft carrier HMS Glorious (77) had taken on board 10 Gloster Gladiators and eight Hawker Hurricanes from 46 Squadron and 263 Squadron Royal Air Force (RAF). These were flown off from land bases to keep them from being destroyed in the evacuation. Glorious left a larger convoy to proceed independently. The next day, while sailing through the Norwegian Sea to return to Scapa Flow, the carrier and her escorts—the destroyers HMS Acasta (H09) and HMS Ardent (H41)—were intercepted by the German battlecruisers GERMAN BATTLESHIP Scharnhorst and GERMAN BATTLESHIP Gneisenau. The carrier and her escorts were sunk with the loss of more than 1,500 men. Scharnhorst was badly damaged by a torpedo from Acasta and both German vessels were hit by a number of medium shells. The damage to the German ships was sufficient to cause the Germans to retire to Trondheim, which allowed the safe passage of the evacuation convoy through the area later that day.

Aftermath
The British had drafted plans to land in Narvik before the German invasion; troops and supplies had been loaded onto ships when they executed their mining operation on 8 April. These had been hastily unloaded when German ships were spotted northbound because the British thought that the German ships were trying to break into the Atlantic to avoid being trapped in German ports and wanted all their ships available to intercept the German fleet. The confusion dogged the troops for weeks, men and equipment were shipped to Norway separately without clear landing sites and orders were changed while en route. It became apparent that the Allies were confused by the many small and large fjords and bays and could not decide where it would be best to start; British, French and Polish units rapidly relieved each other which added to the lack of local knowledge.

The cold and snow was a common enemy for all troops at Narvik but most of the Allies were poorly prepared for it. The Norwegians were the only ones fully equipped with skis and able to use them. The British tried skis but their troops were largely untrained and supply was scarce. German sailors faced the same problems, even within the Gebirgsjäger (mountain troops) and French mountain specialists, only a few units were equipped with skis and the Polish mountain brigade had no mountain training.

Most troops were untested in battle. The Gebirgsjäger had participated in the invasion of Poland and some of the troops that had been air dropped over Bjørnfjell had fought in the Netherlands. Some of the French Foreign Legionnaires came directly from fighting in North Africa and most of the Polish officers and many of the soldiers had participated in the defence of Poland, some even in the Spanish Civil War and were highly motivated.

The Allies had sea and air superiority until the very last stage of the operation, but did not take full advantage. The Germans lost the naval battle, but achieved the main goal of their operation: the successful Operation Weserübung and occupation of Norway. Around Narvik, German naval losses were high: they lost 10 destroyers (50 percent of their entire destroyer force), one submarine, and several support ships. In exchange, they sank one aircraft carrier, four Allied destroyers and damaged several others. The reason for their defeat lay in the German plans, which made it impossible for their destroyers to retire quickly, even if they had had adequate supplies. This was compounded by the design of German destroyers: despite their relatively large size and armament, they had inadequate fuel and ammunition storage. The British forces achieved an indisputable local naval victory but were unprepared to follow it up with any land operation. This allowed the Germans to consolidate their foothold in Norway and made the subsequent Allied counter-invasion more difficult.

Post-war
In 1964, a war museum opened in Narvik; since 2016, the collections have been displayed in the Narvik War Museum—located inside the Narvik War and Peace Centre.

Parts of the bow of the German destroyer Georg Thiele remain visible above the water in Rombaksbotn to this day. The wrecks at Narvik remain popular diving spots, although some are off-limits because they still contain undetonated ammunition. Three of the German destroyers were raised in 1964 and moved to Framnesodden, near Eidsvoid, to clear the shipping lane. The destroyers Anton Schmitt, Diether von Roeder, and Wilhelm Heidkamp rest in 12 m of water there and were opened for diving. A number of other wrecks are also accessible, but most have been preserved as historic sites and it is forbidden to dive to them.

Medals
At least 1,200 French, British, and Polish participants in the battle were awarded the Norwegian War Cross for their contribution to the battle. Among the Norwegians who took part in the battle, only the top two military leaders were awarded the medal. Norwegian media has complained about this limited award.

All German forces (8,577 military personnel) who partook in the battles of Narvik were awarded with the Narvik Shield.

title: Battles of Narvik