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Fighting new nuclear power stations in the UK
EDF is Eagerly Destroying Fields even though it doesn’t yet have permission to build the reactors - nor does it have approval for the reactor design, or even a final investment decision.
The new EPR reactor design will produce radioactive waste that is so toxic that it will have to be stored on site for over 100 years. The dangers associated with flooding, terrorist attack and accidental leakage are totally unacceptable.
NO MORE NUCLEAR BAILOUTS
The movement against the government's so-called 'nuclear renaissance' is winning….but we must keep up the pressure. Out of the eight new nuclear power stations supported by the coalition government when it came into power, only two are still on the table: Hinkley in Somerset and Sizewell in Suffolk.
French-owned EDF Energy - the owner of Hinkley and Sizewell - is pressuring the government to increase the range of hidden subsidies on offer in a desperate bid to attract interest from sceptical investors. THIS MUST NOT HAPPEN.
If EDF gets its way, it will be a double whammy for us - and for future generations. It will mean we pay twice: once as taxpayers and once as consumers through our energy bills.
We say put the £60bn earmarked for 'new nuclear' into a cleaner, greener, fairer future. The way forward is through energy reduction and greater investment into research and development to make renewable energy and energy storage fit for the 21st century.
We need to create a long term sustainable energy plan that is based on meeting people's needs rather than making profits for investors. In May, energy secretary Charles Hendry told ministers at a select committee hearing that the government’s energy policy would be robust enough without including nuclear in the mix. It's time we moved energy policy forwards rather than backwards.
NUCLEAR IS NOT THE ANSWER
....Chernobyl
The crisis is far from over: the sarcophagus covering the doomed Russian reactor is falling apart. Only this year, governments finally approved the funding for a new one. The human population in the most heavily contaminated territories is in decline. In Belarus 80% of children were born healthy before Chernobyl. Now, just 26 years later, only 20% of children are born healthy.
.....Fukushima
Thanks to people power, all of Japan's reactors have now been turned off. For the first time in over half a century Japan is nuclear free. However, the crisis at Fukushima is far from over.
The Japanese people are footing the bill. The company behind the power station, Tepco, has had to be re-nationalised because of the spiralling cost of compensation and the ongoing attempts to stabilise the reactors.
Many people are still living in heavily contaminated areas that should have been evacuated.
Food across Japan is heavily contaminated and people are being encouraged to support the farmers of Fukushima by eating it.
The triple meltdown is still in full swing.
All of the fuel pools in reactors 1,2,3 & 4 are in bad condition.
The pool in reactor 4 is of particular concern. Thousands of highly radioactive spent fuel rods are at risk of further explosions. If such an event occurs, high levels of radioactive contamination could spread as far as Tokyo and wipe out Japan's commercial infrastructure.
WE WANT A FUTURE, NOT A DISASTER
More information coming soon.
Subscribe to our newsletter and get regular updates on the latest developments in the campaign against 'new nuclear'. Please send any queries to: campaign@stopnewnuclear.org.uk
What's New
Apologies for the delay but the flyer for the action weekend and mass trespass is now available to download/print. Please spread far and wide! Please use the attachment below as this contains both the front and back pages of the flyer.
EDF is Eagerly Destroying Fields even though it doesn’t yet have permission to build the reactors - nor does it have approval for the reactor design, or even a final investment decision.
The new EPR reactor design will produce radioactive waste that is so toxic that it will have to be stored on site for over 100 years. The dangers associated with flooding, terrorist attack and accidental leakage are totally unacceptable.
Hello everyone,
Just a quick run down of coming events and an update on whats happening at the nuclear sites.
First the good news:
Plans for a third nuclear power station at Heysham in Lancashire have been put on ice. French company EDF Energy has cancelled an agreement with the National Grid to set up any new connection to the grid from Heysham.
this is only a brief and quick newsletter to say "Thank you!" to everyone who came to Hinkley last weekend, and helped to make our action a huge success. On Saturday, more than 1,000 protesters joined our commemoration of Fukushima, and demanded an end to plans for new nuclear power stations in Britain (and elsewhere). About 100 stayed on for the first ever 24 hour blockade of a nuclear power station in Britain. We all did it!
Visit Stop New Nuclear on Facebook
Stop New Nuclear is a campaign to stop new nuclear power stations and is an alliance of Campaign for Nuclear Disarmament, CND Cymru, Stop Nuclear Power Network UK, Kick Nuclear, South West Against Nuclear, Shutdown Sizewell, Sizewell Blockaders, Trident Ploughshares, Stop Hinkley, and Rising Tide UK | 2024-07-12T01:26:35.434368 | https://example.com/article/4903 |
Civilian abdominal gunshot wounds in Lagos.
This prospective study of 78 patients who sustained abdominal gunshot wounds was performed to evaluate the pattern of injuries, treatment outcome and the role of selective conservative management. Three (3.8%) patients died before laparotomy. Four (5.1%) patients with superficial wounds were managed by local wound care. Fourteen (18%) patients who had equivocal or minimal abdominal signs were selected for conservative management. Laparotomy was performed in 57 (73.1%) patients who presented with an acute abdomen. The commonly injured organs were the small bowel (56.1%), colon (38.6%), liver (22.8%) and stomach (19.3%). Prolonged injury to arrival and surgical intervention time were contributing factors to the high incidence of sepsis (63.2%) and mortality (22.8%) after laparotomy. Two patients selected for conservative management required delayed laparotomy, one of which was negative. A 10-fold increase in prevalence of abdominal gunshot wounds has occurred in our institution in the 1990s. Selective conservative management is feasible without the use of expensive investigations. | 2023-11-02T01:26:35.434368 | https://example.com/article/1826 |
This vendor-written tech primer has been edited by Network World to eliminate product promotion, but readers should note it will likely favor the submitter’s approach.
The amount of data that is being generated on a daily basis is growing rapidly, placing more and more demand on data centers. Not only do we have connected users actively engaged in generating and storing large amounts of content, machines such as autonomous cars and connected planes generate greater amounts of content by orders of magnitude (Figure 1).
Samsung Semiconductor Figure 1: Data Generated Each Day
As there is value in almost any data, it is rarely, if ever, deleted. This leads to increasing demands on storage capacity. The alternatives are hard disk drives (HDDs) and solid state drives (SSDs). HDD capacities have been increasing steadily over time, and have been the mainstream form of storage in the enterprise until now. But last year the capacity of HDDs was surpassed for the first time by SSDs – and because SSDs are scaling at a faster rate than HDDs, we will never look back.
Samsung Semiconductor Figure 2: SSD Densities Scaling Much Faster
SSDs use NAND memory, which has an amazing ability to scale. NAND memory is comprised of storage cells formed on semiconductor material. Improved density was achieved via process geometry shrinks at the die level. However, this method of gaining greater density was nearing its physical limitations based on how closely the memory cells were being squeezed together. Undeterred, the industry introduced a breakthrough in the past three years with the introduction of 3D or vertical NAND. Instead of attempting to squeeze memory cells ever closer together, 3D NAND stacks them vertically on top of each other. This allows SSDs to continue to aggressively scale in capacity for the foreseeable future. Another inflection point took place during the past year – enterprise SSDs became less expensive than 15K HDDs when taking data reduction technologies such as compression and deduplication into account. Compression reduces bits and hence the amount of storage needed for a set amount of data by identifying and eliminating statistical redundancy. This is possible because most real-world data exhibits statistical redundancy. For example, an image may have areas of color that do not change over several pixels. So instead of coding “red pixel, red pixel ...,” the data may be encoded as “100 red pixels.” Deduplication is a special form of data compression that eliminates duplicate copies of repeating data. While compression takes care of repeated substrings inside individual files, deduplication inspects volumes of data to identify large sections (such as entire files) that are identical and stores only a single copy. Storage vendors claim they can achieve approximately a 3x data reduction using SSDs without negatively impacting system performance. The same cannot be said for HDDs due to their inherently slower nature. Therefore, when comparing SSDs and HDDs in a storage array, the relative cost for SSDs is divided by three when taking data reduction technologies into account. SSDs have become more cost-effective than 15K performance HDDs on a per gigabyte basis (Figure 3). This cross-over to SSDs, compared to 10K HDDs, will happen very soon as well. This has triggered a massive transition to flash in the enterprise. SSDs have always had a good value proposition versus HDDs – faster, more reliable and lower power. Adding lower cost and higher density makes the SSD alternative all the more compelling.
Samsung Semiconductor Figure 3: Relative Drive Costs with Data Reduction
Leading vendors recognize the need to offer the densest storage arrays possible and have aggressively designed products that incorporate the latest, high capacity SSDs. At a system level, the benefits of dense SSDs are amplified. For example, the largest HDD available is 10TB in a 3.5” form factor. A maximum of 12 of these drives could be installed in a standard 2U server, providing 120TB capacity. Alternatively, the same server could be equipped with 24 2.5” 16TB SSDs, providing 384TB capacity – or 3x the density. System equipment cost aside, the resources needed to build and operate a data center are considerable. To get a good sense of their significance, consider total cost of ownership (TCO) calculators that estimate the capital and operational expenditures for a given data center. As an example, a modest, tier 3 data center (which supports 99.982% availability) with 10 cabinets of system equipment using SSDs would cost approximately $887,000 of construction and operational costs over three years. The same amount of HDD storage would require a 30-cabinet system (SSDs having 3x the density), resulting in estimated construction and operational costs of $1,423,000. The density benefit alone results in over half a million dollars in savings over 3 years.
Samsung Semiconductor Figure 4: Data Center Build-Out is Expensive
It is clear that storage requirements are growing exponentially, driven by inexhaustible content generators that include human and non-human sources. Great value is being derived from this information stream through data analytics, which requires much of the information to be stored on a faster medium than archival tape. This faster medium is transitioning from HDDs to SSDs. Not only are SSDs higher performing and more reliable, they are now also higher capacity and lower cost than performance HDDs. The density advantage translates to even lower costs when building out and operating data centers that host the storage. Businesses looking for a distinct competitive advantage should waste no time in taking note of this trend. | 2023-10-11T01:26:35.434368 | https://example.com/article/8829 |
Part of NYC goes dark in massive power outage...
Part of NYC goes dark in massive power outage
Part of NYC goes dark in massive power outage
New York power outage: What we know so far
Power is returning after parts of New York City suffered an outage at 6:47 p.m.
Con Edison CEO John McAvoy said about 72,000 customers were affected at the height of the outage.
8th Ave. was closed from 42nd St. to 72nd St.
The cause is being investigated.
Four subway stations lost power, impacting several subway lines.
Several Broadway productions canceled Saturday night's shows, but some actors took to the streets to perform.
Parts of New York City went dark Saturday in a massive power outage that affected 72,000 customers at its height, the CEO of New York City's utility company, Con Edison, said. John McAvoy said the cause was still under investigation, but said it was unlikely to be a manhole fire or an excessive load of power.
The power went out at 6:47 p.m. from West 42nd St. to West 72nd St. and from 5th Ave. west to the Hudson River. Five of the six networks were restored by 10:30 p.m., McAvoy said.
Get Breaking News Delivered to Your Inbox
There were no reported injuries, the New York City Office of Emergency Management said.
New York City Mayor Bill de Blasio, who is campaigning in Iowa as he seeks the 2020 Democratic nomination, said he would be returning to New York City by Sunday morning.
New York City Council Speaker Corey Johnson tweeted that Con Edison's CEO told him there was a "a major disturbance" at West 49th Street Substation.
The New York City Office of Emergency Management activated its emergency operations center. The New York City transit system worked with Con Ed to restore power in affected subway stations. Photos of darkened subway stations were shared on social media.
The Fire Department of New York said it responded to multiple calls of people stuck in elevators.
The CBS Broadcast Center was affected and temporarily turned to generator power. NBC's 30 Rockefeller Plaza also lost power.
Jennifer Lopez was performing at Madison Square Garden when the power went out. The venue was evacuated due to security concerns.
The Millennial Choirs and Orchestras took their performance to the streets outside Carnegie Hall.
A power outage in New York, but it couldn’t stop the Millennial Choirs and Orchestras, creating a makeshift stage right outside Carnegie Hall. #nycblackout pic.twitter.com/fPQJzvTS1t — Ravi Agrawal (@RaviReports) July 14, 2019
Several Broadway shows canceled their Saturday night performances, including Hamilton, Hadestown, Aladdin, Frozen, Ain't Too Proud to Beg and The Cher Show.
Erich Bergen, who is in the Waitress musical, tweeted video of show's stars taking their performance to the street.
Chad Kimball of Come From Away also tweeted those stars were performing.
Coincidentally, Saturday's power outage struck on the 41st anniversary of the 1977 blackout, which lasted until July 14. New York City went dark during the 2003 blackout of the East Coast and again after Superstorm Sandy struck in 2012. | 2024-05-20T01:26:35.434368 | https://example.com/article/9927 |
Surveillance for the identification of cases of acute respiratory infection by enterovirus D68 in children in a tertiary level care hospital during 2014-2016.
The reemergence of enterovirus D68 (EV-D68) infections in the United States was reported from August-October 2014 (691 cases). In Mexico, an outbreak at the National Institute of Respiratory Diseases was reported (24 cases). The results of epidemiological surveillance of Enterovirus sp. (EV) and other respiratory viruses in a national pediatric tertiary care level hospital are presented. Following the alert issued by the reemergence of EV-D68 in 2014, epidemiological surveillance -which only detected respiratory viruses by PCR in patients with influenza-like illness using nasopharyngeal swabs- expanded to include children with asthma exacerbation or acute respiratory distress. Positive samples to EV were confirmed and typed by sequencing. Subsequent sequencing was used to obtain the complete viral genome. Of 1705 samples, 13 were positive to EV. Patients with EV presented the following comorbidities: chronic lung disease (7.7%), neoplastic disease (15.4%), allergic asthma/rhinitis (23%), recurrent pneumonia (23%), and other (23%). Of the 13 samples positive for EV, three were positive for EV-D68. These cases required invasive mechanical ventilation, presented no neurological involvement and survived. The impact of the population studied by EV-D68 was lower than that reported in Mexico during the same period. Cases of EV-D68 infection had multiple comorbidities, but few pulmonary comorbidities, which could explain the low attack rate. The epidemiological surveillance and infection prevention system may have contained the outbreak. | 2024-06-01T01:26:35.434368 | https://example.com/article/9932 |
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100 Ton Marine Travel Lift Parameters Lifting Capacity: 10-1200t
Span: 6.5-25m
Lifting Speed : 0-3m/min
Travelling Speed : 0-40m/min
Provide Custom Option Get a Free Quote
Features Fully electric remote control choice UV protected hoses Choice of height and width Very low maintenance winch and trolley devices Choice of steering options A reliable safety protection system Advantages Advanced technology and professional engineers ensure top quality A strict quality inspection system, stable performance Excellent design, simple structure, easy to install, operate, transport and maintain Durable material, long service life Powerful production capacity, convenient transportation condition, fast delivery time Customers first, perfect service system, excellent after-sales services International marine travel lift manufacturer, professional and reliable Affordable and competitive 100-ton travel lift price Parameters Technical Parameter of AQ-MBH Mobile Boat Hoist Capacity t 30 50 75 100 125 150 Span S(m) 6.5 8 9 10.5 11 12.5 Lifting speed m/min 0~1 (full load) 0~1 (full load) 0~1 (full load) 0~1 (full load) 0~1 (full load) 0~1 (full load) m/min 0~3 (non-load) 0~3 (non-load) 0~3 (non-load) 0~3 (non-load) 0~3 (non-load) 0~3 (non-load) Running speed m/min 0~20 (full load) 0~20 (full load) 0~20 (full load) 0~20 (full load) 0~20 (full load) 0~20 (full load) m/min 0~40 (non-load) 0~40 (non-load) 0~40 (non-load) 0~40 (non-load) 0~40 (non-load) 0~40 (non-load) Grade abiliby 4% 4% 4% 4% 4% 4% Capacity t 200 300 400 500 600 700 Span S(m) 13 13.5 15.5 17 18.5 20 Lifting speed m/min 0~1 (full load) 0~1 (full load) 0~1 (full load) 0~1 (full load) 0~1 (full load) 0~1 (full load) m/min 0~2 (non-load) 0~2 (non-load) 0~2 (non-load) 0~2 (non-load) 0~2 (non-load) 0~2 (non-load) Running speed m/min 0~20 (full load) 0~20 (full load) 0~20 (full load) 0~20 (full load) 0~20 (full load) 0~20 (full load) m/min 0~40 (non-load) 0~35 (non-load) 0~35 (non-load) 0~35 (non-load) 0~35 (non-load) 0~35 (non-load) Grade abiliby 4% 4% 4% 4% 4% 4% Capacity t 800 1000 1200 Span S(m) 15.5 18.5 25 Lifting speed m/min 0~1 (full load) 0~1 (full load) 0~1 (full load) m/min 0~2 (non-load) 0~2 (non-load) 0~2 (non-load) Running speed m/min 0~20 (full load) 0~20 (full load) 0~20 (full load) m/min 0~40 (non-load) 0~30 (non-load) 0~30 (non-load) Grade abiliby 4% 4% 4%
100 Ton Travel Lift for Sale
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Get a Free Quote
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| 2024-03-10T01:26:35.434368 | https://example.com/article/2103 |
ETHLend est une application décentralisée sur la blockchain de l’Ethereum permettant d’effectuer des prêts entre particuliers de façon sécurisée et transparente.
C’est un moyen efficace pour les emprunteurs d’accéder à des financements à l’échelle mondiale et pour les prêteurs de financer des demandes de prêts à travers le monde.
ETHLend décentralise la finance
Grâce à la blockchain de l’Ethereum, ETHLend décentralise la finance pour créer un marché mondial du crédit. Ainsi, un emprunteur au Brésil n’est pas limité aux prêteurs locaux et aux banques brésiliennes, il peut en effet accéder à des financements venant d’Asie, d’Amérique du Nord ou d’ailleurs.
Cela signifie pour les prêteurs davantage de possibilités d’investissement. ETHLend permet donc l’internationalisation du marché du crédit ainsi qu’un accès plus rapide à celui ci par rapport à l’utilisation du système bancaire. Les transactions sont effectuées en quelques secondes ou minutes comparés aux jours d’attente que l’on rencontre dans le système bancaire traditionnel.
Par ailleurs, en offrant plus de liquidités au niveau local ETHLend favorise la compétition sur les taux d’intérêts et grâce à l’utilisation de cryptomonnaies, il n’est pas nécessaire d’avoir un compte en banque pour obtenir un prêt.
Les atouts de la start-up ? Désintermédiation, transparence et sécurité
Lorsqu’un préteur décide de financer une demande de prêt, ces derniers se mettent d’accord sur une prime de risque ou un taux d’intérêt. Une fois l’accord établi et validé par les deux parties, il devient un « Smart Contract » ; un contrat auto-exécutant correspondant à des lignes de code inviolables au sein de la blockchain.
Ainsi les institutions bancaires, qui servent aujourd’hui de tiers de confiance, n’ont plus d’utilité lors de telles transactions. Par ailleurs, l’ensemble des transactions effectuées sur ETHLend est consultable à l’aide de n’importe quel explorateur de blockchain. (Par exemple http://etherscan.io/ )
Auparavant, il était impossible d’avoir une garantie que l’emprunteur rembourserait un prêt en cryptomonnaie. ETHLend a trouvé la solution pour sécuriser les prêts en utilisant des tokens compatibles ERC-20 qui peuvent représenter presque n’importe quelle valeur, entre autres l’or (DigixDAO), le baril de Brent (Bilur) ou des propriétés immobilières (REXmls).
Toutes les données des opérations de prêt sont stockées sur la blockchain Ethereum. Par conséquent elles ne peuvent pas être falsifiées. Le collatéral est détenu par le contrat auto-exécutant, ce qui signifie que même ETHLend n’est pas en capacité de déplacer ces tokens une fois envoyés au contrat auto-exécutant. Les collatéraux mis par l’emprunteur sont ainsi bloqués dans le contrat et ne seront débloqués qu’une fois que les conditions choisis seront rencontrées.
Leur but ? Que chacun puisse avoir accès au même marché du crédit
Aujourd’hui ETHLend est constitué d’une équipe de 18 personnes aux compétences complémentaires ainsi que de conseillers locaux à travers le monde. Nous sommes à Hong Kong, en Uruguay, en Inde, en Indonésie, en Finlande, en Corée, en Australie mais également à San Francisco, New York ou encore Paris.
Être avant tout une entreprise décentralisée, nous permet d’avancer plus vite dans la création de ce marché mondial du crédit entre particuliers. En effet, en participant à de nombreux Meet Up avec la communauté Ethereum dans l’ensemble des pays dans lesquels nous sommes présents, nous profitons de feedback permanent ainsi que d’une diversité de point de vue que nous aurions très difficilement pu avoir autrement.
En ce qui concerne notre développement, nous venons d’ajouter un système de réputation, un « credit score » décentralisé. En 2018, il sera possible d’obtenir des prêts dans d’autres cryptomonnaies telles que le Bitcoin ou le Litecoin. Le reste de nos fonctionnalités à venir est à découvrir dans notre livre blanc. Par ailleurs certains pays comme la Suède ou le Japon ont entrepris de créer un registre des propriétés immobilières sur la blockchain, ces systèmes dit de « tokenization » permettront notamment de placer une propriété représentée par un token sur la blockchain en collatéral pour obtenir un prêt en cryptomonnaie.
La multiplication de systèmes décentralisés et transparents est une opportunité pour les entrepreneurs des pays peu bancarisés, où les taux d’intérêt sont généralement très élevés et, où aujourd’hui le micro crédit est plus un frein qu’une opportunité.
Notre but est que chacun puisse avoir accès au même marché du crédit, et que les taux d’intérêt et prime de risque soient décidé individuellement, au cas par cas entre le prêteur et l’emprunteur. Plutôt que limités par des frontières et imposés par des banques centrales. | 2023-10-28T01:26:35.434368 | https://example.com/article/1916 |
Q:
AIS and RTL-SDR Dongles
I am looking for an Windows-based AIS Decoder for RTL Dongles. Currently, there is a solution available using GNU Radio and SDR# but it is complicated to set up and keep running.
ADSB has a dedicated solution called RTL1090 that connects directly to the RTL-Sdr stick and decodes the ADSB messages in one application.
Does anyone know of a project like this for AIS Ship Tracking?
A:
You could check out ShipPlotter which appears to be a windows-based AIS receiver. It mentions in the webpage that it accepts audio through your sound card. In the case of RTL-SDR, you'll want to use something like "Virtual Audio Cable" or "VB-Audio Cable" to route the audio from sdrsharp to ShipPlotter.
A:
Check out AISMon; I've never used it, but it looks like it fits the bill. Here's a thorough tutorial: http://www.rtl-sdr.com/rtl-sdr-tutorial-cheap-ais-ship-tracking/
| 2024-04-21T01:26:35.434368 | https://example.com/article/5848 |
Q:
ReactTable - Toggle row background color onClick/ onExpandRow
in ReactTable I want to make the row background color toggle when that row is expanded. In the link below, the first image is what I have, the second is what I want it to be. I've tried playing around with onExpandedChange and a few things without success. Any idea how to accomplish this. Thanks for any help.
https://imgur.com/a/HLOigDC
A:
According to documentation, you can use custom props (there is no direct link to the example, try search for You can use these callbacks for dynamic styling as well!):
<ReactTable
getTrProps={(state, rowInfo, column) => {
return {
style: {
background: state.expanded[rowInfo.index] ? "blue" : "white"
}
};
}}
/>
| 2023-08-21T01:26:35.434368 | https://example.com/article/2024 |
Q:
Integration by parts: $\int e^{ax}\cos(bx)\,dx$
I need to evaluate the following function and then check my answer by taking the derivative:
$$\int e^{ax}\cos(bx)\,dx$$
where $a$ is any real number and $b$ is any positive real number.
I know that you set $u=\cos(bx)$ and $dv=e^{ax} dx$,
and the second time you need to integrate again you set $u=\sin(bx)$ and $dv=e^{ax}dx$ again.
It eventually simplifies down to
$$\int e^{ax}\cos(bx)dx = \frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a}\left(\frac{1}{a}e^{ax}\sin(bx) - \frac{b}{a}\int e^{ax}\cos(bx)\,dx\right).$$
Now I know to move the integral on the left side to the right side so that I can just divide by the constant to solve.
Here is my problem:
I know I need to solve the right side to be:
$$\frac{e^{ax}\left(a\cos(bx) + b\sin(bx)\right)}{a^2+b^2} + C.$$
To divide by the constant, I multiplied everything on the right side by
$$\frac{a^2}{b^2+1}.$$
but this leads me to get $b^2 + 1$ on the bottom instead of $a^2 + b^2$.
I will show what I am doing in detail:
After setting the initial integral equal to:
$$\frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a}\left(\frac{1}{a}e^{ax}\sin(bx) - \frac{b}{a}\int e^{ax}\cos(bx)\,dx\right) + C$$
I simplify:
$$\int e^{ax}\cos(bx)\,dx = \frac{a^2}{b^2+1}\left(\frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a}\left(\frac{1}{a}e^{ax}\sin(bx)\right)\right) + C$$
If this is already wrong, can someone point be in the right direction?
If I have not gone wrong yet, I can edit to show the rest of my work.
A:
So you have
$$\int e^{ax}\cos(bx)dx = \frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a}\left(\frac{1}{a}e^{ax}\sin(bx) - \frac{b}{a}\int e^{ax}\cos(bx)\,dx\right).$$
Multiplying out you get
$$\int e^{ax}\cos(bx)\,dx = \frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a^2}e^{ax}\sin(bx) - \frac{b^2}{a^2}\int e^{ax}\cos(bx)\,dx.$$
At this point, you should move that last integral on the right hand side to the left hand side and add in the constant of integration on the right.
Moving the last integral to the left hand side, you get
$$\left(1 + \frac{b^2}{a^2}\right)\int e^{ax}\cos(bx)\,dx = \frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a^2}e^{ax}\sin(bx) + C,$$
and I think this is where you made your mistake.
You tried to clear that $1 + \frac{b^2}{a^2}$ by multiplying through by $\frac{a^2}{1+b^2}$. But this is incorrect:
$$1 + \frac{b^2}{a^2} = \frac{a^2+b^2}{a^2} \neq \frac{1+b^2}{a^2}$$
so that what you multiplied through did not clear that factor. You need to multiply by $\frac{a^2}{a^2+b^2}$ (or, more horribly, by
$$\frac{1}{1+\frac{b^2}{a^2}}$$
which is too horrible for words) for things to cancel out.
If you do that, from
$$\frac{a^2+b^2}{a^2}\int e^{ax}\cos(bx)\,dx = \frac{1}{a}e^{ax}\cos(bx) + \frac{b}{a^2}e^{ax}\sin(bx) + C,$$
multiplying both sides by $\frac{a^2}{a^2+b^2}$, we get:
$$\int e^{ax}\cos(bx)\,dx = \frac{a}{a^2+b^2}e^{ax}\cos(bx) + \frac{b}{a^2+b^2}e^{ax}\sin(bx) + C$$
the intended answer.
By the way: you don't need to have the "$+C$" on the right hand side until there are no more indefinite integrals there; the constant of integration is implicit in the indefinite integral, so for example, in your penultimate displayed equation, the "$+C$" is superfluous.
A:
Another solution to your original question can be using complex numbers.
$$\begin{align}
I&=\displaystyle\int e^{ax}\cos {bx}dx \\
&=\Re\left(\displaystyle\int e^{ax}(\cos {bx}+i\sin {bx})\right)dx\\
&=\Re\left(\displaystyle\int e^{(a+ib)x}dx\right)\\
&=\Re\left(\dfrac{e^{(a+ib)x}}{a+ib}\right)\\
&=\Re\left(\dfrac{e^{ax}(\cos {bx}+i\sin {bx})}{a+ib}\right)\\
&=\Re\left(\dfrac{e^{ax}}{a^2+b^2}(\cos {bx}++i\sin {bx})(a-ib)\right)+C\\
\therefore I&=\dfrac{e^{ax}}{a^2+b^2}(a\cos {bx}+b\sin {bx})+C
\end{align}$$
| 2023-08-28T01:26:35.434368 | https://example.com/article/6118 |
1. Introduction
===============
Magnetic nanomaterials are nowadays widely studied in many fields, such as medicine \[[@B1-nanomaterials-04-00242],[@B2-nanomaterials-04-00242]\], materials science \[[@B3-nanomaterials-04-00242],[@B4-nanomaterials-04-00242],[@B5-nanomaterials-04-00242]\], environmental science \[[@B6-nanomaterials-04-00242],[@B7-nanomaterials-04-00242]\] or chemistry \[[@B8-nanomaterials-04-00242],[@B9-nanomaterials-04-00242],[@B10-nanomaterials-04-00242]\]. Research based on these nanomaterials is a great deal bearing in mind the improvements that they can introduce in many applications of these fields. One of the most promising applications for magnetic nanomaterials is the use as sorbent materials, since they combine high adsorption capacity with the interesting magnetic properties of magnetic nanoparticles (NPs).
In recent years, one of the trends of analytical nanotechnology has been focused on developing magnetic nanomaterials as sorbent materials for sample pretreatment \[[@B11-nanomaterials-04-00242]\]. Particularly, these nanomaterials have been described for solid phase extraction (SPE), liquid-liquid microextraction (LLME) or solid phase microextraction (SPME) giving rise to the development of dispersive or magnetic SPE \[[@B7-nanomaterials-04-00242],[@B12-nanomaterials-04-00242],[@B13-nanomaterials-04-00242]\], dispersive LLME \[[@B14-nanomaterials-04-00242],[@B15-nanomaterials-04-00242]\] and magnetic SPME \[[@B16-nanomaterials-04-00242],[@B17-nanomaterials-04-00242]\] based procedures. These techniques take advantage of the large surface area of NPs and the interaction of magnetic nanomaterials with magnetic fields, and the advantages of its use have been demonstrated to improve conventional extraction procedures for several compounds in environmental, biological and clinical analysis.
While in the abovementioned approaches, the magnetic nanomaterials have been exploited in off-line modalities, there is a growing interest in developing on-line extraction procedures using magnetic nanomaterials, where the sample pretreatment step is coupled with the separation and/or detection technique. The main advantages of the on-line procedures rely on reduced analysis times and minimized sample handling, since samples can be directly processed. Furthermore, sensitivity and selectivity can be also improved. However, the challenge to be addressed in on-line devices is focused on the implementation of a magnetic field source.
In this context, several efforts have been made to develop on-line pretreatment techniques using magnetic nanomaterials, mainly in-capillary electrophoretic methods \[[@B18-nanomaterials-04-00242]\] and in-tube SPME (IT-SPME) \[[@B19-nanomaterials-04-00242],[@B20-nanomaterials-04-00242]\] coupled to chromatographic techniques (Magnetic-IT-SPME). In the first approach, the magnetic field, supplied by permanent magnets nipped to the capillary, is used to generate a NPs coating on the surface of a capillary column, so the column efficiency is improved due to the large surface area of nanoparticles. The second approach is based on the functionalization of a capillary column with silica supported magnetic NPs. The capillary column, placed on a magnetic coil, is then used as the loop of the injection valve of a Capillary LC (CapLC). The main feature of this system is that the adsorption is not only governed by the surface area of the capillary column, but also the magnetic field plays an important role in the extraction efficiency and preconcentration, particularly for diamagnetic compounds. The adsorption mechanism is based on the partially adsorption of diamagnetic compounds on the silica supported magnetic NPs deposited capillary, combined with the influence of a magnetic field on superparamagnetic NPs. The magnetization of these NPs inside of the capillary generates regions with different magnetic field gradients, thus, diamagnetic analytes tend to be trapped in those regions where the magnetic field is minimal, yielding to improved adsorption efficiencies. Compared to typical off-line devices, Magnetic IT-SPME can be a powerful tool in the sample pretreatment step since it takes advantage of the high surface area of magnetic nanomaterials combined with the superparamagnetic behavior of magnetic NPs to develop more efficient on-line extraction techniques. This approach has been successfully proposed for several pharmaceutical compounds \[[@B19-nanomaterials-04-00242]\] and organophosphorous compounds \[[@B21-nanomaterials-04-00242]\] in the environmental field. Nevertheless, further investigations are still needed in order to advance in the knowledge of this technique and to extent potential applications in environmental studies and in other fields.
Herein, this work is focused on the study of the adsorption behavior of triazines on SiO~2~ supported Fe~3~O~4~ as sorbent material for magnetic-IT-SPME. A systematic study of triazines adsorption was conducted as function of the magnetic field and the relationship with triazines magnetic susceptibility. Finally, taking advantage of the enhanced adsorption properties, an analytical procedure have been developed and characterized for determining triazines in water samples.
2. Results and Discussion
=========================
2.1. Magnetic Characterization of the Capillary Columns and Target Analytes
---------------------------------------------------------------------------
Atrazine, simazine and terbutylazine are diamagnetic analytes, so susceptible to be extracted from aqueous medium with Magnetic-IT-SPME using SiO~2~ supported Fe~3~O~4~ deposited on the capillary column. Previous studies have reported that this sorbent nanomaterial improves the extraction efficiency of compounds such as acetylsalicylic acid, atenolol, acetaminophen, diclofenac, ibuprofen, chlorfenvinphos and chlorpyrifos \[[@B19-nanomaterials-04-00242],[@B21-nanomaterials-04-00242]\]. It has been shown how this improvement is directly related with the influence of an external magnetic field on the SiO~2~ supported Fe~3~O~4~ nanomaterial deposited on the capillary column. Fe~3~O~4~ nanoparticles with an average size of 5 nm and in a percentage of 5 wt.% in the silica composite (data not shown), gave rise to the synthesis of magnetic capillary column \[[@B19-nanomaterials-04-00242]\]. The NPs inside of the capillary column are superparamagnetic and well isolated as can be deduced of the magnetic characterization of the NPs. In order to determine the type of interaction between NPs, dynamics of superspins have been studied by *AC* magnetic susceptibility measurements in frequency range of 1--1000 Hz. [Figure 1](#nanomaterials-04-00242-f001){ref-type="fig"}a shows the frequency dependence of the *AC* susceptibility for the Fe~3~O~4~ nanoparticles. As one can see, by increasing of the applied frequency, the *T~B~* shifts to higher temperature. Relation between *T~B~* and relaxation time (inverse of applied frequency) for non-interacting nanoparticles is given by the Neel-Arrhenius law as: , where *E~a~* = *KV* is energy barrier (where *K* is magnetic anisotropy constant and *V* is the volume of nanoparticle), *K~B~* is Boltzmann constant, τ = 1/*f* and τ~0~ is about 10^−9^--10^−13^ s. [Figure 1](#nanomaterials-04-00242-f001){ref-type="fig"}b shows the results of fitting the experimental data (real part) by the Arrhenius expression. The obtained values of τ~0~ and *E~a~* were 2.536·× 10^−13^ s and *E~a~*/*K~B~* = 878.22 ± 57.66 K, respectively. As mentioned above, the value of τ~0~ is about 10^−9^--10^−13^ s for noninteractiong nanoparticles. As we expected, no strong dipole-dipole interactions are between the magnetic nanoparticles. It has been already reported that this magnetic capillary columns are formed by well isolated and superparamagnetic NPs, thus are easily magnetized under the application of an external magnetic field.
{#nanomaterials-04-00242-f001}
By another hand, the nature of the analytes is the major factor affecting the extraction efficiency; pharmaceutical compounds showed a better enhancement of the adsorption capacity than organophosphours compounds when a magnetic field is applied. Therefore, in a first study, the magnetic susceptibilities of the different compounds were compared. [Table 1](#nanomaterials-04-00242-t001){ref-type="table"} shows the energy level calculated for each compound.
nanomaterials-04-00242-t001_Table 1
######
B3LYP/6-31G\*\* total energies (*E*, au) *in vacuo* and in water.
Compound In vacuo In H~2~O
---------------------- -------------- --------------
Acetylsalicilic acid −648.709453 −648.720605
Acetaminophen −515.494917 −515.507984
Diclofenac −1665.736440 −1665.748421
Ibuprofen −656.734267 −656.741794
Atenolol −881.951314 −881.969818
Chlorpyrifos −2671.570830 −2671.582537
Chlorfenvinphos −2409.975077 −2409.986882
Simazine −1007.990723 −1008.000696
Atrazine −1047.309710 −1047.319747
Terbutylazina −1086.624906 −1086.633924
Once we calculated the energy level, the magnetic susceptibilities for acetylsalicylic acid, atenolol, acetaminophen, diclofenac, ibuprofen, chlorfenvinphos and chlorpyrifos were evaluated, and these values were compared with the values for simazine, atrazine and terbutylazine. [Table 2](#nanomaterials-04-00242-t002){ref-type="table"} shows the magnetic susceptibility values obtained for the studied compounds in vacuo and water. All the analytes are diamagnetic and as it was expected, there were not significant differences in the magnetic susceptibilities. Therefore, the differences on the adsorption capacity of the magnetic adsorbent toward each compound cannot be explained by the differences in the magnetic susceptibilities of these compounds, but must be crucially depending on the polarity of each compound and the chromatographic conditions, deeply influenced by the interaction of the external magnetic field with the magnetic adsorbent \[[@B19-nanomaterials-04-00242],[@B22-nanomaterials-04-00242]\].
nanomaterials-04-00242-t002_Table 2
######
Isotropic diamagnetic susceptibility (IDS), isotropic paramagnetic susceptibility (IPS) and isotropic total susceptibility (ITS) ^a^ in au.
Compound In vacuo In H~2~O
---------------------- ------------ ----------- ---------- ------------ ----------- ----------
Acetylsalicilic acid −375.1256 354.4428 −20.6827 −376.0739 355.3678 −20.7061
Acetaminophen −361.7369 342.8417 −18.8952 −361.2246 342.2788 −18.9458
Diclofenac −1073.6967 1037.0720 −36.6247 −1071.6524 1035.0105 −36.6419
Ibuprofen −784.5031 754.6211 −29.8820 −784.0887 754.2092 −29.8795
Atenolol −1895.5223 1858.5274 −36.9949 −1905.1243 1868.0617 −37.0626
Chlorpyrifos −1070.6714 1033.9535 −36.7179 −1070.5282 1033.7223 −36.8059
Chlorfenvinphos −1254.5588 1216.6838 −37.8751 −1257.4740 1219.5444 −37.9296
Simazine −588.8682 563.8451 −25.0230 −591.2717 566.3096 −24.9621
Atrazine −716.3337 688.7578 −27.5760 −717.3796 689.8408 −27.5388
Terbutylazine −787.0130 757.0138 −29.9993 −786.0579 756.1178 −29.9401
^a^ ITS = IDS + IPS.
2.2. Adsorption of Triazines in the SiO~2~ Supported Fe~3~O~4~ Capillary Column
-------------------------------------------------------------------------------
Adsorption of simazine, atrazine and tertubylazine in the magnetic sorbent phase was studied following the procedure described in \[[@B19-nanomaterials-04-00242]\] with minimal modification. Typically, 100 μL of a mixture of triazines was passed through the capillary column in the load position (see [Figure 5](#nanomaterials-04-00242-f005){ref-type="fig"}, Experimental Section) at variable magnetic fields (from 50 to 400 G). Once the sample is processed, the injection valve is rotated to the inject position ([Figure 5](#nanomaterials-04-00242-f005){ref-type="fig"}, Experimental Section) at the same time that the polarity of the magnetic field is changed. Then, the adsorbed analytes are transferred from the magnetic capillary column to the chromatographic system for their separation and detection. [Figure 2](#nanomaterials-04-00242-f002){ref-type="fig"} shows the variation of the extraction efficiency as function of the magnetic field for the three target compounds. Note that the extraction efficiencies were calculated taking into account the slope of the calibration curve when standards at different concentration level were directly injected (2 μL) into the chromatographic system. As seen in [Figure 2](#nanomaterials-04-00242-f002){ref-type="fig"}, the adsorption capacity increased as function of the magnetic field applied. Similar results have been reported \[[@B19-nanomaterials-04-00242],[@B21-nanomaterials-04-00242]\]. These results indicated that the application of an external magnetic field induces the magnetization of Fe~3~O~4~ NPs inside of the capillary column, creating regions with different magnetic field gradients that depend on the intensity of the magnetic field. Under these conditions, diamagnetic analytes are inside of a paramagnetic medium, and they are submitted to repulsion forces, in such a way that analytes tend to be trapped in the minima of the magnetic field forces. This effect influenced the partitioning coefficients of the analytes in the mobile phase flow and the stationary phase with a maximum on the extraction efficiency at 150 G.
{#nanomaterials-04-00242-f002}
The enhancement on the adsorption led to an improvement of the extraction efficiency for simazine, atrazine and terbutylazine induced by the application of a magnetic field when the SiO~2~ supported Fe~3~O~4~ capillary column is used. In fact, control experiments showed that in absence of a magnetic field (B = 0 G), the percentage of extracted compound decreased till 30%, 50% and 45% for simazine, atrazine and terbutylazine, respectively. The mechanism by which analytes are entrapped into the sorbent material is based not only on the hydrophobic interactions between the analytes and the sorbent material, but also, on the influence of the magnetic field on the magnetic capillary column within the used configuration \[[@B19-nanomaterials-04-00242]\] (see [Figure 5](#nanomaterials-04-00242-f005){ref-type="fig"}, Experimental Section).
Regardless to the adsorption capacity of the SiO~2~ supported Fe~3~O~4~ material, it has been demonstrated that hydrophobic interactions between the analytes and the sorbent take place through the alkyl chain of CTAB that are structural units of the material \[[@B7-nanomaterials-04-00242]\]. In the case of Magnetic IT-SPME, a contribution of a difference force needs to be considered. Notice that the SiO~2~ matrix supported the Fe~3~O~4~ NPs and CTAB micelles. As it was demonstrated in \[[@B7-nanomaterials-04-00242]\], the material is formed by two types of micelles, CTAB micelles and Fe~3~O~4~-CTAB micelles and the main functions of SiO~2~ matrix were to support the NPs, but also to disperse and isolate Fe~3~O~4~ NPs. The injected compounds in the IT-SPME device are partially adsorbed on the surface of the capillary column. When a magnetic field is applied, the Fe~3~O~4~ NPs embedded on the silica matrix and deposited on the surface of the capillary column, are magnetized; this magnetization yield to the formation of different magnetic field gradients on the surface of the capillary column. Under these conditions, diamagnetic compounds are strongly affected, and they tend to be trapped in the minimal magnetic field regions, increasing the adsorption capacity. Once the analytes have been adsorbed, the desorption step was carried out by changing the polarity of the magnetic field. As it was previously demonstrated, that change is necessary to generate rapid changes in the magnetic strengths, and so the analytes can be detrapped for their subsequent separation and detection in the chromatographic system. [Figure 3](#nanomaterials-04-00242-f003){ref-type="fig"} shows the chromatogram obtained for a mixture of triazines the magnetic capillary column applying a magnetic field (a); and without magnetic field (b). As a result of the magnetic field interaction, the analytical response of the analytes increased and the analytes eluted at higher retention times, owing to the higher adsorption of the analytes. It should be noted that unknown compounds eluted at similar retention times than simazine and atrazine, however, they were not considered interferent species since satisfactory chromatographic resolution and quantification could be carried out.
{#nanomaterials-04-00242-f003}
In an attempt to evaluate the benefits of the SiO~2~ supported Fe~3~O~4~ material for triazines, the adsorption of triazines in a typical IT-SPME device using a commercial capillary column (polydimethylsiloxane (PDMS), TRB-5) was studied, under the same conditions (length of the capillary: 15 cm; volume of sample: 100 μL of a mixture of simazine, atrazine and terbutylazine at 30 μg L^−1^). The extraction efficiencies for simazine, atrazine and terbutylazine were 3%, 9% and 11%, respectively. [Figure 4](#nanomaterials-04-00242-f004){ref-type="fig"} compares the adsorption capacity for the commercial capillary column in IT-SPME modality, the SiO~2~ supported Fe~3~O~4~ capillary column in IT-SPME modality and the SiO~2~ supported Fe~3~O~4~ capillary column in magnetic-IT-SPME modality. Triazines exhibited a higher adsorption on the magnetic capillary column (between 30% and 40%), compared with the typically used commercial capillary column, lower than 15%. It should be noted that these values can be even lower (0.8%--3%) when higher volumes of samples are processed. In addition, the use of the magnetic capillary column in the magnetic-IT-SPME modality even improved these results, and in some cases, such as for atrazine, the extraction efficiency was almost quantitative (87%).
{#nanomaterials-04-00242-f004}
Moreover, the magnetic capillary column also exhibited a good stability for its use in on-line devices. Fe~3~O~4~ NPs were stable inside of the SiO~2~ matrix, since this matrix avoided NPs interaction, agglomerations and also their incorporation to the column flow \[[@B19-nanomaterials-04-00242]\]. In fact, the capillary column was used almost 200 times without loss in the adsorption capacity.
Taking into account the features of this methodology, some analytical characteristics were established in order to characterize the procedure. The analytical response was lineal in the working concentration interval from 3 to 40 μg L^−1^. [Table 3](#nanomaterials-04-00242-t003){ref-type="table"} shows the detection limit (LOD, calculated as 3*S*~blank~/*b*, *b*: slope of the calibration graph), quantification limit (LOQ) and precision values (at 2.5 μg L^−1^; expressed as relative standard deviation, RSD) values for simazine, atrazine and terbutylazine, respectively.
nanomaterials-04-00242-t003_Table 3
######
Detection limit (LOD), quantification limit (LOQ) and relative standard deviation (RSD) for simazine, atrazine and terbutylazine achieved with Magnetic-IT-SPME-CapLC-DAD.
Compound LOD (μg L^−1^) LOQ (μg L^−1^) RSD (%)
--------------- ---------------- ---------------- ---------
Simazine 0.4 1.4 10
Atrazine 0.3 1.1 9
Terbutylazine 0.3 1.0 7
These results demonstrated that this methodology has direct applicability for the determination of triazines in environmental samples, such as water samples. The LODs are comparable but a little bit higher than those previously reported in the literature \[[@B23-nanomaterials-04-00242]\]. Note, however, that in this work, we have processed 100 μL of samples; thus, the sensitivity can be even improved by processing higher volumes of water samples.
2.3. Application of the Magnetic Capillary Column for the Analysis of Triazines in Water Samples
------------------------------------------------------------------------------------------------
Magnetic-IT-SPME-CapLC has been proposed for analytical purposes, therefore, in this section we evaluated the applicability of this methodology to analyse real water samples. For this aim, four river water samples were analyzed. The results showed that the simazine, atrazine and terbutylazine were not detected at the concentration levels assayed.
A recovery study was also carried out in order to evaluate the possible matrix effects, caused by components of the water samples. This effect was evaluated by spiking the water samples with a mixture of triazine (2.5 μg L^−1^, each). The recovery values were between 99% ± 1% and 110% ± 5%. Therefore, Magnetic-IT-SPME-Cap-LC did not shown matrix effects under the optimized conditions.
3. Experimental Section
=======================
3.1. Synthesis of Fe~3~O~4~ NPs and SiO~2~ Supported Fe~3~O~4~ Capillary Columns
--------------------------------------------------------------------------------
Syntheses were carried out by the method described in \[[@B19-nanomaterials-04-00242]\]. Fe(acac)~3~ (0.706 g, Aldrich) 1,2-hexanodiol (2.013 g, Aldrich), oleic acid (1.695 g, Aldrich) and oleyamine (1.605 g, Aldrich) were mixed in 20 mL of phenyl ether (Aldrich) under Ar in order to ensure an inert atmosphere. After refluxing the mixture during 30 min at 263 °C, ethanol (80 mL) was added. Then, the mixture was centrifuged and redissolved in 20 mL of hexane. Finally, water soluble NPs Fe~3~O~4~-CTAB were prepared.
The silica supported Fe~3~O~4~ nanomaterial was synthetized using the method described earlier \[[@B19-nanomaterials-04-00242]\], in this procedure PEG (0.9 g) and urea (0.9 g) were dissolved in 10 mL of acetic acid (10 mM). Then, 2.5 mL of this solution were mixed with Fe~3~O~4~-CTAB water dispersion (1 mL) and the pH was adjusted to 11 with NaOH (1 M). After, TEOS was added (1 mL) to the solution and stirred until a homogenous gel was obtained.
Finally, a fused silica capillary column (*id* = 75 μm) was pretreated with NaOH (1 M), and then the gel was injected into the capillary column. Rapidly, the capillary ends were sealed and place into an oven. The capillary coating was achieved using the temperature program described in \[[@B19-nanomaterials-04-00242]\].
3.2. Physical Characterization
------------------------------
Magnetic characterization was carried out in a MSMS Squid Magnetometer (Quantum Design, San Diego, CA, USA) with variable temperature (*T* = 2 K).
3.3. Instruments and Chromatographic Conditions
-----------------------------------------------
The capillary chromatographic system consisted of a liquid chromatography isocratic capillary pump (Jasco Corporation, Tokyo, Japan) connected to a UV-Vis diode array detector 1200 series (Agilent, Waldbronn, Germany) with a 80 nL flow cell.
The separation of the triazines was carried out with a particulate column Zorbax C18 (150 mm × 0.5 mm, 3.5 μm). The mobile phase was a mixture of methanol:water 70:30 at a flow rate of 6 μL min^−1^. All solvent were filtered through 0.45 mm nylon membranes (Teknokroma) before use.
3.4. Magnetic---IT-SPME Device
------------------------------
[Figure 5](#nanomaterials-04-00242-f005){ref-type="fig"} shows the schematic diagram of the Magnetic-IT-SPME coupled to a CapLC system. The SiO~2~ supported capillary column (15 cm) wrapped with a magnetic coil, was connected to the six port injection valve of the CapLC system. The magnetic coil was connected to a power supply (PS) in order to control the magnetic field intensity. The adsorption of the analytes was carried out in the load position of the injection valve (\-\--), 100 μL of samples were manually processed at different magnetic fields (from 50 to 400 G). Then, the analytes were desorbed and transferred to the analytical column for their separation and detection by rotating the valve to the inject position () at the same time that the polarity was changed \[[@B19-nanomaterials-04-00242]\]. After each injection, the capillary column was rinsed with 300 μL of methanol.
) desorption (injection position of the injection valve).](nanomaterials-04-00242-g005){#nanomaterials-04-00242-f005}
3.5. Computancional Methods
---------------------------
All calculations were carried out with the Gaussian 09 suite of programs \[[@B24-nanomaterials-04-00242]\]. Density functional theory \[[@B25-nanomaterials-04-00242],[@B26-nanomaterials-04-00242]\] calculations (DFT) have been carried out using the B3LYP \[[@B27-nanomaterials-04-00242],[@B28-nanomaterials-04-00242]\] exchange-correlation functionals, together with the standard 6-31G\*\* basis set \[[@B29-nanomaterials-04-00242]\]. The inclusion of solvent effects has been considered by using a relatively simple self-consistent reaction field (SCRF) method \[[@B30-nanomaterials-04-00242],[@B31-nanomaterials-04-00242]\] based on the polarizable continuum model (PCM) of Tomasi's group \[[@B32-nanomaterials-04-00242],[@B33-nanomaterials-04-00242],[@B34-nanomaterials-04-00242]\]. Geometries have been fully optimized with PCM. The solvent we used was H~2~O (common solvent in HPLC). Calculations of magnetic susceptibility using gauge including atomic orbital method (GIAO) were carried out using NMR = Susceptibility.
3.6. Analysis of Water Samples
------------------------------
River water samples collected from several points of the Comunidad Valenciana were analysed. They were filtered through 0.45 μm nylon membranes (Teknokroma) in order to remove any particulate matter, and directly processed in the Magnetic-IT-SPME-CapLC system. The analyses were carried out in triplicate.
4. Conclusions
==============
Rapid developments on the synthesis of magnetic nanomaterials have given to the analytical nanotechnology attractive materials to improve several steps of the analytical procedure. Among them, the use of magnetic nanomaterials in the sample pretreatment step is one of most exploited, although, most of these nanomaterials have been used in off-line procedures. Herein, in this work we have demonstrated the applicability of SiO~2~ supported Fe~3~O~4~ magnetic nanomaterial to develop an on-line extraction and preconcentration tool, Magnetic-IT-SPME, for the determination of triazines. The magnetic nanomaterial deposited on a capillary column, takes advantage of the adsorption properties of the sorbent combined with the influence of an external magnetic field on the analytes to enhance the adsorption capacity. Reduction of the analysis time and increment of the extraction efficiency are the most attractive characteristic of this analytical procedure. In addition, the use of this material in an on-line device represents a cost effective analytical methodology for the determination of triazines in environmental samples. This procedure has been successfully applied for determining triazines in the water samples.
Financial support from the Spanish Ministerio de Economía y Competitividad (Projects with FEDER cofinancing MAT2011-22785, CTQ-2011-26507, CTQ2011-26760). Generalitat Valenciana (PROMETEO, ACOMP/2013/155 and ISIC-Nano programs) is gratefully acknowledged.
The manuscript was written through contributions of all authors and all authors have given approval to the final version.
The authors declare no conflict of interest.
| 2024-05-14T01:26:35.434368 | https://example.com/article/2373 |
High Demand Leads MakerDAO to Raise Debt Ceiling to $100 Million
The Decentralized Autonomous Organization, Maker, has achieved a major milestone with raising its debt ceiling to 100 million Dai. This is a doubling from the previous 50 million Dai in circulation. In this article, we explore the reasons behind this and look at the future implications of this event for MakerDAO and its decentralized stablecoin.
Raising the Debt
The original debt ceiling was set at 50 million Dai. As the value of the Dai is pegged to the value of the US Dollar, this debt ceiling had a value of $50 million. This was set to stress-test the Dai system and ensure stability. As the Dai is still in its experimental phase, and so is MakerDAO and DAOs in general, steady growth and the stability of the Dai stablecoin are essential to proof both novel concepts.
As both concepts are increasingly accepted, adoption and demand are growing. Just days before raising the debt ceiling, a record amount of Dai was created based on demand and caused a 16.7% increase in the number of Dai in circulation. This sudden spike in demand caused the decentralized community to propose a raise of the debt ceiling, which was then voted on.
As the governance of MakerDAO is decentralized, big decisions like this can only be made based on governance vote. This particular vote concerned a new authority in the system—the new authority being a smart contract that replaced the previous smart contract controlling the debt ceiling and enabled a 100 million Dai debt ceiling.
The proposal was accepted by the Maker community and means that 50 million more Dai can now be created by cryptocurrency enthusiasts looking for some peace of mind in this crazy market.
Future
MakerDAO and its Dai stablecoin live completely on the blockchain, which is both exciting and highly experimental. The substantiated increase of the debt ceiling by $50 million worth of Dai indicates an increase in the confidence people have in this decentralized project.
The rise of the debt ceiling also comes in light of other good news for the MakerDAO, as just recently the DAO announced a new partnership with supply chain payments company Tradeshift. This new addition to the MakerDAO network is yet another company willing to work with the decentralized stablecoin solution.
Previous additions to the MakerDAO network were:
Bifrost, a company focused on delivering foreign aid payments
Airswap, which is planning to use the Dai stablecoin in the decentralized marketplaces they are launching
Dether, a blockchain startup devoted to providing easy access of cryptocurrencies to the unbanked that see a valuable tool in MakerDAO’s stablecoin
A big event to look forward to is the launch of the multi-collateral Dai this summer. Once this multi-collateral Dai goes live, public voting will go live. This enables a whole new array of decentralized elements such as debating mechanisms, signalling, proposal overviews, and new processes for governance.
Adoption of the Dai stablecoin has steadily increased over the past 6 months. This can be especially attributed to the fact that the Dai has managed to keep stable against the US Dollar, which is its core purpose.
The fact that demand has increased so much that the DAO was forced to double its debt ceiling indicates strong confidence in the MakerDAO and its Dai. The market really needs a trusted stablecoin and the decentralized solution of MakerDAO is becoming a serious candidate.
Related: What is a Stable Coin and Does the Crypto Market Need Them? | 2023-08-09T01:26:35.434368 | https://example.com/article/3188 |
JACK ROBINSON is determined to repay Liverpool FC’s faith in him after penning a new long-term contract.
The 18-year-old left-back has been rewarded for his progress which has already seen him make five first team appearances.
“I’m delighted,” Robinson said. “I was going for my lunch and I saw (director of football) Damien Comolli on my way through.
“He pulled me to one side and said the club wanted to offer me a new contract. There was no doubt in my mind, I was just so excited the club were offering me a contract.
“I’ve just got to keep working hard in training. I can’t just sit back on this contract. I’ve got to keep improving and showing people what I’m about.”
Robinson, who joined the Academy at under-10s level, became the Reds’ youngest ever player when he came on against Hull on the final day of the 2009/10 campaign.
Last season Robinson impressed in games against Arsenal and Birmingham City and he has played in the Carling Cup against Exeter and Brighton this term.
The arrival of Jose Enrique has increased competition for the left-back slot but Robinson says he’s benefiting from working with the Spaniard.
“Jose’s been fantastic in every game he’s played,” he added. “I need to learn from him. He’s the perfect role model because he’s got everything as a left-back.”
Comolli believes Robinson has all the attributes to be a big success at Anfield.
“He’s bright, which is very important to succeed at the top level,” he said. “He’s dedicated, he’s committed, he’s very professional. He’s one of those who is very positive and he listens to what other people have got to say.
“He’s still got a long way to go, he’s still got a lot of work to do physically, mentally, tactically and technically.
“He knows this, but all the elements are there to make him a very good player. At 18, he’s the future of the club.” | 2023-08-02T01:26:35.434368 | https://example.com/article/7535 |
Q:
Console Application Error "Index (zero based) must be greater than or equal to zero and less than the size of the argument list"
STATIC VOID MAIN GOES HERE
string[] dayNames = { "Sun", "Mon", "Tues", "Wed", "Thur", "Fri", "Sat" };
string m = "";
double average = 0;
double total = 0;
int[] bCalories = new int[7];
int[] lCalories = new int[7];
int[] dCalories = new int[7];
int[] dayTotal = new int[7];
for (int i = 0; i < 7; i++)
{
Console.Write("Please enter calories for {0} breakfast: ", dayNames[i]);
bCalories[i] = int.Parse(Console.ReadLine());
Console.Write("Please enter calories for {0} lunch: ", dayNames[i]);
lCalories[i] = int.Parse(Console.ReadLine());
Console.Write("Please enter calories for {0} dinner: ", dayNames[i]);
dCalories[i] = int.Parse(Console.ReadLine());
dayTotal[i] += bCalories[i];
dayTotal[i] += lCalories[i];
dayTotal[i] += dCalories[i];
total += dayTotal[i];
Console.WriteLine();
}
average = total /7;
Console.Clear();
Console.WriteLine("Day\t\tBreakfast\tLunch\tDinner\tDay Total");
for (int i = 0; i < 7; i++)
{
if (dayTotal[i] > average)
{
m = "*** Above Average";
}
else if(dayTotal[i] <= average)
m = "";
I only recieve the error Index (zero based) must be greater than or equal to zero and less than the size of the argument list", after i add the string m to the writeline below. If i do not have the string m at the end of the statement then the program runs fine, its only when i add it that i get AN ERROR
Console.Write("{0}\t\t{1}\t\t{2}\t{3}\t{4}\t{5}\n", dayNames[i],
bCalories[i], lCalories[i], dCalories[i], dayTotal[i] + m);
}
Console.Write("Average daily calories: {0}", average);
Console.ReadLine();
}
A:
The problem is here:
Console.Write("{0}\t\t{1}\t\t{2}\t{3}\t{4}\t{5}\n", dayNames[i],
bCalories[i], lCalories[i], dCalories[i], dayTotal[i] + m);
You have 6 specifiers (0 - 5), but only 5 arguments being passed in. If you change this to only include up to {4}, it should work properly:
Console.WriteLine("{0}\t\t{1}\t\t{2}\t{3}\t{4}", dayNames[i],
bCalories[i], lCalories[i], dCalories[i], dayTotal[i] + m);
I would also recommend using Console.WriteLine instead of Console.Write with a \n. This makes it obvious that your intending to add a line, which in turn makes the code easier to read and maintain.
| 2024-05-25T01:26:35.434368 | https://example.com/article/6061 |
Q:
Native windows c++ programming?
I have quick question about native c++, along with others, programming on windows-- I recently wrote a small c++ program in Visual Studio on my own computer that does a little math for me. I compiled it successfully and moved the .exe from the VS debug folder to my desktop. It runs fine on my computer, regardless of where the .exe is located. But then I gave the program to my friend, and when he tries to run it, it says he's missing all kinds of dll files. Now I have a feeling this is because there is a c++ environment that is included in VS, that allows it to run on mine and not his. But my question is why should it matter what language the program was originally written in? Isn't the point of compiling it into a .exe to turn the code into machine language so that it can run on any computer regardless of whether or not that have the dev tools?
A:
Compiling a debugging version will dynamically link to debug version(s) of dll files that don't come standard with Windows. You're also not technically/legally allowed to redistribute debug versions of dll files. Either compile a release version, or include whatever .dll files you are linking to with your exe file. You might also have to worry about whether or not the target computer has the proper Microsoft Visual Studio C++ Redistributable Packages installed.
Alternately, you can statically link by setting Runtime Library->Multithreaded /MT under Code Generation in your project's properties, thereby bypassing dll hell, although for various reasons I won't go into, this is generally frowned upon.
| 2023-11-29T01:26:35.434368 | https://example.com/article/1682 |
Oxlow Rake lead mines
A Scheduled Monument in Peak Forest, Derbyshire
If Google Street View is available, the image is from the best available vantage point looking, if possible,
towards the location of the monument. Where it is not available, the satellite view is shown instead.
Coordinates
Latitude: 53.3197 / 53°19'10"N
Longitude: -1.8082 / 1°48'29"W
OS Eastings: 412870.422516
OS Northings: 380322.617283
OS Grid: SK128803
Mapcode National: GBR HZT1.9P
Mapcode Global: WHCCL.6T6F
Entry Name: Oxlow Rake lead mines
Scheduled Date: 20 June 2000
Source: Historic England
Source ID: 1019001
English Heritage Legacy ID: 29961
County: Derbyshire
Civil Parish: Peak Forest
Traditional County: Derbyshire
Lieutenancy Area (Ceremonial County): Derbyshire
Church of England Parish: Peak Forest and Dove Holes
Church of England Diocese: Derby
Details
The monument includes the earthwork, buried, standing and rock cut remains of
Oxlow Rake, a post-medieval lead mining complex. The monument is a linear
feature which includes the rake and a number of intermediate concentrations of
activity including Old Moor Mine and Clear The Way Mine. The term rake is
given to extraction and ore processing features which follow the line of a
lead bearing vein, this was a typical form of lead mining in the Peak
District.
Oxlow Rake is aligned north east to south west on ground which gradually
slopes to the south west. Geologically, the rake follows the line of lead
bearing veins which cut across the Bee Low Limestones and outcrop to the west
of Oxlow Rake and Old Moor Mine.
Workings on Oxlow Rake have been documented from at least 1709 when it is
recorded that `John Bradley's Grove on Oxlow was in production'. However,
another branch of Oxlow Rake, known as Daisy or Deasy Rake was recorded on the
Castleton enclosure map of 1691 suggesting that lead working in this area
started before this date.
The mines would have been worked under the jurisdiction of the Barmote Courts,
the legal administrative unit governing Derbyshire lead mining. The Derbyshire
system of mining was largely based on local mining customs and consisted of
individual groups of miners or small mining companies working relatively short
lengths of the vein.
The monument survives as a series of earthwork, buried, standing and rock cut
remains which include belland yard walls (substantial walls built around
processing areas in order to prevent cattle straying and eating grass
contaminated by lead), ruined coes (stone built shelters or sheds), open cuts
(veins worked open to daylight), a bouse team (a bin into which ore was
stored before processing), water channels, washing floors, leats, buddling dam
(an earth dam used in the process of separating small sized ore from adhering
dirt (buddling)), crushing floor (an area where ore was crushed ready for
further treatment), gin circle (remains of horse powered winding apparatus)
and the remains of a horizontal winding engine.
Towards the eastern end of the monument are the remains of Old Moor Mine.
Here, a belland yard wall surrounds the remains of a crushing floor, a gin
circle and several shafts including the main engine shaft. The shaft mounds
are the result of extraction, but despite their long history suggest low level
mining technology.
Clear The Way Mine which is centred at national grid reference SK12908038, is
enclosed by another belland yard wall which surrounds an area of open cuts and
very large undisturbed hillocks of waste material. The remains of an engine
shaft which is known to be 330ft (100.5m) deep, survives just south of a
large bulge in the northern side of the belland yard wall.
To the south west of Clear The Way Mine, and continuing to the south west end
of Oxlow Rake, are a series of hillocks made up of limestone deads (waste
rock which contains no ore or insufficient quantities to warrant extraction)
and finely crushed vein material. The hillocks are particularly large and
virtually undisturbed. Steep sided open cuts are also a characteristic feature
of this section of the monument. At national grid reference SK12608010 the
well preserved remains of a bouse team associated with the remains of washing
floors and water leats are evident. Bouse teams are particularly rare in
Derbyshire and are more generally associated with 19th century lead workings
in the Northern Pennines. Included in this area of activity are the remains of
coes and ore bins and at national grid reference SK12157980 are the remains of
a late 19th century winding engine bed which is believed to have been used in
conjunction with a trial sinking beneath the Peak Forest Sill which outcrops
immediately to the west.
The modern track surface is excluded from the scheduling although the ground
beneath this is included.
MAP EXTRACT
The site of the monument is shown on the attached map extract.
Source: Historic England
Reasons for Scheduling
Approximately 10,000 lead industry sites are estimated to survive in England,
spanning nearly three millennia of mining history from the later Bronze Age
(c.1000 BC) until the present day, though before the Roman period it is likely
to have been on a small scale. Two hundred and fifty one lead industry sites,
representing approximately 2.5% of the estimated national archaeological
resource for the industry, have been identified as being of national
importance. This selection of nationally important monuments, compiled and
assessed through a comprehensive survey of the lead industry, is designed to
represent the industry's chronological depth, technological breadth and
regional diversity.
Lead rakes are linear mining features along the outcrop of a lead vein
resulting from the extraction of relatively shallow ore. They can be broadly
divided between: rakes consisting of continuous rock-cut clefts; rakes
consisting of lines of interconnecting or closely-spaced shafts with
associated spoil tips and other features; and rakes whose surface features
were predominantly produced by reprocessing of earlier waste tips (normally in
the 19th century). In addition, some sites contain associated features such as
coes (miners' huts), gin circles (the circular track used by a horse operating
simple winding or pumping machinery), and small-scale ore-dressing areas and
structures, often marked by tips of dressing waste.
The majority of rake workings are believed to be of 16th-18th century date,
but earlier examples are likely to exist, and mining by rock-cut cleft has
again become common in the 20th century. Rakes are the main field monuments
produced by the earlier and technologically simpler phases of lead mining.
They are very common in Derbyshire, where they illustrate the character of
mining dominated by regionally distinctive Mining Laws, and moderately common
in the Pennine and Mendip orefields; they are rare in other lead mining areas.
A sample of the better preserved examples from each region, illustrating the
typological range, will merit protection.
The mining remains on Oxlow Rake are particularly well preserved and include a
diverse range of components relating to the mining of this vein. Rake workings
of such veins are now rare, and this example is one of the best preserved
examples in the Peak District. The standing, earthwork, buried and rock cut
remains provide evidence for both the historical and technological development
of what was once a far more extensive, multi-period mining landscape. They
incorporate a wide range of mining and processing features which enable the
development of the mine working and its chronological range to be
reconstructed. The large rake, shafts, hillocks and other features provide
evidence for methods of extraction whilst other processing areas will contain
deposits showing the effectiveness of these techniques. The mining remains
also provide an insight into the Derbyshire Barmote Court system of mining and
the constraints this imposed on the miners of the area.
AncientMonuments.uk is an independent online resource and is not associated with any government department. All government data published here
is used under licence. Please do not contact AncientMonuments.uk for any queries related to any individual ancient or schedued monument,
planning permission related to scheduled monuments or the scheduling process itself. | 2024-03-08T01:26:35.434368 | https://example.com/article/3798 |
Abstract: Irritable bowel syndrome (IBS) is a chronic functional gastrointestinal disorder that affects about 9%–13% of the general population. IBS is one of the main reasons to consult a primary care physician, and nearly 30% of visits to a gastroenterologist are for IBS. The diagnosis of IBS relies on subjective, patient-reported symptoms, thus making urgent the need for IBS-specific biomarkers. The same biomarkers, or perhaps different ones, can also be used to monitor disease evolution and response to treatment. A significant number of studies have looked in the immune system for establishing IBS biomarkers, based on the concept that IBS might represent a condition of immune dysregulation somewhere in the spectrum between health and inflammatory bowel disease. Such biomarkers can be detected in blood, intestinal biopsies, or luminal contents. Overall, results are rarely consistent between studies; small sample size, patient and disease heterogeneity, presence of comorbidities, and variation in sampling might contribute to these discrepancies. So far, studies have failed to provide a diagnostic immune biomarker for IBS, but they have considerably advanced our understanding of the disease pathophysiology, including the role of the individual's genetic make-up, and of the host–microbial interactions. High throughput analysis of a large number of well characterized patients holds promise for developing appropriate biomarkers for IBS.
This work is published by Dove Medical Press Limited, and licensed under Creative Commons Attribution - Non Commercial (unported, v3.0) License.
The full terms of the License are available at http://creativecommons.org/licenses/by-nc/3.0/.
Non-commercial uses of the work are permitted without any further permission from Dove Medical Press Limited, provided the work is properly attributed.
Permissions beyond the scope of the License are administered by Dove Medical Press Limited.
Information on how to request permission may be found at: http://www.dovepress.com/permissions.php | 2024-03-16T01:26:35.434368 | https://example.com/article/3707 |
61st Writers Guild of America Awards
The 61st Writers Guild of America Awards honored the best film, television, and videogame writers of 2008. Winners were announced on February 7, 2009.
Nominees
Names in bold denote the winners.
Film
Best Adapted Screenplay
The Curious Case of Benjamin Button – Eric Roth (screenplay), Eric Roth and Robin Swicord (story); F. Scott Fitzgerald (author)
The Dark Knight – Jonathan and Christopher Nolan (screenplay), Christopher Nolan and David S. Goyer (story); Bob Kane and Bill Finger (creators)
Doubt – John Patrick Shanley (screenplay and playwright)
Frost/Nixon – Peter Morgan (screenplay and playwright)
Slumdog Millionaire – Simon Beaufoy (screenplay); Vikas Swarup (author)
Best Original Screenplay
Burn After Reading – Joel Coen and Ethan Coen
Milk – Dustin Lance Black
Vicky Cristina Barcelona – Woody Allen
The Visitor – Tom McCarthy
The Wrestler – Robert Siegel
Best Documentary Feature Screenplay
Boogie Man: The Lee Atwater Story - Stefan Forbes and Noland Walker
Chicago 10 - Brett Morgen
Fuel - Johnny O'Hara
Gonzo: The Life and Work of Dr. Hunter S. Thompson - Alex Gibney; from the words of Hunter S. Thompson
Waltz with Bashir - Ari Folman
Television
Dramatic Series
Comedy Series
New Series
Episodic Drama
Episodic Comedy
Long Form - Original
Long Form - Adaptation
Animation
Comedy/Variety (Including Talk) Series
Comedy/Variety – Music, Awards, Tributes – Specials
Daytime Serials
Children's
Episodic & Specials
Long Form or Special
Documentary
Current events
Other than current events
News
Regularly scheduled, bulletin, or breaking report
Analysis, feature, or commentary
Video games
Videogame Writing
Star Wars: The Force Unleashed - Haden Blackman, Shawn Pitman, John Stafford and Cameron Suey
Command & Conquer: Red Alert 3 - Writer Haris Orkin, story producer Mical Pedriana
Dangerous High School Girls in Trouble! - Writing Keith Nemitz, additional writing Adrianne Ambrose
Fallout 3 - Lead Writer Emil Pagliarulo, quest writing Erik J. Caponi, Brian Chapin, Jon Paul Duvall, Kurt Kuhlmann, Alan Nanes, Bruce Nesmith and Fred Zeleny, additional quest writing Nate Ellis, William Killeen, Mark Nelson and Justin McSweeney
Tomb Raider: Underworld - Story Eric Lindstrom and Toby Gard, screenplay Eric Lindstrom
Paul Selwin Civil Rights Award
Dustin Lance Black, "to the member whose script best embodies the spirit of constitutional and civil rights and liberties."
References
External links
2008
W
Category:2008 guild awards
W
Category:2008 awards in the United States | 2024-07-28T01:26:35.434368 | https://example.com/article/9460 |
Knee pads are commonly used to protect knees from hard surfaces and to provide padding and comfort to users of knee pads engaged in activities that may require the user to rest on his/her knees for long periods of time. Knee pads are generally strapped around a person's leg at the knee. Attachment can be with any combination of flexible straps and/or buckles. The straps assure that knee pads remain in contact with the front of a person's leg at their knee. Furthermore, straps keep a knee pad on a knee if a person had to stand up and walk to another location.
The problem with knee pads is that they can sometimes limit a person's movement over a hard surface. Knee pads are often made of a rubbery material so the knee pads tend to stick to a smooth surface such as floor tile or concrete as a person moves along the surface to work. The user must often pick up their knee/leg and move over the surface to adjust their position on the work surface (e.g., flooring). What the present inventor believes there is a need for are knee pads that can move easily over a flat surface such as flooring. The present inventor believes that an improved knee pad system would ease a user's required effort when working on a flat surface. | 2024-04-11T01:26:35.434368 | https://example.com/article/8528 |
---
abstract: |
We study the time evolution of quantum systems with a time-dependent non-Hermitian Hamiltonian given by a linear combination of SU(1,1) and SU(2) generators.With a time-dependent metric, the pseudo-Hermitian invariant operator is constructed in the same manner as for both the SU(1,1) and SU(2) systems. The exact common solutions of the Schrödinger equations for both the SU(1,1) and SU(2) systems are obtained in terms of eigenstates of the pseudo-Hermitian invariant operator.
PACS: 03.65.Ca, 03.65.-w
author:
- |
[Mustapha Maamache]{}$^{a}$[^1], [Oum Kaltoum Djeghiour]{}$^{a,b}$[^2], [Walid Koussa]{}$^{a}$[^3] [and Naima Mana]{}$^{a}$[^4]\
$^{(a)}$[Laboratoire de Physique Quantique et Systèmes Dynamiques,]{}\
[Faculté des Sciences, Université Ferhat Abbas Sétif 1, Sétif 19000, Algeria]{}*.*\
$^{(b)}$[Département de Physique, Université de Jijel, ,]{}\
[BP 98 Ouled Aissa, 18000 Jijel, Algeria.]{}
title: 'Time evolution of quantum systems with time-dependent non-Hermitian Hamiltonian and the pseudo Hermitian invariant operator'
---
Introduction
============
The use of invariants theory to solve quantum systems, whose Hamiltonian is an explicit function of time, has the advantage to offer an exact solution for problems solved by the traditional time-dependent perturbation theory. The existence of invariants (constants of the motion or first integral) introduced by Lewis [@lewis2] and Lewis- Riesenfeld [@lewis] is a factor of central importance in the study of such systems. The invariants method is very simple due to the relationship between the eigenstates of the invariant operator and the solutions of the Schrödinger equation by means of the phases; in this case the problem is reduced to find the explicit form of the invariant operator and the phases. In most cases, use is made of the Lewis–Riesenfield quadratic invariant to study two archetypal examples. One of these is the time-dependent generalized harmonic oscillator, the Hamiltonian of which is a time-dependent function of the SU(1,1) generator and the other is the spin in a time-dependent varying magnetic field with Hamiltonian consisting of the SU(2) generator. In [@lai1; @lai2; @cerv; @mus1], the SU(1, 1) and SU(2) time-dependent systems are exactly integrated and the time evolution operator are obtained thanks to the invariant Hermitian operator orto the unitary transformation approach.
There is a growing interest in the study of non-Hermitian Hamiltonian operators due to the fact that these operators may constitute valid quantum mechanical systems [@Scholz; @Carl1; @Carl5; @most1; @most3; @most4], because under certain conditions, non-Hermitian Hamiltonians may have a real spectrum and therefore may describe realistic physical systems. It has been clarified [@most1; @most3; @most4] , that a non-Hermitian Hamiltonian having all eigenvalues real is connected to its Hermitian conjugate through a linear, Hermitian, invertible and bounded metric operator $\eta=\rho^{+}\rho$ with a bounded inverse, satisfying $H^{+}=\eta H\eta^{-1}$ i.e. $H$ is Hermitian with respect to a positive definite inner product defined by $\left\langle
.,.\right\rangle _{\eta}=\left\langle .\left\vert \eta\right\vert
.\right\rangle $ and called as $\eta$ -pseudo-Hermitian. Essentially the same idea had appeared previously under the name of quasi-Hermiticity by Scholtz et al [@Scholz]. It is also established [@most1; @most3; @most4] that the non Hermitian Hamiltonian $H$ can be transformed to an equivalent Hermitian one given by $h=\rho
H\rho^{-1}$, where $h$ is the equivalent Hermitian analog of $H$ with respect to the standard inner product $\left\langle .,.\right\rangle .$
All these efforts have been devoted to study time-independent non-Hermitian systems. Whereas the treatment for systems with time-dependent non-Hermitian Hamiltonians with time-independent metric operators have been extensively studied [@Faria1; @Faria2], the generalization to time-dependent metric operators is quite controversial [@znojil1; @most5; @most6; @znojil2; @znojil3; @Bila; @wang1; @wang2; @mus; @fring1; @fring2; @khant; @frith; @luiz1; @luiz2].
Recent contributions [@fring1; @fring2] have advanced the grounds for treating time-dependent non-Hermitian Hamiltonians through time dependent Dyson maps. It has been argued that it is incompatible to maintain unitary time evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time dependent.
In light of the above discussion, one important question motivates our work here: How can we treat a non-Hermitian SU(1, 1) and SU(2) time-dependent quantum problems and investigate the possibility of finding the exact solution of the Schrödingerr equation in terms of eigenstates of the pseudo- invariant operator as well the real associated phases?
Let’s first briefly recall the pseudo-Hermitian invariants theory [@khant; @mus2]. The invariant operator $I^{PH}(t)$ is said to be pseudo-Hermitian with respect to $\eta(t)$ if$$I^{PH\dag}\left( t\right) =\eta(t)I^{PH}\left( t\right) \eta^{-1}(t)\text{
}\Leftrightarrow I^{h}(t)=\rho(t)I^{PH}(t)\rho^{-1}(t)=I^{h\dag}(t),\label{quasi}$$ where $\eta(t)=\rho^{+}(t)\rho(t)$ is a linear time dependent Hermitian invertible operator. Thus $I^{PH}\left( t\right) $ may be mapped to the Hermitian invariant operator $I^{h}\left( t\right) $, by a similarity transformation $\rho(t)$.
The solutions of the time-dependent Schrödinger equation ( $\hbar=c=1$ are used throughout) $$i\frac{\partial}{\partial t}\left\vert \Phi^{H}(t)\right\rangle
=H(t)\left\vert \Phi^{H}(t)\right\rangle , \label{shro}$$ for the non- Hermitian Hamiltonian $H(t)$ can be found with the aid of the quantum pseudo invariant method of Lewis and Riesenfeld. A pseudo-Hermitian invariant operator $I^{PH}(t)$ for a given non-Hermitian Hamiltonian $H(t)$ is defined to satisfy $$\frac{\partial I^{PH}(t)}{\partial t}=i\left[ I^{PH}\left( t\right)
,H(t)\right] , \label{lewisPH}$$ where $I^{PH}\left( t\right) $ has a finite number of nondegenerate eigenstates $\left\vert \phi_{n}^{H}(t)\right\rangle $ satisfying $$\text{ \ }I^{PH}\left( t\right) \left\vert \phi_{n}^{H}(t)\right\rangle
=\lambda_{n}\left\vert \phi_{n}^{H}(t)\right\rangle ,$$ and$$\left\langle \phi_{m}^{H}(t)\right\vert \eta(t)\left\vert \phi_{n}^{H}(t)\right\rangle =\delta_{m,n}$$ with time-independent eigenvalues $\lambda_{n}$ . Since the Hermitian invariant $I^{h}(t)$ and the non-Hermitian invariant $I^{PH}(t)$ are related by a similarity transformation (\[quasi\]), they belong to the same similarity class and therefore have the same eigenvalues. The reality of the eigenvalues $\lambda_{n}$ is guaranteed, since one of the invariants involved, i.e. $I^{h}(t),$ is Hermitian.
Now, if the exact invariant $I^{PH}\left( t\right) $ (constant of motion) exists and does not contain any time derivative operators, we can write the solutions of the Schrödinger equation (\[shro\]) in terms of the eigenfunctions $\left\vert \phi_{n}^{H}(t)\right\rangle $ of $I^{PH}\left( t\right) $,$$\left\vert \Phi_{n}^{H}(t)\right\rangle =e^{i\varphi_{n}(t)}\left\vert
\phi_{n}^{H}(t)\right\rangle , \label{sol}$$ the phase functions $\varphi_{n}(t)$ are derived from the equation:$$\frac{d\varphi_{n}(t)}{dt}=\left\langle \phi_{n}^{H}(t)\right\vert
\eta(t)\left[ i\hbar\frac{\partial}{\partial t}-H(t)\right] \text{\ }\left\vert \phi_{n}^{H}(t)\right\rangle . \label{Phase}$$ In Eq. (\[Phase\]), the first term is parallel to a familiar non-adiabatic geometrical phase, but the second term$,$ representing effects due to a time-dependent Hamiltonian, is a dynamical phase. The sum of these two terms that can ensure that the phase functions $\varphi_{n}(t)$ are real.
The general solution of the Schrödinger equation for the system with non-Hermitian time-dependent Hamiltonians $H(t)$ and pseudo-Hermtian invariant operator are readily obtained as follows: $$\left\vert \Phi^{H}(t)\right\rangle ={\textstyle\sum_{n}}
C_{n}e^{i\alpha_{n}(t)}\left\vert \phi_{n}^{H}(t)\right\rangle \label{Gensol}$$ where the $C_{n}$ = $\left\langle \phi_{n}^{H}(0)\right\vert \eta(0)\left\vert
\Phi^{H}(0)\right\rangle $ are time-independent coefficients.
Let’s note that, it then follows immediately by direct substitution of (\[quasi\]) into (\[lewisPH\]) that the two invariants operators $I^{PH\dag}\left( t\right) $ and $I^{h}(t)$ satisfy the following equations: $$\frac{\partial I^{PH+}(t)}{\partial t}=i\left[ I^{PH\dag}\left( t\right)
,\eta\left( t\right) H\left( t\right) \eta^{-1}\left( t\right)
+i\dot{\eta}\left( t\right) \eta^{-1}\left( t\right) \right] ,$$ $$\frac{\partial I^{h}(t)}{\partial t}=i\left[ I^{h}\left( t\right)
,\rho\left( t\right) H\left( t\right) \rho^{-1}\left( t\right)
+i\dot{\rho}\left( t\right) \rho^{-1}\left( t\right) \right] ,$$ which show that the non-Hermitian Hamiltonian $H(t)$ is related to its Hermitian conjugate $H^{\dag}\left( t\right) $ as $$H^{\dag}\left( t\right) =\eta\left( t\right) H\left( t\right) \eta
^{-1}\left( t\right) +i\dot{\eta}\left( t\right) \eta^{-1}\left(
t\right) , \label{PHH1}$$ and the Hermitian Hamiltonian $h(t)$ is linked to the non-Hermitian Hamiltonian $H\left( t\right) $ by the time-dependent Dyson equation$$h\left( t\right) =\rho\left( t\right) H\left( t\right) \rho^{-1}\left(
t\right) +i\dot{\rho}\left( t\right) \rho^{-1}\left( t\right) ,
\label{PHH2}$$ The above equations have been obtained by Fring and Moussa [@fring1; @fring2] by assuming that the two solutions $\left\vert \Phi
^{H}(t)\right\rangle $ and $\left\vert \Psi^{h}(t)\right\rangle $ of the two time-dependent Schrodinger equations ruled by $H\left( t\right) $ and $h\left( t\right) $ respectively, are related by a time-dependent invertible operator $\eta(t)$ as $\left\vert \Psi^{h}(t)\right\rangle =\eta(t)\left\vert
\Phi^{H}(t)\right\rangle $. Then, they argued that the time-dependent quasi-Hermiticity relation and the time-dependent Dyson equation can be solved consistently in such scenario for a time-dependent Dyson map and time-dependent metric operator, respectively.
Our approach is different from Fring’s and Moussa’s one, because we resolve the standard quasi-Hermiticity relation and the standard Dyson equation (\[quasi\]) for a time-dependent invariant operator with time-dependent $\eta(t)$ and a time-dependent similarity transformation $\rho(t).$ While the key feature in Fring’s and Moussa’s approach is that the relation (\[PHH1\]) is stated as the time-dependent quasi-Hermiticity relation. We believe that the resolution of the time-dependent Dyson equation and the time-dependent quasi-Hermiticity relation stated by Fring and Moussa become more difficult due to the presence of the last term in equations (\[PHH1\]) and (\[PHH2\]).
In this paper, we answer this question from a new perspective by studying the time-dependent non-Hermitian Hamiltonian systems given by a linear combination of SU(1, 1) and SU(2) generators using a pseudo-invariant operator theory which is constructed in a manner as for both the SU(1, 1) and SU(2) systems. An advantage of the pseudo- invariant operator is that it allows to obtain the exact solution of the Schrödinger equation in terms of eigenstates of the invariant operator as well as the time-evolution operator.
Evolution of non-Hermitian SU(1, 1) and SU(2) time-dependent systems
====================================================================
The SU(1, 1) and SU(2) time-dependent systems that we consider are described by the non-Hermitian Hamiltonian$$H(t)=2\omega(t)K_{0}+2\alpha(t)K_{-}+2\beta(t)K_{+}, \label{HH}$$ where $\left( \omega(t),\alpha(t),\beta(t)\right) $ $\in C$ are arbitrary functions of time. $K_{0}$ is a Hermitian operator, while $K_{+}=\left(
K_{-}\right) ^{+}$. The commutation relations between these operators are $$\left\{
\begin{array}
[c]{c}\left. \left[ K_{0},K_{+}\right] =K_{+}\right. \\
\left. \left[ K_{0},K_{-}\right] =-K_{-}\right. \\
\left. \left[ K_{+},K_{-}\right] =DK_{0}\right.
\end{array}
\right. . \label{lie}$$ The Lie algebra of SU(1, 1) and SU(2) consists of the generators $K_{0}$, $K_{-}$ and $K_{+}$ corresponding to $D=-2$ and $2$ in the commutation relations (\[lie\]), respectively.
In what follows, we investigate the quantum dynamics of our time-dependent systems (\[shro\]) associated with the Hamiltonian (\[HH\]) . To this end, we consider the most general invariant $I^{PH}(t)$ in the form $$I^{PH}(t)=2\delta_{1}(t)K_{0}+2\delta_{2}(t)K_{-}+2\delta_{3}(t)K_{+},
\label{IH}$$ where $\delta_{1}(t)$, $\delta_{2}(t)$, $\delta_{3}(t)$ are time dependent real parameters$.$ The invariant (\[IH\]) is of course manifestly non-Hermitian when $\delta_{2}(t)\neq$ $\delta_{3}(t).$
As is well known [@cheng; @kli; @bar] an element of the group of SU(1, 1) or SU(2) can be obtained by exponentiation of an element of the corresponding algebra. It is also well known that we can write down this element in many equivalent factorized ways. The Baker–Hausdorff–Campbell formula allows us to express all elements of SU(1, 1) or of SU(2) obtained by exponentiation of an Hermitic element of SU(1, 1) or of SU(2) as $$\begin{aligned}
\rho\left( t\right) & =\exp\left\{ 2\left[ \epsilon\left( t\right)
K_{0}+\mu\left( t\right) K_{-}+\mu^{\ast}\left( t\right) K_{+}\right]
\right\} ,\nonumber\\
& =\exp\left[ \vartheta_{+}\left( t\right) K_{+}\right] \exp\left[
\ln\vartheta_{0}\left( t\right) K_{0}\right] \exp\left[ \vartheta
_{-}\left( t\right) K_{-}\right] , \label{metr}$$ where $$\begin{aligned}
\vartheta_{+}\left( t\right) & =\frac{2\mu^{\ast}\sinh\theta}{\theta
\cosh\theta-\epsilon\sinh\theta}=-\zeta(t)e^{-i\varphi(t)},\nonumber\\
\vartheta_{0}\left( t\right) & =\left( \cosh\theta-\frac{\epsilon}{\theta}\sinh\theta\right) ^{-2}=-\frac{D}{2}\zeta^{2}(t)-\chi(t),
\label{TDC}\\
\vartheta_{-}\left( t\right) & =\frac{2\mu\sinh\theta}{\theta\cosh
\theta-\epsilon\sinh\theta}=-\zeta(t)e^{i\varphi(t)},\nonumber\\
\chi(t) & =-\frac{\cosh\theta+\frac{\epsilon}{\theta}\sinh\theta}{\cosh\theta-\frac{\epsilon}{\theta}\sinh\theta}\text{ \ \ \ \ \ \ ,\ \ \ }\theta=\sqrt{\epsilon^{2}+2D\left\vert \mu\right\vert ^{2}}.\nonumber\end{aligned}$$ This factorization is valid for SU(1, 1) ($D=-2$) and for SU(2) ($D=2$).
The key point of our method is to solve the standard quasi-Hermiticity relation (\[quasi\]) by making, for simplicity, the Hermitian ansatz (\[metr\]) for time-dependent invertible operator $\rho\left( t\right) $ Let us solve the standard quasi-Hermiticity relation (\[quasi\]) by making the following general and, for simplicity, Hermitian ansatz for a time dependent metric$\ \rho\left( t\right) .$We obtain, after some algebra, the transformed invariant operator $I^{h}(t)=\rho(t)I^{PH}(t)\rho^{-1}(t)$ $$\begin{aligned}
I^{h}(t) & =\frac{2}{\vartheta_{0}}\left[ \left[ \left( \frac{D}{2}\vartheta_{-}\vartheta_{+}-\chi\right) \delta_{1}+D\left( \vartheta
_{+}\delta_{2}+\chi\vartheta_{-}\delta_{3}\right) \right] K_{0}\right.
\nonumber\\
& \left. +\left( \vartheta_{-}\delta_{1}+\delta_{2}-\frac{D}{2}\vartheta_{-}^{2}\delta_{3}\right) K_{-}+\left( \chi\vartheta_{+}\delta
_{1}-\frac{D}{2}\vartheta_{+}^{2}\delta_{2}+\chi^{2}\delta_{3}\right)
K_{+}\right] . \label{invh}$$ The derivation of equation (\[invh\]) is made of the following identities: $$\left\{
\begin{array}
[c]{c}\exp\left[ \vartheta_{-}K_{-}\right] K_{0}\exp\left[ -\vartheta_{-}K_{-}\right] =K_{0}+\vartheta_{-}K_{-}\\
\exp\left[ \vartheta_{+}K_{+}\right] K_{0}\exp\left[ -\vartheta_{+}K_{+}\right] =K_{0}-\vartheta_{+}K_{+}\end{array}
\right. ,$$ $$\left\{
\begin{array}
[c]{c}\exp\left[ \ln\vartheta_{0}K_{0}\right] K_{-}\exp\left[ -\ln\vartheta
_{0}K_{0}\right] =\frac{K_{-}}{\vartheta_{0}}\\
\exp\left[ \vartheta_{+}K_{+}\right] K_{-}\exp\left[ -\vartheta_{+}K_{+}\right] =K_{-}+D\vartheta_{+}K_{0}-\frac{D}{2}\vartheta_{+}^{2}K_{+}\end{array}
\right. ,$$ $$\left\{
\begin{array}
[c]{c}\exp\left[ \ln\vartheta_{0}K_{0}\right] K_{+}\exp\left[ -\ln\vartheta
_{0}K_{0}\right] =\vartheta_{0}K_{+}\\
\exp\left[ \vartheta_{-}K_{-}\right] K_{+}\exp\left[ \vartheta_{-}K_{-}\right] =K_{+}-D\vartheta_{-}K_{0}-\frac{D}{2}\vartheta_{-}^{2}K_{-}\end{array}
\right. .$$ For $I^{h}(t)$ to be Hermitian ($I^{h}(t)=I^{+h}(t)$) we require the coefficient of $K_{0}$ is real, and the coefficients of $K_{-}$ and $K_{+}$ are complex conjugate of one another. Using these two requirements, we have: $$\begin{aligned}
\left[ \left( \frac{D}{2}\vartheta_{-}\vartheta_{+}-\chi\right) \delta
_{1}+D\left( \vartheta_{+}\delta_{2}+\chi\vartheta_{-}\delta_{3}\right)
\right] & =\left[ \left( \frac{D}{2}\vartheta_{-}\vartheta_{+}-\chi\right) \delta_{1}+D\left( \vartheta_{-}\delta_{2}+\chi\vartheta
_{+}\delta_{3}\right) \right] ,\nonumber\\
\left( \vartheta_{-}\delta_{1}+\delta_{2}-\frac{D}{2}\vartheta_{-}^{2}\delta_{3}\right) & =\left( \chi\vartheta_{-}\delta_{1}-\frac{D}{2}\vartheta_{-}^{2}\delta_{2}+\chi^{2}\delta_{3}\right) ,\\
\left( \chi\vartheta_{+}\delta_{1}-\frac{D}{2}\vartheta_{+}^{2}\delta
_{2}+\chi^{2}\delta_{3}\right) & =\left( \vartheta_{+}\delta_{1}+\delta_{2}-\frac{D}{2}\vartheta_{+}^{2}\delta_{3}\right) ,\nonumber\end{aligned}$$ from the first constraint we derive the equality $$\delta_{2}=\delta_{3}\chi, \label{delta1}$$ while the other two constraints leads to $$\begin{aligned}
\delta_{1} & =\frac{\left( \frac{D}{2}\vartheta_{-}^{2}-\chi\right)
}{\vartheta_{-}}\delta_{3},\nonumber\\
\delta_{1} & =\frac{\left( \frac{D}{2}\vartheta_{+}^{2}-\chi\right)
}{\vartheta_{+}}\delta_{3}. \label{delta}$$ From the equations (\[delta\]), it follows that $\vartheta_{+}(t)=$ $\vartheta_{-}(t)\equiv-\zeta(t)$ implying that the time dependent parameter $\mu(t)$ must be real, i.e. $\mu(t)=\mu^{\ast}(t)$. Finally the similarity transformation (\[metr\]) maps the non-Hermitian quadratic invariant (\[IH\]) into $I^{h}(t)$ given by $$I^{h}\left( t\right) =\frac{2}{\vartheta_{0}}\left[ \left( \frac{D}{2}\zeta^{2}-\chi\right) \delta_{1}-2D\chi\zeta\delta_{3}\right] K_{0}.
\label{invh1}$$
Let $\left\vert \psi_{n}^{h}\right\rangle $ be the eigenstate of $K_{0}$ with eigenvalue $k_{n}$ i.e.$$K_{0}\left\vert \psi_{n}^{h}\right\rangle =k_{n}\left\vert \psi_{n}^{h}\right\rangle .$$ The eigenstates of $I^{h}\left( t\right) $ (\[invh1\]) are obviously given by $$I^{h}\left( t\right) \left\vert \psi_{n}^{h}(t)\right\rangle =\frac
{2}{\vartheta_{0}}\left[ \left( \frac{D}{2}\zeta^{2}-\chi\right) \delta
_{1}-2D\chi\zeta\delta_{3}\right] k_{n}\left\vert \psi_{n}^{h}\right\rangle
\text{, \ }$$ because of the time-dependence, the invariant $I^{h}\left( t\right) $ is a conserved quantity whose eigenvalues are real constants. However, without loss of generality, the factor $\left[ \left( D\zeta^{2}/2-\chi\right)
\delta_{1}-2D\chi\zeta\delta_{3}\right] /\vartheta_{0}$ can be taken equal to $1.$ It follows that the eigenstate $\left\vert \phi_{n}^{H}(t)\right\rangle
$ of $I^{PH}(t)$ can be directly deduced from the basis $\left\vert \psi
_{n}^{h}\right\rangle $ of its Hermitian counterpart $I^{h}\left( t\right) $ through the similarity transformation $\left\vert \phi_{n}^{H}(t)\right\rangle
=$ $\rho^{-1}(t)\left\vert \psi_{n}^{h}\right\rangle $ with time-independent eigenvalue $k_{n}.$
According to the above discussions, the problem is reduced to find a pseudo Hermitian invariant operator and the suitable real phases of its eigenfunctions to take them as a solution for the Schrödinger equation. In a first step, we will determine the real parameters $\delta_{1},\delta
_{2},\delta_{3}$ so that our invariant operator $I^{PH}(t)$ (\[IH\]) is pseudo Hermitian. Imposing the quasi- Hermiticity condition (\[quasi\]) on $I^{h}\left( t\right) ,$ we get $$\begin{aligned}
I^{\dag PH}(t) & =\rho^{+}\left( t\right) I^{h}\left( t\right)
\rho^{-1+}\left( t\right) =2\delta_{1}\hat{K}_{0}+2\delta_{3}\hat{K}_{-}+2\delta_{2}\hat{K}_{+}\nonumber\\
& =\frac{2}{\vartheta_{0}}\left[ \left( \frac{D}{2}\zeta^{2}-\chi\right)
\hat{K}_{0}-\zeta\hat{K}_{-}-\chi\zeta\hat{K}_{+}\right] .\end{aligned}$$ From the above equation the real parameters $\delta_{1},\delta_{2},\delta_{3}$ follow straightforwardly:$$\delta_{1}=\frac{\left( \frac{D}{2}\zeta^{2}-\chi\right) }{\vartheta_{0}}\text{ , }\delta_{2}=-\frac{\chi\zeta}{\vartheta_{0}}\text{ , }\delta
_{3}=-\frac{\zeta}{\vartheta_{0}}.$$ Therefore, the pseudo Hermitian invariant operator $I^{PH}(t)$ is written in the following form $$I^{PH}(t)=\frac{2}{\vartheta_{0}}\left[ \left( \frac{D}{2}\zeta^{2}-\chi\right) K_{0}-\chi\zeta K_{-}-\zeta K_{+}\right] . \label{PH1}$$
The second step in the method is imposing for $I^{PH}(t)$(\[PH1\]) the invariance condition (\[lewisPH\]) which lead to the following relations : $$\dot{\vartheta}_{0}=\frac{2\vartheta_{0}}{\zeta}\left[ -2\zeta\left\vert
\omega\right\vert \sin\varphi_{\omega}+\left\vert \alpha\right\vert
\sin\varphi_{\alpha}+\left( \chi-D\zeta^{2}\right) \left\vert \beta
\right\vert \sin\varphi_{\beta}\right] , \label{cont1}$$ $$\overset{\cdot}{\zeta}=-2\zeta\left\vert \omega\right\vert \sin\varphi
_{\omega}+2\left\vert \alpha\right\vert \sin\varphi_{\alpha}-D\zeta
^{2}\left\vert \beta\right\vert \sin\varphi_{\beta}, \label{cont2}$$ $$\
\begin{array}
[c]{c}\chi\left\vert \beta\right\vert \cos\varphi_{\beta}=\left\vert \alpha
\right\vert \cos\varphi_{\alpha}\\
\left( \chi-\frac{D}{2}\zeta^{2}\right) \left\vert \alpha\right\vert
\cos\varphi_{\alpha}=\chi\zeta\left\vert \omega\right\vert \cos\varphi
_{\omega}\\
\zeta\left\vert \omega\right\vert \cos\varphi_{\omega}=\left( \chi-\frac
{D}{2}\zeta^{2}\right) \left\vert \beta\right\vert \cos\varphi_{\beta}\end{array}
, \label{rel}$$ here, $\varphi_{\omega}$, $\varphi_{\alpha}$ , and $\varphi_{\beta}$ are the polar angles of $\omega$, $\alpha$, and $\beta$, respectively.
The final step consists in determining the Schrodinger solution (\[sol\]) which is an eigenstate of the pseudo Hermitian invariant (\[PH1\]) multiplied by a time-dependent factor (\[Phase\]) $$\begin{aligned}
\frac{d\varphi_{n}(t)}{dt} & =\left\langle \phi_{n}^{H}(t)\right\vert
\eta(t)\left[ i\frac{\partial}{\partial t}-H(t)\right] \text{\ }\left\vert
\phi_{n}^{H}(t)\right\rangle \nonumber\\
& =\left\langle \psi_{n}^{h}\right\vert \left[ i\rho\dot{\rho}^{-1}-\rho
H\rho^{-1}\right] \text{\ }\left\vert \psi_{n}^{h}\right\rangle .
\label{Phase1}$$ Using the non-Hermitian Hamiltonian $H(t)$ (\[HH\]) and then deriving the transformed Hamiltonian $\left[ i\rho\dot{\rho}^{-1}-\rho H\rho^{-1}\right]
$ through the metric operator $\rho(t)$ (\[metr\]), we further identify this transformed Hamiltonian as $$i\rho\dot{\rho}^{-1}-\rho H\rho^{-1}=2W\left( t\right) K_{0}+2U\left(
t\right) K_{-}+2V\left( t\right) K_{+},$$ where the coefficient functions are$$\begin{aligned}
W\left( t\right) & =-\frac{1}{\vartheta_{0}}\left[ \omega\left( \frac
{D}{2}\zeta^{2}-\chi\right) -D\zeta\left( \alpha+\beta\chi\right) +\frac
{i}{2}\left( \dot{\vartheta}_{0}+D\zeta\overset{\cdot}{\zeta}\right)
\right] ,\\
U\left( t\right) & =\frac{1}{\vartheta_{0}}\left[ \omega\zeta
-\alpha+\frac{D}{2}\beta\zeta^{2}+i\frac{\overset{\cdot}{\zeta}}{2}\right]
,\\
V\left( t\right) & =\frac{1}{\vartheta_{0}}\left[ \omega\chi\zeta
+\frac{D}{2}\alpha\zeta^{2}-\beta\chi^{2}-\frac{i}{2}\left( \zeta
\dot{\vartheta}_{0}-\vartheta_{0}\overset{\cdot}{\zeta}+\frac{D}{2}\vartheta^{2}\overset{\cdot}{\zeta}\right) \right] .\end{aligned}$$ By using Eqs. (\[rel\]), the above time-dependent coefficients $U$ $,V$ are identically equal to zero ($U$ $=V=0$), whereas the coefficients $W$ is reduced to $$W\left( t\right) =-\frac{1}{\vartheta_{0}}\left\{ \left( \frac{D}{2}\zeta^{2}-\chi\right) \left\vert \omega\right\vert \cos\varphi_{\omega
}-2D\zeta\left\vert \alpha\right\vert \cos\varphi_{\alpha}-i\frac
{\vartheta_{0}}{\zeta}\left[ \zeta\left\vert \omega\right\vert \sin
\varphi_{\omega}-\left\vert \alpha\right\vert \sin\varphi_{\alpha}-\chi\left\vert \beta\right\vert \cos\varphi_{\beta}\right] \right\} .$$ Knowing that the phase $\varphi_{n}(t)$ (\[Phase1\]) must be real, we need to impose that the frequency $W\left( t\right) $ is real. Then, we obtain the exact phase of the eigenstate $$\varphi_{n}(t)=-2k_{n}{\displaystyle\int\limits_{0}^{t}}
\frac{1}{\vartheta_{0}}\left[ \left( \frac{D}{2}\zeta^{2}-\chi\right)
\left\vert \omega\right\vert \cos\varphi_{\omega}-2D\zeta\left\vert
\alpha\right\vert \cos\varphi_{\alpha}\right] dt^{\prime}. \label{phase1}$$ Therefore, the general solution (\[Gensol\])of the Schrödinger equation is given by $$\left\vert \Phi^{H}(t)\right\rangle ={\textstyle\sum_{n}}
C_{n}(0)\exp\left( -ik_{n}{\displaystyle\int\limits_{0}^{t}}
\frac{2}{\vartheta_{0}}\left[ \left\vert \omega\right\vert \left( \frac
{D}{2}\zeta^{2}-\chi\right) \cos\varphi_{\omega}-2D\zeta\left\vert
\alpha\right\vert \cos\varphi_{\alpha}\right] dt^{\prime}\right) \left\vert
\phi_{n}^{H}(t)\right\rangle .$$
Few special examples
=====================
$\bigskip$Generalized time dependent non-Hermitian Swanson Hamiltonian
----------------------------------------------------------------------
We now consider the SU(1,1) case first where $D=-2$. The SU(1,1) Lie algebra has a realization in terms of boson creation and annihilation operators $a^{+}$ and $a$ such that$$K_{0}=\frac{1}{2}\left( a^{+}a+\frac{1}{2}\right) ,\text{ \ \ }K_{-}=\frac{1}{2}a^{2},\text{ \ \ \ \ }K_{+}=\frac{1}{2}a^{+2}.$$
When the Hamiltonian (\[HH\]) is expressed in terms of position $x$ and momentum $p,$ it describes the generalized quadratic time-dependent non-Hermitian harmonic oscillator. The celebrated model of a non-Hermitian PT-symmetric Hamiltonian quadratic in position and momentum was studied first by Ahmed [@ahmed] and made popular by Swanson [@swanson] when it was$\ $expressed in terms of the usual harmonic oscillator creation $a^{+}$ and annihilation $a$ operators with $\omega,\alpha$ and $\beta$ time-independent real parameters, such that $\alpha\neq$ $\beta$ and $\omega^{2}-4\alpha\beta>0$. This Hamiltonian has been studied extensively in the literature by several authors [@jones; @bagchi; @musumbu; @quesne; @sinha; @eva].
We construct here, by employing the Lewis-Riesenfeld method of invariants, the solutions for the generalized version of the non-Hermitian Swanson Hamiltonian with time-dependent coefficients[@fring2]$$H(t)=\omega(t)\left( a^{+}a+\frac{1}{2}\right) +\alpha(t)a^{2}+\beta(t)a^{+2},$$ where $\left( \omega(t),\alpha(t),\beta(t)\right) $ $\in C$ are time-dependent parameters. The form for $I^{PH}(t)$, which is both convenient for calculations , is$$\begin{aligned}
I^{PH}(t) & =\exp\left[ \frac{\zeta}{2}a^{2}\right] \exp\left[ -\frac
{\ln\vartheta_{0}}{2}\left( a^{+}a+\frac{1}{2}\right) \right] \exp\left[
\frac{\zeta}{2}a^{+2}\right] \text{ }\left( a^{+}a+\frac{1}{2}\right)
\text{ }\nonumber\\
& \times\exp\left[ -\frac{\zeta}{2}a^{+2}\right] \exp\left[ \frac
{\ln\vartheta_{0}}{2}\left( a^{+}a+\frac{1}{2}\right) \right] \exp\left[
-\frac{\zeta}{2}a^{2}\right] ,\end{aligned}$$ which brings out the Hamiltonian $2K_{0}=\left( a^{+}a+\frac{1}{2}\right) $ of the usual harmonic oscillator whose eigenstates $\left\vert n\right\rangle
$ ($n=0,1,3...$) and eigenvalues $\left( n+\frac{1}{2}\right) $ are well known. As eigenstates of $I^{PH}(t)$ one can then take $$\left\vert \phi_{n}^{H}(t)\right\rangle =\exp\left[ \frac{\zeta}{2}a^{2}\right] \exp\left[ -\frac{\ln\vartheta_{0}}{2}\left\{ \left(
a^{+}a+\frac{1}{2}\right) -\left( n+\frac{1}{2}\right) \right\} \right]
\exp\left[ \frac{\zeta}{2}a^{+2}\right] \left\vert n\right\rangle ,$$ the corresponding phase ( \[phase1\] ) $\varphi_{n}(t)$ is $$\varphi_{n}(t)=(n+\frac{1}{2}){\displaystyle\int\limits_{0}^{t}}
\frac{1}{\vartheta_{0}}\left[ \left( \zeta^{2}+\chi\right) \left\vert
\omega\right\vert \cos\varphi_{\omega}-4\zeta\left\vert \alpha\right\vert
\cos\varphi_{\alpha}\right] dt^{\prime}.$$
A spinning particle in a time-varying magnetic field
----------------------------------------------------
Now, we consider $D=2$ where the Hamiltonian (\[HH\]) and the invariant (\[PH1\]) possesse the symmetry of the dynamical group SU(2). There is substantial literature on the time evolution of two-level system governed by a non-Hermitian Hamiltonian $H(t)=\mathbf{B}(t)\mathbf{\sigma}$ [@1; @2; @3; @4; @5; @6; @7], where $\mathbf{\sigma}$ is the vector of Pauli and the components of the field $\mathbf{B}(t)$ are complex.
Knowing that, the ferromagnetic materials like Cobalt and Iron produce magnetic fields whose magnitudes are measured by real numbers. Imaginary or complex fields are, however, essential in the fundamental theory that underlies the statistical physics of phase transitions, such as those associated with the onset of magnetization. Long thought to be merely mathematical constructs, a realization of these imaginary fields has now been observed in magnetic resonance experiments performed on the spins of a molecule [@8], following an earlier theoretical proposal. A spin in a time-varying complex magnetic field is a practical example for the case $D=2$ . Let $$K_{0}=J_{z},\ \ K_{-}=J_{-},\ \ \ \ K_{+}=J_{+},$$ the Hamiltonian and the invariant are $$\begin{aligned}
H(t) & =2\left[ \omega(t)J_{z}+\alpha(t)J_{-}+\beta(t)J_{+}\right] ,\\
I^{PH}(t) & =\frac{2}{\vartheta_{0}}\left[ \left( \zeta^{2}-\chi\right)
J_{z}-\chi\zeta J_{-}-\zeta J_{+}\right] ,\end{aligned}$$ where $\mathbf{J}$ is the spin angular momentum of the particle. The form for $I^{PH}(t)$, which is both convenient for calculations , is$$I^{PH}(t)=\exp\left[ \zeta J_{-}\right] \exp\left[ -\ln\vartheta_{0}J_{z}\right] \exp\left[ \zeta J_{+}\right] \text{ }J_{z}\text{ }\exp\left[
-\zeta J_{+}\right] \exp\left[ \ln\vartheta_{0}J_{z}\right] \exp\left[
-\zeta J_{-}\right] .$$ The instantaneous eigenstates of $I^{PH}(t)$ can be written in terms of the eigenstates of $J_{z}$ denoted by $\left\vert m\right\rangle $, as $$\left\vert \phi_{m}^{H}(t)\right\rangle =\exp\left[ \zeta J_{-}\right]
\exp\left[ -\ln\vartheta_{0}\left( J_{z}-m\right) \right] \exp\left[
\zeta J_{+}\right] \left\vert m\right\rangle ,$$ the corresponding eigenvalues are $m$. With the factor of $\exp\left[
m\ln\vartheta_{0}\right] $ included in the definition of $\left\vert \phi
_{m}^{H}(t)\right\rangle $, the vector potential is singular only at the south pole.
For this case, the phase ( \[phase1\] )$\varphi_{m}(t)$ is easy to calculate and is given by $$\varphi_{m}(t)=-m{\displaystyle\int\limits_{0}^{t}}
\frac{2}{\vartheta_{0}}\left[ \left( \zeta^{2}-\chi\right) \left\vert
\omega\right\vert \cos\varphi_{\omega}-4\zeta\left\vert \alpha\right\vert
\cos\varphi_{\alpha}\right] dt^{\prime}.$$ Before concluding this paper, we give a particular case when the parameters of $H(t)$ are reals ; i.e., $\left( \omega(t),\alpha(t),\beta(t)\right) $ $\in
R$ .
The Hamiltonian $H(t)$ with real coefficients $\omega
(t),\alpha(t),\beta(t)$
-----------------------------------------------------
When considering the time-dependent coefficients $\omega(t),\alpha
(t),\beta(t)$ to be real functions instead of complex ones, the polar angles the polar angles $\varphi_{\omega}$, $\varphi_{\alpha}$, and $\varphi_{\beta}$ of $\omega$, $\alpha$, and $\beta$, vanish. By imposing that $\varphi_{\omega
}=\varphi_{\alpha}=$ $\varphi_{\beta}=0$, the Eqs.( \[cont1\]- \[rel\]) are simplified to $$\dot{\vartheta}_{0}=0,$$ $$\overset{\cdot}{\zeta}=0,$$ $$\
\begin{array}
[c]{c}\chi\left\vert \beta\right\vert =\left\vert \alpha\right\vert \\
\left( \chi-\frac{D}{2}\zeta^{2}\right) \left\vert \alpha\right\vert
=\chi\zeta\left\vert \omega\right\vert \\
\zeta\left\vert \omega\right\vert =\left( \chi-\frac{D}{2}\zeta^{2}\right)
\left\vert \beta\right\vert
\end{array}
. \label{fin}$$ As one can see from the last equations that the metric parameters $\left(
\ref{TDC}\right) \ \zeta$, $\vartheta_{0}$ are constants. Thus, the time-dependent real coefficients $\omega(t),\alpha(t),\beta(t)$ of $H(t)$ provide a time-independent metric and consequently the gaugelike term $i\hbar\dot{\eta}\left( t\right) \eta^{-1}\left( t\right) $ in the quasi-Hermiticity relation $\left( \ref{PHH1}\right) $disappears and the standard quasi-Hermiticity relation $\eta\left( t\right) H\left( t\right)
=H^{\dag}\left( t\right) \eta\left( t\right) $ for the Hamiltonian $H(t)$ itself is recovered in complete analogy with the time-independent scenario. Thus $H(t)$ is self-adjoined operator and therefore observable and can be written in the following simple form $$H(t)=2\frac{\omega(t)}{\left( \frac{D}{2}\zeta^{2}-\chi\right) }\left\{
\left( \frac{D}{2}\zeta^{2}-\chi\right) K_{0}-\chi\zeta K_{-}-\zeta
K_{+}\right\} =\frac{\omega(t)\vartheta_{0}}{\left( \frac{D}{2}\zeta
^{2}-\chi\right) }I^{PH}(t),$$ which reveal its self-adjoined character and therefore its observability. From Eqs.( \[fin\]), we derive the metric parameter $\zeta$ in terms of parameters of the Hamiltonian $H(t)$ $$\zeta=\frac{1}{2\left\vert \beta\right\vert }\left( -\frac{D}{2}\left\vert
\omega\right\vert \pm\sqrt{\left\vert \omega\right\vert ^{2}+2D\left\vert
\alpha\right\vert \left\vert \beta\right\vert }\right) .$$
Conclusion
==========
The results we have presented offer a general and comprehensive treatment of the non-Hermitian dynamics of SU(1,1) and SU(2) quantum systems. Non-Hermitian Hamiltonian operators have been the subject of considerable interest during the last years within the framework of the PT symmetry and pseudo-Hermiticity theories.
Recently, It has demonstrated that a time-dependent metric operator cannot ensure the unitarity of the time evolution simultaneously with the observability of the Hamiltonian and thus the general framework for a description of a time evolution for time-dependent non-Hermitian Hamiltonians has been stated [@fring1; @fring2]. A well-known method based on a time-dependent unitary transformation for the treatment of time-dependent Hermitian Hamiltonians [@mus1; @mizrahi], has been adapted by the authors of Ref. [@fring2] to solve the the time-dependent Dyson and the time-dependent quasi-Hermiticity relations for non-Hermitian Swanson Hamiltonian with time-dependent coefficients, where the time-dependent unitary transformation is replaced by a non-unitary transformation to conform to non-Hermitian Hamiltonians.
In this work, using the standard quasi-Hermiticity relation (\[quasi\]) between a non-Hermitian invariant operator $I^{PH}(t)$ and a Hermitian one $I^{h}(t)$, we have considered the dynamical behavior of SU(1,1) and SU(2) non-Hermitian time-dependent quantum systems by presenting an alternative approach to solve it. We investigated in detail the main frames of time-dependent non-Hermitian SU(1,1) and SU(2) systems in the framwork of the Lewis and Riesenfeld method which ensures that a solution of the Schrödinger equation governed by a time-dependent non-Hermitian Hamiltonian is an eigenstate of an associated pseudo-Hermitian invariant operator $I^{PH}(t)$ with a time-dependent global real phase factor $\varphi_{n}(t)$.
The properties derived here help us to understand better systems described by time-dependent non-Hermitian Hamiltonians and should play a central role in time-dependent non-Hermitian quantum mechanics. After going through these properties, we then have presented two illustrative examples: the generalized Swanson model and a spinning particle in a time-varying magnetic field. When a time dependent parameters $\omega(t),\alpha(t),\beta(t)$ are supposed real, the standard quasi-Hermiticity relation for the time dependent Hamiltonian $H\left( t\right) $ occur and the metric operator become time-independent.
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[^1]: E-mail: maamache@univ-setif.dz
[^2]: E-mail: k.djeghiourjijel@gmail.com
[^3]: E-mail: koussawalid@yahoo.com
[^4]: E-mail: na3ima\_mn@hotmail.fr
| 2024-03-29T01:26:35.434368 | https://example.com/article/7003 |
Lithium neurotoxicity at therapeutic level--a case report.
A 30 years old Hindu male presenting with symptoms of lithium toxicity. On investigation, serum lithium level was found to be 0.5 meq/l. Though toxicity at this level of lithium is unusual, still neurotoxicity happened to be the cause of his hospital admission. He was debarred from taking lithium further and carbamazepine was started as mood elevator. He responded favourably. | 2024-06-01T01:26:35.434368 | https://example.com/article/4561 |
‘Hey, have you ever heard of a beer called IPA? Apparently it’s a really bitter…’ — And that’s when your face goes dull with that ‘You so 2000 and late’ look and you stop listening. That’s being nice- you’d probably tune out at ‘IPA’.
Just like how Christopher Columbus thought he was the first to discover America, so too are foodies, trendies, and fledgling craft beer enthusiasts of late discovering sour beer. Hipsters heard about them after NPR broke the story on sours in October of 2013, but then promptly gave up drinking them a week later out of principle. My mom even forwarded me a snippet from February’s Bon Appétit magazine¹ where the author dishes out food pairing advice, remarking how the “elegant Champagne fizz and acidic twang” of this sour style, beloved by “beer nerds” [thanks?], “chainsaws through fatty or salty foods, yet is delicate enough for sushi.” Domo arigato Mr. Foodboto, but having an appreciation for sour beer does not qualify one as a “beer nerd” (whatever that means) any more than eating at a food truck makes one a culinary aficionado.
The truth is that if NPR, Bon Appétit, USA Today, the New York Times, and my mom have already heard about them, sours have officially reached critical mainstream mass. Though to be fair to the late comers, sour brews have only gained this new found pop culture popularity over the last two or three years. Prior to that, sour craft beers were something of a rarity stateside, let alone the majority of the modern beer drinking world.
Go back 150 years though, and sour beers weren’t simply a regional specialty or a brewer’s attempt at passion-driven innovation, nor were they altogether uncommon. Even so, it was seldom the brewery’s intention to pour their publicans a sour pint. In fact, in many circles of the brewing industry, sour beer was often referred to as “diseased beer” and was almost without exception considered the bane of the brewhouse. Because once a brewery noticed one of its beers becoming unintentionally sour, to its helpless devastation, it was usually only a matter of time before the rest of the production line followed sour suit, thereby risking the life of the brewery itself. And beer wasn’t the only fermentable becoming “diseased”. Nope, wine and some spirit producers suffered the same fate as well.
That was until 1866 when Louis Pasteur, under the commission of Emperor Napoleon III- nephew to the Napoleon (oh my), published his book Etudes sur le Vin (Studies on Wine) as a remedy to both the economic and reputational loss within the French winemaking industry due to diseased wine. Both brewers and winemakers alike were plagued by “spoilage”, or the unintentional souring of their products, and it was Pasteur, doctor of boozeology, who identified that the culprits responsible for the souring were primarily tiny black rod shaped lactic acid producing micro-organisms presumably introduced into the fermenting beverages via germ-ridden dust in the air (an idea that was largely groundbreaking for the day).
[Lactobacillus bacteria responsible for producing lactic acid.]
What was Pasteur’s solution to these ATDs (Aerially Transmitted Diseases)? Practice safe fermentation. Clean up the winery and the staff, limit exposure of the wine to the souring critters in the air, and last but not least, master the art of Pasteurization, i.e. heating the wine to about 122-144 °F for a specific period of time in order to kill off any potential souring microorganisms. Many of these tactics were soon adopted by the brewing industry along with other methods including temperature control, increased hopping rates, and yeast purification, all of which were prescribed in Pasteur’s follow-up blockbuster (and Amazon Best Seller of 1876) Etudes sur la Bière²; literally “Studies on Beer”, but masterfully translated into English as “Studies on Fermentation: The Diseases of Beer”.
And with this, the days of sour beers appeared to be numbered; however the final curtain call wouldn’t come from Pasteur, but rather a man on an island over 600 miles away.
One Yeast Strain to Rule Them All
Around the time Pasteur was releasing his book Studies on Beer, Danish scientist Emil Hansen was set with the task of separating out unwanted microorganisms in a yeast culture in order to cultivate a pure strain of yeast. But this was no random undertaking in the vacuum of science. No, Hansen was employed by the Carlsberg Laboratory in Copenhagen, a facility created in 1875 by the founder of the Carlsberg Brewery and established for the purpose of advancing biochemical knowledge particularly related to brewing. It turns out that Hansen was triumphantly successful at his task and in 1883 he was able to isolate one very particular yeast strain that would go on to form the basis of a certain style of beer that quickly dominated the world.
This singular variety of yeast in conjunction with the techniques Hansen used to ensure a pure culture brought about not only the absolute monarchy of a single beer style (which established the reign of at least one King of Beers in the U.S.), but also led to the growth of multi-billion dollar corporations so powerful that it would take a revolution to even slightly loosen their soul-crushing stranglehold on the industry.
The beer style in question is none other than lager.
Hansen’s pure lager yeast was offered to other breweries when their beers turned sour, and eventually this lager yeast made its way around the world, changing the entire landscape of beer along with it. In honor of Hansen’s industry revolutionizing accomplishment, the Carlsberg Brewing consort named this world-famous pure yeast strain after him, calling it “Saccharomyces Carlsbergensis”— wait, umm, well close enough.
But it was to be Hansen who would have the last laugh as S. Carlsbergensis was later renamed, to the delight of Francophiles, “S. Pastorianus”, which of course is Latin for “let’s pretend that Pasteur figured out how to produce pure yeast cultures and give no credit to Hansen”. I guess if you really wanted to get technical, Hansen actually “borrowed” his yeast separating technique from German microbiologist Robert Koch.³ So if I were Germany, I’d throw my vote in for renaming the yeast “S. Kochianus”, but that’s just me.
Brewers became so efficient at isolating and controlling souring bacteria and yeast that with the exception of a number of breweries in Belgium and a few regional ones in Germany, sour beers nearly went extinct.
Certainly some sour styles of beer did go extinct, and perhaps more would have if it weren’t in large part for the craft beer revolution sweeping the globe today. Country after country is walking up from its lager/pilsner saturated slumbers and realizing there’s something else out there. Something better. Something sour. And we want it.
It’s said that a full 70 percent of the production of the world-renowned Belgian sour beer producer, Cantillon, is exported to the U.S. To those who’ve ever had the pleasure of sipping a sour from Cantillon, you’ll know why the U.S., as with other desirable finite commodities, wants as much of it as we can get our greedy little fingers on.
And sours aren’t just the realm of traditional continental breweries or the more specialized Russian River or Crooked Stave types in the U.S. Big names are getting in on the action too. Boston Beer Company, Sierra Nevada, Widmer Brothers, Flying Dog, Magic Hat, Odell, Avery, Anderson Valley, Great Lakes, Bell’s, Allagash, Ballast Point, Deschutes, New Belgium, Goose Island, Three Floyds, and Grand Teton have all brewed sours or have one in the rotation. I wouldn’t be surprised to see a weak, watery pseudo sour in the pipe from one of the mega un-craft breweries trying to cash in on this craze, albeit disguised in the predictable faux-craft fashion as is now the custom (think Bluemoon and Shocktop- brewed by Coors and Anheuser Busch respectively, and both go out of their way to hide that fact on the bottles). Alanis couldn’t have written a better irony.
To be honest, I’m shocked that the last major brewery in Berlin that still brews Berliner Weisse hasn’t gotten the message. As far as I know, the Berliner-Kindl-Schultheiss-Brauerei GmbH (yeah, yeah, German words are long), doesn’t even distribute their sours to the U.S., let alone much outside of Berlin. Talk about missing Das Boot.
Despite the bandwagon, sour beers aren’t universally welcomed. To this day, some breweries are so concerned about the souring boogiemen bacteria, many brewmasters have sworn that they will never brew a sour beer lest their entire brewery become infected. I know of at least one brewery owner who told me that not only will he never brew a sour, but that sour beers will never become popular enough to sell.
I guess only time will tell if sour beers ever catch on.
Ok, Desert Island time:
Santé!
[¹Bernstein, J. M. “Sour Beer Primer: How (and Why) to Drink These Funky Wild Ales” bon appetit 26 Feb., 2014. Web. 10 July, 2014; Pasteur, L. (1879) Studies on Fermentation: The Diseases of Beer, London. Macmillan & Co.; ³Rogers, A. (2014) Proof: The Science of Booze. Boston, MA. Houghton Mifflin Harcourt]
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Hi, I’m Dan: Beer Editor for Beer Syndicate, Beer and Drinking Blogger, Gold Medal-Winning Homebrewer, Beer Reviewer, AHA Member, Beer Judge, Shameless Beer Promoter, and Beer Traveler. Interests? Beer. | 2023-09-10T01:26:35.434368 | https://example.com/article/6931 |
Q:
How do I draw double height text using Graphics.DrawString?
I am trying to emulate a POS printer with System.Drawing and one of the functions I need is to draw text at double height. Any idea how I can do this using .Net's Graphics class?
Do I need to draw the text twice as large and condense it or draw normal size and then stretch? Both seem like messy options but is there an alternative?
A:
Look at the transformation matrix on the Graphics object - you can control horizontal and vertical scaling independently.
| 2024-05-26T01:26:35.434368 | https://example.com/article/1849 |
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| 2023-10-31T01:26:35.434368 | https://example.com/article/9512 |
---
abstract: 'Let ${\operatorname{Diff}^1(M)}$ be the set of all $C^1$-diffeomorphisms $f:M\rightarrow M$, where $M$ is a compact boundaryless d-dimensional manifold, $d\geq2$. We prove that there is a residual subset $\mathfrak R$ of ${\operatorname{Diff}^1(M)}$ such that if $f\in\mathfrak R$ and if $H(p)$ is the homoclinic class associated with a hyperbolic periodic point $p$, then either $H(p)$ admits a dominated splitting of the form $E\oplus F_1\oplus \dots\oplus F_k\oplus G$, where $F_i$ is not hyperbolic and one-dimensional, or $f|_{H(p)}$ has no symbolic extensions.'
address:
- 'Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil.'
- 'Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil.'
- 'Faculdade de Matemática, Universidade Federal de Uberlândia.'
- 'Instituto de Matemática, Universidade Federal do Rio de Janeiro, P. O. Box 68530, 21945-970 Rio de Janeiro, Brazil.'
author:
- 'A. Arbieto'
- 'A. Armijo'
- 'T. Catalan'
- 'L. Senos'
title: 'Symbolic Extensions and dominated splittings for Generic $C^1$-Diffeomorphisms'
---
Introduction
============
*Expansiveness* is an important notion in the theory of dynamical systems. Let $M$ be a compact manifold and $f:M\to M$ be a homeomorphism. Roughly, it says that if the orbits of different points must separate in finite time. More precisely, there exists ${\varepsilon}>0$ such that for any point $x$, the ${\varepsilon}$-set of $x$, given by the points $y$ such that $d(f^n(x),f^n(y))<{\varepsilon}$ for every integer $n$, reduces to the point $x$. This notion is somewhat related with the well know notion of sensitivity to initial conditions, commonly known as *chaos*, which means that for any point, there exists a point such that the future orbit of these two points separated. Moreover, expansiveness naturally appears in hyperbolic sets, and together with the shadowing property, play a central role to prove their stability.
However, it is important to look for weaker forms of expansivity. Clearly, expansivity implies *h-expansivity*, i.e. for some ${\varepsilon}>0$ the entropy of the ${\varepsilon}$-set of any point $x$ is zero. This notion implies semicontinuity of the entropy map, henceforth leading to the existence of equilibrium states, which is a well know problem in ergodic theory. We remark that $h$-expansiveness do not imply expansivity. This weaker property holds for partially hyperbolic diffeomorphisms such that their central subbundle admits a dominated splitting by one-dimensional subbundles, see [@D-F-P-V]. It also holds for diffeomorphisms away from tangencies see [@L-V-Y].
It turns out that $h$-expansiveness implies the existence of *symbolic extensions*, see [@B-F-F]. This means that the system is a quotient of a subshift of finite type. Actually, we can ask if the residual entropy of this extension is zero, in this case we say that the extension is *principal*. However, the existence of symbolic extensions does not imply any kind of expansiveness, even asymptotic $h$-expansiveness, which requires that the entropy of the ${\varepsilon}$-sets goes to zero if ${\varepsilon}$ goes to zero. In particular, *the non existence* of symbolic extensions implies that a positive amount of entropy, far from zero, can be found in arbitrarily small sets, given some complexity of the dynamics, see [@BD]. In the other hand, symbolic extensions are used in the theory of data transmission, see [@Down]. It is worthing to remark that any $C^{\infty}$ diffeomorphism is asymptotically $h$-expansive, see [@Bu].
The existence of symbolic extensions is somewhat rare in non-hyperbolic dynamics. Indeed, it was proved by [@D-N] that $C^1$-generic non-Anosov symplectic diffeomorphisms in surfaces do not have symbolic extensions. This result was extended to higher dimensions by [@C-T]. By generic, we mean that this holds for systems in a residual subset of such diffeomorphisms.
A natural question in dynamical systems is to know whether the presence of a dynamical property in a $C^1$-robust way implies some hyperbolicity. For instance, [@B-D-P] shows that robust transitivity implies the existence of a dominated splitting. Naturally, some authors asked this question using expansivity. Indeed, Mañé [@Mane] shows that any robustly expansive diffeomorphisms is Axiom A. The same question can be asked in a semi-local way. More precisely, we can ask if a homoclinic class has some expansiveness in a robust way then it is hyperbolic. By homoclinic class we mean the closure of the transversal homoclinic intersections of a periodic orbit. The series of papers [@PPV], [@PPSV], [@SV1] and [@SV2], essentially proves that robustly expansive homoclinic classes are hyperbolic, see the articles for more details. In [@P-V], it was proved that any robustly $h$-expansive homoclinic class has a dominated splitting of the form $E\oplus F_1\oplus \dots\oplus F_k\oplus G$, where $F_i$ is not hyperbolic and one-dimensional. A related result was proved by Li in the context of R-robustly h-expansive homoclinic classes, see [@LI] for more details.
Another related question is the existence of a residual subset where the presence of a dynamical property implies hyperbolicity in the global and semi-local case. For instance, in [@Ar] it is proved that any generic expansive diffeomorphism is Axiom A. In [@C], it was proved that generic volume preserving diffeomorphisms have symbolic extensions if, and only if, they are partially hyperbolic. In the semi-local case, [@GY] proved that for a generic diffeomorphisms, any expansive homoclinic class is hyperbolic.
In this article we study these questions for generic diffeomorphisms in the semi-local case but using symbolic extensions, that as we saw before, is much weaker than expansiveness. Another results dealing with the non-existence of symbolic extensions are: [@D-F] constructed a locally residual subset of $C^1$-partially hyperbolic diffeomorphisms without symbolic extensions, [@A] also constructed other examples, for smoother systems [@D-N] conjectured that $C^r$-diffeomorphisms have symbolic extensions if $r\geq 2$, [@B] proved this conjecture for surfaces diffeomorphisms, [@BF] extended this result for higher dimensions with 2-dimensional center subbundle. Any $C^r$-one-dimensional transformation, with $r>1$, has symbolic extensions, this was proved by [@DM].
Now, we give precise definitions and state our main results.
We consider a compact boundaryless $d$-dimensional Riemmanian manifold $M$, $d\geq2$, and denoting by ${\operatorname{Diff}}^r(M)$ the set of $C^r$ diffeomorphisms on $M$ endowed with the $C^r$ topology.
A dynamical system $f:M\to M$ has a *symbolic extension* if there exists a subshift $\sigma:N\to N$ and a continuous surjective map $\pi:N\rightarrow M$ such that $\pi\circ \sigma = f \circ \pi$. In this case the system $\sigma:N\to N$ is called an *extension* of $f:M\to M$ and $f$ is called a *factor* of $\sigma$. If $h_{\pi^*\mu}(f)=h_{\mu}(\sigma)$ for every invariant measure $\mu$ of $\sigma$ then the extension is called *principal*.
We say that $f:M^n\to M^n$ has a good decomposition in $\Lambda$ if there exists a dominated splitting $T_{\Lambda}M=E_1\oplus\dots\oplus E_k$ such that $dim(E_1)=s$, $dim(E_k)=n-u$ and for every $1<j<k$ we have $dim(E_j)=1$. Here, $s$ (resp. $u$) denotes the smallest (resp. greatest) index of a hyperbolic periodic point in $\Lambda$. Recall that the [*index*]{} of a hyperbolic periodic point $p$ is the dimension of its stable manifold.
\[maintheo\] There is a residual subset $\mathcal{R}$ of ${\operatorname{Diff}^1(M)}$ such that if $f\in\mathcal{R}$, then for every homoclinic class $H(p,f)$,
- either $H(p,f)$ has a good decomposition,
- or $f|_{H(p,f)}$ has no symbolic extensions.
To prove this theorem we will use criterions to the non existence of symbolic extensions developed by Downarowicz and Newhouse in [@D-N]. Moreover, we also use a dichotomy between good decompositions and the existence of a homoclinic tangency, see [@A-B-C-D-W]. Even so, once that one obtain a good decomposition, is somewhat folklore to obtain partial hyperbolicity when the class is isolated. In particular, we obtain the following theorem and prove it just for sake of completeness.
There is a residual subset $\mathcal{R}$ of ${\operatorname{Diff}^1(M)}$ such that if $f\in\mathcal{R}$, then for every isolated homoclinic class $H(p,f)$
- either $H(p,f)$ is partially hyperbolic,
- or $f|_{H(p,f)}$ has no symbolic extensions.
However, this theorem together with the result of Diaz, Fisher, Pacífico and Vieitez [@D-F-P-V] has an interesting directly consequence.
There is a residual subset $\mathcal{R}$ of ${\operatorname{Diff}^1(M)}$ such that if $f\in\mathcal{R}$, any isolated homoclinic class of $f$ has a symbolic extension if, and only if, it has a principal symbolic extension.
Finally, as a byproduct of the techniques used in the proof of the main theorem we also get the following interesting consequence, which is somewhat related to the previous result by Pacífico and Vieitez [@P-V] mentioned before.
Let $HT\subset{\operatorname{Diff}^1(M)}$ be the set of diffeomorphisms exhibiting a homoclinic tangency, and $NAHE\subset{\operatorname{Diff}^1(M)}$ be the set of diffeomorphisms that are not asymptotically $h-$expansive. Then $\overline{HT}=\overline{NAHE}$. \[prophexp\]
As a consequence, if a diffeomorphism is stably asymptotically $h$-expansive then it has a dominated splitting in the pre-periodic set, using a result of Wen, see [@W]. Moreover, if the diffeomorphism is generic then it is partially hyperbolic due to [@C-S-Y].
This article is organized as follows: In Section \[definition\], we define precisely the notions and objects used in this paper, in Section \[SNP\] we define and study the ${{\mathcal S}}_{n,p}$ property, which is our tool to find diffeomorphisms that has no symbolic extensions, in Section \[localversion\] we prove a local version of the Theorem \[maintheo\], in Section \[mainproof\] we give a proof for Theorem \[maintheo\], in Section \[isolated\] we consider the isolated case and, finally, in Section \[hexpansivity\] we prove Proposition \[prophexp\].
Definitions {#definition}
===========
In this section we define precisely the notions and objects used in the introduction.
We say that $p$ is a *periodic point* if $f^n(p)=p$ for some $n\geq 1$, the minimal such natural is called the *period* of $p$ and it is denoted by $\tau(p,f)$, or simply by $\tau(p)$ if the diffeomorphisms $f$ is fixed. The periodic point is *hyperbolic* if the eigenvalues of $Df^{\tau(p)}(p)$ do not belong to $S^1$.
If $p$ is a hyperbolic periodic point then its *homoclinic class* $H(p,f)$ is the closure of the transversal intersections of the stable manifold and unstable manifold of the orbit of $p$: $$H(p,f)=\overline{W^s(p)\pitchfork W^u(p)}.$$ It is well known that a homoclinic class is transitive. Moreover, we say that a hyperbolic periodic point $q$ is *related* to $p$ if $W^s(p)\pitchfork W^u(q)\neq \emptyset$ and $W^u(p)\pitchfork W^s(q)\neq \emptyset$, it can be proved that the homoclinic class of $p$ is also the closure of the hyperbolic periodic points related to $p$.
Let $Per^n_h(f)$ be the collection of hyperbolic periodic points of $f$ of period less than or equal to $n$, and let $Per_h(f)=
{\displaystyle\bigcup_{n\geq 1} Per^n_h(f)}$.
Domination
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We say that a compact $f$-invariant set ${\Lambda}\subset M$ admits a *dominated splitting* if the tangent bundle $T_{\Lambda}M$ has a continuous $Df$-invariant splitting $E_1\oplus \cdots \oplus E_k$ and there exist constants $C > 0$, $0 < \lambda < 1$, such that $$||Df^n|{E_i(x)}||\cdot ||Df^{-n}|E_j(f^n(x))||\leq C\lambda^n,\quad\forall x\in\Lambda,\; n\geq0, \text{ for every } i<j.$$
We say that $T_{\Lambda}M=E_1\oplus\ldots\oplus E_k$ is the finest dominated splitting if there is no dominated splitting of $E_l$ for every $1<l<k$.
Hyperbolicity
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If ${\Lambda}$ is a compact invariant set of a diffeomorphism $f$ then ${\Lambda}$ is said to be a *hyperbolic set* if we have a $Df$-invariant continuous splitting $T_{\Lambda}M=E^s\oplus E^u$ and constants $C > 0$ and $\kappa < 1$ such that $$||Df^{-n}(x)_{|E^u_x}||\leq C\kappa^n\mbox{ and }||Df^n(x)_{|E^s_x}||\leq C\kappa^n,$$ for every $x \in {\Lambda}$ and $n \in {\mathbb{N}}$.
Let $E\oplus F_1\oplus\dots\oplus G$ be a dominated splitting over $\Lambda$. If $E$ contracts and $G$ expands, like in the previous paragraph then we say that $\Lambda$ is *partially hyperbolic*.
Let ${\Lambda}$ be a hyperbolic set for $f$. We call ${\Lambda}$ a *hyperbolic basic set* if
- it is *isolated*, i.e. there is a neighborhood $U$ of ${\Lambda}$ such that $$\bigcap_{n \in {\mathbb{Z}}} f^n(U) = {\Lambda}\,\ \textsl{and}$$
- $f$ has a dense orbit in ${\Lambda}$.
Genericity
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We say that a subset $\mathfrak R\subset {\operatorname{Diff}^1(M)}$ is a *residual subset* if contains a countable intersection of open and dense sets.
The countable intersection of residual subsets is also a residual subset. Since ${\operatorname{Diff}^1(M)}$ is a Baire space when endowed with the $C^1$-topology, any residual subset of ${\operatorname{Diff}^1(M)}$ is dense.
We will say that a property (P) holds *generically* if there exists a residual subset $\mathfrak R$ such that any $f\in \mathfrak R$ has the property (P).
Measures and Exponents
----------------------
A measure $\mu$ is $f$-invariant if $\mu(f^{-1}(B))=\mu(B)$ for every measurable set $B$. An invariant measure is ergodic if the measure of any invariant set is zero or one. Let ${{\mathcal M}}(f)$ be the space of $f$-invariant *probability measures* on $M$, and let ${{\mathcal M}}_e(f)$ denote the ergodic elements of ${{\mathcal M}}(f)$.
For a hyperbolic periodic point $p$ of $f$ with period $\tau(p)$, we let $ \mu_p$ denote the periodic measure given by $$\mu_p =\frac{1}{\tau(p)} \sum_{ x\in O(p)} \delta_x$$ where $O(p)$ denotes the orbit of $p$ and $\delta_x$ is the Dirac measure at $x$.
A measure $\mu \in {{\mathcal M}}(f)$ is called a *hyperbolic measure* for $f$ if its topological support $supp(\mu)$ is contained in a hyperbolic basic set for $f$. [^1]
Let $C(M,{\mathbb{R}})$ be the set of all continuous functions $h:M\rightarrow{\mathbb{R}}$. If $h\in C(M,{\mathbb{R}})$ then $\mu(h)=\int_Mhd\mu$. Let us denote by $\rho$ the metric on ${{\mathcal M}}(f)$ which defines the weak-\* topology as follows. Let $\phi_1, \phi_2,\ldots$ be a countable dense subset of the unit ball in $C(M,{\mathbb{R}})$ and set $$\rho(\mu,\nu)= \sum_{i\geq1} \frac{1}{2^i} |\mu(\phi_i) - \nu(\phi_i)|.$$
Given a periodic ergodic measure $\mu_p \in {{\mathcal M}}_e(f)$, we denote by $\chi^{+}(p,f)$ and $\chi^{-}(p,f)$ the smallest positive Lyapunov exponent and the biggest negative Lyapunov exponent of $\mu_p$, respectively. Then we define $\chi(p,f)=\min\{\chi^+(p,f),\, -\chi^-(p,f)\}$.
The property ${{\mathcal S}}_{n,p}$ {#SNP}
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In this section, we define and study the ${{\mathcal S}}_{n,p}$ property. This property is in the spirit of [@D-N], in order to find diffeomorphisms that has no symbolic extensions.
Given a positive integer $n$, we say that a diffeomorphism $f$ satisfies property ${{\mathcal S}}_{n,p}$ if $p$ is a hyperbolic periodic point of $f$, and for any $\tilde{p} \in Per_h^n(f)$ related to $p$ there is a zero dimensional periodic hyperbolic basic set ${\Lambda}(\tilde{p}, n)\subset H(p,f)$ for $f$ with the same index that $p$, such that the following happens:
- there is $\nu \in {{\mathcal M}}_e({\Lambda}(\tilde{p}, n))$ such that $$h_\nu(f) >\chi(\tilde{p},f)- \frac{1}{n},$$
- for every $\mu \in {{\mathcal M}}_e({\Lambda}(\tilde{p}, n))$, we have $$\rho(\mu,\mu_{\tilde{p}}) <\frac{1}{n}.$$
- for every hyperbolic periodic point $q \in {\Lambda}(\tilde{p}, n)$, we have $$\chi(q,f)>\chi(\tilde{p},f)-\frac{1}{n}.$$
The following result concern about the abundance of diffeomorphisms satisfying property $S_{n,p}$ near diffeomorphism with homoclinic classes admitting no dominated splittings.
Let $f$ be a Kupka-Smale generic diffeomorphism with a hyperbolic periodic point $p$ of index $i$. If $H(p,f)$ is a non-trivial homoclinic class admitting no $i-$dominated splitting, then for any neighborhood $\mathcal{U}$ of $f$ and any positive integer $n$, there exists an open subset $\mathcal{V}\subset\mathcal{U}$ such that every $g\in \mathcal{V}$ satisfies property ${{\mathcal S}}_{n,p(g)}$. \[mainprop\]
The idea to prove this Proposition is to produce many nice horseshoes, as done by Downarowicz and Newhouse in [@D-N]. However, in their context, there is an abundance of homoclinic tangencies to produce such horseshoes. In our context we will use Lemma \[mainlemma\], which is a key and technical lemma, to overcome the lack of such abundance in general.
We can suppose that every periodic orbit of $Per_h^n(f)$ and the orbit of $p$ has an analytic continuation on ${{\mathcal U}}$. Moreover, by semicontinuity arguments, there exists $k$ such that for every $g\in {{\mathcal U}}$ we have $$\#\{q\in Per_h^n(g);\textrm{ homoclinically related with $p$}\}=k.$$We denote the elements of this set for $f$ by $\{p_1,\dots,p_k\}$.
Since $H(p,f)=H(p_1,f)$ admits no $i-$dominated splitting, Gourmelon’s result [@G] implies that, after some perturbation, we can suppose that $f$ exhibits a homoclinic tangency for $p_1$, i.e., there exists a non transversal intersection between $W^s(O(p_1),f)$ and $W^u(O(p_1),f)$.
Now we state a technical lemma.
If $n$ is large enough, there exist a diffeomorphism $g\in {{\mathcal U}}$ and a small neighborhood $\mathcal{V}\subset{{\mathcal U}}$ of $g$ such that for every $h\in \mathcal{V}$ the items of property $S_{n,p(h)}$ holds for $p_1(h)$, and moreover $g$ exhibits a homoclinic tangency for $p_2(g)$. \[mainlemma\]
We postpone the proof of this lemma and finish the proof of the Proposition.
We consider now $g_1$ and the neighborhood $\mathcal{V}_1$ of $g_1$ given by Lemma \[mainlemma\]. Now, since $g_1$ exhibits a homoclinic tangency for $p_2(g_1)$, and $p_3(g_1)$ is homoclinically related to $p_2(g_1)$, we can use Lemma \[mainlemma\] again to obtain a diffeomorphism $g_2$ and a neighborhood $\mathcal{V}_2\subset \mathcal{V}_1$ of $g_2$ such that for every diffeomorphism $h\in \mathcal{V}_2$ the items of property $S_{n,p(h)}$ holds for $p_2(h)$, and moreover $g_2$ exhibits a homoclinic tangency for $p_3(g)$.
Now, we repeat the process finitely many times, to obtain a diffeomorphism $g=g_k$ and a neighborhood $\mathcal{V}=\mathcal{V}_k\subset \mathcal{V}_{k-1}\ldots \subset \mathcal{V}_1\subset {{\mathcal U}}$ of $g$ such that the items of property $S_{n,p(h)}$ holds for $p_i(h)$ with $i=1,\dots, k$ for every $h\in \mathcal{V}$. And then, by choice of ${{\mathcal U}}$, every diffeomorphism $h\in \mathcal{V}$ satisfy property $S_{n,p(h)}$.
Proof of Lemma \[mainlemma\]
----------------------------
First of all, we observe that many times in this proof we use expressions like “by some perturbation", or “we can perturb $f$", to say we can take a diffeomorphism arbitrary close to $f$. Sometimes, in order to not complicate the notation we use the same letter to denote the new diffeomorphism. Also, when we say “by a local perturbation" we mean that we can perform a perturbation of $f$ keeping the new diffeomorphism equal to $f$ outside some small open set.
Let $q$ be a point of homoclinic tangency of $p_1$, and $V$ be a small neighborhood of $O(p_1)$ such that $f^{-1}(q)$ is not in $V$. Shrinking $V$, if necessary, we can suppose $f^{\tau(p_1,f)}=Df^{\tau(p_1,f)}$ (in local coordinates on $V$) after a perturbation (see Franks’ lemma [@F]). We remark that after this perturbation the homoclinic tangency could disappear. Nevertheless, since $f^{-1}(q)$ is not in $V$, using the continuity of compact parts of unstable and stable manifolds of $p_1$, by a local perturbation in some neighborhood of $f^{-1}(q)$ we can recover the homoclinic tangency.
Up to take another point of the orbit of $q$, we can suppose that $q\in V$ and $f^{-1}(q)\not\in V$. So, we can take a neighborhood $U$ of $q$ such that $f^{-1}(U)\cap V=\emptyset$. We denote by $D$ the connected component of $W^u(p_1,f)\cap U$ that contains $q$.
Now, we look to $U$ in some local coordinates with the splitting $T_qD\oplus T_qD^{\bot}$, and such that $q=0$ in these coordinates. Since $D\subset W^u(p_1,f)$ we have that $D$ is a graph of a $C^1$ map $r:T_{q}D\rightarrow T_{q}
D^{\bot}$, i.e. $D=(x,r(x))$. Moreover, $Dr(q)$ is close to zero. Hence, the diffeomorphism $\phi(x,y)=(x,y-r(x))$ is $C^1$ close to identity in a small neighborhood of $q$. In particular, there exists a diffeomorphism $h$, $C^1$-close to identity, such that $h=\phi$ in some small neighborhood of $q$, and $h=Id$ for points far away from $q$. Thus, $f_1:=h\circ f$ is a $C^1$ local perturbation of $f$ such that $T_qD\cap U\subset W^u(p_1,f_1)$. Since $f^{-1}(U)\cap V=\emptyset$, we have that $f_1=f$ in $V$, as a consequence $f_1|V$ is still linear, and $W^s_{loc}(p_1,f_1)$ remains unchanged in $U$. Since $q$ is a non transversal homoclinic point we have that $T_q D\cap E^s(p_1,f)$ is a non trivial subspace. Actually, we can assume that $T_q D\cap E^s(p_1,f)$ is an one-dimensional subspace, after some local perturbation if necessary. Thus, $f_1$ exhibits an interval of homoclinic tangencies containing $q$. Let $I$ be this interval of homoclinic tangencies. Replacing the local coordinates in $U$, if necessary, we can suppose that $\{(x_1,0,...,0), \, -3a\leq x_1\leq 3a\} \subset I$, for some $a>0$ small enough.
Let $N$ be a large positive integer. Taking $I$ smaller, if necessary, we can construct a diffeomorphism $\Theta:M\rightarrow M$, such that $\Theta=Id$ in $B(0,2a)^c$ and $$\Theta(x,y)=\left(x_1,...,x_s,\,y_1+A\cos\frac{\pi x_1 N}{2a},\, y_2,...,y_u\right), \text{ for } (x,y)\in B(0,a)\subset U,$$ for $A=\displaystyle\frac{2Ka\delta }{\pi N}$, where $K$ is a constant which depends only on the local coordinates over $U$ and $\delta>0$ is so small as we want. Hence, taking $g=\Theta\circ f_1$, we have that $g$ is $\delta-C^1$ close to $f_1$ and moreover $g=f_1$ in the complement of $f_1^{-1}(B(q,2a))$. Note that $g$ depends on $N$ but to not complicate the notation we denote this diffeomorphism by $g$, independent of $N$.
The most important properties of this new diffeomorphim is that $g$ has $N$ transversal homoclinic points for $p_1$ inside $U$, but $g$ still has an interval of homoclinic tangency inside $U$, in fact there are two intervals of homoclinic tangency in $U$: one inside $\{(x_1,0,...,0), \, -3a\leq x_1\leq -2a\}$ and other inside $\{(x_1,0,...,0), \, 2a\leq x_1\leq 3a\} $, in local coordinates. \[tangency\]
To simplify notation we assume $p_1$ is a fixed point, being similar the general case.
We remark that $g|V$ is still linear in local coordinates, since $f$ is equal $g$ in $V$. Let $D_t=D^s\times D^u_t$ be a small rectangle, with $D^s=W^s_{loc}(p_1,g)\cap U$, and $D^u_t$ a small disk in $\{(0,\ldots,0,y_1,\ldots,y_n),\, y_i\in{\mathbb{R}}^+ \text{ and } |y_i|<A/4\}$, such that $t$ is the smallest positive integer such that $g^t(D_t)$ is a disk $A/4-C^1$ close to the connected component of $W^u(p_1,g)\cap U$ containing the $N$ transversal homoclinic points built before. We remark that $t$ depends on $N$, and $t\to\infty$ when $N\to \infty$.
Observe that $A$ is small if $N$ is large, and by choice of $D_t$, we have that $g(D_t)\cap D_t$ has $N$ disjoint connected components. Moreover, we have that the maximal invariant set in $D_t$ for $g^t$ $$\tilde{\Lambda}(p_1,N)=\bigcap_{j\in{\mathbb{Z}}} g^{tj}(D_t)$$ is a hyperbolic set inside $H(p_1,g)$. Let $\Lambda(p_1,N)={\displaystyle\bigcup_{0\leq j\leq t} g^j(\tilde{\Lambda}(p_1,N))}$ be the hyperbolic periodic set of $g$ induced by $\tilde{\Lambda}(p_1,N)$. Since $g|\tilde{\Lambda}(p_1,N)$ is conjugated with the full shift of $N$ symbols, we have that $h(g|\Lambda(p_1,N))=\displaystyle\frac{1}{t}\log N$,
We recall that $g|V$ is linear. So, if $m$ is the largest positive integer such that $g^j(x)\in V$ for $0\leq j\leq m$, there exist constants $K_1$ and $K_2$ depending on the local coordinate on $V$ such that $$K_1\|Dg(p_1)^{m}|E^u\|^{-1}\leq d(x,W^s_{loc}(p_1,g))\leq K_2 \|Dg(p_1)^{-m}|E^u\|, \label{desigualdade 1}$$ for $x\in V$. Analogously, if $m$ is the largest positive integer such that $g^{-j}(x)\in V$ for $0\leq j\leq m$, then there exist constants $K_3$ and $K_4$ such that $$K_3 \|Dg(p_1)^{-m}|E^s\|^{-1} \leq d(x,W^u_{loc}(p_1,g))\leq K_4 \|Dg(p_1)^{m}|E^s\|. \label{desigualdade 2}$$
Another consequence of $g|V$ be linear and the choice of $t$ is the following result, which also appears in [@C-T].
\[Lemma 4.2 of [@C-T]\] \[afirma\] For $A$ and $t$ defined as before, there exists a positive integer $K_5$, which is independent of $A$, such that $$A<K_5\max \{ \|Dg(p_1)^{-t}|E^u\|,\,
\|Dg(p_1)^{t}|E^s\|\}.$$
Let $n$ be a large positive integer. Since $A=\displaystyle\frac{2Ka\delta}{\pi N}$, using Lemma \[afirma\] and recalling that $N\to \infty$ implies $t\to \infty$, we can select a large positive integer $N$, such that $$\displaystyle\frac{1}{t}\log N> \min\left\{\frac{1}{t}\log\|Dg(p_1)^{-t}|E^u\|^{-1},\, \frac{1}{t}\log\|Dg(p_1)^{t}|E^s\|^{-1} \right\} -\frac{1}{2n}.$$ But, when $t$ goes to infinity the above minimum converges to $\chi(p_1,g)$, by definition. Therefore, there exists a large positive integer $N_1$ such that $$\displaystyle\frac{1}{t}\log N_1> \chi(p_1,g)-\frac{1}{n}.$$ So, it is possible to find a $C^1-$perturbation $g$ of $f$ such that $$h(g|\Lambda(p_1,N_1))> \chi(p_1,g)-\frac{1}{n}.$$
Now, by the variational principle there exists an ergodic measure $\mu_N\in\mathcal{M}(\Lambda(p_1,N))$ such that $$h_{\mu_N}(g)> \chi (p_1,g)-\frac{1}{n}, \text{ for } N\geq N_1.\label{item b}$$
Observe that the orbit of points in the hyperbolic set $\Lambda(g,N)$, when $N$ is large enough, stay almost all the time inside the neighborhood $V$ of $p_1$, which one could be assumed so small as we wanted. Hence, there exists a positive integer $N_2$ such that if $\mu\in \mathcal{M}(f|\Lambda(g,N))$ is ergodic then $\rho(\mu,\mu_{p_1})<1/n$, for every $N\geq N_2$.
Finally, we find $N_3$ in order to obtain property (e) of $S_{n,p(g)}$ for $\Lambda(p_1,N)$ with $N\geq N_3$.
We define $$V_k^{u}=V\cap g(V)\cap...\cap g^{k}(V), \text{ and }$$ $$V_k^{s}=V\cap g^{-1}(V)\cap...\cap g^{-k}(V).$$
Given vectors $v,w\in{\mathbb{R}}^{2n}$ and subspaces $E,F\subset{\mathbb{R}}^{2n}$ we define $$ang(v,w):=\left|\tan\left[\arccos\left(\frac{<v,w>}{\|v\|\|w\|}\right)\right]\right|,$$
$$ang(v,E)=\min_{w\in E,\, |w|=1}\, ang(v,w)\quad \text{and}\quad ang(E,F)=\min_{w\in E,\, |w|=1} \, ang(w,F).$$
The following lemma, is also a straightforward consequence of $g|V$ be linear, as in Lemma 4.4 in [@C-T].
With above definitions, there exists positive constants $K_6$ and $K_7$, such that
- if $z\in V^{u}_k$, $v\in {\mathbb{R}}^{2n}\backslash E_{p_1}^u$ and $ang(g^{-k}(v),E_{p_1}^u)\geq
1$, then $$K_6 \|Dg_{p_1}^{k}|E^s\|^{-1}|v| \,\min \{ang(v,E_{p_1}^{u}),\, 1\}\leq |Dg^{-k}(z)(v)|\leq K_7 \|Dg_{p_1}^{-k}|E^s\||v|$$
- if $z\in V^{s}_k$, $v\in {\mathbb{R}}^{2n}\backslash E_{p_1}^s$ and $ang(g^{k}(v),E_{p_1}^s)\geq
1$, then $$K_6 \|Dg_{p_1}^{-k}|E^u\|^{-1}|v| \,\min \{ang(v,E_{p_1}^{s}),\, 1\}\leq |Dg^{k}(z)(v)|\leq K_7 \|Dg_{p_1}^k|E^u\||v|$$
\[lema\]
Now, since $\Lambda(p_1,N)=\cup_{i=0}^{t-1} g^i(\tilde{\Lambda}(p_1,N))$ with $\tilde{\Lambda}(p_1,N)\subset
V$, then we can take positive integers $k$ and $T$ such that $t=k+T$, and $g^{i}(\tilde{\Lambda}(p_1,N))\subset V$ for $0\leq i\leq k$. Moreover, by construction of $\tilde{\Lambda}(p_1,N)$ this $T$ can be taken independent of $N$. Hence, provided $t$ goes to infinity when $N$ goes to infinity, we have that $k$ also goes to infinity. Now, we know that the hyperbolic decomposition $T_{\tilde{\Lambda}(p_1,N)}M=\tilde{E}^s\oplus \tilde{E}^u$ of the hyperbolic set $\tilde{\Lambda}(p_1,N)$ is such that $\tilde{E}^s(g^{-k}(z_1))$ and $\tilde{E}^u(g^{k}(z_2))$ are close to $E^s_{p_1}$ and $E^u_{p_1}$, respectively, for every $z_1\in g^{k}(\tilde{\Lambda}(p_1,N))$ and $z_2\in\tilde{\Lambda}(p_1,N)$. In particular, $$ang(Dg^{-k}(z_1)(v),E^u_{p_1})>1\textrm{ for }v\in \tilde{E}^s(z_1)\textrm{ and }$$ $$ang(Dg^{k}(z_2)(v),E^s_{p_1})>1\textrm{ for }v\in \tilde{E}^u(z_2).$$ Moreover, and the most important argument in this case, is that although $ang(v,E_{p_1}^{u})$ for $v\in \tilde{E}^s(z_1)$, and $ang(v,E_{p_1}^{s})$ for $v\in \tilde{E}^u(z_2)$ are a very small constant, independent of $N$, we have ensured that $$ang(Dg^{-k}(z_1)(v),E^u_{p_1})>1\textrm{ and }ang(Dg^{k}(z_2)(v),E^s_{p_1})>1.$$
So, using these informations and Lemma \[lema\] we can find constants $K_6$ and $K_7$, such that for every $z\in \tilde{\Lambda}(p_1,N)$, $r=l(k+T)$ and for every $l\in{\mathbb{N}}$:
- if $v\in \tilde{E}^s(z)$ then $$|Dg^{-r}(z)(v)| \geq (C_1\, K_6)^l \, \|Dg_{p_1}^{k}|E^s\|^{-l}|v| \label{equa 2}$$
- if $v\in \tilde{E}^u(z)$ then $$|Dg^r(z)(v)|\geq (C_1\, K_7)^l \, \|Dg_{p_1}^{-k}|E^u\|^{-l}|v|, \label{equa 2}$$
where $$C_1=\inf_{z\in V\backslash g^{-1}(V), \; |v|=1} \|Dg^{T}(z)(v)\|.$$
Therefore, for $N$ large enough, all points in $\tilde{\Lambda}(p,N)$ have Lyapunov exponents with absolute values bigger than $\chi(p,g)-1/n$. In particular, we can choose $N_3$, in order to get $k>>T$, such that for any periodic point $\tilde{q}\in \Lambda(p_1,N)$, with $N>N_3$, we have $$\chi(\tilde{q})> \chi(p_1,g)-\frac{1}{n}.$$ Hence, if we take $\Lambda(p_1,n)=\Lambda(p_1,N)$ for $N=\max\{N_1,\, N_2,\, N_3\}$, the items of property $S_{n,p(g)}$ are satisfied for the perturbation $g$ of $f$ and the hyperbolic periodic point $p_1$ of $g$.
By the construction of $\Lambda(p_1,n)$, observe that every item in the property $S_{n,p}$ is robust. That is, if $\tilde{g}$ is close to $g$, then the continuation of $\Lambda(p_1,n)$ for $\tilde{g}$ is such that all the items of property $S_{n,p(\tilde{g})}$ is still true for $p_1(\tilde{g})$. This is because item (a) is a robust property; item (b) is a consequence of the continuation of $\Lambda(p_1,n)$ be also inside $V$ and item (c) still is true for continuations of $\Lambda(p_1,n)$ by Lemma \[lema\]. \[open\]
Hence, by the previous remark there exists a neighborhood $\mathcal{V}\subset \mathcal{U}$ of $g$, such that every diffeomorphism $h\in\mathcal{V}$ satisfies the items of property $S_{n,p(h)}$ for $p_1(h)$.
Now, since the diffeomorphism $g$ belongs to $\mathcal{U}$, we know that the hyperbolic periodic point $p_2(g)$ still is homoclinic related with $p_1(g)$. Also, by Remark \[tangency\], $g$ still exhibits a homoclinic tangency for $p_1(g)$. Now, by a perturbation using Franks Lemma, we can find a transversal homoclinic point to $p_1(g)$, such that the angle between $W^s(p_1(g),g)$ and $W^u(p_1(g),g)$ is so small as we want. Hence, since $p_1(g)$ and $p_2(g)$ are related, there exists a transversal homoclinic point for $p_2(g)$ such that the angle between $W^s(p_2(g),g)$ and $W^u(p_2(g),g)$ is so small, too. Finally, using Franks Lemma once more, we can perturb $g$ such that this transversal homoclinic point become a homoclinic tangency. Since this perturbation can be find in $\mathcal{V}$, we finish the proof.
A local version of the main theorem {#localversion}
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First we recall some knowns residual subsets. We denote by $\mathcal{R}_1\subset{\operatorname{Diff}}^1(M)$ the residual subset given by [@C-M-P], such that for every diffeomorphism $g\in \mathcal{R}_1$ two homoclinic classes are either disjoint or coincide. By $\mathcal{R}_2\subset {\operatorname{Diff}}^1(M)$ the residual subset given by [@A-B-C-D-W], such that for every diffeomorphism $g\in \mathcal{R}_2$, every homoclinic class having a hyperbolic periodic point with index $i$ and a hyperbolic periodic point with index $j$, with $i<j$, has a dense set of hyperbolic periodic points with index $k$ for every $i\leq k\leq j$. And by $KS$ the residual subset of Kupka-Smale diffeomorphisms. Hence, we define $\mathcal{R}_4=\mathcal{R}_1\cap\mathcal{R}_2\cap KS$.
\[local\] Let $f \in \mathcal{R}_3$, $p$ be a hyperbolic periodic point of $f$. If ${{\mathcal U}}(f)\subset{\operatorname{Diff}^1(M)}$ is a small enough neighborhood of $f$, there is a residual subset $\mathcal{R} \subset {{\mathcal U}}(f)$ such that every $g \in \mathcal{R}$ satisfies only one of the following statements:
- $H(p_g,g)$ has a good decomposition;
- $g|_{H(p_g,g)}$ has no symbolic extensions.
**Proof:**
Since $f\in \mathcal{R}_3$ if $\mathcal{U}(f)$ is small enough then there exist $i$ and $j$, and hyperbolic periodic points $p_i, \, p_{i+1},\ldots, \, p_{j}$ of $f$ with $ind\, p_k=k$, for $i\leq k\leq j$, such that:
- $H(p,f)=H(p_i,f)=H(p_{i+1},f)=\ldots=H(p_j,f)$,
- for every hyperbolic periodic point $q\in H(p,f)$ we have $i\leq ind\, q\leq j$.
By [@A-B-C-D-W Lemma 4.2, pg.20], there exists an open and dense subset of $\mathcal{U}(f)$ over $\mathcal{R}_3$ such that for every $g$ in this subset, we still have that:
- $H(p(g),g)=H(p_i(g),g)=H(p_{i+1}(g),g)=\ldots=H(p_j(g),g)$,
- for every hyperbolic periodic point $q\in H(p(g),g)$ we have $i\leq ind\, q\leq j$.
Now, for any positive integer $n$ and any $i\leq k\leq j$, we define $\mathcal{B}_{n,p_k}\subset \mathcal{U}(f)$ as the subset of diffeomorphisms that robustly satisfies property $S_{n,p_k}$, i.e., $g\in\mathcal{B}_{n,p_k}$ if there is a small neighborhood of $g$ where every diffeomorphism $h$ satisfy property $S_{n,p_k(h)}$.
\[residual\] There is a residual subset of $\mathcal{R}_4\subset \mathcal{U}(f)$, such that for any positive integer $n$ and any $i\leq k\leq j$, if $g \in \mathcal{R}_4$ and there is a sequence of diffeomorphisms $\{g_m\}\in \mathcal{B}_{n,p_k}$ that converges to $g$, then $g$ satisfies property ${{\mathcal S}}_{n,p_k(g)}$.
Let us define $\mathcal{V}_{n,k}=\mathcal{B}_{n,p_k}\cup \overline{\mathcal{B}_{n,p_k}}^c$ be an open and dense subset in $\mathcal{U}(f)$, for every positive integer $n$ and every $i\leq k\leq j$. Then, $\mathcal{R}_4=\cap_{n\geq 0}\cap_{i\leq k\leq j} \mathcal{V}_{n,k}$ is a residual subset in $\mathcal{U}(f)$. To finish the proof, let $g\in \mathcal{R}_4$. Given a positive integer $n$ and $i\leq k\leq j$, if there exists diffeomorphisms $g_m\in \mathcal{B}_{n,p_k}$ converging to $g$, then $g\not\in\overline{\mathcal{B}_{n,p_k}}^c$. Therefore, since $g\in \mathcal{V}_{n,k}$ we have that $g\in\mathcal{B}_{n,p_k}$ and then satisfies property $S_{n,p_k(g)}$.
$\hfill\square$
Using Lemma \[residual\], we define $\mathcal{R}=\mathcal{R}_3\cap \mathcal{R}_4$, which is a residual subset in $\mathcal{U}(f)$. Now, we will verify that a diffeomorphism in this residual subset satisfies one of the two properties claimed in the proposition which finishes the proof.
For this we will use the following result of Burguet.
\[Corollary 1 of [@B1]\] Let $f:M\to M$ be a dynamical system admitting a symbolic extension. Then the entropy function $h: \mathcal{M}(f)\rightarrow {\mathbb{R}}$ is a difference of nonnegative upper semicontinuous functions. In particular the entropy function $h$ restrict to any compact set of measures has a large set of continuity points. \[propburguet\]
Let $g\in \mathcal{R}$, by choice of $\mathcal{R}$, $i$ and $j$ are the two extreme indices in $H(p(g),g)$ and $H(p(g),g)=H(p_i(g),g)=H(p_{i+1}(g),g)=\ldots=H(p_j(g),g)$.
Suppose $H(p(g),g)$ admits no good decomposition. Hence, there is some $i\leq k\leq j$ such that $H(p(g),g)=H(p_k(g),g)$ admits no $k-$dominated splitting. By Proposition \[mainprop\], for every $n>0$, we can find a sequence of diffeomorphisms $\{g_{n,m}\}_{m\in {\mathbb{N}}}$ converging to $g$, such that each $g_{n,m}\in \mathcal{B}_{n,p_k}$. Therefore, by Lemma \[residual\], $g$ satisfies property $S_{n,p_k(g)}$ for every $n>0$, since $g\in \mathcal{R}_4$.
We define $\rho_0=\max\{\chi(\tilde{p},g); \; \tilde{p}\in Per_h(g) \text{ and related to } p_k(g)\}$, and $$\xi_1(g)=\Big\{\mu_{\tilde{p}} : \tilde{p}\in Per_h(g), \text{ related to } p_k(g) \,\text{ and }\,\ \chi(\tilde{p},g)>{\displaystyle\frac{\rho_0}{2}}\Big\}$$ which is a non empty subset in ${{\mathcal M}}(f)$. Then, we consider the compact subset $\xi(g)=\overline{\xi_1(g)}$ in ${{\mathcal M}}(g)$. Now, let $\mu_{\tilde{p}}\in \xi_1$ and $t$ be a positive integer. Since $g$ satisfies property $S_{n,p_k(g)}$ for every positive integer $n$, there exist ergodic measures $\nu_m\rightarrow \mu_{\tilde{p}}$ such that $h_{\nu_m}(g)>\rho_0/2$, for every $m$. Moreover, since these measures are supported on hyperbolic sets with the same index that $p_k(g)$, by Sigmund [@S-I], they are approximated by hyperbolic periodic measures also supported in these hyperbolic sets, and by item (c) of property $S_{n,p_k(g)}$, they belong to $\xi_1(g)$. Hence, $\nu_m\in \xi(g)$ for every $m$, and then $$\limsup_{\nu_m\rightarrow \mu_{\tilde{p}}, \nu_m\in\xi(g)}h_{\nu_m}(g)>\frac{\rho_0}{2}.$$
Therefore, since $p$ is arbitrary and $\xi_1(g)$ has dense periodic measures, there is no continuity point for the entropy function $h$. Thus, by Proposition \[propburguet\], this implies that $f$ has no symbolic extensions.
$\Box$
Non existence of symbolic extensions versus good decomposition {#mainproof}
==============================================================
In this section we use Proposition \[local\] and the generic machinery to prove Theorem \[maintheo\].
**Proof of Theorem \[maintheo\]:**
Since ${\operatorname{Diff}^1(M)}$ is separable, there is a countable and dense subset $\mathcal{A}\subset {\operatorname{Diff}^1(M)}$. Moreover, we can assume that $\mathcal{A}\subset \mathcal{R}_3$, the residual subset of ${\operatorname{Diff}^1(M)}$ in the hypothesis of Proposition \[local\].
Now, for any $f\in \mathcal A$ and a small enough neighborhood $\mathcal{U}(f)$ of $f$, we consider the residual subset $\tilde{\mathcal{R}}_f$ in $\mathcal{U}(f)$ given by Proposition \[local\]. Thus, we define $$\mathcal{R}_f=\tilde{\mathcal{R}}_f\cup (\mathcal{U}(f))^c,$$ which is a residual subset in ${\operatorname{Diff}^1(M)}$, indeed. Also, since $\mathcal{A}$ is a dense subset $$\mathcal{U}=\bigcup_{f\in \mathcal{A}} \mathcal{U}(f),$$ is an open and dense subset of ${\operatorname{Diff}^1(M)}$.
Finally, we define the following residual subset $$\mathcal{R}=\bigcap_{f\in \mathcal{A}} \mathcal{R}_f\cap \mathcal{U}.$$
Now, let $g\in \mathcal{R}$ and $H(p,g)$ be a homoclinic class of $g$. Since $g\in \mathcal{U}$, there exists $f\in \mathcal{A}$ such that $g\in \mathcal{U}(f)$, and then provided $g$ also belongs to $\mathcal{R}_f$, $g$ should belongs to $\tilde{\mathcal{R}}_f$. Therefore, by Proposition \[local\] we have that either $H(p,g)$ has a good decomposition, or $f\,|\,H(p,g)$ has no symbolic extensions. This completes the proof.
The isolated case {#isolated}
=================
It is enough to prove that for $f\in {{\mathcal R}}$ of Theorem \[maintheo\], if $H(p,f)$ has a good decomposition and it is isolated then it is partially hyperbolic. Let $U$ be a neighborhood of $H(p,f)$ such that $H(p,f)=\bigcap_{n\in {\mathbb{Z}}}f^n(U)$. Also, let $E\oplus E_1\oplus\dots\oplus E_l\oplus F$ be the good decomposition. We will prove that $E$ is contracting, a similar argument will prove that $F$ is expanding.
We recall that $dim(E)$ is the smallest index of a periodic point in the class. By [@A-B-C-D-W], there is another residual subset where we know that there exists a neighborhood ${{\mathcal U}}$ of $f$ such that $dim(E)$ is still the smallest index of a periodic point in the class $H(p_g,g)$, for any $g\in {{\mathcal U}}$, where $p_g$ is the analytic continuation of $p$. The intersection of this two residual subsets is the one claimed in the statement of the theorem.
Now, if $E$ does not contract, using the Ergodic Closing Lemma, as Mañé did in [@M], then it is possible to find $g\in {{\mathcal U}}$ with a periodic orbit $O(q)\subset U$ with index smaller than $dim(E)$.
However, we can consider the result of Abdenur proved in [@Ab] to relative homoclinic class. Here, a relative homoclinic class of $p$ for $U$ is the subset of $H(p,f)$ of points that have the whole orbit inside $U$, which we denote by $H_U(p,f)$. Therefore, since $H_U(p,f)=H(p,f)$ isolated homoclinic class, for any $h\in \mathcal{R}$ close enough to $f$, $H_U(p(h),h)=\bigcap_{n\in {\mathbb{Z}}}h^n(U)$ and then $q\in H_U(p(h),h)\subset H(p(h),h)$, which is a contradiction.
Proof of Proposition \[prophexp\] {#hexpansivity}
=================================
First, note that one inclusion is a directly consequence of the result of Liao, Viana and Yang [@L-V-Y]. More precisely, they have proved that far away from homoclinic tangency every diffeomorphism is $h-$expansive. For the other inclusion we will use Lemma \[mainlemma\].
Let $f\in HT$, that is, $f$ exhibits a homoclinic tangency, say $q$, for a hyperbolic periodic point $p$. Given $\epsilon > 0$ small, let us consider a small neighborhood $\mathcal{U}$ of $f$, with $diam(\mathcal{U})<\epsilon$. Then by Lemma \[mainlemma\] there is a perturbation $f_1\in \mathcal{U}$ of $f$ such that $f_1$ has a periodic hyperbolic basic set ${\Lambda}_1$ satisfying $$h(f_1|{\Lambda}_1) >\chi(p(f_1),f_1)- \frac{1}{n_0+1},$$ for a big positive integer $n_0$ fixed, and moreover $f_1$ still exhibits a homoclinic tangency for $p(f_1)$. As we can see in the proof of the Lemma \[mainlemma\], $\Lambda_1$ can be found such that the base set $\overline{\Lambda}_1$, i.e., $\Lambda_1=\cup f_1^j(\overline{\Lambda}_1)$, is contained in a ball of radius so small, in particular, we can assume it is in a ball with radius $\frac{1}{n_0+1}$.
In the sequence, we consider a small neighborhood $\mathcal{U}_1$ of $f_1$, such that for all diffeomorphisms in $\mathcal{U}_1$ there is a continuation for $\Lambda_1$, and moreover $diam( \mathcal{U}_1)<\frac{{\varepsilon}}{n_0+1}$. Now, using again Lemma \[mainlemma\] we can find a diffeomorphism $f_2\in \mathcal{U}_1$, and a periodic hyperbolic basic set ${\Lambda}_2$, with base set contained in a ball with radius $\frac{1}{n_0+2}$, such that $$h(f_2|{\Lambda}_2) >\chi(p(f_2),f_2)- \frac{1}{n_0+2},$$ and $f_2$ still exhibits a homoclinic tangency for $p(f_2)$.
Following this process inductively we can find a sequence of diffeomorphism $f_n\in \mathcal{U}_{n-1}$, with $diam( \mathcal{U}_n)<\frac{{\varepsilon}}{n_0+n}$, $\mathcal{U}\supset \mathcal{U}_1\supset \ldots \supset \mathcal{U}_n\supset\ldots$, and moreover, by construction, $f_n$ is such that there exists periodic hyperbolic sets $\Lambda_1, \ldots, \Lambda_n$ with $diam( \Lambda_i)<\frac{1}{n_0+i}$, for every $1\leq i \leq n$, and $$h(f_n|{\Lambda}_i) >\chi(p(f_n),f_n)- \frac{1}{n_0+i}.$$ Since this sequence of diffeomorphism is a Cauchy sequence, it converges to a diffeomorphism $g$, that is $\epsilon$-close to $f$. Now, by choice of the open sets $\mathcal{U}_n$, $g$ has periodic hyperbolic basic sets with diameter so small as we want with topological entropy away from zero, since $\chi(p(f),f)$ varies continuously with the diffeomorphism $f$. Therefore, $g$ can not be asymptotically h-expansive. And then, we have proved that $\overline{HT}\subset \overline{NAHE}$.
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[^1]: This differs from usual definition, where one ask that the Lyapunov exponents of the measure are non-zero.
| 2023-12-02T01:26:35.434368 | https://example.com/article/2936 |
Trailer for Paul Verhoeven's Elle starring Isabelle Huppert
There's a new Paul Verhoeven movie coming out. Need we say more? And even while, based on the first trailer for it, the film doesn't come across as the maniacal/subversive/bleakly funny Verhoeven we all truly love, just to have the director back in the game after a long hiatus is very good news indeed.
Verhoeven's latest is ELLE, a revenge thriller starring veteran French actress Isabelle Huppert. (The film itself is French, which I believe is a first for Verhoeven.) This flick looks to come from the same man who gave us THE FOURTH MAN and BASIC INSTINCT; that is to say, this material appeals to the Dutch helmer's kinkier sensibilities. We'll definitely take it!
In ELLE, Huppert plays...
Michele, head of a successful video game company, she brings the same ruthless attitude to her love life as to business. Being attacked in her home by an unknown assailant changes Michèle's life forever. When she resolutely tracks the man down, they are both drawn into a curious and thrilling game - a game that may, at any moment, spiral out of control.
ELLE hits theaters in France in September; hopefully a U.S. distributor nabs it soon for stateside release. (Trailer doesn't have English subtitles, sorry folks.) | 2024-06-18T01:26:35.434368 | https://example.com/article/1092 |
Q:
How to detect when a usb cable is connected/disconnected on the device side in Linux 2.6.37?
I have a embedded device that runs linux 2.6.37.
I want my application to know when the USB is connected.
Currently I can achieve this by pooling
/sys/devices/platform/musb/musb-hdrc.0/vbus.
However this approach does not distinguish between a USB charger or a USB host.
I found this udev approach but I don't think it's available in my version of the kernel. because I did not find any USB related nodes in my /dev. This discussing also shows that it might not be feasible, ether.
I also found linux hotplug and tried the netlink example, but I didn't see any output running the example when I connect/disconnect the USB cable.
What I want to do is to detect connection type on the device, when USB is connected, and prepare (unmount file system) and switch to g_file_storage if device is connected to a host, and do nothing if device is connect to a charger.
How shall I achieve this?
A:
On 2.6.37 kernel, this could be done by polling
/sys/devices/platform/musb-omap2430.0/musb-hdrc.0/mode
If handshake with host is successful then it will read as "peripheral", if fail it'll be "idle".
| 2023-09-01T01:26:35.434368 | https://example.com/article/1388 |
Introduction
============
Hospitals play an important role in preventing, treating, and rehabilitating patients; and also the bulk of healthcare resources are spent by them ([@R1]--[@R3]). In this regard, quality control of health services is considered as the first step in providing effective services for better responsiveness ([@R4]). The application of standards is similarly one of the strategies to achieve appropriate levels of quality ([@R5]). Additionally, standards are regarded as expectations that are designed to ensure quality of service ([@R6]). Within health systems, strengthening an evaluation system is known as one of the most effective tools used to attain a responsive and effective system ([@R7]). Accreditation is currently one of the most widely used systems for evaluating health systems. The given approach is exploited in most countries due to its positive impacts on healthcare indicators ([@R8]--[@R10]). Accordingly, accreditation of hospitals can bring about operational effectiveness ([@R8]), professional development ([@R11]), reinforced inter- and intraorganizational relationships ([@R12]), development of quality and safety-oriented culture ([@R13]), increase in compliance with safety standards ([@R14]), improvement in outcomes of patients ([@R15]) and their satisfaction ([@R16]) as well as an enhanced public image of hospitals ([@R17]).
In this regard, Joint Commission on Accreditation of Healthcare Organizations (JCAHO) established Joint Commission International (JCI) to respond to the growth in global demands for standardized assessment in healthcare organizations ([@R18]). For this purpose, the JCI investigated 500 international healthcare organizations in 2013. In this case, there have been numerous studies evaluating the impacts of external accreditation systems on hospital performance and patient outcomes ([@R8], [@R19]--[@R21]). The concept of accreditation also refers to the systematic assessment of hospitals using certain and explicit indicators, and it is considered as a process implemented by an independent organization based on codified standards in order to evaluate units of an organization and decide on granting executive competence to that organization ([@R22]).
For the first time, Iranian hospitals were evaluated with a limited number of structural standards in 1962. Then, structural and procedural standards were developed in 1997; and finally an accreditation system was established in 2012. It should be noted that the tasks of policy-making, planning, and directing accreditation in Iran are assumed as the responsibilities of the Office for Accreditation of Healthcare Institutions in the Ministry of Health, Treatment, and Medical Education (MOHTME) ([@R23]). In this respect; medical accreditation standards for hospitals were publicized in Iran in March 2011 ([@R24]). Over time, accreditation standards of Iranian hospitals have also seen a number of revisions to their comprehensiveness ([@R25]). However, there has always been a challenge for teaching hospitals because of their wide variety of activities and measures. A teaching hospital is one that has educational and research responsibilities for training doctors, rescuers, medical and paramedical students, and also providing advancement in medical science along with treating patients ([@R26]).
Teaching hospitals are also the main providers of care services in the public sector of Iran; therefore, operation of these centers has a direct and significant impact on health system ([@R27]). Teaching hospitals now account for about 50% of hospital beds and 68% of academic beds ([@R28]). Due to the diversity of missions as well as insufficient transparency of relevant rules and regulations, such hospitals are exposed to numerous problems in their roles, which need to be addressed and resolved. In this regard, one of the main issues is the accreditation of these hospitals as teaching and research institutions providing health services ([@R29]). Multiple measures have been correspondingly taken in the domain of accreditation of teaching hospitals in Iran following international programs. It should be noted that criteria and measures regarding the accreditation of teaching hospitals were developed by the MOHTME and announced for the first time in 2015 after reviewing international documents as well as holding scientific and specialized meetings ([@R30]). At the same time; following evaluation of hospitals by universities in Iran and providing feedback on the results, hospital accreditation guidelines were reviewed and their third generation was developed and presented in 2016 ([@R31]).
It is noteworthy that old standards in the domain of education have a structure-oriented nature, and there is still no fundamental standards regarding outcomes and educational processes in the world ([@R32]). However, examples have emerged in the last decade on accreditation standards of teaching hospitals and medical education. For example, Huang et al. developed accreditation standards for teaching hospitals in Taiwan ([@R33]) and the Word Federation for Medical Education (WFME) codified standards for medical education ([@R34]). However, none of previous studies on accreditation in Iran had pointed to educational accreditation ([@R18], [@R35]--[@R38]). Some of these research studies had been solely conducted for the purpose of adapting the standards employed in Iran to international standards, and no specific standards had been developed for teaching hospitals ([@R18]). Some other investigations had also provided models for accreditation of health system in its broad terms in academic centers ([@R38]), which could not be applicable to assess teaching hospitals. Based on the reported results of studies conducted in Iran and other countries, tangible points could be addressed in the domain of accreditation of teaching hospitals in Iran. Firstly, Iran had no specific program for accreditation of these hospitals before 2012. Secondly, instructions used in teaching hospitals by Iran after this period had been taken from models in other countries, and given the reviews, they were still not well suited to the status of Iranian hospitals. Finally; design and development of a localized model, considering current laws and regulations, expert opinions, as well as those of executives as the most related ones to accreditation program, could lead to the development of a comprehensive model and provide conditions for the effectiveness of accreditation to improve the status of medical education in Iran. Therefore, the present study was conducted to respond to this issue and to design an accreditation model for Iranian teaching hospitals.
Materials and Methods
=====================
The current qualitative study was conducted from January 1st, 2017 to March 6th, 2018. To this end, four stages were taken to develop the accreditation model. In the first stage, existing accreditation models of teaching hospitals and medical education were extracted through a comprehensive review. For this purpose, the search was carried out on websites of relevant international institutions, databases and websites of health ministries, as well as the ministry of higher education in selected countries. The criterion for selecting the given countries and models of accreditation was accessibility to information. In the case of countries, pioneers in the domain of medical education and its accreditation as well as regional countries similar to Iran were selected. The models of relevant international institutions were also extracted to compare them with the current Iranian model. In this stage, the dimensions and components of the selected models were extracted and compared, and finally the shortcomings of the current Iranian model were delineated.
In the second stage, semi-structured interviews (with open-ended questions about the drawbacks of the current model and suggestions for complementing its dimensions) were used to extract the components and the dimensions required for the accreditation of Iranian hospitals. Given the nature of the required data as well as the objectives of the study, purposeful sampling method was employed. Moreover, there were attempts to use key informants for interviews and finally 19 interviews with a mean duration of 45 minutes were fulfilled until data saturation. Manifest content analysis method was also utilized to analyze qualitative data. In this method, semantic units were initially extracted and then classified and merged to form categories and subcategories. Finally, the main themes were specified by examining overlapping and semantic relationships of the categories. The criteria provided by Guba and Lincoln reporting that there were four criteria for increasing reliability and credibility in qualitative studies including credibility, confirmability, dependability, and transformability were similarly used to increase rigor in research ([@R39]). In this regard, the results were given to the interviewees during the interviews, after their completion, and following their analysis; feedback was received, and then they were corrected if there were contradictions. All the research team participated in its implementation and analysis. Three faculty members outside the research team also contributed to this study. The coding procedure was performed separately by two researchers. In all cases, there were over 90% agreements in the comments. Moreover, direct quotations were used and enough time was allocated to all stages of the study. Participation in interviews was fulfilled with prior coordination, agreement on time and place, as well as rights to interrupt the interviews by the interviewees. Data were then analyzed using MAXQDA-10.
In the third stage, the findings from the first and the second stages were integrated by the research team to develop a new model for the accreditation of Iranian teaching hospitals. In this stage, overlaps and drawbacks of the current model used in Iran and international models in selected countries were extracted. Then, the dimensions and components of the accreditation model were formulated by integrating them with the findings from the analysis of qualitative data obtained from the interviews.
In the final (fourth) stage, the model was validated by experts to address the deficiencies. In the first phase (the first round of Delphi method), a template was developed in the form of a survey by experts in which dimensions and items in the primary accreditation model were scored based on necessity, relevance, clarity, and simplicity of each item by experts. At this phase, content validity ratio (CVR) and content validity index (CVI) were employed for model validation ([@R40]). A total number of 30 experts who had experience in authorized specialist work teams or had published research articles in the domain of accreditation, or were involved in accreditation units at the MOHTME or medical universities participated in this phase. During the second round of Delphi method, the results of the first round were shared with the participants who were asked to submit their suggestions to complement the extracted model. A total number of 12 participants also submitted their own comments for completing the developed model. After collecting and analyzing the suggestions by the research team, the required modifications were applied in the developed model. In the final phase of the model validation, a meeting was also held with the presence of 9 experts, during which the proposed model was evaluated by calculating CVI and modified Cohen\'s kappa coefficient. At this phase, the status of the extracted model was evaluated for applicability, adherence to top-level documents, acceptance by beneficiaries, simplicity, coherence and integrity, as well as comprehensiveness. Additionally, in an overall item, the opinion of participants was assessed about the suitability of the extraction model for teaching hospitals. The approach developed by Polit (2007) was correspondingly used to calculate CVI and modified Cohen\'s kappa coefficient. According to Polit, Cohen\'s kappa coefficient ranged from 0.40--0.59 as a fairly good index and it was good and excellent if it was at the range of 0.60--0.74 as good and over 0.75; respectively ([@R41]). Inclusion criteria for participants in the specialized forums were similar to the ones defined for participation in Delphi method.
The ethical considerations of this study were reviewed by the Ethics Committee of Iran University of Medical Sciences (code: IR.IUMS.REC1395.9223652205). An informed consent was also obtained from all individuals. Furthermore, they were ensured for the confidentiality of information.
Results
=======
Along with the current model used in Iran, eight models were extracted by searching and considering the defined criteria (accessibility to information, models of relevant international institutions, pioneering of the selected country in the domain of educational accreditation, and similarity of the countries with Iran). The accreditation model of academic medical centers was first presented by the JCI in 2012 and then released in 2017. A model of the WFME in the field of educational accreditation was also selected for evaluation. Similarly; the models from the United States, Canada, Australia, and Japan were extracted as countries of interest in this field, as well as from Turkey and Taiwan as similar regional countries. The results of a comparative study of the models extracted and the model used in Iran in terms of dimensions and core components were presented in [Table 1](#T1){ref-type="table"} which suggested no financial support and counseling for students, interactions with society and industry, and internationalization in the model used in Iran. The participants in the interviews on the extracted dimensions included 19 individuals. Most of them were under the age of 40 years (36.8%) and male (62.2%). Almost three-quarters of these individuals (73.7%) were holding Ph.D. degree (clinical and non-clinical). All the participants with Ph.D. degree in non-clinical major were graduates of healthcare management. Most of these participants (36.8%) also had working experience of 10 to 20 years and this value was less than 10 years in 78.8% of the individuals in their current position. Most of the participants agreed on quality and quantity of dimensions and measures regarding the accreditation of teaching hospitals. In some cases, the participants provided recommendations to improve the nature and the content of the instruction associated with educational accreditation.
######
Comparative study results of selected educational accreditation models
--
--
In this context, some participants emphasized the active role of ethical components in research into teaching hospitals. In this respect, one of the participants said that: "*Limited attention has been paid to the role of research. Research into teaching hospitals is also commonplace. The dimensions of ethical considerations and thus the material and moral rights of participants must be explicitly monitored and evaluated*" (Participant No. 5).
In the field of research; considering strategies to attract funding sources, moving in the direction of obtaining grants, and holding relationships with the industry were presented as suggestions. For example, a participant reiterated that: "*There are different conditions to fund universities in advanced countries. Universities, as firms, must be able to meet their costs and be profitable institutions. Some actions have been also developed towards this direction in Iran; the speed and the strength of these movements can be enhanced through inclusion in accreditation programs. Additionally, more points should be given to the centers wherein industry is flourishing and research needs to be conducted through attracting grants so that differences can induce motivation*" (Participant No. 14).
Another issue noted by the given participants was the ongoing reviews and revisions of educational programs for students within hospital environment. Accordingly, it was stated that: "*Practical training takes place entirely in hospital environment. Therefore, new principles of education should be used in the clinical and theoretical fields. There should be further codified programs and mechanisms for continuous reviews and reconsideration of educational programs and contents. The training methods and contents used should be always reviewed. Existence of educational development units in hospitals or close collaboration of centers and colleges with hospitals can be useful in this respect*" (Participant No. 11).
Educational achievement and monitoring were other dimensions mentioned by the interviewees. "*The funding system through public resources may not provide sufficient incentives for productivity promotion interventions at universities and teaching hospitals. However, it should be noted that costs can be reduced in most cases, and a certain number of students can be trained effectively at varying costs, so the lowest costs will always be more acceptable if the quality is satisfied. These items should be considered in educational accreditation. In these circumstances, several plans are required to improve productivity*" (Participant No. 13).
The findings showed that accreditation guidelines should be more in line with the conditions of hospitals in Iran; educational centers in this country can adapt themselves to the given status while respecting standards and taking them into consideration. This factor also requires the integration of existing guidelines with international standards in the domain of medical education as well as the views of experts and professionals in order to formulate guidelines in an appropriate manner.
Synthesizing the findings from the interviews and combining them with international accreditation models as well as the latest model employed in Iran, the raw model for accreditation of teaching hospitals was extracted with 12 dimensions and 94 standards, including 1- Governance and educational management, 2- Monitoring and evaluating educational system, 3- Evaluation of students, 4- Faculty members, 5-Learners, 6- Management of facilities, spaces, equipment, and financial and human resources of education and research, 7- Training learners in emergency and para-clinical departments, 8-Educational programs and processes, 9-Respecting patient rights in educational processes, 10- Considering teaching hospitals as an area of clinical research, 11- Educational productivity, and 12- Continuous reviews and revisions.
During the first step of the validation model (the first round of Delphi method) in this study, there were 30 participants in the accreditation program, including 10 executives and managers, 10 faculty members, as well as 10 key staff members. Moreover, 60% of the participants were within the age of less than 45 years, 60% of the individuals were male, and 40% of them were women. The proportion of participants with bachelor\'s and master\'s degrees was equal (each one was 20%). The rest of the participants were general practitioners and Ph.D. graduates (each one was 23.33%), while the proportion of clinical specialists was the lowest (13.34%). In addition, 43% of these individuals had working experience between 10 and 20 years. Based on the number of survey participants (n=30), the minimum acceptable CVR was 0.33 and the minimum acceptable CVI was equal to 0.79. The results also showed that the minimum and maximum CVR in 94 standards tested were 0.40 and 0.80, respectively; hence, all the items were confirmed in this regard. The minimum and maximum CVI were estimated by 0.80 and 0.95, respectively; so that was at an acceptable level for all items. In the second step of validation (the second round of Delphi method) for the developed model, the results of the first step were presented to the participants who were then requested to provide their suggestions to complement the extracted model. A total number of 12 participants also submitted suggestions for completing the developed model. After collecting and analyzing the proposals by the research team, three items were added to the original model including a standard in the domain of monitoring and evaluating educational system, a standard in the domain of continuous reviews and revisions, and a standard in the domain of educational productivity. Eventually, the number of standards developed for the model was increased to 97.
In the next step, for the final validation of the model, a meeting was held with the participation of nine experts consisting of 5 staff from the MOHTME, 2 faculty members, and 2 staff from the teaching hospitals. The mean age of the participants in this step was estimated to be 43.6 years, 6 (66.66) of them were male and 5 (55.55) individuals were general practitioners or holding Ph.D. degrees. The results of the reviews of the CVI and modified Cohen\'s kappa agreement coefficient were shown in [Table 2](#T2){ref-type="table"}.
######
Comparison of opinions and agreement among experts on the validity of the proposed model
Dimensions I-CVI K\* Scores
----------------------------------------------------- ------- ------ -----------
Applicability 0.90 0.89 Excellent
Adherence to top-level documents 0.90 0.71 Good
Welcoming by beneficiaries 0.80 0.86 Excellent
Simplicity 0.90 0.85 Excellent
Coherence and integrity 0.80 0.81 Excellent
comprehensiveness 0.80 0.89 Excellent
Suitability of model for Iranian teaching hospitals 0.90 0.91 Excellent
Considering the above findings, the developed model had an acceptable status for six factors. In general, participants agreed on the suitability of the extraction model for teaching hospitals in Iran. Based on various validation steps, the final model for the accreditation of educational hospitals was approved with 12 dimensions and 97 standards ([Table 3](#T3){ref-type="table"}).
######
Dimensions and number of standards for the accreditation model of Iranian teaching hospitals
-------------------------------------------------------------------------------------------------------
Dimensions Number of\
standards
------------------------------------------------------------------------------------------ ------------
Governance and educational management 12
Monitoring and evaluating the educational system 5
Evaluation of students 6
Faculty members 13
Learners 9
Management of facilities, spaces, equipment, financial and human resources of education\ 13
and research
Training learners in emergency and para-clinical departments 6
Educational program and process 11
Respecting the rights of patient in the educational process 8
Considering the teaching hospitals as an area of clinical research 7
Continuous review and revision 3
Educational productivity 4
12 dimensions 97
-------------------------------------------------------------------------------------------------------
Discussion
==========
In this study, the accreditation model of Iranian teaching hospitals was developed through four stages in the form of 12 dimensions and 97 standards. The results of the components of educational accreditation models also showed that there were components of governance and leadership, missions and objectives, learners, student evaluation and its mechanisms, and educational environment and resources in all the extracted models. Governance and leadership have been so far considered as the most effective and necessary components in validation systems. In this context, the main custodian of education in a hospital should be identified, and the roles should be formulated in a clear and defined manner. Transparency of responsibilities and roles can also increase monitoring potential and reduce probability of negligence ([@R33], [@R35], [@R42]). Similarly, evaluation of students and related mechanisms has been among the most significant joint items in all extracted models. In this respect, students are considered as clients and ultimate products of medical education systems. A codified and comprehensive assessment system should be also available to truly measure the capabilities of medical students and enable the possibility of improving the status quo, in addition to realizing the principles such as merits and fairness. The last joint item in the extracted accreditation models was facilities, environments, and resources of education and research. Undoubtedly, the educational environment and resources are of the most effective components in the domain of training human resources. Educational environment can also affect attitudes and motivations of students as well as educational productivity ([@R43]).
The subjects of interactions with society and industry, internationalization, and patient rights in were the least frequent ones in educational processes. Today, universities are moving beyond their second generation and directing towards Third Generation Universities (TGUs). One of the characteristics of TGUs is a potential and high-level interaction with society and industry. The TGUs are also moving towards self-sufficiency in financing, and this necessarily involves moving towards interacting with industry and commercializing science ([@R44]). On the other hand, attention to society as a fundamental principle in teaching medical science has always been considered. Community-oriented medical education can also help educational systems meet the needs of populations efficiently. One of the goals of integrating education and treatment in 1985 in Iran and its establishment by MOHTME has been providing motivations to drive medical education towards society and its real needs ([@R45]).
Internationalization of education was another item with the lowest frequency among the models. Currently, economics of education has become one of the most commonly used terms in the world. Pioneering in the field of education can thus become a benefit to attract students from other countries, which will definitely have an effect on economics of education and other economic areas of countries ([@R46]). Considering patient rights in medical science education was the third item with a low frequency among the studied models. However, since the 18th century and along with the development of therapeutic and anatomical methods, discussions on patient rights have gradually become the focus of attention. The need for students to attend patient bedside and their access to patients\' personal information require clarity in order to provide confidentiality of patient information. Moreover, conditions must be such that prescribing treatments and their implementation by students are carried out under the supervision of a competent person and with full knowledge of patients. With regard to medical research, patient rights must be met in the field of awareness on research and its objectives as well as outcomes and other necessary information ([@R47], [@R48]). The analysis of interviews resulted in the extraction of three dimensions of accreditation model of teaching hospitals. One of the most prominent items to consider was focus on research issues in teaching hospitals. Funding research projects and likelihood of attracting grants were also the priority of research-related issues. According to the participants; research should be directed towards commercialization and attraction of grants with adherence to ethical and legal considerations ([@R44]). The TGUs-related policies in the MOHTME Department of Education in Iran have also been discussed as evolutions in education. Continuous reviews and revisions in educational programs and related processes have been also the main dimensions proposed by interviewees to add to the current educational accreditation model. The rapid and growing trend of science production, especially in the domain of medical sciences, requires continuous consideration of educational programs and contents, as well as clinical training methods and revisions on the basis of the best available evidence ([@R49]). Another area proposed by the interviewees to complete the accreditation model was educational productivity. Today, the economics of education is similarly regarded as one of the most globally well-known economic areas. Despite the aspects of income, expenditures and cost management in this branch of economy are of utmost importance ([@R46]). At present, costs of education are on a rise considering advances in medical education and specialization of this knowledge ([@R50]). Therefore, attention to educational productivity is essential for achieving sustainability in resources and possibility of growth and development.
Moreover, the feedback of findings from the first step of validation by the participants and the demands for suggestions in completing the model led to the addition of three items to monitoring and evaluation domains of the program, continuous reviews and revisions, and educational productivity. Monitoring and evaluation of the program was also added by the item of the system of sharing the results of the evaluation program and the conditions for application in order to improve the status. Benchmarking is also one of the low-cost and effective strategies to use the successful experiences of similar systems ([@R51]). The organizational conditions were almost the same in teaching hospitals and medical faculties. Therefore, there is the possibility of transferring experiences that can result in effectiveness of training and declining costs by reducing trial and error. Continuous reviews and revisions were also strengthened by the item of mechanisms used to apply international (evidence-based) scientific and empirical advances in education to revise and enhance educational programs and processes. As noted earlier, implementation of successful experiences and modeling was considered as a low-cost approach to improve the status quo. Finally, an item entitled conditions for transfer of experience and cost control in educational centers was added to the domain of educational productivity. Hospitals and academic centers can thus transfer their own experiences in reducing and managing costs during reasoning and specialized sessions, and can consequently predispose the enhancement of educational productivity through sharing knowledge. In extensive systems such as college systems, the transfer of knowledge and experience as one of the areas of knowledge management could promote efficiency and effectiveness ([@R52]). Finally, the triple process of validation resulted in the approval of the accreditation model of Iranian teaching hospitals in 12 dimensions and 97 standards. The current model used in Iran was comprised of 9 dimensions and 81 standards ([@R31]) whose quantitative and qualitative development could improve the state of executive conditions and the consequences of accreditation in teaching hospitals using the new model of accreditation.
The onset of each program would face many challenges and shortcomings that should be recast and completed through frequent revisions, forums and discussions, as well as use of international experiences. The experience of educational accreditation in Iranian university hospitals is a new step as well. The model used in this regard was based on patterns from other countries. Despite extensive efforts to nationalize this model and its adaptation to the conditions of hospitals in Iran, there are problems with the implementation of accreditation as well as its consequences. Through reviewing documentation, combining and comparing global approaches, and integrating them with the views of domestic experts; the results of the present study could scientifically predispose a basis for improving the status of educational accreditation, quality of services, and safety in Iranian hospitals.
The present study had limitations in terms of its external validity given the nature of its design (qualitative research). One of other limitations in this study was that accreditation models were selected among a number of countries and international organizations which might not be a representative of entire countries and related organizations across the world. Differences in the instructions of other countries and organizations could also increase the comprehensiveness of the model designed in this study. Moreover, since the introduction of the current model for accreditation of teaching hospitals in Iran, it might have affected the mentality of participants and challenged their creativity in terms of expressing new ideas. So, there were attempts to compensate somewhat for this limitation through conducting the study in four stages and selecting samples from different levels.
The current article has been adapted from the Ph.D. thesis in Health Services Management approved at Iran University of Medical Sciences. Authors would like to thank and appreciate the University officials as well as all the people who participated in this study.
[^1]: **Funding:** Nil
[^2]: **Competing Interests:** The authors declare that this manuscript was approved by all authors in its form and that no competing interest exists.
| 2024-05-08T01:26:35.434368 | https://example.com/article/8899 |
Maidenform The Ultimate Push Up Bra 9359 Reviews
This has way too much padding to be any good. The padding is very stiff so it makes you look ridiculous. Stiffest bra ever. It's obvious you are wearing a heavily padded bra. It doesn't work well with smaller chests. (My ideal size is 30C or 32B, depending on manufacturer) It gaps too much at the top b/c it doesn't have enough coverage for the amount of padding. As another reviewer stated, you have to stand perfectly straight with your chest pushed out for it not to gap. I think it would work better w/ bigger chests where it's better balanced (better padding to chest ratio). Otherwise, it's like you're putting fake boobs on a board.
Maidenform Response:
This bra is guaranteed to increase bust size 2 sizes. Pads on this bra have always been on the stiff side but washing does help.
Sue from Baltimore, MD
Height:
Average Height (5'4"-5'8")
Age:
30s
Posted:
August, 2012
Size:
34D
This probably won't matter since this one has been discontinued anyway. I think if they had made it clearer that this is a heavily padded bra it would have been better. I don't really need this much padding and I don't think it makes sense to make this thing in a D-cup, but if you are looking for something to make your bust look huge this would do it and I have to admit the bra itself is comfy. Being a seamstress, I may try to remove part of the padding so I can use it. If not, maybe I'll do a Jessica Rabbit cos-play in it sometime!
Maidenform Response:
This bra is made to increase you 2 cup sizes and it does.
Heidi from Salt Lake City, Ut
Height:
Petite (5'3" and under)
Age:
30s
Posted:
July, 2012
Size:
36B
Added cup size and comfort
Submitted from TheUndies.com
Height:
Average Height (5'4"-5'8")
Posted:
April, 2012
Size:
32A
I absolutely love this bra. I won't wear any other. I can never find my size in a retail store so I will only order my bras from HerRoom!
Christina from fl
Height:
Petite (5'3" and under)
Age:
20s
Posted:
April, 2012
Size:
38DD
great support
looks fabulous under clothes
Submitted from TheUndies.com
Height:
Average Height (5'4"-5'8")
Posted:
April, 2012
Size:
34B
I love this bra. Is like have a surgery without pain and looks great and feels amazing. I have 3 kids and after breastfeed them my breasts are not the same anymore,but this bra makes me feel sexy. The only little thing that I don't like is that cover too much for some of my low tops. (Me encanta este bra)
vanessa from utah
Height:
Petite (5'3" and under)
Age:
20s
Posted:
March, 2012
Size:
32A
I absolutely LOVE this bra! I bought the Ultimate Push Up bra and it is the best bra I have ever had. I am petite and small chested. I am 31 years old and feel like a woman trapped in a girls body sometimes. This bra gives me the look of a full chest and cleavage, which makes me feel more like a woman. The bra is very comfortable too. It is a little stiffer than natural breasts of course, but you can't tell without touching, which won't be happening by anyone else but me! Also, I first bought this bra , the Miraculous Push Up Bra. I loved it and wanted another one in a different color, but it cost $50. I knew that Maidenform made the bra and was only $25 from MF website. So I gave it shot and the Maidenform bra is better than the other one...at half the price! The bras are pretty much the same both places, but with a few differences. The Maidenform one is more sturdy in the front center of the bra and the straps are stronger. The cup covers a tiny bit more on the Maidenform one too, but not too much coverage so it's still good for low tops. I like the Maidenform bra better than the other one. I will definitely buy this bra from MF again.
Terry from Venice, FL USA
Height:
Petite (5'3" and under)
Age:
30s
Posted:
January, 2012
Size:
38B
This is just too much of an increase of one's bustline.
Maidenform Response:
Thank you for your comment, but this style is to increase your bust 2 sizes.
Jennifer from Goleta, CA
Height:
Tall (5'9" and over)
Age:
50s
Posted:
January, 2012
Size:
36A
Way too much padding.
Sarah from New Orleans
Height:
Tall (5'9" and over)
Age:
50s
Posted:
December, 2011
Size:
36D
The most comfortable bra I have worn in a long time, I love the support and my Husband always notices when I have it on.
Linda from South Carolina
Height:
Tall (5'9" and over)
Age:
20s
Posted:
December, 2011
Size:
34C
This is one great bra. It does it exactly what it says it will do to enhance your bust line. It is smooth under my clothes and my entire wardrobe looks better on me in this bra. It is not heavy like some padded bras. I would have never thought that I had cleavage potential, Whoo-hoo!
Denise from Reidsville NC
Height:
Average Height (5'4"-5'8")
Age:
50s
Posted:
September, 2011
Size:
38B
I finally bought this bra and am I ever happy I did. All I can say is wow it looks like there was an explosion in my blouse, a fantastic explosion. This does add a lot to what is, or in my case what isn't there I LOVE IT. Certainly not for every day wear, at least for me, but when I want to feel "Wow Look at Me" this is the perfect bra. PLEASE more pretty colors, love the bright pink.
happy TS lady from National City CA
Height:
Tall (5'9" and over)
Age:
30s
Posted:
September, 2011
Size:
36C
I really like this bra, it fits nice and looks great.
christine from cenral islip
Height:
Petite (5'3" and under)
Age:
40s
Posted:
July, 2011
Size:
34B
Bought this for my 17 year old daughter. It fit beautifully, was comfortable, and certainly did what it promised. I feared for my daughter's safety because instead of looking ahead of herself, she was walking while at the same time gazing down at her new cleavage. Ah, the amazing placement of foam and the shaping all hidden away from sight. She reported it was comfortble, did what it said it would do, and she wanted MORE!
Paulette from Wytheville, VA
Height:
Petite (5'3" and under)
Age:
60s
Posted:
July, 2011
Size:
34C
Very comfortable, good cleavage
Submitted from TheUndies.com
Height:
Average Height (5'4"-5'8")
Posted:
April, 2011
Size:
34C
I ordered this item in a 34C because that is what size I normally wear in another brand I got the bra, I noticed there was a bit of a gap at the top if I wasn't standing completely straight with my chest out. This bra actually made my chest look TOO big for my frame, (i didn't realize that was possible!). I ordered the bra in several colors. I wore the leopard one for a day and felt awkward. The print shows through every shirt I had, including polos. The bra really does increase you by two cup sizes, I would recommend ordering a size smaller than usual. I would not recommend the print. I would order this again in a smaller size in black or nude and probably only wear it on special occasions to fill out a low cut dress better.
Liss from Chicago, IL USA
Height:
Average Height (5'4"-5'8")
Age:
20s
Posted:
April, 2011
Size:
34B
The girls need all the help they can get.
Submitted from TheUndies.com
Height:
Average Height (5'4"-5'8")
Posted:
April, 2011
Size:
34B
Great for almost anything I wear.
Submitted from TheUndies.com
Height:
Average Height (5'4"-5'8")
Posted:
April, 2011
Size:
34B
This amazing push-up bra works like magic to add TWO cup sizes to your bustline right before your very eyes! This bra features heavy graduated padding along the bottom and sides of the cups for incredible lift while maintaining a natural shape and profile. Convertible, adjustable straps for convenience. HerRoom.com
Submitted from TheUndies.com
Height:
Petite (5'3" and under)
Posted:
April, 2011
Size:
34A
The bra was made well, but it was too much padding for me, so I exchanged it for another bra.
Kathie from dumas/TX/USA
Height:
Petite (5'3" and under)
Age:
40s
Posted:
April, 2011
Size:
34C
I found it comfortable and my husband found it very sexy as it does what it says it does - look 2 cup sizes bigger.
LRK from Kansas City/MO/USA
Height:
Average Height (5'4"-5'8")
Age:
40s
Posted:
March, 2011
Size:
38C
awesome....just as good as competing brand....only less expensive!!!
me
Height:
Average Height (5'4"-5'8")
Age:
40s
Posted:
March, 2011
Size:
36B
WOW....VAAVOOM...this is the one...great fit...was buying from a competitor...found them cheaper here...my boyfriend loves it..he cant take his eyes off my,well... you know.......
dorothy from pa
Height:
Average Height (5'4"-5'8")
Age:
40s
Posted:
January, 2011
Size:
36C
Like a previous reviewer stated, this bra does what it says it will. However, I found this bra to be too extreme for me. It didn't fit quite right on me as well. This bra has very molded and firm cups and is made well. It does give you a nice shape. I think women with smaller breasts would appreciate this bra...or women who want that va-va-voom factor!
Jenny from MI
Height:
Average Height (5'4"-5'8")
Age:
30s
Posted:
January, 2011
Size:
36B
Comfortable even with the extreme padding. Has a natural-looking shape and certainly increases ones bust size. It provides attractive cleavage. Makes one dress fits well now with more balance proportions. Probably not for every day but is nice to have available.
Jennifer from Goleta, CA, USA
Height:
Tall (5'9" and over)
Age:
50s
Posted:
December, 2010
Size:
36B
I love this bra! I can finally wear some of my clothes and feel like they fit me correctly. This bra is so comfortable that I want to wear it every day. I will definitely be buying more soon. I am so glad I searched before I spent double on another bra. This is so much better!
Jennifer from Goleta, CA
Height:
Petite (5'3" and under)
Age:
40s
Posted:
December, 2010
Size:
34B
This did what it said it would. I went from a B to a D without surgery and was my husband excited.
Kitty from New Mexico
Height:
Petite (5'3" and under)
Age:
50s
Posted:
October, 2010
Size:
36D
Va, va, Voom! It makes your breasts look massive!
Christina
Height:
Average Height (5'4"-5'8")
Age:
20s
Posted:
October, 2010
Size:
36D
This bra fits like a dream and is easily comparable to the more expensive versions of it. I have recommended it to all of my friends who are looking for a bra to give them a little OOMPH for the evening! You should buy this bra.
Tona from Ohio
Height:
Petite (5'3" and under)
Age:
30s
Posted:
October, 2010
Size:
38B
This is definitely an extreme bra. I guess I am no longer an extreme type of woman. I had to return this one. Even though I was hoping to add a bit of cleavage, and it certainly did that, I found it very uncomfortable. This one was just not for me.
Cary from Michigan
Welcome to HerRoom – the ultimate online lingerie store. Founded by Tomima Edmark in 1998, HerRoom has grown from bras and panties to swimwear, sleepwear, and intimate apparel and beyond. From petite to plus size we offer over 200 brand names - including Chantelle, Maidenform, Playtex and Wacoal - with more of your favorites brands and products being added almost daily to our collections. Our team works hard to provide photos and detailed product information including Customer Reviews, on every page to assist in your product selections. From bathing suits to sexy yoga pants to hosiery, HerRoom offers an unparalleled selection of products, combined with great pricing and top-notch service, to provide the most outstanding lingerie shopping experience for every customer. Enjoy the pleasure and excitement of lingerie shopping from the comfort and convenience of your own home! | 2024-04-04T01:26:35.434368 | https://example.com/article/5085 |
mmon multiple of 80 and 32?
160
What is the common denominator of -79/560 and 93/1400?
2800
Calculate the lowest common multiple of 42 and 1350.
9450
Find the common denominator of -1/2 and -68/15.
30
What is the smallest common multiple of 456 and 570?
2280
Calculate the least common multiple of 55 and 55.
55
Calculate the least common multiple of 84 and 252.
252
What is the lowest common multiple of 135 and 297?
1485
Calculate the lowest common multiple of 20916 and 6.
20916
What is the smallest common multiple of 740 and 30?
2220
Find the common denominator of 55/63 and 11/175.
1575
Calculate the lowest common multiple of 312 and 264.
3432
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270
Find the common denominator of 55/423 and 115/564.
1692
Find the common denominator of 91/30 and 62/63.
630
Calculate the lowest common multiple of 140 and 364.
1820
What is the common denominator of 7/752 and 40/423?
6768
What is the common denominator of -26/203 and -77/290?
2030
What is the lowest common multiple of 153 and 1105?
9945
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7810
Calculate the common denominator of -24/7 and -20/7.
7
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952
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808
Calculate the least common multiple of 592 and 252.
37296
Calculate the common denominator of -139/36 and -99/124.
1116
Calculate the smallest common multiple of 165 and 44.
660
Calculate the smallest common multiple of 2 and 1945.
3890
What is the least common multiple of 198 and 60?
1980
What is the smallest common multiple of 4 and 1476?
1476
Calculate the common denominator of 53/492 and 13/192.
7872
Calculate the smallest common multiple of 110 and 60.
660
What is the lowest common multiple of 33 and 99?
99
Find the common denominator of 11/542 and 85/4.
1084
Find the common denominator of -49/27 and -91/108.
108
Calculate the common denominator of -5/6 and 37/182.
546
Calculate the lowest common multiple of 6 and 1370.
4110
Calculate the smallest common multiple of 3396 and 5094.
10188
What is the least common multiple of 22 and 4606?
50666
What is the least common multiple of 150 and 300?
300
Calculate the common denominator of -59/798 and 20/49.
5586
Find the common denominator of -17/844 and -67/20.
4220
What is the smallest common multiple of 17 and 51?
51
Calculate the common denominator of 13/18 and -47/9.
18
Calculate the smallest common multiple of 72 and 274.
9864
What is the common denominator of 35/493 and 32/29?
493
Find the common denominator of 87/22 and -137/18.
198
What is the least common multiple of 11 and 310?
3410
What is the smallest common multiple of 495 and 225?
2475
Find the common denominator of 17/20 and -155/504.
2520
Calculate the lowest common multiple of 48 and 3280.
9840
Find the common denominator of 1/40 and -11/5.
40
What is the least common multiple of 462 and 1092?
12012
Calculate the common denominator of -37/288 and -17/192.
576
Calculate the smallest common multiple of 357 and 2907.
20349
Find the common denominator of -61/63 and 54/371.
3339
Calculate the smallest common multiple of 9 and 63.
63
Calculate the least common multiple of 75 and 250.
750
What is the lowest common multiple of 288 and 18?
288
Calculate the least common multiple of 104 and 234.
936
What is the lowest common multiple of 75 and 15?
75
Calculate the least common multiple of 8 and 388.
776
Calculate the least common multiple of 10 and 101.
1010
What is the lowest common multiple of 1076 and 2690?
5380
What is the smallest common multiple of 2 and 902?
902
What is the least common multiple of 12 and 18?
36
Calculate the smallest common multiple of 550 and 80.
4400
What is the common denominator of 7/80 and 73/10?
80
Calculate the lowest common multiple of 210 and 3297.
32970
What is the smallest common multiple of 280 and 140?
280
Find the common denominator of 44 and -46/59.
59
Find the common denominator of 34/27 and 73/105.
945
What is the lowest common multiple of 408 and 714?
2856
Calculate the common denominator of 137/336 and -117/28.
336
Calculate the common denominator of 63/64 and 55/104.
832
What is the smallest common multiple of 192 and 1504?
9024
What is the least common multiple of 63 and 1596?
4788
Calculate the least common multiple of 462 and 1302.
14322
What is the smallest common multiple of 4 and 674?
1348
What is the common denominator of -23/14 and -149/990?
6930
Calculate the least common multiple of 738 and 492.
1476
Calculate the lowest common multiple of 12 and 303.
1212
What is the common denominator of -71/232 and -74/261?
2088
Calculate the lowest common multiple of 80 and 64.
320
Calculate the lowest common multiple of 234 and 10.
1170
What is the smallest common multiple of 32 and 20?
160
Calculate the common denominator of -1/39 and 19/60.
780
Calculate the lowest common multiple of 98 and 70.
490
Find the common denominator of -41/12 and 41/1646.
9876
Find the common denominator of -41/43 and -73/10.
430
What is the common denominator of 103/150 and -63/550?
1650
What is the smallest common multiple of 5 and 62?
310
Calculate the lowest common multiple of 90 and 20.
180
What is the lowest common multiple of 4 and 6?
12
What is the common denominator of 149/390 and 103/910?
2730
What is the least common multiple of 3 and 278?
834
What is the smallest common multiple of 25 and 160?
800
Calculate the smallest common multiple of 420 and 420.
420
Find the common denominator of -113/448 and -169/336.
1344
Calculate the common denominator of -103/762 and 7/9398.
28194
Find the common denominator of 4/1467 and -179/30.
14670
Calculate the lowest common multiple of 1100 and 2970.
29700
What is the common denominator of -155/204 and 113/6?
204
Calculate the lowest common multiple of 6267 and 27.
56403
Find the common denominator of -151/468 and -43/312.
936
What is the least common multiple of 280 and 380?
5320
Find the common denominator of 37/609 and 53/435.
3045
Find the common denominator of 57/112 and -57/112.
112
What is the least common multiple of 1264 and 948?
3792
Calculate the smallest common multiple of 12 and 21874.
131244
Calculate the common denominator of 59/16 and 34/15.
240
What is the lowest common multiple of 14 and 1890?
1890
What is the common denominator of 29/48 and 11/18?
144
Calculate the smallest common multiple of 4 and 8.
8
What is the least common multiple of 1120 and 20?
1120
Calculate the common denominator of 85/36 and -17/12.
36
Calculate the smallest common multiple of 57 and 12768.
12768
What is the lowest common multiple of 8 and 10?
40
Find the common denominator of -47/52 and 85/2.
52
What is the common denominator of -47/3710 and 48/55?
40810
What is the common denominator of -107/360 and -88/45?
360
What is the least common multiple of 480 and 64?
960
Calculate the least common multiple of 56 and 3017.
24136
Calculate the common denominator of -35/144 and 83/64.
576
What is the least common multiple of 556 and 12?
1668
What is the common denominator of 77/24 and 49/72?
72
Calculate the least common multiple of 118 and 43.
5074
Calculate the least common multiple of 4 and 3643.
14572
What is the lowest common multiple of 2 and 8?
8
Find the common denominator of 23/55 and -113/100.
1100
What is the smallest common multiple of 1360 and 1360?
1360
Calculate the lowest common multiple of 72 and 126.
504
Calculate the lowest common multiple of 21 and 63.
63
Calculate the lowest common multiple of 14 and 18.
126
Calculate the smallest common multiple of 104 and 26.
104
What is the smallest common multiple of 2196 and 488?
4392
What is the common denominator of 67/174 and -101/474?
13746
Find the common denominator of -13/10 and -9/326.
1630
Find the common denominator of -83/1419 and -17/774.
8514
What is the common denominator of 38/11 and 83/50?
550
Calculate the least common multiple of 31 and 127.
3937
What is the common denominator of -149/1776 and 139/1332?
5328
Calculate the lowest common multiple of 39 and 39.
39
Calculate the common denominator of 145/1092 and 47/65.
5460
What is the lowest common multiple of 1078 and 770?
5390
Calculate the common denominator of -85/132 and -81/154.
924
Calculate the common de | 2024-02-23T01:26:35.434368 | https://example.com/article/9139 |
Q:
Jquery second change not firing
I'm having an issue where my second event listener does not seem to be properly performing. I am looking to update the text in my div descrip with each selection from a dropdown, but the text only gets changed for the first change. After that, despite the dropdown menus properly firing, the text is not updated at any point with any of the changes. I feel as though it must be a problem with the selectors, but I'm not 100% certain and I'm very new to Jquery. I have attached the fiddle below showing my issue. Any help is greatly appreciated.
https://jsfiddle.net/042swvdx/4/
HTML:
<h1 style='text-align:center;'>Accu Tab Submittal Builder</h1>
<br>
<div style='text-align:center;'>
<div id='descrip'>
<p>Please select a chlorinator model</p>
</div>
<form id='first'>
<select>
<option selected disabled>Chlorinator Models</option>
<option value='Accu-tab 2075'>Accu-Tab 2075</option>
<option value='Accu-tab 2150'>Accu-Tab 2150</option>
<option value='Accu-tab 2300'>Accu-Tab 2300</option>
<option value='Accu-tab 2600'>Accu-Tab 2600</option>
<option value='POWER PRO 3075'>3075 Power Pro</option>
<option value='POWER PRO 3150'>3150 Power Pro</option>
<option value='POWER PRO 3530'>3530 Power Pro</option>
<option value='POWER PRO 30600'>30600 Power Pro</option>
<option value='POWER PRO 361000'>361000 Power Pro</option>
<option value='POWER PRO 481200'>481200 Power Pro</option>
</select>
<select id='second' style="display:none;">
<option selected disabled>Select Flow</option>
<option value='Gravity'>Gravity</option>
<option value='Standard'>Standard</option>
</select>
<select id='third' style='display: none;'>
<option value='1 PH'>1 Phase</option>
<option value='3 PH'>3 Phase</option>
</select>
<select id='fourth' style="display:none;">
<option disabled selected>Control Type</option>
<option>No Control</option>
<option>WEG</option>
<option>VFD</option>
</select>
<button style='display: none'>Submit</button>
JQUERY:
$("#first").change(function() {
$("#descrip").html("<p>Please select the flow type for this system.</p>");
$("#second").show();
});
$("#second").change(function() {
$("#descrip").html('<p>Please select the phase of the motor for this unit.</p>');
$("#third").show();
});
$("#third").change(function() {
$("#descrip").html("<p>Please select units control type.</p>");
$("#fourth").show();
});
$("#fourth").change(function() {
$("#descrip").html("");
$("button").show();
});
A:
The problem is not that the second event is not firing. Your first 'change' event is set to your <form id='first'> tag. This means that each time something inside your form tag gets changed by the user it will fire a new event. I persume that you would like to set your first event to the first select element. I changed the id of your first select like this:
<form> <select id='first'>
Look here for the working Version at JSFiddle.
| 2023-11-24T01:26:35.434368 | https://example.com/article/7680 |
Bacteriology and risk factors associated with periprosthetic joint infection after primary total knee arthroplasty: retrospective study of 2543 cases.
Periprosthetic joint infection after total knee arthroplasty is a serious complication. This study aimed to identify risk factors and bacteriological features associated with periprosthetic joint infection after primary total knee arthroplasty performed at a teaching hospital. We reviewed 2543 elective primary total knee arthroplasties performed at our institution from 1993 to 2013. Data were collected from the Hong Kong Hospital Authority's Clinical Data Analysis and Reporting System, the Infection Control Team, and the joint replacement division registry. The association between potential risk factors and periprosthetic joint infection was examined by univariable analysis and multivariable logistic regression. Univariable analyses were also performed to examine the association between potential risk factors and bacteriology and between potential risk factors, including bacteriology, and early-onset infection. The incidence of periprosthetic joint infection in our series was 1.34% (n=34). The incidence of early-onset infection was 0.39% (n=24). Of the periprosthetic joint infections, 29.4% were early-onset infections. In both univariable and multivariable analyses, only rheumatoid arthritis was a significant predictor of periprosthetic joint infection. Methicillin-sensitive Staphylococcus aureus was the most common causative organism. We did not identify any significant association between potential risk factors and bacteriology. Periprosthetic joint infection caused by skin flora was positively associated with early-onset infection but the association was not statistically significant. The incidence of periprosthetic joint infection after elective primary total knee arthroplasty performed at our institution from 1993 to 2013 was 1.34%. Rheumatoid arthritis was a significant risk factor for periprosthetic joint infection. | 2024-03-28T01:26:35.434368 | https://example.com/article/5767 |
Photo from here.
I’m no fan of startup jargon—there’s a very thin line between innovation and bullshit—but there’s one term I’m a big fan of: “achieving failure.” It’s from Lean Startup, and essentially, it means spending a lot of time and money to perfectly execute something that it turns out nobody wants. If you want a case study, look no further than the Toronto Star’s tablet app, Star Touch. They thought it up in early 2014, announced it in January 2015, and only launched it in September 2015. It has cost the company $32.8 million, nearly two years, and two rounds of layoffs for “between 55,000 and 60,000 readers” each week. That’s nothing for a media company with a combined daily print and digital readership that’s somewhere north of two million, and it’s also an audience that I’d bet is no more attractive to advertisers buying ads or sponsored content than what the Star’s other products have.
Over the last few weeks, I’ve talked to J-Source and Marketing Magazine about building new digital things within an established but small media company like mine, in particular 12:36—Marc Weisblott’s wonderful daily tabloid newsletter that I’m in charge of strategy and product for. One thing I’ve learned, and that I hinted at in both stories, is that when you have what you think is a good idea for something, there’s no shame in starting meagrely and a little messily, which we did when we launched 12:36. That wasn’t easy for me; I’m fussy, and much happier when things are perfect. But trying to create something that’s perfect when it launches, rather than seeing perfection as the goal you are going to be forever working towards, is dangerous. You don’t know if anyone is going to give a shit about your great idea. And if they do give a shit, they might not give a shit in the way you thought they would.
That’s why you’re supposed to use your vision to create what’s called a minimum viable product — I tell people that that means something one notch above something they’d be embarrassed by — get it out into the world, then pay attention to how people actually use it, a thing that’s never been easier thanks to the ever-increasing amount and detail of data you can get for any and all digital products. Then you use that data to keep making the thing better. Or, if you can’t make it work, you stop. Failure is totally an option; it’s when it’s not that you’re in trouble.
It’s not that the Star having a tablet app like Star Touch was necessarily a bad idea, and in the few times I’ve used it, I’ve liked it just fine. It’s that they went about it exactly backwards, spending a year and a half and tens of millions of dollars, not to mention restructuring the entire newsroom, to get things just so before their readers ever saw it. They should’ve put six employees in a room and given them a month to launch something that would’ve quickly given the company a much better sense of just how good of an idea a tablet app was. If that project had failed, no sweat.
But this one? They’ve spent so much on this now—in money, in time, in reputation, in staff—that they feel like they can’t stop, even though they should. In the memo that went out this week when dozens of journalists working on the app were laid off, the paper’s new publisher David Holland wrote that:
…as we move forward with these changes, I want to re-affirm our continued commitment to Star Touch as an integral part of the Star’s multi-platform future. While our current audience size is not yet what we had initially anticipated, we are pleased that Star Touch has developed a highly engaged and loyal audience of committed readers. Continuing to grow from this core audience base is a key priority.
Back in January, when ten Star Touch employees lost their jobs, the publisher at the time, John Cruickshank, told staff this:
Growing our digital operation in 2014–15, and launching Toronto Star Touch last fall, were moves we made with a degree of experimentation and uncertainty about what was needed in the marketplace and what the revenue impacts would be.
“Uncertainty about what was needed in the marketplace and what the revenue impacts would be”? That sure sounds like a pretty good example of when to not spend tens of millions of dollars and two years on something before you know whether it’s a good idea. Not in Canada, not in journalism, and not right now. Instead, with Star Touch, the Star put itself in a position it never needed to be in: first, they made it so that failure wasn’t an option, and then, they failed. | 2023-11-05T01:26:35.434368 | https://example.com/article/8285 |
2019 Kentucky 3- Day Event Big Horse Racing Tote
The simple elegant printed silhouette of the iconic Land Rover Kentucky Three Day Event jumping horse rocks this bag. Printed on a heavy cotton duck canvas, the Gray Exterior is completed by a crisp navy interior. Two outer snaps open to up to allow for more space when needed. The interior has three drop pockets and magnetic closure. This bag is finished with a footed bottom. Truly one of a kind! | 2024-07-21T01:26:35.434368 | https://example.com/article/4146 |
[LDL-Cholesterol--Is there an "LDL hypothesis"?].
The term "LDL-Hypothesis" is frequently used to describe the association between LDL cholesterol (LDL-C) and cardiovascular outcomes. In the light of recent results of randomized trials the question arises whether the term hypothesis is still adequate. Considering the causal importance of LDL for the pathogenesis of atherosclerosis, epidemiological evidence and the clear genetic association of LDL-C with cardiovascular risk as well as the large statin trials and the reduction of events by a non-statin intervention in the IMPROVE-IT study, the term "hypothesis" appears to be outdated and should be replaced by "LDL-causality". | 2024-03-29T01:26:35.434368 | https://example.com/article/2494 |
Democratic New York State Senator Brad Hoylman was sick of him and his husband having to change his 4-year-old daughter on a "pee-covered floor next to a urinal," he told BuzzFeed News. He wants to do something about it.
The installation of the changing table in the men's room would be at the expense of the business.
Hoylman just finished drafting a bill for the New York State Senate that would require all new buildings or largely renovated bathrooms in New York state to have changing tables in both female and male public bathrooms.
"This is a personal issue for me," the 49-year-old senator told BuzzFeed News, "but it's also about men needing to pick up the slack in parenthood."
Recently, celebrities like Ashton Kutcher have been speaking up in anger over the lack of changing tables in men's restrooms.
Kutcher and Change.org created a petition for more changing tables, and now two bills on the subject are being considered in California.
Hoylman, who is the former president of the Gay & Lesbian Independent Democrats, has decided to take the issue to New York, but with a slightly different angle.
The Senator said that more and more gay men are becoming parents all over America and its time for public businesses to accommodate that. | 2023-11-22T01:26:35.434368 | https://example.com/article/8806 |
Product Description
Carpet color and texture vary; please allow us to select a color for you
Additional Information
Make your cat happy, distract him from clawing your furniture and rugs and help the environment all at once with this 26" Carpeted Cat Scratching Post Furniture made from recycled carpet remnants. The recycled remnants used on this Cat Scratching Furniture come in a variety of colors and textures, giving your cat hours of varied scratching and climbing pleasure. This pet scratching post can be used in many places in your home, keeping your cat from destroying furniture. Please note that the carpet color and texture of this 26" Carpeted Cat Scratching Post Furniture may vary.
Reviews
PonderosaRanch
Tall Enough For Adult Cats
Whoa! A bargain! Easily $25 at a pet specialty store. Details should include the fact that scratcher is catnip-infused, so my cats readily took to it and abandoned their old shredded, shedding sisal scratch post. This post is tall enough for the biggest adult cat to stretch full-length as he scratches. Only drawback: glued seam will eventually give way, but I will then simply cover seam with decorative duct tape; they avoid that tape, I have noticed. Excellent buy!
Bowlerchick58
Cat scratch fever
My recent purchase of this cat scratching post replaced one that I had bought several years ago and my cats had loved. I fully expect it to this new post to become their "go to" scratching post, just as the old one was. The extra height helps out also. I would purchase this again.
Judy
Cat scratch fever
Barely got it out and put down and my 16 year old big boy cat started scratching. It's the perfect size.
readerofreviews
great scratcher
My cat only likes carpet scratch post. This one is tall so she gets to stretch. She goes for it every morning. Very good price and we'll made.
enaid3
Just the right size for my big kitty.
My female kitty who isn't a light weight can easily scratch and play on this scratching post without it falling over. She played on it a few minutes after I took it out of the box | 2024-02-21T01:26:35.434368 | https://example.com/article/2847 |
Genetic variation in the non-coding genome: Involvement of micro-RNAs and long non-coding RNAs in disease.
It has been found that the majority of disease-associated genetic variants identified by genome-wide association studies are located outside of protein-coding regions, where they seem to affect regions that control transcription (promoters, enhancers) and non-coding RNAs that also can influence gene expression. In this review, we focus on two classes of non-coding RNAs that are currently a major focus of interest: micro-RNAs and long non-coding RNAs. We describe their biogenesis, suggested mechanism of action, and discuss how these non-coding RNAs might be affected by disease-associated genetic alterations. The discovery of these alterations has already contributed to a better understanding of the etiopathology of human diseases and yielded insight into the function of these non-coding RNAs. We also provide an overview of available databases, bioinformatics tools, and high-throughput techniques that can be used to study the mechanism of action of individual non-coding RNAs. This article is part of a Special Issue entitled: From Genome to Function. | 2023-08-15T01:26:35.434368 | https://example.com/article/9303 |
Q:
col/bg for plotting ecdf
I would like to highlight certain points (without the adjacent lines) in an ecdf plot. The problem is, that either
a) using col, the lines left of these points get labelled as well:
b) using bg has absolutely no effect even if specifying a pch that normally uses bg:
Where is my mistake? Is there an easy way to do that (other then to extract the ecdf function data and create the plot by hand)? I prefer plain plotting over ggplot etc. Thanks in advance!
set.seed(seed=123)
dta=rnorm(20)
plot(1:2, pch=c(19, 25), col="blue", bg="red", cex=5, lwd=4)
# works perfectly (note: pch=19 only has col, no bg, whereas others (e.g. 25) have col (border) and bg (fill))
# a)
plot(ecdf(dta), pch=19, col=c("gray","red"))
# colored symbols AND lines, but I only want to color the symbols (see 1st figure above)
# b)
plot(ecdf(dta), pch=25, col="gray",bg="red")
# specifying bg does not work from plot.ecdf (see 2nd fig. above)
A:
Would this work for you?
set.seed(seed=123)
dta=rnorm(20)
##
plot(ecdf(dta), pch=19,
col="gray",
col.01line = "gray")
lines(ecdf(dta),col="gray",
col.points=c(
rep(c("gray","red"),20)))
##
EDIT: even easier (without the additional lines call) incorporating at the aditional parameters available for plot.stepfun directly:
# nonsense colors, just to illustrate the possibility to set further parameters:
? plot.stepfun # has many more parameters!!
plot(ecdf(dta), pch=19,
col="blue",
col.points=c(
rep(c("gray","red"),20)),
verticals=TRUE, col.vert="pink",
col.01line = "green")
| 2023-08-03T01:26:35.434368 | https://example.com/article/1520 |
Oestrogens and obesity as risk factors for endometrial cancer in Italy.
In a case-control study to evaluate risk factors for endometrial cancer, obesity, history of various diseases, reproductive and menstrual characteristics, marital status, education, and lifetime use of female hormones were examined in 173 histologically proven endometrial cancers and 347 controls. Obesity, non-contraceptive oestrogen use, late menopause, low parity and history of uterine fibromyomas were associated with an increased risk of endometrial cancer. The relative risks of obesity and oestrogen use seem to fit well for an additive model. Histological differentiation was positively correlated both to oestrogen use and to level of overweight, supporting the hypothesis of a specific role of oestrogens in endometrial cancer. | 2023-10-01T01:26:35.434368 | https://example.com/article/5377 |
//
// CDEGlobalIdentifier.m
// Test App iOS
//
// Created by Drew McCormack on 4/20/13.
// Copyright (c) 2013 The Mental Faculty B.V. All rights reserved.
//
#import "CDEGlobalIdentifier.h"
#import "CDEDefines.h"
@implementation CDEGlobalIdentifier
@dynamic globalIdentifier;
@dynamic storeURI;
@dynamic nameOfEntity;
- (void)awakeFromInsert
{
[super awakeFromInsert];
if (!self.globalIdentifier) self.globalIdentifier = [[NSProcessInfo processInfo] globallyUniqueString];
}
+ (NSArray *)fetchGlobalIdentifiersForObjectIDs:(NSArray *)objectIDs inManagedObjectContext:(NSManagedObjectContext *)context
{
if (objectIDs.count == 0) return @[];
NSFetchRequest *fetch = [NSFetchRequest fetchRequestWithEntityName:@"CDEGlobalIdentifier"];
NSArray *uriStrings = [objectIDs valueForKeyPath:@"URIRepresentation.absoluteString"];
fetch.predicate = [NSPredicate predicateWithFormat:@"storeURI IN %@", uriStrings];
NSError *error;
NSArray *globalIds = [context executeFetchRequest:fetch error:&error];
if (!globalIds) {
CDELog(CDELoggingLevelError, @"Fetch for global ids failed: %@", error);
return nil;
}
// Sort in same order
NSDictionary *globalIdsByURI = [NSDictionary dictionaryWithObjects:globalIds forKeys:[globalIds valueForKeyPath:@"storeURI"]];
NSMutableArray *result = [NSMutableArray arrayWithCapacity:objectIDs.count];
for (NSManagedObjectID *objectID in objectIDs) {
CDEGlobalIdentifier *globalId = globalIdsByURI[objectID.URIRepresentation.absoluteString];
[result addObject:globalId ? : [NSNull null]];
}
return result;
}
+ (NSArray *)fetchGlobalIdentifiersForIdentifierStrings:(NSArray *)idStrings withEntityNames:(NSArray *)entityNames inManagedObjectContext:(NSManagedObjectContext *)context
{
NSParameterAssert(idStrings.count == entityNames.count);
NSFetchRequest *fetch = [NSFetchRequest fetchRequestWithEntityName:@"CDEGlobalIdentifier"];
fetch.predicate = [NSPredicate predicateWithFormat:@"globalIdentifier IN %@", idStrings];
NSError *error;
NSArray *globalIds = [context executeFetchRequest:fetch error:&error];
if (!globalIds) {
CDELog(CDELoggingLevelError, @"Fetch for global ids failed: %@", error);
return nil;
}
// Group results by id string, and index on entity
NSMutableDictionary *globalIdsByIdString = [NSMutableDictionary dictionaryWithCapacity:globalIds.count];
for (CDEGlobalIdentifier *globalId in globalIds) {
NSMutableDictionary *globalIdsByEntity = globalIdsByIdString[globalId.globalIdentifier];
if (!globalIdsByEntity) globalIdsByEntity = [[NSMutableDictionary alloc] init];
[globalIdsByEntity setObject:globalId forKey:globalId.nameOfEntity];
[globalIdsByIdString setObject:globalIdsByEntity forKey:globalId.globalIdentifier];
}
// Create result in same order as input
NSMutableArray *result = [NSMutableArray arrayWithCapacity:idStrings.count];
NSUInteger i = 0;
for (NSManagedObjectID *idString in idStrings) {
NSDictionary *globalIdsByEntity = globalIdsByIdString[idString];
NSString *entityName = entityNames[i++];
CDEGlobalIdentifier *entityGlobalId = globalIdsByEntity[entityName];
[result addObject:entityGlobalId ? : [NSNull null]];
}
return result;
}
+ (NSArray *)fetchUnreferencedGlobalIdentifiersInManagedObjectContext:(NSManagedObjectContext *)context
{
NSError *error = nil;
NSFetchRequest *fetch = [NSFetchRequest fetchRequestWithEntityName:@"CDEGlobalIdentifier"];
fetch.predicate = [NSPredicate predicateWithFormat:@"objectChanges.@count == 0"];
NSArray *globalIds = [context executeFetchRequest:fetch error:&error];
if (!globalIds) {
CDELog(CDELoggingLevelError, @"Fetch for global ids failed: %@", error);
return nil;
}
return globalIds;
}
@end
| 2024-07-09T01:26:35.434368 | https://example.com/article/2817 |
There is a growing sense that America’s tech entrepreneurs are no longer making useful things that solve difficult problems.
Worse than that, Silicon Valley is exhibiting some of Wall Street’s amoral behaviors.
Ankur Jain, of Kairos Society, has created a fund aimed at solving big problems that are particularly tough on middle-class Americans.
At some point in between coming up with the tagline “Don’t be evil” and bringing Soylent into this world – between building the cloud and cheerleading the disaster that is Theranos – Silicon Valley became a place it hates.
Silicon Valley became Wall Street.
I don’t cover Silicon Valley. But I do cover Wall Street. I know Wall Street.
And it takes one to know one. I also know that in private and not-so-private conversations, the two centers of capitalism see themselves as symbiotic rivals.
Over the past few years, the Ivy League graduates who used to pour into Wall Street have started opting for Silicon Valley instead. So have some of the Wall Streeters themselves. Stanford has outshone Harvard, and America’s business hero has become Amazon’s Jeff Bezos, not JPMorgan’s Jamie Dimon.
It’s not hard to see why. Like Silicon Valley’s technology, Bezos has managed to reach his business into almost every facet of daily life in America.
Lees ook op Business Insider Daimler stort zich op de markt voor elektrische trucks met 2 nieuwe modellen van Mercedes – en gaat strijd aan met Tesla en Nikola
The most important distinction for this story is that the purported ethos of each place couldn’t be more different. Wall Street stands practically naked in its acknowledgment that greed is the driver of many its dealings. Silicon Valley, on the other hand, has always sold itself as a place that made good things that help the world and solve problems.
And this is where it has now run into problems.
At the moment, it is not difficult to argue that Silicon Valley is not living up to its ideals – that its former ethos is just a veneer over what has become a bubble of tone-deaf ideas and money chasing money for money’s sake. At dinners with venture capitalists, investments are measured not by the brilliance of the idea behind them or the scope of the problems they solve, but by how much money they’ve managed to raise.
Every guy wearing Louis Vuitton sneakers at The Battery – a members-only San Francisco club for the Valley’s elite – wants to interrupt your conversation to talk about the growth metrics he’s seeing on his bitcoin sticker company.
Let me tell you: It sounds a lot like a guy in Gucci loafers at the Hunt and Fish Club in New York City bragging about how much money his hedge fund raised.
Meanwhile, since the 2016 US presidential election, Facebook, Google, and Twitter have managed to anger just about every single American with a smartphone.
“Silicon Valley has gotten out of touch in a time when it’s more powerful than ever and the work that it does affects more people than ever,” said Ankur Jain, the 27-year-old founder of the Kairos Society, which includes a venture-capital fund. “Ninety percent of VC funds say they want to change the world, and they don’t.”
In that sense, Wall Street has Silicon Valley beat. At least Wall Street is doing what it set out to do.
What good is a maker?
It’s not just making something that matters. It’s what you make.
Perhaps you looked at the Forbes “30 Under 30” list for startups. If you didn’t, let me tell you about some things you’ll find there: a company that’s like Airbnb but for pets, a glorified catering service for Silicon Valley startups, an app that helps you decorate, and a point-of-sale platform that can help you finance that Jet Ski you’ve always had your eye on.
America has so many big problems, and part of Silicon Valley’s pride was helping us solve them.
Of course, there’s nothing wrong with getting an Airbnb for your labradoodle. But this isn’t just about startups.
Apple is a tax avoider, and Google, Facebook, and Twitter – where to even start with them? We’ll call them the big three.
At a Senate hearing last month on how Russian bots used social media to spread misinformation during the 2016 campaign, Democratic Sen. Al Franken of Minnesota couldn’t get any of the lawyers representing the big three to say they wouldn’t accept payment for US political ads in foreign currency.
Foto: Sen. Al Franken. source Getty
And by the way, a shout-out to the big three’s CEOs for sending their lawyers and not answering questions themselves about a hostile foreign power on their platforms. That beats Wall Street too – every major US Wall Street bank head has had a turn in the hot seat in Congress. But I guess the seat’s too hot for Mark Zuckerberg.
Slowly, the big three have been trickling out troubling data about the number of people who’ve seen misinformation on their platforms. Facebook was throwing around numbers like 10 million at first, then it hiked that up to 126 million.
It’s like when Dimon says “open kimono” and every journalist on Wall Street shudders, knowing that whatever ugly thing is under there the reality is probably 10 times worse.
Google, Facebook, and Twitter never wanted the responsibility of patrolling their platforms. They just wanted to sell your data. The problem with that, of course, is that they run spaces that need to be filled with something, anything, good or otherwise. That has consequences.
Th opposite of good isn’t nothing – it’s evil. And in the absence of good, that is what will often fill the void.
Put more simply: “Don’t be evil” is no longer enough. (Google, incidentally, dropped it a few years ago as a motto.)
How to get back to good
Foto: Ankur Jain, the founder of Kairos Society, which includes a venture fund.sourceSarah Jacobs/Business Insider
What has happened, it seems quite clear, is that instead of innovating for America or the world, Silicon Valley is innovating for itself.
Instead of asking, “What does the world need?” – a big, bold question if there ever was one – more often it’s asking, “What do I want?”
And “I,” a wealthy, tech-savvy urban dweller, would like an app that delivers a burrito on command, or a $400 juicer.
Enter Jain, who has decided that this is enough. At a time when middle-class America – a massive market, as he repeatedly pointed out to me – is hurting more than ever, it’s time for Silicon Valley to be bold. It’s time for it to be useful. It’s time for it to be what it says it is.
“The everyday person is getting squeezed at every phase of their life,” he told me. And not just middle-class people.
“The decision-makers [in Silicon Valley] assume their engineers are just fine, but when rent is 50% of your after-tax income, you’re struggling,” he said.
On Thursday, Jain announced he had dedicated a fund to fixing the following big problems in America:
Student debt.
Sky-high rent in urban centers.
Childcare.
The cost of unemployment and retraining.
Retirement income.
The fund’s board include Vicente and Marta Fox, the former president and first lady of Mexico; Mark Thompson, the CEO of The New York Times; Bobbi Brown, the founder of Bobbi Brown Cosmetics; Roger Goodell, the NFL commissioner; and more. There are, however, no venture capitalists.
“We’re going to feel deal-flow FOMO by passing up deals everyone is working on, but we’re going to have to do that to stay focused,” Jain said.
Now a place where money likes to follow money, Silicon Valley has become risk-averse and cowardly. On Wall Street, we call this a herd.
Silicon Valley, welcome to Wall Street. | 2024-03-01T01:26:35.434368 | https://example.com/article/9747 |
/*
Copyright (c) 2006-2012, Arvid Norberg
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modification, are permitted provided that the following conditions
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CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/
#ifndef NODE_ID_HPP
#define NODE_ID_HPP
#include <algorithm>
#include <boost/cstdint.hpp>
#include "libtorrent/config.hpp"
#include "libtorrent/peer_id.hpp"
#include "libtorrent/assert.hpp"
#include "libtorrent/address.hpp"
namespace libtorrent { namespace dht
{
typedef libtorrent::big_number node_id;
// returns the distance between the two nodes
// using the kademlia XOR-metric
node_id TORRENT_EXTRA_EXPORT distance(node_id const& n1, node_id const& n2);
// returns true if: distance(n1, ref) < distance(n2, ref)
bool TORRENT_EXTRA_EXPORT compare_ref(node_id const& n1, node_id const& n2, node_id const& ref);
// returns n in: 2^n <= distance(n1, n2) < 2^(n+1)
// usefult for finding out which bucket a node belongs to
int TORRENT_EXTRA_EXPORT distance_exp(node_id const& n1, node_id const& n2);
node_id TORRENT_EXTRA_EXPORT generate_id(address const& external_ip);
node_id TORRENT_EXTRA_EXPORT generate_random_id();
node_id TORRENT_EXTRA_EXPORT generate_id_impl(address const& ip_, boost::uint32_t r);
bool TORRENT_EXTRA_EXPORT verify_id(node_id const& nid, address const& source_ip);
} } // namespace libtorrent::dht
#endif // NODE_ID_HPP
| 2024-06-25T01:26:35.434368 | https://example.com/article/6306 |
---
abstract: |
We establish a canonical and unique tensor product for commutative monoids and groups in an $\infty$-category ${\mathcal C}$ which generalizes the ordinary tensor product of abelian groups. Using this tensor product we show that ${\mathbb{E}}_n$-(semi)ring objects in ${\mathcal C}$ give rise to ${\mathbb{E}}_n$-ring spectrum objects in ${\mathcal C}$. In the case that ${\mathcal C}$ is the $\infty$-category of spaces this produces a multiplicative infinite loop space machine which can be applied to the algebraic K-theory of rings and ring spectra.
The main tool we use to establish these results is the theory of smashing localizations of presentable $\infty$-categories. In particular, we identify preadditive and additive $\infty$-categories as the local objects for certain smashing localizations. A central theme is the stability of algebraic structures under basechange; for example, we show ${\mathcal{R}\mathrm{ing}}({\mathcal D}\otimes{\mathcal C})\simeq{\mathcal{R}\mathrm{ing}}({\mathcal D})\otimes{\mathcal C}$. Lastly, we also consider these algebraic structures from the perspective of Lawvere algebraic theories in $\infty$-categories.
author:
- 'David Gepner, Moritz Groth and Thomas Nikolaus'
bibliography:
- 'add\_final.bib'
title: Universality of multiplicative infinite loop space machines
---
Introduction {#sec:intro}
============
The Grothendieck group $\mathrm{K}_0{(M)}$ of a commutative monoid $M$, also known as the group completion, is the universal abelian group which receives a monoid map from $M$. It was a major insight of Quillen that higher algebraic K-groups can be defined as the homotopy groups of a certain spectrum which admits a similar description: more precisely, from the perspective of higher category theory, the algebraic K-theory spectrum of a ring $R$ can be understood as the group completion of the groupoid of projective $R$-modules, viewed as a symmetric monoidal category with respect to the coproduct.
When $R$ is commutative, the algebraic K-groups inherit a multiplication which stems from the tensor product of $R$-modules. Just as the K-groups arise as homotopy groups of the K-theory spectrum, it is essential for computational and theoretical purposes to understand the multiplication on these groups as coming from a highly structured multiplication on the K-theory spectrum itself. Unfortunately it turned out to be hard to construct such a multiplication directly, partly because for a long time the proper framework to deal with multiplicative structures on spectra was missing. Important work on this question was pioneered by May et. al. [@May82], and the general theory of homotopy coherent algebraic structures goes back at least to Boardman-Vogt [@BV], May [@Operad], and Segal [@segal_categories].
It was first shown by May that the group completion functor from ${\mathbb{E}}_\infty$-spaces to spectra preserves multiplicative structure [@May82]; see also the more recent accounts [@May_WhatI; @May_WhatII; @May_WhatIII]. Since then, several authors have given alternative constructions of multiplicative structure on K-theory spectra: most notably, Elmendorf and Mandell promote the infinite loop space machine of Segal to a multifunctor in [@EM06] and in [@EM09] they extend the K-theory functor from symmetric monoidal categories to symmetric multicategories (a.k.a. coloured operads), and Baas-Dundas-Richter-Rognes show how to correct the failure of the ‘phony multiplication’ on the Grayson-Quillen $S^{-1}S$-construction in [@BDRR], as identified by Thomason [@phony].
All of these approaches are very carefully crafted and involve for example the intricacies of specific pairs of operads or indexing categories. Here we take a different approach to ‘multiplicative infinite loop space theory’, replacing the topological and combinatorial constructions of specific machines by the use of *universal properties*. The main advantage of our approach is that we get strong uniqueness results, which follow for free from the universal properties. The price we pay is that we use the extensive machinery of $\infty$-categories and argue in the abstract, without the aid of concrete models. Similar results for the case of Waldhausen K-theory, also using the language of $\infty$-categories, have been obtained by Barwick in the recent paper [@Bar].\
In this paper we choose to use the language of (presentable) $\infty$-categories. But we emphasize the fact that every combinatorial model category gives rise to a presentable $\infty$-category, and that all presentable $\infty$-categories arise in this way. Moreover the study of presentable $\infty$-categories is basically the same as the study of combinatorial model categories, so that in principle all our results could also be formulated in the setting of model categories.
Let us begin by mentioning one of our main results. Associated to an $\infty$-category ${\mathcal C}$ are the $\infty$-categories ${\mathcal C}_*$ of pointed objects in ${\mathcal C}$, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ of commutative monoids in ${\mathcal C}$, ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ of commutative groups in ${\mathcal C}$, and ${\mathrm{Sp}}({\mathcal C})$ of spectrum objects in ${\mathcal C}$. For these $\infty$-categories we establish the following:
() [*Let ${\mathcal C}^\otimes$ be a closed symmetric monoidal structure on a presentable $\infty$-category ${\mathcal C}$. The $\infty$-categories ${\mathcal C}_*$, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$, ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$, and ${\mathrm{Sp}}({\mathcal C})$ all admit closed symmetric monoidal structures, which are uniquely determined by the requirement that the respective free functors from ${\mathcal C}$ are symmetric monoidal. Moreover, each of the following free functors also extends uniquely to a symmetric monoidal functor $${\mathcal C}_*\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Sp}}({\mathcal C})\, .$$*]{}
Note that these symmetric monoidal structures allow us to talk about ${\mathbb{E}}_n$-(semi)ring objects and ${\mathbb{E}}_n$-ring spectrum objects in ${\mathcal C}$. Before we sketch the general ideas involved in the proof, it is worth indicating what this theorem amounts to for specific choices of ${\mathcal C}$.
1. If ${\mathcal C}$ is the ordinary category of sets, then the symmetric monoidal structures of recover for instance the tensor product of abelian monoids and abelian groups. This also reestablishes the easy result that the group completion functor $\mathrm{K}_0$ is symmetric monoidal.
2. In the case of the 2-category ${\mathcal{C}\mathrm{at}}$ of ordinary categories, functors, and natural isomorphisms we obtain a symmetric monoidal structure on the $2$-category of symmetric monoidal categories. The symmetric monoidal structure on ${\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}})$ has been the subject of confusion in the past due to the fact that ${\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}$ only has the desired symmetric monoidal structure when considered as a 2-category and not as a 1-category. In this case, ${\mathbb{E}}_n$-(semi)ring objects are *${\mathbb{E}}_n$-(semi)ring categories* (sometimes also called *rig categories*), important examples of which are given by the bipermutative categories of [@May_WhatII]. We also obtain higher categorical analogues of this picture using ${\mathcal{C}\mathrm{at}}_n$ and ${\mathcal{C}\mathrm{at}_\infty}$.[^1]
3. Finally, and most importantly for this paper, we consider in the special case of the $\infty$-category ${\mathcal{S}}$ of spaces (which can be obtained from the model category of spaces or simplicial sets). That way we get canonical monoidal structures on ${\mathbb{E}}_\infty$-spaces and grouplike ${\mathbb{E}}_\infty$-spaces. The resulting ${\mathbb{E}}_n$-algebras are *${\mathbb{E}}_n$-(semi)ring spaces*; more precisely, they are an $\infty$-categorical analogue of the ${\mathbb{E}}_n$-(semi)ring spaces of May (see, for example, [@May_WhatI]). Moreover, we obtain unique multiplicative structures on the group completion functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ and the ‘delooping’ functor ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Sp}}$ which assigns a spectrum to a grouplike ${\mathbb{E}}_\infty$-space. In particular, the spectrum associated to an ${\mathbb{E}}_n$-(semi)ring space is an ${\mathbb{E}}_n$-ring spectrum, which amounts to *‘multiplicative infinite loop space theory’*.
These facts can be assembled together to obtain a new description of the multiplicative structure on the algebraic K-theory functor ${\mathrm{K}}\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\to {\mathrm{Sp}}$ and its $\infty$-categorical variant ${\mathrm{K}}\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty \to {\mathrm{Sp}}$ (§\[sec:infinite\]). In particular, the algebraic K-theory of an ${\mathbb{E}}_n$-semiring ($\infty$-)category is canonically an ${\mathbb{E}}_n$-ring spectrum. By a ‘recognition principle’ for ${\mathbb{E}}_n$-semiring ($\infty$-)categories, this applies to many examples of interest. More precisely, we show that these semiring $\infty$-categories can be obtained from ${\mathbb{E}}_n$-monoidal $\infty$-categories with coproducts such that the monoidal structure preserves coproducts in each variable separately (). For instance ordinary closed monoidal, braided monoidal, or symmetric monoidal categories admit the structure of ${\mathbb{E}}_n$-semiring categories (for $n=1,2,\infty$, respectively) in which the ‘addition’ is given by the coproduct and the ‘mutliplication’ is given by the tensor product. More specific examples are given by ($\infty$-)categories of modules over ordinary commutative rings or ${\mathbb{E}}_n$-ring spectra.[^2]\
One central idea to prove as stated above, which is also of independent interest, is to identify the assignments $$\label{assignments}
{\mathcal C}\mapsto {\mathcal C}_*, \qquad {\mathcal C}\mapsto {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}),\qquad {\mathcal C}\mapsto {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}),\qquad {\mathcal C}\mapsto {\mathrm{Sp}}({\mathcal C})$$ as universal constructions. The first and the last case have already been thoroughly discussed by Lurie in [@HA], where it is shown that, in the world of presentable $\infty$-categories, ${\mathcal C}_*$ is the *free pointed* $\infty$-category on ${\mathcal C}$ and ${\mathrm{Sp}}({\mathcal C})$ is the *free stable* $\infty$-category on ${\mathcal C}$. We extend this picture by introducing *preadditive* and *additive* $\infty$-categories (see also [@TV] and [@Joyal]). These notions are obtained by imposing additional exactness conditions on pointed $\infty$-categories, just as is done in the case of ordinary categories. In fact, a presentable $\infty$-category ${\mathcal C}$ is (pre)additive if and only if its homotopy category ${\mathrm{Ho}}({\mathcal C})$ is (pre)additive in the sense of ordinary category theory. We show that, again in the framework of presentable $\infty$-categories, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is the *free preadditive* $\infty$-category on ${\mathcal C}$ and that ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is the *free additive* $\infty$-category on ${\mathcal C}$ ().
As an application of this description as free categories one can deduce the existence and uniqueness of the functors $${\mathcal C}\to{\mathcal C}_*\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Sp}}({\mathcal C}_\ast)$$ from the fact that every stable $\infty$-category is additive, every additive $\infty$-category is preadditive and every preadditive $\infty$-category is pointed. More abstractly, the assignments give rise to endofunctors of the $\infty$-category ${\mathcal{P}\mathrm{r^L}}$ of presentable $\infty$-categories and left adjoint functors. The aforementioned universal properties are equivalent to the observation that these endofunctors are localizations (in the sense of Bousfield) of ${\mathcal{P}\mathrm{r^L}}$ with local objects the pointed, preadditive, additive, and stable presentable $\infty$-categories, respectively.\
A second main theme of the paper is the stability of algebraic structures under basechange. For example we show that we have equivalences $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}\otimes {\mathcal D}) \simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \otimes {\mathcal D}\qquad {\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal C}\otimes {\mathcal D}) \simeq {\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal C}) \otimes {\mathcal D}\ ,$$ where $\otimes$ denotes the tensor product on ${\mathcal{P}\mathrm{r^L}}$ as constructed in [@HA] ( and ). Such basechange properties are satisfied by many endofunctors of ${\mathcal{P}\mathrm{r^L}}$ which arise when considering algebraic structures of certain kinds, e.g. ${\mathcal C}\mapsto {\mathrm{Mod}}_{\mathbb{T}}({\mathcal C})$ for a Lawvere algebraic theory ${\mathbb{T}}$. We give a brief account of algebraic theories in .
A key insight here is to consider endofunctors of ${\mathcal{P}\mathrm{r^L}}$ which satisfy both properties: namely, they are simultaneously localizations and satisfy basechange. In keeping with the terminology of stable homotopy theory we refer to such functors as *smashing localizations* of ${\mathcal{P}\mathrm{r^L}}$. The endofunctors $(-)_\ast, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}, {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}$ and ${\mathrm{Sp}}$ are the main examples treated in this paper. Then the proof of follows as a special case of the general theory of smashing localizations $L\colon{\mathcal{P}\mathrm{r^L}}\to {\mathcal{P}\mathrm{r^L}}$. For example we prove that if ${\mathcal C}\in {\mathcal{P}\mathrm{r^L}}$ is closed symmetric monoidal, then the $\infty$-category $L{\mathcal C}$ admits a [*unique*]{} closed symmetric monoidal structure such that the localization map ${\mathcal C}\to L{\mathcal C}$ is a symmetric monoidal functor ().\
**Organization of the paper.** In §\[sec:monoids\], we recall the definition of the $\infty$-category of monoid and group objects in an $\infty$-category. They form the generic examples of (pre)addtive $\infty$-categories which we introduce in §\[sec:pre\]. In §\[sec:smash\], we study smashing localizations of ${\mathcal{P}\mathrm{r^L}}$, which turns out to be the central notion needed to deduce many of the subsequent results in this paper. We then show, in §\[sec:mon\], that the formation of commutative monoids and groups in presentable $\infty$-categories are examples of smashing localizations of ${\mathcal{P}\mathrm{r^L}}$, and we identify these localizations with the free (pre)additive $\infty$-category functor. This leads to the existence of the canonical symmetric monoidal structures described in §\[sec:spec\], and the next §\[sec:more\] is devoted to studying the functoriality of these structures. Then in §\[sec:ring\] we consider $\infty$-categories of (semi)ring objects in a closed symmetric monoidal presentable $\infty$-category; these are used in §\[sec:infinite\] to show that the algebraic K-theory of an ${\mathbb{E}}_n$-semiring $\infty$-category is an ${\mathbb{E}}_n$-ring spectrum. Finally, in Appendix \[comonoids\] we show a relation of functors with comonoids, and in Appendix \[sec:app\] we consider monoid, group, and ring objects from the perspective of Lawvere algebraic theories.\
**Conventions.** We freely use the language of $\infty$-categories throughout this paper. In particular, we adopt the notational conventions of [@HTT] and [@HA] and provide more specific references where necessary.\
**Acknowledgements.** We would like to thank Ulrich Bunke for suggesting that we work out these results in the setting of $\infty$-categories and for carefully reading a previous draft. We’d also like to thank Peter May, Tony Elmendorf and Mike Mandell for helpful comments and discussions.
Infinity-categories of commutative monoids and groups {#sec:monoids}
=====================================================
Given an $\infty$-category ${\mathcal C}$ with finite products, we may form the $\infty$-category ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ of ${\mathbb{E}_\infty}$-monoids in ${\mathcal C}$. By definition, an ${\mathbb{E}_\infty}$-monoid $M$ in ${\mathcal C}$ is a functor $M\colon{\mathrm{N}(\mathcal{F}\mathrm{in}_*)}\to{\mathcal C}$ such that the morphisms $M({\langle n\rangle})\to M({\langle 1\rangle})$ induced by the inert maps $\rho^i\colon{\langle n\rangle}\to{\langle 1\rangle}$ exhibit $M({\langle n\rangle})$ as an $n$-fold power of $M({\langle 1\rangle})$ in ${\mathcal C}$ (see [@HA 2.1.1.8, 2.4.2.1, 2.4.2.2] for details). In the terminology of [@segal_categories], $M$ is called a *special* $\Gamma$-object of ${\mathcal C}$. In what follows we will sometimes abuse notation and also use the same name for the underlying object of such an ${\mathbb{E}_\infty}$-monoid. Given an ${\mathbb{E}_\infty}$-monoid $M$, we obtain a (coherently associative and commutative) multiplication map $$m\colon M\times M\to M\, ,$$ uniquely determined up to a contractible space of choices.
\[prop:gpl\] Let ${\mathcal C}$ be an $\infty$-category with finite products and let $M$ be an ${\mathbb{E}}_\infty$-monoid in ${\mathcal C}$. Then the following conditions are equivalent:
1. The ${\mathbb{E}_\infty}$-monoid $M$ admits an *inversion* map, i.e., there is a map $i\colon M\to M$ such that the composition $$M \xrightarrow{\Delta} M \times M \xrightarrow{id \times i} M \times M \xrightarrow{m} M$$ is homotopic to the identity.
2. The commutative monoid object of ${\mathrm{Ho}}({\mathcal C})$ underlying the ${\mathbb{E}_\infty}$-monoid $M$ is a *group* object.
3. The *shear map* $s\colon M \times M \to M \times M$, defined as the projection $pr_1\colon M \times M \to M$ on the first factor and the multiplication $m\colon M \times M \to M$ on the second factor, is an equivalence.
4. The special $\Gamma$-object $M\colon{\mathrm{N}(\mathcal{F}\mathrm{in}_*)}\to{\mathcal C}$ is *very special* (again in the terminology of [@segal_categories]).
This follows immediately from the fact that ${\mathcal C}\to \mathrm{N}({\mathrm{Ho}}({\mathcal C}))$ is conservative and preserves products.
Let ${\mathcal C}$ be an $\infty$-category with finite products. An object $M\in{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is called an [*${\mathbb{E}}_\infty$-group*]{} in ${\mathcal C}$ if it satisfies the equivalent conditions of . We write ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ for the full subcategory of ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ consisting of the ${\mathbb{E}_\infty}$-groups.
There are similar equivalent characterizations as in the proposition for ${\mathbb{E}}_n$-monoids, $n\geq 1$. In fact, they can be applied more generally to algebras for monochromatic $\infty$-operads ${\mathcal{O}}$ equipped with a morphism ${\mathbb{E}}_1\to{\mathcal{O}}$. In this case, these characterizations serve as a definition of ${\mathcal{O}}$-*groups*. Since an ordinary monoid having right-inverses is a group, we can use the fact that every morphism in ${\mathrm{Ho}}({\mathcal C})$ lifts to a morphism in ${\mathcal C}$ to conclude that also the characterizations (i) and (iii) are equivalent to their respective ‘two-sided variants’, but in characterization (iv) one must instead use (very) special simplicial objects in ${\mathcal C}$.
Recall (cf. [@HA Remark 5.1.3.3]) that an ${\mathbb{E}}_n$-monoid object $M$ of an $\infty$-topos ${\mathcal C}$ is said to be [*grouplike*]{} if (the sheaf) $\pi_0 M$ is a group object. In more general situations, such as for instance ${\mathcal C}={\mathcal{C}\mathrm{at}}_\infty$, the correct $\pi_0$ is unclear, and in any case the resulting notion of ‘grouplike monoid’ may not agree with that of ‘group’.
In our definition of a group object we force the ‘inversion’ morphism to be an actual morphism of the underlying objects in ${\mathcal C}$. In many situations, however, there is a natural inversion which is naturally only an anti-morphism. For example, this is the case in a tensor category with tensor inverses or in the category of Poisson Lie groups. This suggests that there should be a notion of group object with such an anti-inversion morphism. It would be interesting to study such a notion, though we will not need this.
Given two $\infty$-categories ${\mathcal C}$ and ${\mathcal D}$ with finite products, we write ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$ for the $\infty$-category of finite product preserving functors from ${\mathcal C}$ to ${\mathcal D}$. If ${\mathcal C}$ and ${\mathcal D}$ are complete, we write ${{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})$ for the $\infty$-category of limit preserving functors. In this situation, the $\infty$-category ${{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})$ is also complete and limits in ${{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})$ are formed pointwise in ${\mathcal D}$. This follows from the corresponding statement for ${\mathrm{Fun}}({\mathcal C},{\mathcal D})$ and from the fact that such a pointwise limit of functors is again limit preserving.
\[lem:algR\] If ${\mathcal C}$ and ${\mathcal D}$ are $\infty$-categories with finite products, then ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$ also has finite products and we have canonical equivalences $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})\big) \simeq {\mathrm{Fun}}^\Pi\big({\mathcal C}, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \big)$$ and $${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}\big({\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})\big) \simeq {\mathrm{Fun}}^\Pi\big({\mathcal C}, {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \big).$$ If ${\mathcal C}$ and ${\mathcal D}$ are complete, then so is ${{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})$, and we have canonical equivalences $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})\big) \simeq {{\mathrm{Fun}}^\mathrm{R}}\big({\mathcal C}, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \big)$$ and $${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})\big) \simeq {{\mathrm{Fun}}^\mathrm{R}}\big({\mathcal C}, {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \big).$$
We only give the proof of the second case, as the first one is entirely analogous. As recalled above, an ${\mathbb{E}_\infty}$-monoid in an $\infty$-category ${\mathcal E}$ is given by a functor $M\colon {\mathrm{N}(\mathcal{F}\mathrm{in}_*)}\to {\mathcal E}$ satisfying the usual Segal condition, i.e., the inert maps ${\langle n\rangle}\to{\langle 1\rangle}$ exhibit $M({\langle n\rangle})$ as the $n$-fold power of $M({\langle 1\rangle})$. We denote the full subcategory spanned by such functors by $${\mathrm{Fun}}^{\times}\big({\mathrm{N}(\mathcal{F}\mathrm{in}_*)}, {\mathcal E}\big) \subseteq {\mathrm{Fun}}\big({\mathrm{N}(\mathcal{F}\mathrm{in}_*)}, {\mathcal E}\big).$$ Using this notation, we obtain a fully faithful inclusion $$\begin{aligned}
{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})\big) &\simeq& {\mathrm{Fun}}^{\times}\big({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})\big) \\
&\subseteq& {\mathrm{Fun}}\big({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathrm{Fun}}({\mathcal C},{\mathcal D})\big) \\
&\simeq& {\mathrm{Fun}}\big({\mathrm{N}(\mathcal{F}\mathrm{in}_*)}\times {\mathcal C}, {\mathcal D}\big)\end{aligned}$$ whose essential image consists of those functors $F$ such that $F(-,C)\colon{\mathrm{N}(\mathcal{F}\mathrm{in}_*)}\to{\mathcal D}$ is special for all $C\in{\mathcal C}$ and such that $F({\langle n\rangle},-)\colon{\mathcal C}\to{\mathcal D}$ preserves limits for all ${\langle n\rangle}\in{\mathrm{N}(\mathcal{F}\mathrm{in}_*)}$. This follows from the fact that limits in ${{\mathrm{Fun}}^\mathrm{R}}({\mathcal C},{\mathcal D})$ are formed pointwise, as remarked above. In a similar vein, we obtain a fully faithful inclusion $$\begin{aligned}
{{\mathrm{Fun}}^\mathrm{R}}\big({\mathcal C}, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\big) & \simeq& {{\mathrm{Fun}}^\mathrm{R}}\big({\mathcal C}, {\mathrm{Fun}}^\times({\mathrm{N}(\mathcal{F}\mathrm{in}_*)}, {\mathcal D})\big) \\
&\subseteq& {\mathrm{Fun}}\big({\mathcal C}, {\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)}, {\mathcal D})\big) \\
&\simeq& {\mathrm{Fun}}({\mathcal C}\times {\mathrm{N}(\mathcal{F}\mathrm{in}_*)}, {\mathcal D}) \\
& \simeq& {\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)}\times {\mathcal C}, {\mathcal D})\end{aligned}$$ with the same essential image, concluding the proof for the case of monoids. The proof for the case of groups works exactly the same. In fact, using characterization (4) of , it suffices to replace special $\Gamma$-objects by very special $\Gamma$-objects.
Preadditive and additive infinity-categories {#sec:pre}
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An $\infty$-category is preadditive if finite coproducts and products exist and are equivalent. More precisely, we have the following definition.
An $\infty$-category ${\mathcal C}$ is *preadditive* if it is pointed, admits finite coproducts and finite products, and the canonical morphism $C_1 \sqcup C_2 \to C_1 \times C_2$ is an equivalence for all objects $C_1, C_2 \in {\mathcal C}$. In this case any such object will be denoted by $C_1 \oplus C_2$ and will be referred to as a *biproduct* of $C_1$ and $C_2$.
Let us collect a few immediate examples and closure properties of preadditive $\infty$-categories.
An ordinary category ${\mathcal C}$ is preadditive if and only if ${\mathrm{N}}({\mathcal C})$ is a preadditive $\infty$-category. Products and opposites of preadditive $\infty$-categories are preadditive. Clearly any $\infty$-category equivalent to a preadditive one is again preadditive. Finally, if ${\mathcal C}$ is a preadditive $\infty$-category and $K$ is any simplicial set, then ${\mathrm{Fun}}(K,{\mathcal C})$ is preadditive. This follows immediately from the fact that (co)limits in functor categories are calculated pointwise ([@HTT Corollary 5.1.2.3]).
We will obtain more examples of preaddtive $\infty$-categories from the following proposition, which gives a connection to §\[sec:monoids\].
\[pro:pre\] Let ${\mathcal C}$ be an $\infty$-category with finite coproducts and products. Then the following are equivalent:
1. \[p1\] The $\infty$-category ${\mathcal C}$ is preadditive.
2. \[p2\] The homotopy category ${\mathrm{Ho}}({\mathcal C})$ is preadditive.
3. \[p3\] The $\infty$-operad ${\mathcal C}^{\sqcup} \to {\mathrm{N}(\mathcal{F}\mathrm{in}_*)}$ as constructed in [@HA Construction 2.4.3.1] is cartesian ([@HA Definition 2.4.0.1]).
4. \[p4\] The forgetful functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathcal C}$ is an equivalence.
Moreover, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is preadditive if ${\mathcal C}$ has finite products.
Let us begin by proving that the first two statements are equivalent. The direction \[p1\]$\Rightarrow $\[p2\] follows from the fact that the functor $\gamma\colon{\mathcal C}\to \mathrm{N}({\mathrm{Ho}}({\mathcal C}))$ preserves finite (co)products. For the converse direction, let us recall that a morphism in ${\mathcal C}$ is an equivalence if and only if $\gamma$ sends it to an isomorphism. Now, by our assumption on ${\mathrm{Ho}}({\mathcal C})$, the canonical map $C_1\sqcup C_2\to C_1\times C_2$ in ${\mathcal C}$ is mapped to an isomorphism under $\gamma$ and is hence an equivalence.
To show \[p1\] $\Rightarrow$ \[p3\] we only need to check that the symmetric monoidal structure ${\mathcal C}^{\sqcup} \to {\mathrm{N}(\mathcal{F}\mathrm{in}_*)}$ exhibits finite tensor products (in this case the disjoint union) as products. But this follows directly from \[p1\].
Now assume \[p3\] holds. Then by [@HA Corollary 2.4.1.8] there exists an equivalence of symmetric monoidal structures ${\mathcal C}^\sqcup \simeq {\mathcal C}^{\times}$. Thus we get an induced equivalence $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \simeq {\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C}^{\times}) \simeq {\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C}^{\sqcup}) .$$ compatible with the forgetful functors to ${\mathcal C}$. But for the latter symmetric monoidal structure the forgetful functor ${\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C}^{\sqcup}) \to {\mathcal C}$ always induces an equivalence, as shown in [@HA Corollary 2.4.3.10].
Finally, assume \[p4\] holds. Then in order to show that ${\mathcal C}$ is preadditive it suffices to show that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is preadditive. To see that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is preadditive we note that limits in ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ are formed as the limits of the underlying objects of ${\mathcal C}$. In particular, the underlying object of the product in ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is given by the product of the underlying objects. Coproducts are more complicated, but it is shown in [@HA Proposition 3.2.4.7] that the underlying object of the coproduct is formed by the tensor product of the underlying objects, i.e., by the product of the underlying objects in our case. Thus, the underlying object of the coproduct and the product are equivalent. But, by assumption, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathcal C}$ is fully-faithful, so that we already have such an equivalence in ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$. This implies \[p1\] and concludes the proof.
\[cor:pipre\] Let ${\mathcal C}$ and ${\mathcal D}$ be $\infty$-categories with finite products and suppose that either ${\mathcal C}$ or ${\mathcal D}$ is preadditive. Then the $\infty$-category ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$ is preadditive.
If ${\mathcal D}$ is preadditive, then ${\mathrm{Fun}}({\mathcal C},{\mathcal D})$ is also preadditive, and clearly ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})\subseteq {\mathrm{Fun}}({\mathcal C},{\mathcal D})$ is stable under products. In particular, given two product preserving functors $f,g:{\mathcal C}\to{\mathcal D}$, the pointwise product $f \times g\colon {\mathcal C}\to{\mathcal D}$ again lies in ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$. Since (co)limits in ${\mathrm{Fun}}({\mathcal C},{\mathcal D})$ are calculated pointwise ([@HTT Corollary 5.1.2.3]), we can use the preadditivity of ${\mathcal D}$ to conclude that $f\times g$ is also the coproduct $f\sqcup g$ of $f$ and $g$ in ${\mathrm{Fun}}({\mathcal C},{\mathcal D})$, and hence, a posteriori, also the coproduct in ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$. A similar reasoning yields a zero object in ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$, and we conclude that ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$ is preadditive.
The case in which ${\mathcal C}$ is preadditive is slightly more involved. Recall that a product preserving functor $f\colon{\mathcal C}\to{\mathcal D}$ induces a functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ (simply by composing a special $\Gamma$-object in ${\mathcal C}$ with $f$). Since products in $\infty$-categories of ${\mathbb{E}_\infty}$-monoids are calculated in the underlying $\infty$-categories, this induced functor preserves products. Thus, we obtain a functor $${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})\to{\mathrm{Fun}}^\Pi({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}),{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})).$$ By we know that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ is preadditive. The first part of this proof implies the same for ${\mathrm{Fun}}^\Pi({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}),{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}))$, and hence we are done if we can show that the above functor is an equivalence. A functor in the reverse direction is given by composition with the equivalence ${\mathcal C}\simeq{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ (use again) and with ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\to{\mathcal D}.$ It is easy to check that the resulting endofunctor of ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$ is equivalent to the identity, as is also the case for the other composition.
\[cor:colmon\] Let ${\mathcal C}$ be an $\infty$-category with finite products and let ${\mathcal D}$ be a preadditive $\infty$-category.
1. The $\infty$-category ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is preadditive.
2. The forgetful functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is an equivalence.
3. There is an equivalence ${\mathrm{Fun}}^\Pi({\mathcal D}, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})) \simeq {\mathrm{Fun}}^\Pi({\mathcal D},{\mathcal C}).$
The first assertion is a consequence of the proof of . The second follows immediately from that same proposition, while the last statement is implied by and the observation that ${\mathrm{Fun}}^\Pi({\mathcal D},{\mathcal C})$ is preadditive whenever ${\mathcal D}$ is as guaranteed by .
We now establish basically the analogous results for additive $\infty$-categories. As it is very similar to the case of preadditive $\infty$-categories, we leave out some of the details. Parallel to ordinary category theory, we introduce additive $\infty$-categories by imposing an additional exactness condition on preadditive $\infty$-categories. Let ${\mathcal C}$ be a preadditive $\infty$-category and let $A$ be an object of ${\mathcal C}$. We know from that $A$ can be canonically endowed with the structure of an ${\mathbb{E}_\infty}$-monoid, and it is shown in [@HA Section 2.4.3] that this structure is given by the fold map $\nabla\colon A\oplus A\to A$. The [*shear map*]{} $$s\colon A\oplus A\to A\oplus A$$ is the projection $pr_1\colon A\oplus A\to A$ on the first factor and the fold map $\nabla\colon A\oplus A\to A$ on the second.
A preadditive $\infty$-category ${\mathcal C}$ is *additive* if, for every object $A\in{\mathcal C}$, the shear map $s\colon A\oplus A\stackrel{\sim}{\to} A\oplus A$ is an equivalence.
\[egs:add\] An ordinary category ${\mathcal C}$ is additive if and only if ${\mathrm{N}}({\mathcal C})$ is an additive $\infty$-category. Products and opposites of additive $\infty$-categories are additive. If ${\mathcal C}$ is an additive $\infty$-category, then any $\infty$-category equivalent to ${\mathcal C}$ is additive $\infty$-category, and any functor $\infty$-category ${\mathrm{Fun}}(K,{\mathcal C})$ is additive.
The connection to ${\mathbb{E}_\infty}$-groups and hence to §\[sec:monoids\] is provided by the following analog of .
\[pro:add\] For an $\infty$-category ${\mathcal C}$ with finite products and coproducts, the following are equivalent:
1. \[pp1\] The $\infty$-category ${\mathcal C}$ is additive.
2. \[pp2\] The homotopy category ${\mathrm{Ho}}({\mathcal C})$ is additive.
3. \[pp3\] The forgetful functor ${{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}}({\mathcal C}) \to {\mathcal C}$ is an equivalence.
Moreover, if ${\mathcal C}$ is an $\infty$-category with finite products, then ${{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}}({\mathcal C})$ is additive.
The proof of the equivalence of \[p1\] and \[pp3\] is parallel to the proof of . To see that \[pp1\] implies \[pp3\] we note that by we have an equivalence ${\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C}^{\sqcup}) \simeq{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathcal C}$. But it is shown in [@HA Section 2.4.3] that an inverse to this equivalence endows an object $A\in{\mathcal C}$ with the algebra structure given by the fold map $\nabla\colon A\oplus A\to A$. Now, the statement that such an algebra object is grouplike is equivalent to the shear map being an equivalence. Thus, invoking \[pp1\], we obtain an equivalence ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\simeq{{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}}({\mathcal C})$, which gives \[pp3\]. Conversely, to see that \[pp3\] implies \[pp1\], we need to show that ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is additive. Preadditivity is clear and additivity follows from the characterization of groups given in .
\[cor:piadd\] Let ${\mathcal C}$ and ${\mathcal D}$ be $\infty$-categories with finite products and suppose that either ${\mathcal C}$ or ${\mathcal D}$ is additive. Then the $\infty$-category ${\mathrm{Fun}}^\Pi({\mathcal C},{\mathcal D})$ is additive.
\[cor:colgrp\] Let ${\mathcal C}$ be an $\infty$-category with finite products and let ${\mathcal D}$ be an additive $\infty$-category.
1. The $\infty$-category ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is additive.
2. The forgetful functor ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is an equivalence.
3. There is an equivalence ${\mathrm{Fun}}^\Pi({\mathcal D}, {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})) \simeq {\mathrm{Fun}}^\Pi({\mathcal D},{\mathcal C}).$
and basically state that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(-)$ and ${{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}}(-)$ are colocalizations of the $\infty$-category of $\infty$-categories with finite products and product preserving functors. Much of the remainder of the paper makes use of this observation, although we prefer to phrase things slightly differently: namely, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(-)$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}(-)$ also induce colocalizations of ${\mathcal{P}\mathrm{r^R}}$, which in turn (using the anti-equivalence between ${\mathcal{P}\mathrm{r^L}}$ and ${\mathcal{P}\mathrm{r^R}}$) induce localizations of ${\mathcal{P}\mathrm{r^L}}$. We have opted to state our results in term of localizations as we think they are slightly more intuitive from this perspective.
Smashing localizations {#sec:smash}
======================
So far we have discussed $\infty$-categories with finite products. We now turn our attention to presentable $\infty$-categories. The primary purpose of this section is to review the notion of *smashing localizations*, which we then specialize to ${\mathcal{P}\mathrm{r^{L,\otimes}}}$ in order to deduce some important consequences which will play an essential role throughout the remainder of the paper.
Let ${\mathcal C}$ be an $\infty$-category. Recall that a [*localization*]{} of ${\mathcal C}$ is functor $L\colon{\mathcal C}\to{\mathcal D}$ which admits a fully faithful right adjoint $R\colon{\mathcal D}\to{\mathcal C}$. If $L\colon{\mathcal C}\to{\mathcal D}$ is a localization, then ${\mathcal D}$ is equivalent (via the fully faithful right adjoint) to a full subcategory $L{\mathcal C}$ of ${\mathcal C}$, called the subcategory of [*local objects*]{}. For this reason we typically identify localizations with reflective subcategories (i.e., full subcategories such that the inclusion admits a left adjoint). We will also sometimes write $L$ for the endofunctor of ${\mathcal C}$ obtained as the composite of $L\colon{\mathcal C}\to{\mathcal D}$ followed by the fully faithful right adjoint $R\colon{\mathcal D}\to{\mathcal C}$. Given such a localization, a map $X\to Y$ is a *local equivalence* if $LX\to LY$ is an equivalence.
Let ${\mathcal C}$ be an $\infty$-category and $M\colon{\mathcal C}\to{\mathcal C}$ an endofunctor equipped with a natural transformation $\eta\colon{\mathrm{id}}\to M$. Then $M$ is equivalent to the composite $R\circ L$ of a localization $L\colon{\mathcal C}\to{\mathcal D}$ if and only if, for every object $X$ of ${\mathcal C}$, the two obvious maps $M(X)\to M(M(X))$ are equivalences.
This is condition (3) of [@HTT Proposition 5.2.7.4].
If ${\mathcal C}$ has a symmetric monoidal structure ${\mathcal C}^\otimes$, then it is sometimes the case that a localization of ${\mathcal C}$ is given by ‘smashing’ with a fixed object $I$ of ${\mathcal C}$. In keeping with the terminology used in stable homotopy theory, we make the following definition.
Let ${\mathcal C}^\otimes$ be a symmetric monoidal $\infty$-category. We say that a localization $L\colon{\mathcal C}\to{\mathcal C}$ is [*smashing*]{} if it is of the form $L\simeq (-)\otimes I$ for some object $I$ of ${\mathcal C}$.
Recall from [@HA Definition 6.3.2.1] that an *idempotent object* in ${\mathcal C}^\otimes$ is an object $I$ together with a morphism from the tensor unit such that the two obvious maps $I\to I\otimes I$ are equivalences. It follows that the endofunctor of ${\mathcal C}$ given by tensoring with $I$ is a localization [@HA Proposition 6.3.2.4]. Conversely for a smashing localization $L\simeq (-)\otimes I$ the object $I$ is necessarily an idempotent commutative algebra object of ${\mathcal C}$. In other words, showing that the functor $(-)\otimes I$ is a localization is the same as endowing $I$ with the structure of an idempotent commutative algebra object of ${\mathcal C}$. This provides a one-to-one correspondence between smashing localizations and idempotent commutative algebra objects.
There are two obvious key features of smashing localizations: first, they preserve colimits (provided the tensor structure is compatible with colimits, which is always the case if it is closed), and second, they are symmetric monoidal in the sense of the following definition.
Let ${\mathcal C}^\otimes$ be a symmetric monoidal $\infty$-category equipped with a localization $L\colon{\mathcal C}\to{\mathcal D}$ of the underlying $\infty$-category ${\mathcal C}$. Then $L$ is [*compatible with the symmetric monoidal structure*]{} (or simply *symmetric monoidal*) if, whenever $X\to Y$ is a local equivalence, then so is $X\otimes Z\to Y\otimes Z$ for any object $Z$ of ${\mathcal C}$.
Given such a localization, the subcategory ${\mathcal D}\simeq L{\mathcal C}$ of local objects inherits a symmetric monoidal structure from that of ${\mathcal C}$. This is the content of the following lemma which also justifies the terminology *symmetric monoidal* localization. Identifying ${\mathcal D}$ with the full subcategory $L{\mathcal C}$ of local objects, let $R^\otimes\colon{\mathcal D}^\otimes\subseteq{\mathcal C}^\otimes$ be the inclusion of the full subcategory consisting of those objects $X_1\oplus\cdots\oplus X_n$ such that each $X_i$ is in ${\mathcal D}$.
\[prop:symmonloc\] Let ${\mathcal C}^\otimes$ be a symmetric monoidal $\infty$-category equipped with a symmetric monoidal localization $L\colon{\mathcal C}\to{\mathcal D}.$ Then there is a symmetric monoidal structure ${\mathcal D}^\otimes$ on ${\mathcal D}$ such that $L$ extends to a symmetric monoidal functor $L^\otimes\colon{\mathcal C}^\otimes\to{\mathcal D}^\otimes$ and such that the right adjoint $R^\otimes\colon{\mathcal D}^\otimes\to{\mathcal C}^\otimes$ is lax symmetric monoidal.
This is a special case of [@HA Proposition 2.2.1.9].
\[rmk\_closed\] If ${\mathcal C}^\otimes$ is a closed symmetric monoidal $\infty$-category equipped with a symmetric monoidal localization $L\colon {\mathcal C}\to {\mathcal C}$. Then $L$ is compatible with the closed structure in the sense that, for every pair of objects $C$ and $D$ of ${\mathcal C}$, the localization $C\to LC$ induces an equivalence $$D^{LC} \simeq D^C$$ whenever $D$ is local. This follows immediately from the definition.
\[prop:algloc\] Let ${\mathcal C}^\otimes$ be a symmetric monoidal $\infty$-category equipped with a symmetric monoidal localization $L\colon{\mathcal C}\to{\mathcal D},$ and let $R\colon{\mathcal D}\to{\mathcal C}$ denote the right adjoint of $L$. Then there is an induced localization $L'\colon{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C})\to{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal D})$ such that the diagram $$\xymatrix{
{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C})\ar[r]^{L'}\ar[d] & {\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal D})\ar[d]\\
{\mathcal C}\ar[r]^L & {\mathcal D}}$$ commutes. Moreover, given $A\in{\mathrm{Alg}}_{{\mathbb{E}_\infty}}({\mathcal C})$, there exists a unique commutative algebra structure on $RLA$ such that unit map $A\to RLA$ extends to a morphism of commutative algebras.
By above, we obtain maps $L'\colon{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C})\to{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal D})$ and $R'\colon{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal D})\to{\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal C})$ by composing sections ${\mathbb{E}}_\infty\to{\mathcal C}^\otimes$ with $L^\otimes$ and sections ${\mathbb{E}}_\infty\to{\mathcal D}^\otimes$ with $R^\otimes$, respectively. In a similar fashion we also obtain unit and counit transformations such that the counit is an equivalence. It follows that $L'$ is a localization.
For the second assertion, we know already that $R'L'A$ comes with a canonical commutative algebra map $\eta'\colon A\to R'L' A$, the adjunction unit evaluated at $A$, and that this map extends the adjunction unit $\eta\colon A\to RLA$ of the underlying objects. If $\eta''\colon A\to R'B$ is a second such map of commutative algebras, then the universality of $\eta'$ implies that $\eta''$ factors essentially uniquely as $$\phi\circ\eta'\colon A\to R'L'A\to R'B.$$ Since the underlying map of $\phi$ is an identity, if follows that $\phi$ itself is an equivalence since ${\mathrm{Alg}}_{{\mathbb{E}_\infty}}({\mathcal C})\to{\mathcal C}$ is conservative. We can now conclude since the space of reflections of a fixed object in a full subcategory is contractible if non-empty.
The second part of the lemma implies that $RLA$ can be turned into an ${\mathbb{E}_\infty}$-algebra such that the unit map $A\to RLA$ can be enhanced to a morphism of ${\mathbb{E}_\infty}$-algebras. Moreover, the space of such enhancements is contractible. In particular, if $RLA$ is endowed with two different ${\mathbb{E}_\infty}$-algebra structures, then the identity morphism of the underlying objects in ${\mathcal D}$ can be essentially uniquely turned into an equivalence of these two ${\mathbb{E}_\infty}$-algebras compatible with the localizations. We will apply this in §\[sec:spec\] to smashing localizations on ${\mathcal{P}\mathrm{r^L}}.$
Now we specialize to the case of the (very large) $\infty$-category ${\mathcal{P}\mathrm{r^L}}$ of presentable $\infty$-categories and colimit-preserving functors. We will write ${\mathcal C}$, ${\mathcal D}$, etc. for objects of ${\mathcal{P}\mathrm{r^L}}$. Recall that ${\mathcal{P}\mathrm{r^L}}$ admits a closed symmetric monoidal structure which is uniquely characterized as follows: given presentable $\infty$-categories ${\mathcal C}$ and ${\mathcal D}$, their tensor product ${\mathcal C}\otimes{\mathcal D}$ corepresents the functor ${\mathcal{P}\mathrm{r^L}}\to\widehat{{\mathcal{C}\mathrm{at}}}_\infty$ which sends ${\mathcal E}$ to $${{\mathrm{Fun}}^\mathrm{L,L}}({\mathcal C}\times{\mathcal D},{\mathcal E})\subseteq{\mathrm{Fun}}({\mathcal C}\times{\mathcal D},{\mathcal E}),$$ the full subcategory consisting of those functors $F\colon{\mathcal C}\times{\mathcal D}\to{\mathcal E}$ which preserve colimits separately in each variable. The unit of this monoidal structure on ${\mathcal{P}\mathrm{r^L}}$ is the $\infty$-category ${\mathcal{S}}$ of spaces, as follows from the fact that ${{\mathrm{Fun}}^\mathrm{L}}({\mathcal{S}},{\mathcal C})\simeq{\mathcal C}$ ([@HA Example 6.3.1.19]). Moreover, by [@HA Proposition 6.3.1.16] this tensor product admits the following description $${\mathcal C}\otimes{\mathcal D}\simeq{{\mathrm{Fun}}^\mathrm{R}}({\mathcal C}\op,{\mathcal D}).$$ Recall that ${{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})$ is presentable ([@HTT Propositon 5.5.3.8]). It is immediate from the definition of ${\mathcal C}\otimes{\mathcal D}$ as a corepresenting object that the symmetric monoidal structure on ${\mathcal{P}\mathrm{r^L}}$ is closed, with right adjoint to ${\mathcal C}\otimes(-):{\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L}}$ given by ${{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},-):{\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L}}$. Lastly, the (possibly large) mapping spaces in ${\mathcal{P}\mathrm{r^L}}$ are given by the formula $$\Map_{{\mathcal{P}\mathrm{r^L}}}({\mathcal C},{\mathcal D})\simeq{{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})^\sim,$$ the maximal subgroupoid. This description will be applied in §\[sec:mon\] to our context of monoids and groups.
\[prop:smmod\] Let $L\colon {\mathcal{P}\mathrm{r^L}}\to {\mathcal{P}\mathrm{r^L}}$ be a smashing localization or, more generally, a symmetric monoidal localization, and let ${\mathcal C}$ and ${\mathcal D}$ be presentable $\infty$-categories such that ${\mathcal D}$ is in the essential image of $L$.
1. The map ${{\mathrm{Fun}}^\mathrm{L}}(L{\mathcal C},{\mathcal D}) \to {{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})$ induced by the localization ${\mathcal C}\to L{\mathcal C}$ is an equivalence.
2. If $L$ is smashing, then, writing $L{\mathcal{P}\mathrm{r^L}}$ for the image of $L$, there is an equivalence of $\infty$-categories $$L{\mathcal{P}\mathrm{r^L}}\simeq {\mathrm{Mod}}_{L{\mathcal{S}}}({\mathcal{P}\mathrm{r^L}}).$$
3. Given a second symmetric monoidal localization $L'\colon{\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L}}$ such that $L'{\mathcal{P}\mathrm{r^L}}\subseteq L{\mathcal{P}\mathrm{r^L}}$, then the canonical morphism $L{\mathcal C}\to L'{\mathcal C}$ induces an equivalence ${{\mathrm{Fun}}^\mathrm{L}}(L'{\mathcal C},{\mathcal D}) \to {{\mathrm{Fun}}^\mathrm{L}}(L{\mathcal C},{\mathcal D})$ for every $L'$-local ${\mathcal D}.$
The first statement follows from and the second from [@HA Proposition 6.3.2.10]. Finally, the third one follows immediately from the first and the 2-out-of-3 property of equivalences.
Let us now consider a presentable $\infty$-category endowed with a closed symmetric monoidal structure ${\mathcal C}^\otimes$. In this context the closedness is equivalent to the fact that the monoidal structure preserves colimits separately in each variable, i.e., ${\mathcal C}^\otimes$ is essentially just a commutative algebra object in ${\mathcal{P}\mathrm{r^L}}$ ([@HA Remark 6.3.1.9]).
\[prop:smmonoidal\] Let $L\colon {\mathcal{P}\mathrm{r^L}}\to {\mathcal{P}\mathrm{r^L}}$ be a smashing localization or, more generally, a symmetric monoidal localization. Let ${\mathcal C}^\otimes$ and ${\mathcal D}^\otimes$ be closed symmetric monoidal presentable $\infty$-categories.
1. The $\infty$-category $L{\mathcal C}$ admits a [*unique*]{} closed symmetric monoidal structure such that the localization map ${\mathcal C}\to L{\mathcal C}$ is a symmetric monoidal functor.
2. The map ${{\mathrm{Fun}}^{\mathrm{L},\otimes}}(L{\mathcal C},{\mathcal D}) \to {{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C},{\mathcal D})$ induced by the localization ${\mathcal C}\to L{\mathcal C}$ is an equivalence whenever ${\mathcal D}$ is $L$-local.
3. Given a second symmetric monoidal localization $L'\colon{\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L}}$ such that $L'{\mathcal{P}\mathrm{r^L}}\subseteq L{\mathcal{P}\mathrm{r^L}}$, the induced morphism $L{\mathcal C}\to L'{\mathcal C}$ admits a unique symmetric monoidal structure. In particular, for every $L'$-local ${\mathcal D}$ the induced map ${{\mathrm{Fun}}^{\mathrm{L},\otimes}}(L'{\mathcal C},{\mathcal D}) \to {{\mathrm{Fun}}^{\mathrm{L},\otimes}}(L{\mathcal C},{\mathcal D})$ is an equivalence.
Statement (i) follows from , which also gives equivalences $$\Map(\Delta^0,{{\mathrm{Fun}}^{\mathrm{L},\otimes}}(L{\mathcal C},{\mathcal D}^K))\simeq\Map(\Delta^0,{{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C},{\mathcal D}^{K}))$$ for any simplicial set $K$ such that ${\mathcal D}^K$ is local. (ii) then follows from the fact that ${\mathrm{Alg}}_{{\mathbb{E}}_\infty}({\mathcal{P}\mathrm{r^L}})$ is cotensored over ${\mathcal{C}\mathrm{at}}_\infty$ in such a way that ${\mathcal D}^K$ is local whenever ${\mathcal D}$ is local; indeed, the cotensor ${\mathcal D}^K$ is given by the internal mapping object ${{\mathrm{Fun}}^\mathrm{L}}({\mathcal{P}}(K),{\mathcal D})$, and this is a local object since $(-)\otimes{\mathcal{P}}(K)$ preserves local equivalences by assumption. Finally, (iii) is obtained by the same argument as (i) after replacing ${\mathcal{P}\mathrm{r^L}}$ with $L{\mathcal{P}\mathrm{r^L}}$, which has an induced closed symmetric monoidal structure, $L\colon{\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L}}$ with the functor $L{\mathcal{P}\mathrm{r^L}}\to L{\mathcal{P}\mathrm{r^L}}$ induced by the composite ${\mathcal{P}\mathrm{r^L}}\to L'{\mathcal{P}\mathrm{r^L}}\subseteq L{\mathcal{P}\mathrm{r^L}}$, and ${\mathcal C}$ with $L{\mathcal C}$, which also inherits a closed symmetric monoidal structure.
We shall see in the next section that formation of $\infty$-categories of commutative monoid and group objects in a presentable $\infty$-category ${\mathcal C}$ are instances of smashing localizations of ${\mathcal{P}\mathrm{r^L}}$. For the moment, it is worth mentioning that there are other well-known examples of smashing localizations of ${\mathcal{P}\mathrm{r^L}}$. The most obvious one is the functor which associates to a presentable $\infty$-category ${\mathcal C}$ its $\infty$-category ${\mathcal C}_*$ of [*pointed objects*]{}; the fact that this is a smashing localization follows from the formula $${\mathcal C}_*\simeq{\mathcal C}\otimes{\mathcal{S}}_*$$ and the fact that ${\mathcal{S}}_*$ is an idempotent object of ${\mathcal{P}\mathrm{r^L}}$ (cf. [@HA Proposition 6.3.2.11]). An important feature of ${\mathcal{S}}_*$ is that it is symmetric monoidal under the [*smash product*]{}, which is uniquely characterized by the requirement that the unit map ${\mathcal{S}}\to{\mathcal{S}}_*$ is symmetric monoidal. Less obvious but possibly more important is the functor which associates to a presentable $\infty$-category ${\mathcal C}$ the $\infty$-category ${\mathrm{Sp}}({\mathcal C})$ of spectrum objects in ${\mathcal C}$ (cf. [@HA Proposition 6.3.2.18]).
Commutative monoids and groups as smashing localizations {#sec:mon}
========================================================
In this section we show that the passage to $\infty$-categories of commutative monoids or groups are instances of smashing localizations of ${\mathcal{P}\mathrm{r^L}}$.
\[prop:monpres\] Given a presentable $\infty$-category ${\mathcal C}$, then also the $\infty$-categories ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ are presentable.
By definition the $\infty$-categories ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ are full subcategories of the presentable $\infty$-category ${\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C}).$ Therefore, it suffices to show that the monoids and groups, respectively, are precisely the $S$-local objects for a small collection $S$ of morphisms in ${\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C})$ ([@HTT Proposition 5.5.4.15]). We will give the details for the case of monoids and leave the case of groups to the reader.
In order to define $S$ we first note that the evaluation functors $${\mathrm{ev}}_{{\langle n\rangle}}\colon{\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C}) \to {\mathcal C}$$ admit left adjoints $F_{{\langle n\rangle}}\colon {\mathcal C}\to {\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C}).$ Now, $M \in {\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C})$ belongs to ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ if for every $n \in \mathbb{N}$ the morphism $M({\langle n\rangle}) \to \prod M({\langle 1\rangle})$ is an equivalence in ${\mathcal C}$, and this is the case if and only if for every $C \in {\mathcal C}$ the morphism $$\label{strmorphisms}
\Map_{\mathcal C}\big(C, M({\langle n\rangle})\big) \longrightarrow \prod \Map_{\mathcal C}\big(C, M({\langle 1\rangle})\big)$$ is an equivalence of spaces. Since ${\mathcal C}$ is accessible it suffices to check this for objects in ${\mathcal C}^\kappa$, the essentially small subcategory of $\kappa$-compact objects for some regular cardinal $\kappa$. Now we use the equivalences $$\Map_{\mathcal C}\big(C, M({\langle n\rangle})\big) \simeq \Map_{{\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C})}(F_{{\langle n\rangle}}(C), M)$$ and $$\qquad\prod \Map_{\mathcal C}\big(C, M({\langle 1\rangle})\big) \simeq \Map_{{\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C})}\big(\bigsqcup F_{{\langle 1\rangle}}(C), M\big)$$ and see that the morphism is induced by a morphism $
\phi_{n,C}\colon\bigsqcup_n F_{{\langle 1\rangle}}(C) \to F_{{\langle n\rangle}}(C)
$ in ${\mathrm{Fun}}({\mathrm{N}(\mathcal{F}\mathrm{in}_*)},{\mathcal C})$. Thus we may take $S$ to consist of the $\phi_{n,C}$, where $C$ ranges over any small collections of objects of ${\mathcal C}$ which contains a representative of each equivalence class of object in ${\mathcal C}^\kappa$.
The proof for groups is similar, though we have to add more maps to the set $S$ to account for the ‘very’ special condition. This tells us in particular that ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is a reflective subcategory of ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}).$
Let ${\mathcal C}$ be a presentable $\infty$-category. Then there are functors $${\mathcal C}\to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$$ which are left adjoint to the respective forgetful functors.
Since limits in ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ are computed as the limits of the underlying objects, this follows from the adjoint functor theorem.
Let ${\mathcal C}$ be a presentable $\infty$-category. The functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ left adjoint to the forgetful functor ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is called the *group completion*. Thus, in the framework of $\infty$-categories, the group completion ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ has the expected universal property, defining a left adjoint to the forgetful functor ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$.
The following theorem, while straightforward to prove, is central.
\[thm:idem\] The assignments ${\mathcal C}\mapsto {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathcal C}\mapsto {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ refine to smashing localizations of ${\mathcal{P}\mathrm{r^L}}$. Thus, we have, in particular, equivalences of $\infty$-categories $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \simeq {\mathcal C}\otimes {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \qquad\text{and}\qquad {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \simeq {\mathcal C}\otimes {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}).$$ The local objects are precisely the preadditive presentable $\infty$-categories and the additive presentable $\infty$-categories, respectively.
The description of the tensor product of presentable $\infty$-categories together with gives us the chain of equivalences $$\begin{aligned}
{\mathcal C}\otimes {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) &\simeq& {{\mathrm{Fun}}^\mathrm{R}}\big({\mathcal C}\op, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\big) \\
&\simeq& {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{R}}({\mathcal C}\op,{\mathcal D})\big) \\
&\simeq& {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}\otimes {\mathcal D}).\end{aligned}$$ In particular, we have ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \simeq {\mathcal C}\otimes {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$. The fact that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}$ is a localization follows from . The local objects are precisely the presentable $\infty$-categories ${\mathcal C}$ for which the canonical functor is an equivalence ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \simeq {\mathcal C}$, hence by precisely the preadditive $\infty$-categories. The case of groups is established along the same lines.
As a consequence we obtain the following result.
\[cormon\] Let ${\mathcal C}$ and ${\mathcal D}$ be presentable $\infty$-category. Then there are canonical equivalences $$\begin{aligned}
&{\mathcal C}\otimes {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}\otimes {\mathcal D}) \simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \otimes {\mathcal D}, \\
&{\mathcal C}\otimes {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\; \simeq {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}\otimes {\mathcal D})\: \simeq {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \otimes {\mathcal D}.\end{aligned}$$
Let us denote the full subcategories of ${\mathcal{P}\mathrm{r^L}}$ spanned by the preadditive and additive $\infty$-categories respectively by $${\mathcal{P}\mathrm{r^L_{Pre}}}\subseteq{\mathcal{P}\mathrm{r^L}}\qquad \text{and} \qquad {\mathcal{P}\mathrm{r^L_{Add}}}\subseteq{\mathcal{P}\mathrm{r^L}}.$$ Then specializes to the following two corollaries.
\[cor:premod\] The forgetful functors $${\mathrm{Mod}}_{{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})}({\mathcal{P}\mathrm{r^L}})\to{\mathcal{P}\mathrm{r^L}}\quad\text{and}\quad{\mathrm{Mod}}_{{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})}({\mathcal{P}\mathrm{r^L}})\to{\mathcal{P}\mathrm{r^L}}$$ induce equivalences of $\infty$-categories $$\mathrm{Mod}_{{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})}({\mathcal{P}\mathrm{r^L}})\simeq{\mathcal{P}\mathrm{r^L_{Pre}}}\qquad \text{and} \qquad {\mathrm{Mod}}_{{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})}({\mathcal{P}\mathrm{r^L}})\simeq{\mathcal{P}\mathrm{r^L_{Add}}}.$$
\[cor:frepre\] Let ${\mathcal C}$ and ${\mathcal D}$ be presentable $\infty$-categories.
1. If ${\mathcal D}$ is preadditive then the free ${\mathbb{E}_\infty}$-monoid functor ${\mathcal C}\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ induces an equivalence of $\infty$-categories $${{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}),{\mathcal D})\stackrel{\simeq}{\to}{{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D}),$$ exhibiting ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ as the *free preadditive presentable $\infty$-category generated by ${\mathcal C}$*. In particular, we have canonical equivalences $${{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}),{\mathcal D})\stackrel{\simeq}{\to}{{\mathrm{Fun}}^\mathrm{L}}({\mathcal{S}},{\mathcal D})\stackrel{\simeq}{\to}{\mathcal D}$$ exhibiting ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ as the free preadditive presentable $\infty$-category on one generator.
2. If ${\mathcal D}$ is additive then the free ${\mathbb{E}_\infty}$-group functor ${\mathcal C}\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ induces an equivalence of $\infty$-categories $${{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}),{\mathcal D})\stackrel{\simeq}{\to}{{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D}),$$ exhibiting ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ as the *free additive presentable $\infty$-category generated by ${\mathcal C}$*. In particular, the free ${\mathbb{E}_\infty}$-group functor ${\mathcal{S}}\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ induces canonical equivalences $${{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}),{\mathcal D})\stackrel{\simeq}{\to}{{\mathrm{Fun}}^\mathrm{L}}({\mathcal{S}},{\mathcal D})\stackrel{\simeq}{\to}{\mathcal D}$$ exhibiting ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ as the free additive, presentable $\infty$-category on one generator.
The results of this section give us a refined picture of the stabilization process of presentable $\infty$-categories as we describe it in the next corollary (we will obtain a further *monoidal* refinement in ). In [@HA Chapter 1] it is shown that the stabilization of a presentable $\infty$-category ${\mathcal C}$ is given by the $\infty$-category ${\mathrm{Sp}}({\mathcal C})$ of *spectrum objects* in ${\mathcal C}$, which is to say the limit $${\mathrm{Sp}}({\mathcal C})\simeq\lim\{{\mathcal C}_*\overset{\Omega}{\longleftarrow}{\mathcal C}_*\overset{\Omega}{\longleftarrow}{\mathcal C}_*\overset{\Omega}{\longleftarrow}\cdots\}\, ,$$ taken in the $\infty$-category of (not necessarily small) $\infty$-categories, or equivalently in the $\infty$-category ${\mathcal{P}\mathrm{r^R}}$ of presentable $\infty$-categories by [@HTT Theorem 5.5.3.18]. Alternatively, ${\mathrm{Sp}}({\mathcal C})$ is equivalent to the $\infty$-category of reduced excisive functors $${\mathrm{Sp}}({\mathcal C})\simeq\mathrm{Exc}_*({\mathcal{S}}_*^\mathrm{fin},{\mathcal C})$$ (see [@HA Section 1.4.2] for details). Recall from [@HA Proposition 1.4.4.4] that for such a ${\mathcal C}$ the $\infty$-category ${\mathrm{Sp}}({\mathcal C})$ is related to ${\mathcal C}$ by the suspension spectrum adjunction $(\Sigma^\infty_+,\Omega^\infty_-)\colon{\mathcal C}{\rightleftarrows}{\mathrm{Sp}}({\mathcal C}).$
\[cor:stab\] The stabilization of presentable $\infty$-categories ${\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L_{St}}}$ factors as a composition of adjunctions $${\mathcal{P}\mathrm{r^L}}{\rightleftarrows}{\mathcal{P}\mathrm{r^L_{Pt}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^L_{Pre}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^L_{Add}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^L_{St}}}.$$ In particular, if ${\mathcal C}$ is a presentable $\infty$-category, then $\Sigma^\infty_+\colon{\mathcal C}\to{\mathrm{Sp}}({\mathcal C})$ factors as a composition of left adjoints $$\Sigma^\infty_+\colon{\mathcal C}\to{\mathcal C}_*\to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Sp}}({\mathcal C}),$$ each of which is uniquely determined by the fact that it commutes with the corresponding free functors from ${\mathcal C}$.
This follows from and the corresponding corollary for the functor $(-)_+\colon{\mathcal C}\to{\mathcal C}_\ast$ together with the facts that ${\mathrm{Sp}}({\mathcal C})$ is additive (by Corollary 1.4.2.17 and Remark 1.1.3.5 in [@HA]), ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is preadditive (even additive by ), and ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is pointed (in fact, preadditive by ). For the second statement, it suffices to use .
Canonical symmetric monoidal structures {#sec:spec}
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Let us now assume that ${\mathcal C}$ is a presentable $\infty$-category endowed with a closed symmetric monoidal structure ${\mathcal C}^\otimes$. In this section we specialize the general results from §\[sec:smash\] (or more specifically ) to the localizations $(-)_\ast, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(-), {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}(-),$ and ${\mathrm{Sp}}(-)$. The two cases of ${\mathcal C}_\ast$ and ${\mathrm{Sp}}({\mathcal C})$ are already essentially covered in [@HA Section 6.1.9], but since these results are not stated explicitly, we include them here for the sake of completeness.
\[thm:tensorproducts\] Let ${\mathcal C}^\otimes$ be a closed symmetric monoidal structure on a presentable $\infty$-category ${\mathcal C}$. The $\infty$-categories ${\mathcal C}_*$, ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$, ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$, and ${\mathrm{Sp}}({\mathcal C})$ all admit closed symmetric monoidal structures, which are uniquely determined by the requirement that the respective free functors from ${\mathcal C}$ are symmetric monoidal. Moreover, each of the functors $${\mathcal C}_*\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Sp}}({\mathcal C})$$ uniquely extends to a symmetric monoidal functor.
Follows directly from the fact that the localizations are smashing using .
From now on, when considered as symmetric monoidal $\infty$-categories, these $\infty$-categories are always endowed with the canonical monoidal structures of the theorem.
The reader should not confuse the two symmetric monoidal structures on ${\mathcal C}$ that are used in the above construction. The first one is the cartesian structure ${\mathcal C}^\times$ which is used to define the $\infty$-category ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ of ${\mathbb{E}_\infty}$-monoids. The second one is the closed symmetric monoidal structure ${\mathcal C}^\otimes$ which induces a monoidal structure on ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ as described in the theorem. In applications, these two monoidal structures on ${\mathcal C}$ often agree, which amounts to assuming that ${\mathcal C}$ is cartesian closed. This is the case in the most important examples, namely $\infty$-topoi (such as ${\mathcal{S}}$) and ${\mathcal{C}\mathrm{at}}_\infty$.
1. The (nerve of the) category ${\mathrm{Set}}$ of sets is a cartesian closed presentable $\infty$-category, and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathrm{Set}})$ is just the (nerve of the) category ${\mathrm{Ab}}$ of abelian groups. The free functor ${\mathrm{Set}}\to{\mathrm{Ab}}$ can then of course be turned into a symmetric monoidal functor with respect to the cartesian product on ${\mathrm{Set}}$ and the usual tensor product on ${\mathrm{Ab}}$. Thus, in this very special case, the theorem reproduces the classical tensor product of abelian groups.
2. The $\infty$-category ${\mathcal{S}}$ of spaces is a cartesian closed presentable $\infty$-category. The $\infty$-category ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ of ${\mathbb{E}_\infty}$-spaces hence comes with a canonical closed symmetric monoidal structure, as does the $\infty$-category ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ of grouplike ${\mathbb{E}_\infty}$-spaces. Since the latter $\infty$-category is equivalent to the $\infty$-category of connective spectra ([@HA Remark 5.1.3.7]), the canonical symmetric monoidal structure on ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ agrees with the smash product of connective spectra.
3. Let ${\mathcal{C}\mathrm{at}}$ denote the cartesian closed presentable $\infty$-category of small ordinary categories (this is actually a 2-category, in the sense of [@HTT Section 2.3.4]). Thus, the $\infty$-category ${\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}})$ of small symmetric monoidal categories admits a canonical closed symmetric monoidal structure such that the free functor ${\mathcal{C}\mathrm{at}}\to {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}$ can be promoted to a symmetric monoidal functor in a unique way. This structure on ${\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}$ has been explicitly constructed and discussed in the literature (see [@Power] and the more explicit [@schmitt2007tensor]). In fact, this tensor product is slightly subtle since, at least to the knowledge of the authors, it can not be realized as a symmetric monoidal structure on the 1-category of small categories (as opposed to the $2$-category ${\mathcal{C}\mathrm{at}}$).
4. The $\infty$-category ${\mathcal{C}\mathrm{at}_\infty}$ of small $\infty$-categories is a cartesian closed presentable $\infty$-category. Thus, as an $\infty$-categorical variant of the previous example, we obtain a canonical closed symmetric monoidal structure on the $\infty$-category ${\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}_\infty}$ of small symmetric monoidal $\infty$-categories.
We have already seen that, for presentable $\infty$-categories ${\mathcal C}$, the passage to commutative monoids and commutative groups has a universal property (). In the case of closed symmetric monoidal presentable $\infty$-categories we now obtain a refined universal property for the symmetric monoidal structures of . For convenience, we also collect the analogous results for the passage to pointed objects and spectrum objects.
\[universalmonoidal\] Let ${\mathcal C}$ and ${\mathcal D}$ be closed symmetric monoidal presentable $\infty$-categories.
1. If ${\mathcal D}$ is pointed then the symmetric monoidal functor ${\mathcal C}\to {\mathcal C}_\ast$ induces an equivalence of $\infty$-categories $${{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C}_\ast, {\mathcal D}) \to {{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C}, {\mathcal D}).$$
2. If ${\mathcal D}$ is preadditive then the symmetric monoidal functor ${\mathcal C}\to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ induces an equivalence of $\infty$-categories $${{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}), {\mathcal D}) \to {{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C}, {\mathcal D}).$$
3. If ${\mathcal D}$ is additive then the symmetric monoidal functor ${\mathcal C}\to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ induces an equivalence of $\infty$-categories $${{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}), {\mathcal D}) \to {{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C}, {\mathcal D}).$$
4. If ${\mathcal D}$ is stable then the symmetric monoidal functor ${\mathcal C}\to {\mathrm{Sp}}({\mathcal C})$ induces an equivalence of $\infty$-categories $${{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathrm{Sp}}({\mathcal C}), {\mathcal D}) \to {{\mathrm{Fun}}^{\mathrm{L},\otimes}}({\mathcal C}, {\mathcal D}).$$
This follows immediately from the second statement of .
Here is the monoidal refinement of the stabilization process which is now an immediate consequence of the third statement of .
\[cor:monstab\]
1. Let ${\mathcal C}$ and ${\mathcal D}$ be closed symmetric monoidal presentable $\infty$-categories and let us consider a symmetric monoidal left adjoint $F\colon{\mathcal C}\to{\mathcal D}.$ In the following commutative diagram, each of the functors induced by $F$ admits a symmetric monoidal structure: $$\xymatrix{
{\mathcal C}\ar[d]\ar[r]&{\mathcal C}_\ast\ar[d]\ar[r]&{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\ar[d]\ar[r]&{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\ar[d]\ar[r]&
{\mathrm{Sp}}({\mathcal C})\ar[d]\\
{\mathcal D}\ar[r]&{\mathcal D}_\ast\ar[r]&{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\ar[r]&{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\ar[r]&{\mathrm{Sp}}({\mathcal D}_\ast)
}$$ Moreover, these symmetric monoidal structures are uniquely characterized by the fact that the functors commute with the free functors from ${\mathcal C}$.
2. The stabilization of presentable $\infty$-categories ${\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L_{St}}}$ admits a symmetric monoidal refinement ${\mathcal{P}\mathrm{r^{L,\otimes}}}\to{\mathcal{P}\mathrm{r^{L,\otimes}_{St}}}$ which factors as a composition of adjunctions $${\mathcal{P}\mathrm{r^{L,\otimes}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^{L,\otimes}_{Pt}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^{L,\otimes}_{Pre}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^{L,\otimes}_{Add}}}{\rightleftarrows}{\mathcal{P}\mathrm{r^{L,\otimes}_{St}}}.$$
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1. One can use the theory of $\Gamma$-objects in ${\mathcal C}$ to obtain a more concrete description of the tensor product on ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ as the convolution product (see [@HA Corollary 6.3.1.12] for the case in which ${\mathcal C}$ is the $\infty$-category of spaces).
2. The uniqueness of the symmetric monoidal structures can be used to compare our results to existing ones. Every simplicial combinatorial, monoidal model category leads to a presentable, closed symmetric monoidal $\infty$-category. Thus for the monoidal model category of $\Gamma$-spaces as discussed in [@Schwede] it follows immediately that the symmetric monoidal structure on the underlying $\infty$-category has to agree with our structure. The same applies to the model structure on $\Gamma$-objects in any nice model category, for example in presheaves as discussed in [@Bergsaker].
More functoriality {#sec:more}
==================
In §\[sec:mon\] we saw that for presentable $\infty$-categories the passages to commutative monoids and groups are smashing localizations and hence, in particular, define functors $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(-),{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}(-): \,{\mathcal{P}\mathrm{r^L}}\to{\mathcal{P}\mathrm{r^L}}\ .$$ But this passage allows for more functoriality. In fact, a product-preserving functor $F\colon {\mathcal C}\to {\mathcal D}$ induces functors $$\underline{F}\colon {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\qquad\text{and}\qquad
\underline{F}\colon {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$$ simply by post-composing the respective (very) special $\Gamma$-objects with $F$. The main goal of this section is to establish , which states that under certain mild assumptions these extensions themselves are lax symmetric monoidal with respect to the canonical symmetric monoidal structures established in . This corollary will be needed in our applications to algebraic K-theory in §\[sec:infinite\]. We begin by comparing these two potentially different functorialities of the assignments ${\mathcal C}\mapsto{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathcal C}\mapsto{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}).$
\[leftright\] Let $L\colon{\mathcal C}\rightarrow{\mathcal D}$ be a functor of presentable $\infty$-categories with right adjoint $R\colon{\mathcal D}\to{\mathcal C}$.
1. If $L\colon{\mathcal C}\to{\mathcal D}$ is product-preserving and if products in ${\mathcal C}$ and ${\mathcal D}$ commute with countable colimits, then the functors $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(L)\colon {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \qquad\text{and}\qquad
\underline{L}\colon {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$$ described above are equivalent.
2. The canonical extension $\underline{R}\colon {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ is right adjoint to the functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(L)$.
The corresponding two statements for ${\mathbb{E}_\infty}$-groups hold as well.
For the first claim we must show that if $L$ preserves products then the two functors agree. This follows if we can show that $\underline {L}$ is a left adjoint and the diagram $$\label{dia:L}
\xymatrix{
{\mathcal C}\ar[rr]^-L\ar[d]_{{\mathrm{Fr}}} && {\mathcal D}\ar[d]^{{\mathrm{Fr}}}\\
{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \ar[rr]_-{\underline{L}} && {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})
}$$ commutes in $\widehat{{\mathcal{C}\mathrm{at}}}_\infty$. To see that $\underline{L}$ is left adjoint we observe that it commutes with sifted colimits, as they are detected by the forgetful functors ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathcal C}$ and ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\to{\mathcal D}$, and also that it commutes with coproducts, as coproducts in ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ are given by the tensor product which is preserved by $L$. To conclude this part of the proof it suffices to show that there is an equivalence ${\mathrm{Fr}}\circ L\simeq\underline{L}\circ{\mathrm{Fr}}$. For this, we consider the mate of the equivalence $L\circ U\simeq U\circ\underline{L}\colon{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathcal D}$, i.e., we form the following pasting with the respective adjunction morphisms: $$\xymatrix{
{\mathcal C}\ar[r]^-{{\mathrm{Fr}}}\ar@/_0.8pc/[dr]_-=&{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\ar[d]_-U\ar[r]^-{\underline{L}}&{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\ar[d]^-U\ar@/^1.0pc/[rd]^-=&\\
&{\mathcal C}\ar[r]_-L&{\mathcal D}\ar[r]_-{{\mathrm{Fr}}}&{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})
}$$ In order to show that the resulting transformation $${\mathrm{Fr}}\circ L\to{\mathrm{Fr}}\circ L\circ U\circ {\mathrm{Fr}}\simeq {\mathrm{Fr}}\circ U\circ \underline{L}\circ{\mathrm{Fr}}\to\underline{L}\circ {\mathrm{Fr}}$$ is an equivalence, it is enough to check that this is the case after applying the forgetful functor $U\colon{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\to{\mathcal D}$. But this follows from the explicit description of the free functors as $${\mathrm{Fr}}(C)\simeq \bigsqcup_n C^n/ \Sigma_n$$ (see [@HA Example 3.1.3.12]) and by unraveling the definitions of $\underline{L}$ and the adjunction morphisms.
To prove the second statement we first remark that $\underline{R}$ has a left adjoint since it preserves all limits and filtered colimits which are formed in the underlying $\infty$-category. Moreover, any such left adjoint has to make diagram commute since this is the case for the corresponding diagram of right adjoints. By the above, this left adjoint has to coincide with ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(L)$. The proof for the case of groups is completely parallel.
This lemma can be applied to adjunctions between cartesian closed presentable $\infty$-categories.
\[symadjoints\] Let ${\mathcal C}$ and ${\mathcal D}$ be closed symmetric monoidal presentable $\infty$-categories, let $L\colon {\mathcal C}\to {\mathcal D}$ be a symmetric monoidal left adjoint functor and let $R\colon {\mathcal D}\to {\mathcal C}$ be right adjoint to $L$.
1. The functors $\underline{R}\colon {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and $\underline{R}\colon {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ have canonical lax symmetric monoidal structures.
2. If ${\mathcal C}$ and ${\mathcal D}$ are cartesian closed, then the canonical extensions $\underline{L}\colon{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ and $\underline{L}\colon{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ both admit structures of symmetric monoidal functors which are determined up to a contractible space of choices by the fact that the following diagrams commute: $$\xymatrix{
{\mathcal C}\ar[r]\ar[d]_L& {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\ar[d]^{\underline{L}}&&
{\mathcal C}\ar[r]\ar[d]_L& {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\ar[d]^{\underline{L}}\\
{\mathcal D}\ar[r]&{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}),&&
{\mathcal D}\ar[r]&{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\,\, .
}$$
tells us that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(L)$ is canonically symmetric monoidal, and the right adjoint of a symmetric monoidal functor always inherits a canonical lax symmetric monoidal structure [@HA Corollary 8.3.2.7]. Together with this establishes the first part. The second part is an immediate consequence of and , and again the case of groups is entirely analogous.
\[factorsym\] Let $F\colon {\mathcal C}\to {\mathcal D}$ be an accessible functor between presentable $\infty$-categories.
1. We can factor $F \simeq L \circ R$ where $R$ is a right adjoint and $L$ is a left adjoint functor.
2. If ${\mathcal C}$ and ${\mathcal D}$ are closed symmetric monoidal, then the factorization can be chosen such that $L$ and the left adjoint to $R$ are symmetric monoidal (this means of course that the intermediate $\infty$-category is symmetric monoidal as well). In particular, $R$ itself is lax symmetric monoidal.
3. If $F$ preserves products and ${\mathcal D}$ is cartesian closed, then $L$ can be chosen to preserve products.
Choose $\kappa$ sufficiently large such that both ${\mathcal C}$ and ${\mathcal D}$ are $\kappa$-compactly generated and $F$ preserves $\kappa$-filtered colimits. Then the restricted Yoneda embedding $R\colon{\mathcal C}\to{\mathcal{P}}({\mathcal C}^\kappa)$ preserves limits and $\kappa$-filtered colimits, and therefore admits a left adjoint. Similarly, the functor $L\colon{\mathcal{P}}({\mathcal C}^\kappa)\to{\mathcal D}$ induced (under colimits) by the composite ${\mathcal C}^\kappa\to{\mathcal C}\to{\mathcal D}$ preserves all colimits, and therefore admits a right adjoint. Since $F$ is equivalent to the composite $L\circ R$, this completes the proof of the first claim.
Now, if in addition ${\mathcal C}$ and ${\mathcal D}$ are closed symmetric monoidal, then it follows from the universal property of the convolution product [@HA Proposition 6.3.1.10] that $L$ is symmetric monoidal and also that the left adjoint ${\mathcal{P}}({\mathcal C}^\kappa)\to{\mathcal C}$ of $R$ is symmetric monoidal, completing the proof of the second claim (the fact that $R$ is lax symmetric monoidal again follows from [@HA Corollary 8.3.2.7]).
Finally, if $F$ preserves products, then $L$ preserves products of representables ${\mathcal C}^\kappa$, and if ${\mathcal D}$ is cartesian closed then products commute with colimits in both variables. Hence $L$ preserves products.
Let ${\mathcal C}$ and ${\mathcal D}$ be closed symmetric monoidal presentable $\infty$-categories and let $F\colon{\mathcal C}\to{\mathcal D}$ be product-preserving, symmetric monoidal, and accessible. If ${\mathcal D}$ is also cartesian closed then the functors $\underline{F}\colon{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ and $\underline{F}\colon{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ admit lax symmetric monoidal structures.
Factor $F$ according to and apply .
\[cor:lax\] Let ${\mathcal C}$ and ${\mathcal D}$ be cartesian closed presentable $\infty$-categories and let $F\colon{\mathcal C}\to{\mathcal D}$ be product-preserving and accessible. Then the canonical extensions $\underline{F}\colon {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ and $\underline{F}\colon {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$ are lax symmetric monoidal.
Infinity-categories of semirings and rings {#sec:ring}
==========================================
In this section we will use the results of §\[sec:spec\] to define and study semiring (a.k.a. ‘rig’) and ring objects in suitable $\infty$-categories. We know by that given a closed symmetric monoidal presentable $\infty$-category ${\mathcal C}$, there are canonical closed symmetric monoidal structures on ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ which will respectively be denoted by $${\mathrm{Mon}_{{\mathbb{E}_\infty}}^\otimes\!}({\mathcal C})\qquad\text{and}\qquad{\mathrm{Grp}_{{\mathbb{E}_\infty}}^\otimes\!}({\mathcal C}).$$
Let ${\mathcal C}$ be a closed symmetric monoidal presentable $\infty$-category and let ${\mathcal{O}}$ be an $\infty$-operad. The $\infty$-category ${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal C})$ of ${\mathcal{O}}$-*semirings* in ${\mathcal C}$ and the $\infty$-category ${\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal C})$ of ${\mathcal{O}}$-*rings* in ${\mathcal C}$ are respectively defined as the $\infty$-categories of ${\mathcal{O}}$-algebras $${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal C}) := {\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}^\otimes\!}({\mathcal C})) \qquad \text{and}\qquad {\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal C}) := {\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Grp}_{{\mathbb{E}_\infty}}^\otimes\!}({\mathcal C})).$$
In the case of ordinary categories and the associative or commutative operad, the alternative terminology *rig objects* is also used for what we call semiring objects, hence the notation. We will be mainly interested in the case of ${\mathcal{O}}= \mathbb{E}_n$ for $n=1,2,\ldots,\infty$. In the case $n=1$, ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_1}({\mathcal C})$ is the $\infty$-category of *associative rings* in ${\mathcal C}$ and, in the case $n=\infty$, ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_\infty}({\mathcal C})$ is the $\infty$-category of *commutative rings* in ${\mathcal C}$. Similarly, there are $\infty$-categories of associative or commutative semirings in ${\mathcal C}$.
Let us take up again the examples of §\[sec:spec\].
1. In the special case of the cartesian closed presentable $\infty$-category ${\mathrm{Set}}$ of sets, our notion of associative or commutative (semi)ring object coincides with the corresponding classical notion.
2. Since the $\infty$-category ${\mathcal{S}}$ of spaces is cartesian closed and presentable, we obtain, for each $\infty$-operad ${\mathcal{O}}$, the $\infty$-category ${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal{S}})$ of ${\mathcal{O}}$*-rig spaces* and the $\infty$-category ${\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal{S}})$ of ${\mathcal{O}}$*-ring spaces*. For the special case of the operads ${\mathcal{O}}=\mathbb{E}_n$ for $n=1,\ldots,\infty$, the point-set analogue of these spaces were intensively studied by May and others using carefully chosen pairs of operads (see the recent articles [@May_WhatI; @May_WhatII; @May_WhatIII] and the many references therein).
3. In the case of the cartesian closed presentable $\infty$-category ${\mathcal{C}\mathrm{at}}$ of ordinary small categories, we obtain the $\infty$-category ${{\mathcal{R}\mathrm{ig}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}$ of ${\mathcal{O}}$*-rig categories* and the $\infty$-category ${{\mathcal{R}\mathrm{ing}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}$ of ${\mathcal{O}}$*-ring categories*. Coherences for ‘lax’ semiring categories have been studied by Laplaza [@Laplaza2], [@Laplaza1]; note that, in our case, all coherence morphisms must be invertible. It should be possible to obtain a precise comparison of our notion with these more classical ones, but we bypass this via a recognition principle () for semiring $\infty$-categories which allows us to work directly with the examples of interest to us, without having to check coherences for distributors.
4. An $\infty$-categorical version of the previous example is obtained by considering the cartesian closed presentable $\infty$-category ${\mathcal{C}\mathrm{at}_\infty}$. Associated to it there is the $\infty$-category ${{\mathcal{R}\mathrm{ig}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}_\infty$ of ${\mathcal{O}}$*-semiring $\infty$-categories* and the $\infty$-category ${{\mathcal{R}\mathrm{ing}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}_\infty$ of ${\mathcal{O}}$*-ring $\infty$-categories*.
For a general closed symmetric monoidal presentable $\infty$-category ${\mathcal C}$ there are two potentially different symmetric monoidal structures playing a role in the notion of an ${\mathcal{O}}$-(semi)ring object. Thus it may be useful to provide an informal description of the structure given by an ${\mathbb{E}_\infty}$-semiring object in ${\mathcal C}$. It consists of an object $R\in{\mathcal C}$ together with an addition map $+\colon R\times R\to R$ and a multiplication map $\times\colon R\otimes R\to R$ such that both maps are coherently associative and commutative. Moreover, the multiplication has to distribute over the addition in a homotopy coherent fashion. In the case of an ordinary category with the Cartesian monoidal structure, our notion reduces to the usual one.
Similarly to the case of commutative monoids and commutative groups, also guarantees that the $\infty$-category ${\mathrm{Sp}}({\mathcal C})$ of spectrum objects associated to a closed symmetric monoidal presentable $\infty$-category ${\mathcal C}$ has a canonical closed symmetric monoidal structure ${\mathrm{Sp}}^\otimes({\mathcal C})$. This allows us to make the following definition.
Let ${\mathcal C}$ be a closed symmetric monoidal presentable $\infty$-category and let ${\mathcal{O}}$ be an $\infty$-operad. The $\infty$-category ${{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}({\mathcal C})$ of ${\mathcal{O}}$-*ring spectrum objects in* ${\mathcal C}$ is defined as $${{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}({\mathcal C}) := {\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Sp}}^\otimes({\mathcal C})).$$
\[thm:rigmon\] Let ${\mathcal C}$ be a closed symmetric monoidal presentable $\infty$-category and let ${\mathcal{O}}$ be an $\infty$-operad. Then the group completion functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and the associated spectrum functor ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Sp}}({\mathcal C})$ refine to functors $${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal C}) \to {\mathcal{R}\mathrm{ing}}_{{\mathcal{O}}}({\mathcal C}) \qquad\text{and}\qquad {\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal C}) \to {{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}({\mathcal C}),$$ called the *ring completion* and the *associated ring spectrum functor*, respectively.
This is clear since the group completion ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C})$ and also the associated spectrum functor ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Sp}}({\mathcal C})$ are symmetric monoidal as shown in .
1. In the special case of the $\infty$-category ${\mathrm{Set}}$ of sets this reduces to the usual ring completion of associative or commutative semirings.
2. Given an $\infty$-operad ${\mathcal{O}}$, we obtain an associated ring completion functor ${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal{S}})\to{\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal{S}})$ from ${\mathcal{O}}$-rig spaces to ${\mathcal{O}}$-ring spaces and an associated ring spectrum functor ${\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal{S}})\to{{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}({\mathcal{S}})$ from ${\mathcal{O}}$-ring spaces to ${\mathcal{O}}$-ring spectra. The latter $\infty$-category will also be written ${{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}.$
3. Let us again consider the cartesian closed presentable $\infty$-category ${\mathcal{C}\mathrm{at}}$ of ordinary small categories. Then for each $\infty$-operad ${\mathcal{O}}$, we obtain a ring completion functor ${{\mathcal{R}\mathrm{ig}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}\to{{\mathcal{R}\mathrm{ing}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}$ from ${\mathcal{O}}$-rig categories to ${\mathcal{O}}$-ring categories.
4. Again, we immediately obtain an $\infty$-categorical refinement of the previous example. For each $\infty$-operad ${\mathcal{O}}$, we obtain a ring completion functor ${{\mathcal{R}\mathrm{ig}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}_\infty\to{{\mathcal{R}\mathrm{ing}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}}_\infty$ from ${\mathcal{O}}$-rig $\infty$-categories to ${\mathcal{O}}$-ring $\infty$-categories. Using explicit models, a similar construction was obtained by Baas-Dundas-Richter-Rognes in [@BDRR].
shows that semirings can be used to produce highly structured ring spectra. Unfortunately, the definition of a semiring object is a bit indirect, so in practice it is often difficult to write down explicit examples of such objects. provides a natural class of semirings in the case of the cartesian closed $\infty$-category ${\mathcal C}= {\mathcal{C}\mathrm{at}}_\infty$. Moreover, this is the class that is of most interest in applications to algebraic K-theory, as we discuss in §\[sec:infinite\].
We conclude this section with a base-change result (similar to ) which sheds some light on the definition of semiring and ring object. This result will also be needed in where we show ${\mathbb{E}}_n$-(semi)rings to be *algebraic*.
\[prop\_rig\_ten\] Let ${\mathcal C}$ be a cartesian closed presentable $\infty$-category and ${\mathcal{O}}$ an $\infty$-operad. Then we have equivalences $${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal C}) \simeq {\mathcal C}\otimes {\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal{S}}) \qquad \text{and} \qquad {\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal C}) \simeq {\mathcal C}\otimes {\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal{S}}).$$
We show more generally that, for ${\mathcal D}$ any closed symmetric monoidal presentable $\infty$-category, there exists a canonical equivalence $$\label{eqn:algbasechange}
{\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal C}\to{\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal C}).$$ Then, taking ${\mathcal D}$ to be ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$, using Theorem \[thm:idem\], we obtain the desired chain of equivalences $${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal C})\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}))\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\otimes{\mathcal C})
\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}))\otimes{\mathcal C}\simeq{\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal{S}})\otimes{\mathcal C}\, .$$ In the case of rings we get an analogous chain of equivalences.
To show , first consider the case in which ${\mathcal C}={\mathcal{P}}({\mathcal C}_0)$ is the $\infty$-category of presheaves of spaces on a (small) $\infty$-category ${\mathcal C}_0$. In this case, we have that ${\mathcal D}\otimes{\mathcal C}\simeq{\mathrm{Fun}}({\mathcal C}^{op}_0,{\mathcal D})$, so that $${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal C}\simeq{\mathrm{Fun}}({\mathcal C}^{op}_0,{\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}))\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathrm{Fun}}({\mathcal C}^{op}_0,{\mathcal D}))\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal C}).$$ A general cartesian closed presentable $\infty$-category ${\mathcal C}$ is a full symmetric monoidal subcategory of some ${\mathcal{P}}({\mathcal C}_0)$, say for ${\mathcal C}_0$ the full subcategory of $\kappa$-compact objects in ${\mathcal C}$ for a sufficiently large regular cardinal $\kappa$. Since ${\mathcal D}\otimes{\mathcal C}\simeq{{\mathrm{Fun}}^\mathrm{R}}({\mathcal C}^{op},{\mathcal D})$, we see that ${\mathcal D}\otimes{\mathcal C}$ is a full symmetric monoidal subcategory of ${\mathcal D}\otimes{\mathcal{P}}({\mathcal C}_0)$, and similarly with ${\mathcal D}$ replaced by ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})$. Thus it suffices to show that ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal C}$ and ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal C})$ define equivalent full subcategories of ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal{P}}({\mathcal C}_0)\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal{P}}({\mathcal C}_0))$.
If ${\mathcal{O}}$ is monochromatic (i.e. if there exists an essentially surjective functor $\Delta^0\to{\mathcal{O}}^\otimes_{\langle 1\rangle}$), then an object of ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal{P}}({\mathcal C}_0))$ lies in the full subcategory ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal C})$ if and only if the projection to ${\mathcal D}\otimes{\mathcal{P}}({\mathcal C}_0)$ factors through ${\mathcal D}\otimes{\mathcal C}$. For arbitrary ${\mathcal{O}}$, an object of ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal{P}}({\mathcal C}_0))$ lies in the full subcategory ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal C})$ precisely when the restriction along any full monochromatic suboperad ${\mathcal{O}}'\to{\mathcal{O}}$ satisfies this same condition. As the analogous results for ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal C}$ hold by the same argument, we see that ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal C}$ and ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal C})$ define equivalent full subcategories of ${\mathrm{Alg}}_{\mathcal{O}}({\mathcal D})\otimes{\mathcal{P}}({\mathcal C}_0)\simeq{\mathrm{Alg}}_{\mathcal{O}}({\mathcal D}\otimes{\mathcal{P}}({\mathcal C}_0))$.
Multiplicative infinite loop space theory {#sec:infinite}
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In this section we apply the results of the previous section to some specific $\infty$-categories; namely, we consider the $\infty$-categories ${\mathcal{S}}$ of spaces, the $\infty$-category ${\mathcal{C}\mathrm{at}}$ of ordinary categories (really a 2-category, but we regard it as an $\infty$-category), and the $\infty$-category ${\mathcal{C}\mathrm{at}_\infty}$ of $\infty$-categories. Let us emphasize that, as a special case of , the group completion and the associated spectrum functor $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Sp}}$$ refine to functors $${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal{S}}) \to {\mathcal{R}\mathrm{ing}}_{\mathcal{O}}({\mathcal{S}}) \to {{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}.$$ This gives us not only a way of obtaining (highly structured) ring spectra, but it also allows us to identify certain spectra as ring spectra.
Recall that the group completion functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\to{\mathrm{Sp}}$ plays an important role in algebraic K-theory. The input data for algebraic K-theory is often a symmetric monoidal category ${\mathcal{M}}$; as a primary example, we have the category ${\mathcal{M}}={\mathrm{Proj}}_R$ of finitely generated projective modules over a ring $R$, which is symmetric monoidal under the direct sum $\oplus$, the coproduct. In any case, given such a category ${\mathcal{M}}$, we form the subcategory of isomorphisms ${\mathcal{M}}^\sim$ and pass to the geometric realization $|{\mathcal{M}}^\sim|$. That way we obtain an ${\mathbb{E}}_\infty$-space $|{\mathcal{M}}^\sim|$, i.e., an object of ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$. The *algebraic K-theory spectrum* ${\mathrm{K}}({\mathcal{M}})$ is then defined to be the spectrum associated to the group completion of $|{\mathcal{M}}^\sim|$, see e.g. [@segal_categories]. In other words, (direct sum) algebraic K-theory is defined as the composition $$\label{ktheory}
{\mathrm{K}}\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\xrightarrow{(-)^\sim} {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\xrightarrow{|-|} {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Sp}}.$$ It is a result of May [@May82], with refinements by Elmendorf-Mandell [@EM06] and Bass-Dundas-Richter-Rognes [@BDRR], that this functor respects multiplicative structures, in the appropriate sense. Our methods give an even more refined result.
The algebraic ${\mathrm{K}}$-theory functor ${\mathrm{K}}\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\to{\mathrm{Sp}}$ is lax symmetric monoidal. In particular, it induces a functor ${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}{\mathcal{C}\mathrm{at}}\to {{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}$ for any $\infty$-operad ${\mathcal{O}}$.
The last two functors in the composition are symmetric monoidal by . The remaining two functors $(-)^\sim\colon{\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\to{\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}$ and $|-|\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ are the canonical extensions of the product preserving functors $(-)^\sim\colon{\mathcal{C}\mathrm{at}}\to{\mathcal{C}\mathrm{at}}$ and $|-|\colon {\mathcal{C}\mathrm{at}}\to {\mathcal{S}}$ respectively. Since these latter functors are accessible, implies that their canonical extensions are lax symmetric monoidal, concluding the proof.
We now have the tools necessary to establish corresponding results in the $\infty$-categorical case. Note that the composition of the first two functors in is the same as the composition of the nerve ${\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\to {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty$ followed by the functor $(-)^\sim\colon{\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$, which sends a symmetric monoidal $\infty$-category to its maximal subgroupoid, and of course is again symmetric monoidal. This allows us to recover the algebraic K-theory of a symmetric monoidal category ${\mathcal{M}}$ by an application of the following $\infty$-categorical version of algebraic K-theory to the nerve of ${\mathcal{M}}$.
Let ${\mathcal{M}}$ be a symmetric monoidal $\infty$-category. The *algebraic $\mathrm{K}$-theory spectrum* ${\mathrm{K}}({\mathcal{M}})$ is the spectrum associated to the group completion of ${\mathcal{M}}^\sim$. Thus, the algebraic K-theory functor is defined as the composition $$\label{ktheory2}
{\mathrm{K}}\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty \xrightarrow{(-)^\sim} {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \longrightarrow {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \longrightarrow {\mathrm{Sp}}.$$
Strictly speaking, this is the [*direct sum*]{} K-*theory*, since it does not take into account a potential exactness (or Waldhausen) structure on the symmetric monoidal $\infty$-categories in question. Nevertheless, in many cases of interest, e.g. that of a connective ring spectrum $R$, the algebraic K-theory of $R$, defined in terms of Waldhausen’s $S_\bullet$ construction applied to the stable $\infty$-category of $R$-modules (which agrees with the K-theory of any suitable model category of $R$-modules, see [@BGT1] for details), is computed as the direct sum K-theory of the symmetric monoidal $\infty$-category $\mathrm{Proj}_R$ of finitely-generated projective $R$-modules ([@HA Definition 8.2.2.4]).
For more sophisticated versions of K-theory, the situation is slightly more complicated but entirely analogous. In [@BGT2] it is shown that the algebraic K-theory $\mathrm{K}\colon{\mathcal{C}\mathrm{at}_\infty}^\mathrm{perf}\to{\mathrm{Sp}}$ of small idempotent-complete stable $\infty$-categories is a lax symmetric monoidal functor, as is the nonconnective version; the methods employed to do so are similar to the ones used in the present paper, in that $\mathrm{K}$ is shown to be the tensor unit in a symmetric monoidal $\infty$-category of all additive (respectively, localizing) functors ${\mathcal{C}\mathrm{at}_\infty}^\mathrm{perf}\to{\mathrm{Sp}}$, so that the commutative algebra structure ultimately relies on the existence of an idempotent object in an appropriate symmetric monoidal $\infty$-category. The case of general Waldhausen $\infty$-categories is treated in [@Bar], where it is shown that the algebraic K-theory $\mathrm{K}\colon\mathrm{Wald}_\infty\to{\mathrm{Sp}}$ of Waldhausen $\infty$-categories is again a lax symmetric monoidal functor.
As already mentioned, the $\infty$-categorical algebraic K-theory $${\mathrm{K}}\colon{\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}_\infty}\to{\mathrm{Sp}}$$ applied to nerves of ordinary symmetric monoidal categories recovers the 1-categorical algebraic K-theory ${\mathrm{K}}\colon{\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}\to{\mathrm{Sp}}.$ Note, however, that the inclusion of symmetric monoidal 1-categories into symmetric monoidal $\infty$-categories given by the nerve functor does not commute with the tensor products. In fact, the tensor product $\mathrm{N}({\mathcal C})\otimes\mathrm{N}({\mathcal D})$ of the nerves of two symmetric monoidal 1-categories ${\mathcal C}$, ${\mathcal D}$ need not again be (the nerve of) a symmetric monoidal 1-category; rather, one can show that $\mathrm{N}({\mathcal C}\otimes{\mathcal D})$ is the 1-categorical truncation of $\mathrm{N}({\mathcal C})\otimes\mathrm{N}({\mathcal D})$.
The algebraic ${\mathrm{K}}$-theory functor ${\mathrm{K}}\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty \to {\mathrm{Sp}}$ is lax symmetric monoidal. In particular, it refines to a functor ${\mathcal{R}\mathrm{ig}}_{\mathcal{O}}({\mathcal{C}\mathrm{at}}_\infty) \to {{\mathcal{R}\mathrm{ing}}{\mathrm{Sp}}}_{\mathcal{O}}$ for any $\infty$-operad ${\mathcal{O}}$.
The proof is almost the same as in the 1-categorical case. The last two functors in the defining composition are symmetric monoidal by . The remaining functor $(-)^\sim\colon{\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}_\infty}\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ is the canonical extension of the accessible, product preserving functors $(-)^\sim\colon{\mathcal{C}\mathrm{at}_\infty}\to{\mathcal{S}}$. Thus, implies that this canonical extension is lax symmetric monoidal as intended.
The ${\mathrm{K}}$-theory functor is defined as the composition of lax symmetric monoidal functors. We know that the last two of these (namely, the group completion and the associated spectrum functor) are actually symmetric monoidal. Thus, one might wonder whether also the first functor (and hence the ${\mathrm{K}}$-theory functor) is symmetric monoidal as well. This is not the case, as the following counterexample shows.
Let us begin by recalling from [@HA Remark 2.1.3.10] that the $\infty$-category $\mathrm{Mon}_{{\mathbb{E}}_0}({\mathcal{C}\mathrm{at}}_\infty)$ is equivalent to $({\mathcal{C}\mathrm{at}}_\infty)_{\Delta^0/}.$ Thus, an object in $\mathrm{Mon}_{{\mathbb{E}}_0}({\mathcal{C}\mathrm{at}}_\infty)$ is just an $\infty$-category ${\mathcal C}$ together with a chosen object $x\in{\mathcal C}.$ The fact that an ordinary monoid gives rise to a category with one object (which is hence distinguished) admits the following $\infty$-categorical variant. There is a functor $$\mathrm{B}\colon\mathrm{Mon}_{{\mathbb{E}}_1}({\mathcal{S}})\to\mathrm{Mon}_{{\mathbb{E}}_0}({\mathcal{C}\mathrm{at}}_\infty)$$ which is left adjoint to the functor which sends $x\colon\Delta^0\to{\mathcal C}$ to the endomorphism monoid $\mathrm{End}_{{\mathcal C}}(x)$ of the distinguished object. Similarly, there is a functor $$\mathrm{B}\colon\mathrm{Mon}_{{\mathbb{E}}_\infty}({\mathcal{S}})\to\mathrm{Mon}_{{\mathbb{E}}_\infty}({\mathcal{C}\mathrm{at}}_\infty)$$ which is left adjoint to the functor which sends a symmetric monoidal $\infty$-category to the ${\mathbb{E}_\infty}$-monoid of endomorphisms of the monoidal unit (we are also using the fact that ${\mathbb{E}}_n\otimes{\mathbb{E}}_\infty\simeq{\mathbb{E}}_\infty$ for $n=0,1$).
Now, let ${\mathcal F}={\mathrm{Fr}}(\Delta^0)$ denote the free symmetric monoidal $\infty$-category on the point, which is to say the nerve of the groupoid of finite sets and isomorphisms. We claim that, for any symmetric monoidal $\infty$-groupoid ${\mathcal C}$, $$(\mathrm{B}{\mathcal F})\otimes{\mathcal C}\simeq\mathrm{B}{\mathcal C}.$$ This is clearly true if ${\mathcal C}={\mathcal F}$, and the general formula follows by the observation that both sides commute with colimits in the ${\mathcal C}$ variable and the fact that every symmetric monoidal $\infty$-groupoid is an iterated colimit of ${\mathcal F}$. But the groupoid core $(\mathrm{B}{\mathcal F})^\sim$ is trivial. Thus, ${\mathrm{K}}(\mathrm{B}{\mathcal F})\otimes{\mathrm{K}}({\mathcal C})=0$ for every ${\mathcal C}$. On the other hand, taking ${\mathcal C}=\mathbb{Z}$, we have that $(\mathrm{B}{\mathcal C})^\sim\simeq\mathrm{B}{\mathcal C}$, so ${\mathrm{K}}(\mathrm{B}{\mathcal C})\simeq\Sigma\mathrm{H}\mathbb{Z}$, the suspension of the Eilenberg-MacLane spectrum.
We have the following ‘recognition principle’ for semiring $\infty$-categories.
\[seminringex\] Let ${\mathcal C}$ be an ${\mathbb{E}}_n$-monoidal $\infty$-category with coproducts such that the monoidal product $$\otimes\colon{\mathcal C}\times{\mathcal C}\to{\mathcal C}$$ preserves coproducts separately in each variable. Then $({\mathcal C},\sqcup,\otimes)$ is canonically an object of ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{C}\mathrm{at}_\infty})$.
Let ${\mathcal{C}\mathrm{at}}_\infty^\Sigma$ be the $\infty$-category of $\infty$-categories which admit finite coproducts and coproduct preserving functor. There is a fully-faithful functor $${\mathcal{C}\mathrm{at}}_\infty^{\Sigma} \to {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty$$ given by considering an $\infty$-category with coproducts as a cocartesian symmetric monoidal $\infty$-category (see [@HA Variant 2.4.3.12]). We want to show that this functor naturally extends to a lax symmetric monoidal functor, essentially by the construction of the tensor product on ${\mathcal{C}\mathrm{at}}_\infty^\Sigma$ of [@HA Proposition 6.3.1.10] . From this the claim follows, since an ${\mathbb{E}}_n$-algebra in ${\mathcal{C}\mathrm{at}}_\infty^\Sigma$ is the same as an ${\mathbb{E}}_n$-monoidal $\infty$-category such that the tensor product preserves finite coproducts in each variable separately.
The first thing we want to observe is that the $\infty$-category ${\mathcal{C}\mathrm{at}}_\infty^{\Sigma}$ is preadditive. To see this, note that ${\mathcal{C}\mathrm{at}}_\infty^{\Sigma}$ has finite coproducts and products, because ${\mathcal{C}\mathrm{at}}_\infty^{\Sigma}$ is presentable (this follows from [@HA Lemma 6.3.4.2] by taking $\mathcal{K}$ to be the collection of finite sets). It remains to check that the product ${\mathcal C}\times{\mathcal D}$, which is calculated as the product in ${\mathrm{Ho}}({\mathcal{C}\mathrm{at}}_\infty)$, satisfies the universal property of the coproduct in ${\mathrm{Ho}}({\mathcal{C}\mathrm{at}}_\infty^\Sigma)$. Given a third $\infty$-category with finite coproducts ${\mathcal E}$, we note that any pair of coproduct preserving functors $f\colon{\mathcal C}\to{\mathcal E}$ and $g\colon{\mathcal D}\to{\mathcal E}$ extends to the coproduct preserving functor $${\mathcal C}\times{\mathcal D}\overset{f\times g}{\longrightarrow}{\mathcal E}\times{\mathcal E}\overset{\sqcup}{\longrightarrow}{\mathcal E}.$$ Moreover, this extension is unique up to homotopy, because $(c,d)\cong(c,\emptyset)\sqcup(\emptyset,d)$ for any $(c,d)\in{\mathcal C}\times{\mathcal D}$.
Using [@HA Proposition 6.3.1.10] again, the inclusion functor $i\colon {\mathcal{C}\mathrm{at}}_\infty^\Sigma \to {\mathcal{C}\mathrm{at}}_\infty$ admits a left adjoint $L$ which is symmetric monoidal. By the functor $L$ extends to a left adjoint functor $$L'\colon {\mathcal{S}\mathrm{ym}\mathcal{M}\mathrm{on}\mathcal{C}\mathrm{at}}_\infty \simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty^\Sigma)\simeq{\mathcal{C}\mathrm{at}}_\infty^\Sigma .$$ The right adjoint of this functor can be described as the functor $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(i)\colon {\mathcal{C}\mathrm{at}}_\infty^\Sigma \simeq {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty^\Sigma) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty).$$
We can now conclude that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(i)$ is lax symmetric monoidal since it is right adjoint to a symmetric monoidal functor. It remains to show that ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}(i)$ is the desired functor. This is obvious.
Preserving coproducts is a condition!
\[cor:awesome\] If ${\mathcal C}$ is an ordinary monoidal category with coproducts such that $\otimes\colon{\mathcal C}\times{\mathcal C}\to{\mathcal C}$ preserves coproducts in each variable separately. Then $({\mathcal C},\sqcup,\otimes)$ is canonically an object of ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_1}({\mathcal{C}\mathrm{at}}) \subset{\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_1}({\mathcal{C}\mathrm{at}_\infty})$. If ${\mathcal C}$ is moreover braided or symmetric monoidal then $({\mathcal C},\sqcup,\otimes)$ is an object of ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_2}({\mathcal{C}\mathrm{at}})$ or ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_\infty}({\mathcal{C}\mathrm{at}})$ respectively.
We only need the identification of the ${\mathbb{E}}_n$-monoids in ${\mathcal{C}\mathrm{at}}$ with the respective monoidal categories. This has been given in [@HA Example 5.1.2.4].
Let ${\mathcal C}$ be an ${\mathbb{E}}_n$-monoidal $\infty$-category with coproducts such that $\otimes\colon{\mathcal C}\times{\mathcal C}\to{\mathcal C}$ preserves coproducts in each variable separately. Then the largest Kan complex ${\mathcal C}^\sim$ inside of ${\mathcal C}$ together with $\sqcup$ and $\otimes$ is an object of ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{S}})\subseteq{\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{C}\mathrm{at}_\infty}).$
The functor $(-)^\sim\colon{\mathcal{C}\mathrm{at}_\infty}\to {\mathcal{S}}\subset{\mathcal{C}\mathrm{at}_\infty}$ preserves products and is accessible. Thus we can apply to deduce that the induced functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}_\infty}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}_\infty})$ is lax symmetric monoidal. But this implies that we obtain a further functor ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{C}\mathrm{at}_\infty}) \to {\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{C}\mathrm{at}_\infty})$ which preserves the underlying object of ${\mathcal{C}\mathrm{at}_\infty}$. Now apply this functor to the semiring $\infty$-category of .
1. For an ordinary commutative ring $R$, let ${\mathrm{Mod}}_R$ denote the (ordinary) category of $R$-modules. Then ${\mathrm{Mod}}_R$ and the $\infty$-groupoid ${\mathrm{Mod}}_R^\sim$, equipped with the operations $\oplus$ and $\otimes_R$, form ${\mathbb{E}_\infty}$-semiring categories. The same applies to the category of sheaves on schemes and other similar variants.
2. For an ${\mathbb{E}}_n$-ring spectrum $R$, the $\infty$-category ${\mathrm{Mod}}_R$ of (left) $R$-modules is a ${\mathbb{E}}_{n-1}$-monoidal $\infty$-category by [@HA Section 6.3 or Proposition 8.1.2.6]. Since the tensor product preserves coproducts in each variable we conclude that ${\mathrm{Mod}}_R$, together with the coproduct $\oplus$ and tensor product $\otimes_R$, is an ${\mathbb{E}}_{n-1}$-semiring $\infty$-category.
Now we want to apply this to identify certain spectra as ${\mathbb{E}_\infty}$-ring spectra. For a connective $\mathbb{E}_{n+1}$-ring spectrum $R$ the $\infty$-category ${\mathrm{Proj}}_R$ of finitely generated projective $R$-modules is an ${\mathbb{E}}_n$-semiring. The K-theory spectrum ${\mathrm{K}}(R)$ can then be defined as ${\mathrm{K}}({\mathrm{Proj}}_R)$. This definition is actually equivalent to the definition using Waldhausen categories: for the variant which uses finitely generated free $R$-modules in place of projective, this is shown in [@EKMM Chapter VI.7], and for the general case this follows from [@BGT Section 4].
For a connective ${\mathbb{E}}_{n+1}$-ring spectrum $R$ the algebraic ${\mathrm{K}}$-theory spectrum ${\mathrm{K}}(R)$ is an ${\mathbb{E}}_{n}$-ring spectrum.
We also have the following proposition, which states roughly that group completion of monoidal $\infty$-categories not only inverts objects, but arrows as well. It also shows why it is necessary to discard all non-invertible morphisms *before* group completion.
The underlying $\infty$-category of an ${\mathbb{E}}_\infty$-group object of ${\mathcal{C}\mathrm{at}}_\infty$ is an $\infty$-groupoid. More precisely, the group completion functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty)\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty)$ factors through the groupoid completion $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty)\to{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty)$$ and induces an equivalence ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\simeq{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_\infty)$.
Let ${\mathcal C}$ be an ${\mathbb{E}}_\infty$-group object of ${\mathcal{C}\mathrm{at}}_\infty$. Then the underlying $\infty$-category of ${\mathcal C}$ is an $\infty$-groupoid precisely if its homotopy category ${\mathrm{Ho}}({\mathcal C})$ is an ordinary groupoid. Thus it suffices to show that ${\mathrm{Ho}}({\mathcal C})$ is a groupoid. But since ${\mathrm{Ho}}({\mathcal C})$ is a group object in ${\mathcal{C}\mathrm{at}}$, this reduces the proof of the proposition to ordinary categories ${\mathcal C}$.
A group object ${\mathcal C}$ in categories is a symmetric monoidal category $({\mathcal C},\otimes)$ together with an ‘inversion’ functor $I\colon {\mathcal C}\to {\mathcal C}$ as in to . We clearly have $I^2 \simeq {\mathrm{id}}$. As a first step we show that all endomorphisms of the tensor unit $\bbone$ in ${\mathcal C}$ are automorphisms. This follows from the Eckman-Hilton argument since $\hom_{\mathcal C}(\bbone,\bbone)$ carries two commuting monoid structures (composition and tensoring), and as one of these is a group structure the other must also be as well. It follows that all endomorphisms in ${\mathcal C}$ are automorphisms by the identification $$I(x) \otimes -\colon \hom_{\mathcal C}(x,x) \cong \hom_{\mathcal C}(\bbone,\bbone).$$ Finally, to show that ${\mathcal C}$ is a groupoid, it now suffices to show that for every morphisms $f\colon x \to y$ in ${\mathcal C}$ there is a morphism $g: y \to x$ in ${\mathcal C}$. By tensoring with $I(y)$ we see that we may assume that $y = \bbone$. Then we have $I(f)\colon I(x) \to \bbone$, and therefore, using the usual identifications, $g:=I(f) \otimes x\colon \bbone \to x$.
Comonoids
=========
In this short section we establish additional universal mapping properties for ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ and ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ respectively. This gives a characterization of these $\infty$-categories among all presentable $\infty$-categories and not only among the (pre)additive ones.
Let us denote by ${{\mathrm{Fun}}^\mathrm{RAd}}({\mathcal C},{\mathcal D})$ the $\infty$-category of right adjoint functors from ${\mathcal C}$ to ${\mathcal D}$, which is a full subcategory of ${\mathrm{Fun}}({\mathcal C},{\mathcal D})$.
If ${\mathcal C}$ and ${\mathcal D}$ are presentable, then we have canonical equivalences $${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{RAd}}({\mathcal C},{\mathcal D})\big) \simeq {{\mathrm{Fun}}^\mathrm{RAd}}\big({\mathcal C}, {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \big) \quad\text{and}\quad {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{RAd}}({\mathcal C},{\mathcal D})\big) \simeq {{\mathrm{Fun}}^\mathrm{RAd}}\big({\mathcal C}, {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal D}) \big).$$
We note that right adjoint functors between presentable $\infty$-categories can be described as accessible functors that preserve limits. Then then the proof works exactly the same as the proof of Lemma \[lem:algR\].
Let ${\mathcal C}$ be an $\infty$-category with finite coproducts. We define the $\infty$-categories of *comonoids* and *cogroups* in ${\mathcal C}$ to be the respective $\infty$-categories $${\mathrm{coMon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) = {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({\mathcal C}\op\big)\op \quad\text{and}\quad
{\mathrm{coGrp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) = {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}\big({\mathcal C}\op\big)\op.$$
The comonoids as defined above are comonoids for the coproduct as tensor product. This is a structure which is often rather trivial. For example in the $\infty$-category ${\mathcal{S}}$ of spaces (or in the ordinary category of sets) there is exactly one comonoid in the sense above, namely the empty set $\emptyset$.
\[mappingproperty\] Let ${\mathcal C}$ and ${\mathcal D}$ be presentable $\infty$-categories. Then there are natural equivalences $${{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) , {\mathcal D}) \simeq {\mathrm{coMon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})\big) \quad\text{and}\quad
{{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) , {\mathcal D}) \simeq {\mathrm{coGrp}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})\big).$$ In particular, for a presentable $\infty$-category ${\mathcal D}$ we have natural equivalences $${{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}), {\mathcal D}) \simeq {\mathrm{coMon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})\quad\text{and}\quad{{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}), {\mathcal D}) \simeq {\mathrm{coGrp}_{{\mathbb{E}_\infty}}\!}({\mathcal D}).$$
Let us recall that given two $\infty$-categories ${\mathcal E}$ and ${\mathcal F}$ then there is an equivalence of categories ${{\mathrm{Fun}}^\mathrm{L}}({\mathcal E},{\mathcal F})$ and ${{\mathrm{Fun}}^\mathrm{RAd}}({\mathcal F},{\mathcal E})\op$ ([@HTT Proposition 5.2.6.2]). The adjoint functor theorem ([@HA Corollary 5.5.2.9]) together with then yield the following chain of equivalences: $$\begin{aligned}
{{\mathrm{Fun}}^\mathrm{L}}({\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) ,{\mathcal D}) & \simeq &{{\mathrm{Fun}}^\mathrm{RAd}}\big({\mathcal D},{\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C})\big)\op\\
& \simeq& {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{RAd}}({\mathcal D},{\mathcal C})\big)\op \\
& \simeq& {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})\op\big)\op \\
& =& {\mathrm{coMon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{L}}({\mathcal C},{\mathcal D})\big).\end{aligned}$$ In the special case of ${\mathcal C}={\mathcal{S}}$ we can use the universal property of $\infty$-categories of presheaves ([@HTT Theorem 5.1.5.6]) to extend the above chain of equivalences by $${\mathrm{coMon}_{{\mathbb{E}_\infty}}\!}\big({{\mathrm{Fun}}^\mathrm{L}}({\mathcal{S}},{\mathcal D})\big)\simeq{\mathrm{coMon}_{{\mathbb{E}_\infty}}\!}({\mathcal D}).$$ This settles the case of monoids and the case of groups works the same.
Algebraic theories and monadic functors {#sec:app}
=======================================
In this section we give a short discussion of Lawvere algebraic theories in $\infty$-categories and show that our examples are algebraic. For other treatments of $\infty$-categorical algebraic theories, see [@cranch], [@cranch2], [@Joyal Section 32] and [@HTT Section 5.5.8]. We write $\mathcal{F}\mathrm{in}$ for the category of finite sets.
An *algebraic theory* is an $\infty$-category ${\mathbb{T}}$ with finite products and a distinguished object $1_{\mathbb{T}}$, such that the unique product-preserving functor $\mathrm{N}(\mathcal{F}\mathrm{in})\op\to\mathbb{T}$ which sends the singleton to $1_\mathbb{T}$ is essentially surjective. A *morphism of algebraic theories* is a functor which preserves products and the distinguished object. We write ${\mathcal{T}\mathrm{h}}\subseteq({\mathcal{C}\mathrm{at}_\infty}^\Pi)_\ast$ for the $\infty$-category of theories and morphisms thereof.
This is the obvious generalization of ordinary algebraic theories, as defined by Lawvere [@Lawvere], to $\infty$-categories.
Let ${\mathcal C}$ be an $\infty$-category with finite products. A *model* (or an *algebra*) in ${\mathcal C}$ for an algebraic theory ${\mathbb{T}}$ is a finite product preserving functor ${\mathbb{T}}\to{\mathcal C}$. We write ${\mathrm{Mod}}_{{\mathbb{T}}}({\mathcal C})$ for the $\infty$-category of models of ${\mathbb{T}}$ in ${\mathcal C}$, i.e., for the full subcategory of ${\mathrm{Fun}}({\mathbb{T}},{\mathcal C})$ spanned by the models.
If ${\mathcal C}$ is a presentable $\infty$-category and ${\mathbb{T}}$ a theory, then ${\mathrm{Mod}}_{{\mathbb{T}}}({\mathcal C})$ is again presentable. This follows since ${\mathrm{Mod}}_{{\mathbb{T}}}({\mathcal C})$ is an accessible localization of the presentable $\infty$-category ${\mathrm{Fun}}({\mathbb{T}},{\mathcal C})$ (the proof is similar to the one of which takes care of the case of commutative monoids). Applying the adjoint functor theorem we also get that the forgetful functor ${\mathrm{Mod}}_{{\mathbb{T}}}({\mathcal C})\to{\mathcal C}$, i.e. the evaluation at the distinguished object $1_{\mathbb{T}},$ has a left adjoint.
\[prop\_ten\_al\] Let ${\mathcal C}$ be a presentable $\infty$-category and $\mathbb{T}$ a theory. Then we have an equivalence $${\mathrm{Mod}}_{\mathbb{T}}({\mathcal C}) \simeq {\mathcal C}\otimes {\mathrm{Mod}}_{{\mathbb{T}}}({\mathcal{S}}).$$
The same proof as for shows that we have an equivalence $${\mathrm{Mod}}_{\mathbb{T}}({{\mathrm{Fun}}^\mathrm{R}}({\mathcal C}^{op},{\mathcal{S}})) \simeq {{\mathrm{Fun}}^\mathrm{R}}({\mathcal C}^{op}, {\mathrm{Mod}}_{\mathbb{T}}({\mathcal{S}})).$$ This then implies the claim since we have ${\mathcal C}\otimes {\mathcal D}\simeq {{\mathrm{Fun}}^\mathrm{R}}({\mathcal C}^{op},{\mathcal D})$ for any presentable $\infty$-category ${\mathcal D}$.
A *monad* on an $\infty$-category ${\mathcal C}$ is an algebra $M$ in the monoidal $\infty$-category ${\mathrm{Fun}}({\mathcal C},{\mathcal C})$ of endofunctors; see [@HA Chapter 6.2] for details. Any such monad $M\in{\mathrm{Alg}}({\mathrm{Fun}}({\mathcal C},{\mathcal C}))$ admits an $\infty$-category of *modules* which we denote ${\mathrm{Mod}}_M({\mathcal C})$. This $\infty$-category comes equipped with a forgetful functor ${\mathrm{Mod}}_M({\mathcal C}) \to {\mathcal C}$ which is a right adjoint. Thus, given an arbitrary right adjoint functor $U\colon {\mathcal D}\to {\mathcal C}$, it is natural to ask whether this functor is equivalent to the forgetful functor from modules over a monad on ${\mathcal C}$. In this case the corresponding monad is uniquely determined as the composition $M = U \circ F$, where $F$ is a left adjoint of $U$. The functors $U$ for which this is the case are called *monadic*.
The Barr-Beck theorem (also called Beck’s monadicity theorem) gives necessary and sufficient conditions for a functor $U$ to be monadic. The conditions are that $U$ is conservative (i.e., reflects equivalences) and that $U$ preserves $U$-split geometric realizations ([@HA Theorem 6.2.2.5]). We will not need to discuss here what $U$-split means exactly since in our cases all geometric realizations will be preserved.
\[prop:monadic\] Let ${\mathcal C}$ be a presentable $\infty$-category and let ${\mathbb{T}}$ be a theory. Then the forgetful functor ${\mathrm{Mod}}_{{\mathbb{T}}}({\mathcal C})\to{\mathcal C}$ is monadic and preserves sifted colimits.
We will show that the evaluation ${\mathrm{Fun}}^\Pi({\mathbb{T}},{\mathcal C})\to{\mathcal C}$ is conservative and preserves sifted colimits. The result then follows immediately from the monadicity theorem. The fact that the functor is conservative is clear, so it remains to check the sifted colimit condition. But the inclusion of the finite product preserving functors $${\mathrm{Fun}}^\Pi({\mathbb{T}},{\mathcal C})\to{\mathrm{Fun}}({\mathbb{T}},{\mathcal C})$$ preserves sifted colimits by (4) of [@HA Proposition 5.5.8.10], and as colimits in functor $\infty$-categories are computed pointwise the evaluation $${\mathrm{Fun}}({\mathbb{T}},{\mathcal C})\to{\mathcal C}$$ also preserves sifted colimits.
We will obtain a converse to the previous proposition in the case of the $\infty$-category of spaces; namely, in this case we will identify algebraic theories with certain monads. To this end, note that an arbitrary monadic functor $U\colon {\mathrm{Mod}}_M({\mathcal{S}}) \to{\mathcal{S}}$ defines a theory ${\mathbb{T}}_M$ by $${\mathbb{T}}_M:={\big({{{\mathrm{Mod}}^\mathrm{ff}}}_M({\mathcal{S}})}\big)\op,$$ where ${{{\mathrm{Mod}}^\mathrm{ff}}}_M({\mathcal{S}})\subseteq{\mathrm{Mod}}_M({\mathcal{S}})$ is the full subcategory spanned by the free $M$-algebras on finite sets (which we abusively refer to as [*finite free*]{} algebras, and should not to be confused with more general free algebras on finite or finitely presented spaces). There is a canonical functor $$R\colon{\mathrm{Mod}}_M({\mathcal{S}}) \to {\mathrm{Mod}}_{{\mathbb{T}}_M}({\mathcal{S}})$$ from modules for $M$ to models to the associated theory ${\mathbb{T}}_M$, which is just the restriction of the Yoneda embedding to the full subcategory ${{{\mathrm{Mod}}^\mathrm{ff}}}_M({\mathcal{S}})$.
\[monadalg\] A monadic functor $U\colon{\mathrm{Mod}}_M({\mathcal{S}})\to{\mathcal{S}}$ is called *algebraic* if $$R\colon{\mathrm{Mod}}_M({\mathcal{S}}) \to {\mathrm{Mod}}_{{\mathbb{T}}_M}({\mathcal{S}})$$ is an equivalence of $\infty$-categories over ${\mathcal{S}}$. We also say that a monad $M$ on spaces is *algebraic* if the associated forgetful functor $U\colon{\mathrm{Mod}}_M({\mathcal{S}})\to{\mathcal{S}}$ is algebraic.
The main result of this section is , which provides necessary and sufficient conditions for a monadic functor to spaces to be algebraic. As preparation, we first collect the following result, a straightforward generalization of a well-known result in ordinary category theory.
\[prop:modpres\] Let ${\mathcal C}$ be a presentable $\infty$-category and let $M\colon{\mathcal C}\to{\mathcal C}$ be a monad which commutes with $\kappa$-filtered colimits for some infinite regular cardinal $\kappa$. Then ${\mathrm{Mod}}_M({\mathcal C})$ is a presentable $\infty$-category.
To begin with let us choose a regular cardinal $\kappa$ such that ${\mathcal C}$ is $\kappa$-compactly generated and $M$ commutes with $\kappa$-filtered colimits. Let ${\mathcal C}^\kappa\subseteq{\mathcal C}$ and ${\mathrm{Mod}}_M({\mathcal C})^\kappa\subseteq{\mathrm{Mod}}_M({\mathcal C})$ be the respective full subcategories spanned by the $\kappa$-compact objects. We claim that there is an equivalence ${\mathrm{Ind}}_\kappa({\mathrm{Mod}}_M({\mathcal C})^\kappa)\simeq {\mathrm{Mod}}_M({\mathcal C}).$ Since ${\mathrm{Mod}}_M({\mathcal C})$ admits $\kappa$-filtered colimits, the inclusion ${\mathrm{Mod}}_M({\mathcal C})^\kappa\subseteq{\mathrm{Mod}}_M({\mathcal C})$ induces a functor $$\phi\colon{\mathrm{Ind}}_\kappa({\mathrm{Mod}}_M({\mathcal C})^\kappa)\to {\mathrm{Mod}}_M({\mathcal C})$$ which we want to show is an equivalence. The fully faithfulness of $\phi$ is a special case of the following: if ${\mathcal D}$ be an $\infty$-category with $\kappa$-filtered colimits, then the inclusion ${\mathcal D}^\kappa\subseteq{\mathcal D}$ of the $\kappa$-compact objects induces a fully faithful functor ${\mathrm{Ind}}_\kappa({\mathcal D}^\kappa)\to{\mathcal D}.$ Thus it remains to show that $\phi$ is essentially surjective.
Because $M$ commutes with $\kappa$-filtered colimits, we see that, if $X\in{\mathcal C}^\kappa$, then $FX\in{\mathrm{Mod}}_M({\mathcal C})^\kappa$, where $F\colon{\mathcal C}\to{\mathrm{Mod}}_M({\mathcal C})$ denotes a left adjoint to the forgetful functor ${\mathrm{Mod}}_M({\mathcal C})\to{\mathcal C}.$ Since the forgetful functor ${\mathrm{Mod}}_M({\mathcal C})\to{\mathcal C}$ is conservative and ${\mathcal C}$ is $\kappa$-compactly generated, a map $f\colon A\to B$ of $M$-modules is an equivalence if and only if $${\mathrm{map}}_{{\mathrm{Mod}}_M({\mathcal C})}(FX,A)\to {\mathrm{map}}_{{\mathrm{Mod}}_M({\mathcal C})}(FX,B)$$ is an equivalence for all $X\in{\mathcal C}^\kappa$. We will apply this criterion to the map $$\colim_{A'\in{\mathrm{Mod}}_M({\mathcal C})^\kappa_{/A}} A'\to A\, ,$$ whose domain is a $\kappa$-filtered colimit, in order to obtain the essential surjectivity of $\phi$. We first show that, for any $X\in{\mathcal C}^\kappa$, the induced map $$\colim_{{\mathrm{Mod}}_M({\mathcal C})^\kappa_{/A}}\pi_0{\mathrm{map}}(FX,A')\to\pi_0{\mathrm{map}}(FX,A)$$ is an isomorphism. Indeed, it is surjective because any (homotopy class of) map $FX\to A$ is the image of the identity map $FX\to A'$ for $A'=FX$, which is by construction a $\kappa$-compact object of ${\mathrm{Mod}}_M({\mathcal C})$. Similarly, injectivity follows because given any two maps $f,g:FX\to A'$, the fact that ${\mathrm{Mod}}_M({\mathcal C})^\kappa_{/A}$ is $\kappa$-filtered implies that there exists an $A''\to A$ which coequalizes $f$ and $g$. Replacing $X$ by $K\otimes X$ for some finite simplicial set $K$, and noting that $K\otimes X$ is a $\kappa$-compact object of ${\mathcal C}$ since $K$ is finite, we obtain an isomorphism $$\pi_0{\mathrm{map}}(K,\colim{\mathrm{map}}(FX,A'))\cong\pi_0{\mathrm{map}}(K,{\mathrm{map}}(FX,A)).$$ It follows that $\colim{\mathrm{map}}(FX,A')\to{\mathrm{map}}(FX,A)$ is a homotopy equivalence, as desired.
\[algebraicity\] A monadic functor $U\colon{\mathrm{Mod}}_M({\mathcal{S}})\to{\mathcal{S}}$ is algebraic if and only if it preserves sifted colimits.
Since the forgetful functor ${\mathrm{Mod}}_{{\mathbb{T}}_M}({\mathcal{S}})\to{\mathcal{S}}$ preserves sifted colimits [(see )]{}, we see that this is a necessary condition. Thus, suppose that $U$ preserves sifted colimits; we must show that $R$ is an equivalence. Note that ${\mathrm{Mod}}_M({\mathcal{S}})$ is presentable by , and ${\mathrm{Mod}}_{{\mathbb{T}}_M}({\mathcal{S}})$ is presentable as an accessible localization of the presentable $\infty$-category ${\mathrm{Fun}}({\mathbb{T}},{\mathcal{S}})$. Because ${{\mathrm{Mod}}^\mathrm{ff}}_M({\mathcal{S}})\subseteq{\mathrm{Mod}}_M({\mathcal{S}})$ is a subcategory of compact projective objects, $R$ preserves sifted colimits, and clearly $R$ also preserves small limits. Thus $R$ admits a left adjoint $L$.
We now check that the adjunction counit $LR\to{\mathrm{id}}$ is an equivalence. Since $R$ is conservative, as both the projections down to ${\mathcal{S}}$ are conservative, this will also imply that the unit ${\mathrm{id}}\to RL$ is an equivalence. Observe that both functors commute with sifted colimits and spaces is freely generated under sifted colimits by the finite sets $\langle n\rangle$, it is enough to check the counit equivalence on objects of the form $F\langle n\rangle$. Now, $RF\langle n\rangle=\widehat{F}\langle n\rangle$, the functor represented by $\widehat{F}\langle n\rangle$, so we must show that we have an equivalence $L\widehat{F}\langle n\rangle\to F\langle n\rangle$. Let $A\in{\mathrm{Mod}}_M({\mathcal{S}})$ and consider the map $${\mathrm{map}}(F\langle n\rangle,A)\to{\mathrm{map}}(L\hat{F}\langle n\rangle,A)\, .$$ The left hand side can be identified with ${\mathrm{map}}(F\langle n\rangle,A)\simeq U(A)^n.$ Similarly, the right hand side is $${\mathrm{map}}(L\widehat{F}\langle n\rangle,A)\simeq{\mathrm{map}}(\widehat{F}\langle n\rangle,RA)\simeq{\mathrm{map}}(\widehat{F}\langle 1\rangle,RA)^n\simeq U(A)^n$$ where we used in the last step that $R$ is compatible with the forgetful functors to ${\mathcal{S}}$.
Finally, we wish to apply the results of this section to the study of semirings and rings in $\infty$-categories. We begin by showing that semirings and rings are algebraic over spaces.
The functors ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{S}}) \to {\mathcal{S}}$ and ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal{S}}) \to {\mathcal{S}}$ are monadic and algebraic over ${\mathcal{S}}$.
We claim that the functors ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{S}}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathcal{S}}$ and ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal{S}})\to{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to{\mathcal{S}}$ all preserve sifted colimits and reflect equivalences. Then the monadicity follows from the Barr-Beck theorem [@HA Theorem 6.2.2.5], and the algebraicity from .
To see that this claim is true note that three of the four functors, namely ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{S}}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}),$ ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\to{\mathcal{S}},$ and ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal{S}})\to {\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$, are forgetful functors from $\infty$-categories of algebras over an $\infty$-operad. These forgetful functors are always conservative and for suitable monoidal structures they also preserve sifted colimits [@HA Proposition 3.2.3.1]. Thus we only have to establish the same properties for ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathcal{S}}$. It is easy to see that this functor is conservative since ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ is a full subcategory of ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ and the given functor factors over the conservative functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})\to{\mathcal{S}}.$ It remains to show that ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal{S}})$ preserves sifted colimits. But for an ${\mathbb{E}}_\infty$-monoid in the $\infty$-category of spaces being a group object is equivalent to being grouplike. Thus, via the left adjoint functor $\pi_0$ it reduces to the statement that the sifted colimit of groups formed in the category of monoids is again a group. And this result is a special case of [@ARV Proposition 9.3].
We denote the algebraic theory corresponding to the functor ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal{S}}) \to {\mathcal{S}}$ by ${\mathbb{T}}_{{{\mathbb{E}}_n}\text{-}{\mathcal{R}\mathrm{ig}}}$ and call it the *theory of ${\mathbb{E}}_n$-semirings*. Accordingly we denote the algebraic theory corresponding to the functor ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal{S}}) \to {\mathcal{S}}$ by ${\mathbb{T}}_{{{\mathbb{E}}_n}\text{-}{\mathcal{R}\mathrm{ing}}}$ and call it the *theory of ${\mathbb{E}}_n$-rings*.
Let ${\mathcal C}$ be a cartesian closed, presentable $\infty$-category. Then we have equivalences $${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal C}) \simeq {\mathrm{Alg}}_{{\mathbb{T}}_{{{\mathbb{E}}_n}\text{-}{\mathcal{R}\mathrm{ig}}}}({\mathcal C}) \qquad \text{and} \qquad {\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal C}) \simeq {\mathrm{Alg}}_{{\mathbb{T}}_{{{\mathbb{E}}_n}\text{-}{\mathcal{R}\mathrm{ing}}}}({\mathcal C}).$$
For ${\mathcal C}= {\mathcal{S}}$ the $\infty$-category of spaces the statement is true by definition of ${\mathbb{T}}_{{{\mathbb{E}}_n}\text{-}{\mathcal{R}\mathrm{ig}}}$ and ${\mathbb{T}}_{{{\mathbb{E}}_n}\text{-}{\mathcal{R}\mathrm{ing}}}$. The general case follows from the base change formulas given in and .
1. Theories of ${\mathbb{E}}_\infty$-semirings and rings have also been constructed in [@cranch] by the use of spans and distributive laws. These two approaches do agree.
2. The theory approach of semirings and rings gives a way of defining ring objects in a much broader generality. One only needs an $\infty$-category ${\mathcal C}$ with finite products. In this way we can drop the assumption that ${\mathcal C}$ is presentable and cartesian closed. However in this case semiring and ring objects do not admit a nice description in terms of a tensor product on monoids. It is also impossible to apply this to different tensor products than the cartesian one.
3. We showed in that an accessible, product preserving functor $F\colon {\mathcal C}\to {\mathcal D}$ between cartesian closed symmetric monoidal categories extends to a lax symmetric monoidal functor ${\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal C}) \to {\mathrm{Mon}_{{\mathbb{E}_\infty}}\!}({\mathcal D})$. This means that $F$ extends to functors ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal C}) \to {\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal D})$ and ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal C})\to{\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal D})$. Therefore we may drop the assumption that $F$ is accessible and conclude that any product preserving functor ${\mathcal C}\to {\mathcal D}$ extends to functors ${\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal C}) \to {\mathcal{R}\mathrm{ig}}_{{\mathbb{E}}_n}({\mathcal D})$ and ${\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal C})\to{\mathcal{R}\mathrm{ing}}_{{\mathbb{E}}_n}({\mathcal D})$.
[^1]: Interestingly, we have equivalences ${\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}({\mathcal{C}\mathrm{at}}_n)\simeq{\mathrm{Grp}_{{\mathbb{E}_\infty}}\!}(\mathrm{Gpd}_{n})$ and ${\mathrm{Sp}}({\mathcal{C}\mathrm{at}}_n) \simeq {\mathrm{Sp}}(\mathrm{Gpd}_{n})$, and the latter is trivial unless $n = \infty$; more generally, ${\mathrm{Sp}}({\mathcal C})$ is trivial for any $n$-category ${\mathcal C}$ if $n$ is finite.
[^2]: But note that the $\infty$-category of modules for an ${\mathbb{E}}_n$-ring spectrum is only an ${\mathbb{E}}_{n-1}$-semiring $\infty$-category.
| 2024-07-03T01:26:35.434368 | https://example.com/article/9923 |
Paul has offered thoughts on the release of the U.S. sailors, all of which I agree with. I want to add a few further observations.
The day began with Joe Biden touting the president’s State of the Union speech on CBS. Near the end of his interview, he was asked about the seizure of American sailors by the Iranians (the sailors by then had been released) and specifically, whether there had been any apology by the U.S. He indignantly denied this suggestion:
Biden: The Iranians picked up both boats, as we have picked up Iranian boats that needed to be rescued….They released them, like ordinary nations would do. That’s the way nations should deal with one another. That’s why it’s important to have channels open. Interviewer: Did we apologize to the Iranians? Biden: No, there was no apology, there was nothing to apologize for. When you have a problem with the boat, do you apologize that the boat had a problem? And there was no looking for any apology. This was just standard nautical practice.
Here he is:
Then there was Secretary of State John Kerry, one of the great blowhards of world history, who praised the Iranians effusively, either unaware that Iran’s treatment of the captive sailors had violated international law, or indifferent to that fact.
Kerry: … I also want to thank the Iranian authorities for their cooperation and quick response. … I’m appreciative for the quick and appropriate response of the Iranian authorities. All indications suggest, tell us, that our sailors were well taken care of, provided with blankets and food [Ed.: and a headscarf] and assisted with their return to the fleet earlier today. And I think we can all imagine how a similar situation might have played out three or four years ago. In fact, it is clear that today, this kind of issue is able to be peacefully resolved, and officially resolved, and that is a testament to the critical role diplomacy plays in keeping out country safe, secure and strong.
In other words: we owe this humiliation to the Iran nuclear deal! Here is Kerry:
Of course, Biden and Kerry were both wrong. There was an apology, and Iran didn’t respond “appropriately,” but rather violated international law by forcing one of the sailors to “confess,” by filming the servicemen and woman in humiliating positions, and by forcing the lone woman in the crew to comply with Sharia law.
Here is the apology that the Iranians filmed and broadcast to the world, trumpeting their victory over the pathetic, weak United States of America:
Iran’s government-controlled press viewed the incident in quite a different light from the Biden/Kerry “nothing to see here” evasion. FARS News was triumphant:
In its statement, the [Islamic Revolution Guards Corps] pointed out that its investigations show that the US combat vessels’ illegal entry into the Iranian waters was not the result of a purposeful act. “Following technical and operational investigations and in interaction with relevant political and national security bodies of the country and after it became clear that the US combat vessels’ illegal entry into the Islamic Republic of Iran’s waters was the result of an unintentional action and a mistake and after they extended an apology, the decision was made to release them,” the statement said. “The Americans have undertaken not to repeat such mistakes,” it added, and continued, “The captured marines were released in international waters under the supervision of the IRGC Navy moments ago.”
***
Following the capture, two US and French aircraft carriers as well as their accompanying fleets and military choppers started maneuvering near Iranian waters. The IRGC statement blamed the US flotilla for its “excited and unprofessional moves”, but said the IRGC navy could handle the situation and restored calm to the region through powerful and wise moves. Senior US officials, including Secretary of State John Kerry, were in contact with their Iranian counterparts on the fate of the marines since Tuesday, and according to Iranian officials, Foreign Minister Mohammad Javad Zarif had told Kerry that the US should extend a formal apology first. According to the statement, the Americans have extended an apology.
It is sad: throughout the nuclear negotiations, Iran’s government gave a more truthful account of what was going on than the Obama administration. That appears to be the case with regard to the seizure of American sailors, as well.
UPDATE: The Daily Mail is no one’s idea of an intellectual web site, but they know humiliation when they see it. Click to enlarge: | 2023-10-17T01:26:35.434368 | https://example.com/article/2731 |
Bone marrow niche in the myelodysplastic syndromes.
The myelodysplastic syndromes (MDS) are a diverse group of clonal hematopoietic malignancies characterized by ineffective hematopoiesis, progressive bone marrow (BM) failure, cytogenetic and molecular abnormalities, and variable risk of progression to acute myeloid leukemia (AML). The BM microenvironment in MDS plays an important role in the development of this disorder. The BM stromal cells of MDS patients often harbor distinct chromosomal aberrations than the hematopoietic elements, suggesting different genetic origins. Perturbed cytokine secretions from BM stromal cells such as multipotent mesenchymal stem cells (MSCs) and endothelial cells are associated with increased proliferation and survival of malignant hematopoietic cells. Within the MDS BM there are also alterations in stromal cell composition, signaling and angiogenesis between Low- and High-risk MDS patients. Several open lines of investigation into the MDS niche remain, including the timing of stromal defects in context to dysplastic hematopoiesis. Another important, unanswered question is the impact of age on BM stroma function and regulation (or dysregulation) or hematopoietic stem/progenitor cells. With a better understanding of the MDS niche, new therapeutic strategies will emerge. | 2024-05-30T01:26:35.434368 | https://example.com/article/8596 |
111 N.W.2d 289 (1961)
STATE of Iowa, Appellee,
v.
Emil SCHLAK, Appellant.
No. 50369.
Supreme Court of Iowa.
October 17, 1961.
*290 Joseph L. Phelan, Fort Madison, for appellant.
Evan Hultman, Atty. Gen., John H. Allen, Asst. Atty. Gen., and R. N. Johnson, County Atty., Lee County, for appellee.
THORNTON, Justice.
The defendant was convicted of committing a lewd act upon the body of a female child under 16 years of age, he being over 18 years of age, contrary to section 725.2, Code of Iowa 1958, I.C.A.
The sole error relied on for reversal is the admitting in evidence of prior distinct and independent offenses of a similar nature upon persons other than the prosecuting witness. The names of the witnesses and the substance of their testimony relating to the distinct offenses of a similar nature were attached to the indictment. The defendant raised the question by motion before trial. During the trial defendant objected to the evidence because it showed another crime and it was too remote as to time and place. The trial court in its instruction limited the consideration of the evidence of similar offenses to show the act charged was intentional rather than accidental, or to show motive, or to establish identity.
The prosecuting witness testified she was 15 years old and lived in Keokuk, on September 18, 1960, at about 4:00 p. m. she was walking north on 14th Street in the city of Keokuk in the vicinity of a junior high school accompanied by a schoolmate of the same age when the defendant drove by in his car and waved, he stopped his car across the street, walked over into their path, spoke to the girls and as the prosecuting witness started to walk by him he put his arm around her waist, released her as a car went by, put his arm around her waist a second time and put his other hand on her breast, he squeezed and had a good grip on her breast for a few seconds. The girl struggled and got away from him, she ran to a nearby house. Defendant ran to his car and left at a fast speed. The girls got the license number of the car. The police were called. Later on the same day the girls identified defendant at the police station. The girl friend's testimony was to a like effect.
The first similar offense testified to was related by two girls 14 years old and to some extent by a lady living in the home in front of which this occurrence took place. The testimony is while these two girls were walking along 12th Street in Fort Madison on their way home from a show at about 9:00 p. m. on April 29, 1960, defendant drove up near them, got out of his car, greeted the girls, started to walk along with them and then put his arm around one of the girls, the girls told him they didn't want him there and to get in his car, he kept walking with them, one girl hit him in the forehead with her purse, he backed away and asked, "Well, what's wrong?", he backed away to his car and the girls ran to *291 the lady's front porch. The two girls and lady were able to get the license number of the car as he drove around the block and past the house a second time. Both girls identified defendant as the man who accosted them, one testified to his license number as did the lady
The second similar offense was testified to by a young girl, 14 years old at the time of the trial and nine at the time of the alleged offense. The offense occurred in September of 1955 on State Highway 16 about two miles from Denmark, Iowa. The girl was riding her bicycle from a driveway onto the highway, a car was parked there, the man in it spoke to her, she rode over to the car, the man got out of the car, he started to say something, he grabbed for her and she screamed. She then testified, "and he sort of jumped back like he thought, `Well, what did you scream for?'" She further testified he grabbed her off the bike, he reached for her and tried to pull her pants down. She screamed and hit him. When a car came along he got in his car and drove off. The sheriff was called, later the same week the sheriff brought the man, evidently to the girl's home, and she identified him. And she testified the man was in court and was the defendant.
I. The state concedes the general rule that one crime cannot be proved by proof of another, but contends the evidence here is admissible as one of the exceptions to the general rule and urges as stated in State v. Vance, 119 Iowa 685, 687, 94 N.W. 204:
"Evidence as to other offenses is competent to establish (1) motive, (2) intent, (3) absence of mistake or accident, (4) a common scheme embracing the commission of two or more crimes so related to each other that proof of one tends to prove the others, and (5) the identity of the person charged with the commission of the crime on trial."
This is the rule in other crimes as well as sex crimes. State v. Linzmeyer, 248 Iowa 31, 79 N.W.2d 206. The question of admissibility of such evidence is, is it material and relevant, does it tend to prove the particular offense or an essential element thereof? State v. Linzmeyer, supra, and State v. Triplett, 248 Iowa 339, 79 N.W.2d 391.
II. In prosecutions under section 725.2 this court held in State v. Marvin, 197 Iowa 443, 197 N.W. 315; State v. Weaver, 182 Iowa 921, 166 N.W. 379; and State v. Kinkade, 241 Iowa 1259, 43 N.W.2d 736, intent may be inferred from the nature of the act itself and that proof of separate distinct acts of similar nature is unnecessary. In Marvin and Weaver showing similar acts with others than the prosecuting witness was held reversible error. In Kinkade the testimony showed a number of similar acts with the same child over a short space of time. The state was required to elect which offense it relied on. This court held it was not error to allow the jury to consider the other acts as tending to show the lascivious lewd disposition of the defendant. See also State v. Neubauer, 145 Iowa 337, 345, 124 N.W. 312, 316. In State v. Leuty, 247 Iowa 251, 73 N.W.2d 64, a prosecution for incest, we held attempts to show other similar acts with another person required a reversal because the defendant did not have a fair and impartial trial.
III. The similar acts shown here are not admissible to show intent. This is clear from the act done. However, the motive, the desire to gratify his lustful desire by grabbing or fondling young girls is shown. And the other similar acts with other girls is admissible for that purpose, see State v. Knox, 236 Iowa 499, 18 N.W.2d 716, as well as to show the identity of the accused. Evidence that the same man had on prior occasions accosted young girls where they were likely to be (this refers to the alleged offense in April, 1960) coupled with the license number tends to refute his claim he was not there. See Annotation 77 A.L.R.2d 841, and Annotation 167 A.L.R. 565.
*292 IV. Both the April, 1960, and the September, 1955, offenses are admissible to show the lewd disposition and identity of defendant if they are not too remote in time and place. We hold they are not too remote as to place. The home of defendant is Fort Madison, the site of the April, 1960, offense. Keokuk is the site of the crime charged, these cities are 25 miles apart. The September, 1955, offense occurred near Denmark, nine miles north of Fort Madison. The area within which the alleged offenses occurred is not more than 35 miles. Today it cannot be said 35 miles is remote.
V. The question as to time is different. Three and a half months elapsed between the April, 1960, offense and the crime charged. Courts generally hold where the similar act does show disposition and identity such a length of time is not too remote. Annotation 77 A.L.R.2d 841. And depending upon the circumstances shown in the evidence remoteness in time is committed to the discretion of the trial court, and the length of time affects the weight rather than the admissibility. 22A C.J.S. Criminal Law § 683, p. 744. However, there is a point beyond which such remoteness may not go. We have examined the cases cited by the state together with the cases cited in the annotations in 77 A. L.R.2d 841 and 167 A.L.R. 565 and we do not find a lascivious acts case, or a case involving a similar sexual offense where testimony of a similar offense with a person other than the prosecuting witness occurring five years before the crime charged has been held admissible. Materiality and relevancy tend to lessen as the length of time increases and the prejudice to the defendant becomes greater. This is particularly true where the disposition and identity of defendant are in issue. Both may change. Further the burden of defending against such a remote charge is increased to the prejudice of the defendant. Its tendency to inflame and prejudice the jury outweighs its evidentiary value. State v. Nicks, 134 Mont. 341, 332 P.2d 904, 77 A.L.R.2d 836, and Annotation 77 A.L.R.2d 841.
The evidence of the similar offense with a person other than the prosecuting witness during September, 1955, was inadmissible because it was too remote in time. The judgment is reversed and the case remanded for a new trial.
Reversed and remanded.
GARFIELD, C. J., and OLIVER, HAYS, THOMPSON and PETERSON, JJ., concur.
LARSON and SNELL, JJ., dissent.
BLISS, J., not sitting.
| 2023-12-28T01:26:35.434368 | https://example.com/article/7822 |
[Irreversible pH-denaturation of tissue thromboplastin].
Irreversible denaturation of tissue thromboplastin from human brain occurred at pH values below 5.0 and above 11.0. Coagulating activity of total phospholipid fraction of thromboplastin was decreased after incubation in acid or alkaline media. | 2024-01-28T01:26:35.434368 | https://example.com/article/1979 |
Damage stemming from Australia's climate policy standoff is an "important" issue that should be better addressed, Environment Minister Greg Hunt says, amid fears that toxic politics around emissions cuts is unsettling investors and hurting the economy.
However, common ground was in short supply when Mr Hunt met Labor environment spokesman Mark Butler at the National Press Club in Canberra on Wednesday, in a pre-election debate dominated by disagreement over the best way to address global warming, and suggestions that Prime Minister Malcolm Turnbull will remain beholden to his party's Abbott-aligned climate sceptics if returned to power.
Mr Butler said the federal government's abolition of Labor's so-called carbon tax had "smashed to pieces" Australia's chances of capitalising on jobs and investment in renewable energy after the successful global climate deal in Paris last year.
The change had also allowed carbon pollution levels from electricity to rise by more than 5 per cent in less than two years and "Australia is now pretty much the only major advanced economy where pollution levels are going up, not coming down", he said. | 2024-06-04T01:26:35.434368 | https://example.com/article/2267 |
Q:
jsf: Calling a method in managedbean giving exception
When I am trying to access the login method of my managed bean by following code in my xhtml:
<p:commandButton value="Login" update="growl"
actionListener="#{loginView.login}"/>
my LoginView class looks like this:
@Component
@ManagedBean(name="loginView",eager=true)
@SessionScoped
public class LoginView {
@Autowired
LoginService loginServiceImpl;
Student student=loginServiceImpl.login(username, password);
public void login(ActionEvent event) {
RequestContext context = RequestContext.getCurrentInstance();
FacesMessage message = null;
boolean loggedIn = false;
if(username != null && student!=null && password != null ) {
loggedIn=True;
try {
FacesContext.getCurrentInstance()
.getExternalContext()
.redirect(location);
} catch (IOException e) {
e.printStackTrace();
}
}
}
when I am calling pressing the button its giving me the following error:
javax.el.ELException: /login1.xhtml @105,62 actionListener="#{loginView.login}": java.lang.NullPointerException
at com.sun.faces.facelets.el.TagMethodExpression.invoke(TagMethodExpression.java:111)
at javax.faces.event.MethodExpressionActionListener.processAction(MethodExpressionActionListener.java:147)
at javax.faces.event.ActionEvent.processListener(ActionEvent.java:88)
at javax.faces.component.UIComponentBase.broadcast(UIComponentBase.java:818)
at javax.faces.component.UICommand.broadcast(UICommand.java:300)
at javax.faces.component.UIViewRoot.broadcastEvents(UIViewRoot.java:790)
at javax.faces.component.UIViewRoot.processApplication(UIViewRoot.java:1282)
at com.sun.faces.lifecycle.InvokeApplicationPhase.execute(InvokeApplicationPhase.java:81)
at com.sun.faces.lifecycle.Phase.doPhase(Phase.java:101)
at com.sun.faces.lifecycle.LifecycleImpl.execute(LifecycleImpl.java:198)
at javax.faces.webapp.FacesServlet.service(FacesServlet.java:646)
at org.apache.catalina.core.ApplicationFilterChain.internalDoFilter(ApplicationFilterChain.java:305)
at org.apache.catalina.core.ApplicationFilterChain.doFilter(ApplicationFilterChain.java:210)
at org.apache.catalina.core.StandardWrapperValve.invoke(StandardWrapperValve.java:222)
at org.apache.catalina.core.StandardContextValve.invoke(StandardContextValve.java:123)
at org.apache.catalina.authenticator.AuthenticatorBase.invoke(AuthenticatorBase.java:472)
at org.apache.catalina.core.StandardHostValve.invoke(StandardHostValve.java:171)
at org.apache.catalina.valves.ErrorReportValve.invoke(ErrorReportValve.java:99)
at org.apache.catalina.valves.AccessLogValve.invoke(AccessLogValve.java:953)
at org.apache.catalina.core.StandardEngineValve.invoke(StandardEngineValve.java:118)
at org.apache.catalina.connector.CoyoteAdapter.service(CoyoteAdapter.java:408)
at org.apache.coyote.http11.AbstractHttp11Processor.process(AbstractHttp11Processor.java:1008)
at org.apache.coyote.AbstractProtocol$AbstractConnectionHandler.process(AbstractProtocol.java:589)
at org.apache.tomcat.util.net.JIoEndpoint$SocketProcessor.run(JIoEndpoint.java:312)
at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
at java.lang.Thread.run(Unknown Source)
Caused by: java.lang.NullPointerException
at org.primefaces.showcase.view.menu.LoginView.login(LoginView.java:62)
at sun.reflect.NativeMethodAccessorImpl.invoke0(Native Method)
at sun.reflect.NativeMethodAccessorImpl.invoke(Unknown Source)
at sun.reflect.DelegatingMethodAccessorImpl.invoke(Unknown Source)
at java.lang.reflect.Method.invoke(Unknown Source)
at org.apache.el.parser.AstValue.invoke(AstValue.java:278)
at org.apache.el.MethodExpressionImpl.invoke(MethodExpressionImpl.java:274)
at com.sun.faces.facelets.el.TagMethodExpression.invoke(TagMethodExpression.java:105)
... 26 more
Strangely, When I am commenting the line
Student student=loginServiceImpl.login(username, password);
The code is working fine. I want my bean to be both, Spring based as I want to autowire loginServiceImpl and jsf based as I want to call my method. If It's not possible, what approach should I chose.
A:
You cannot inject a Spring bean by using @Autowired inside JSF managed bean.
You should change to
@ManagedProperty(value="#{something}")
private LoginService loginServiceImpl; // getter and setter.
See also:
Null pointer when autowiring the bean into JSF Managed bean
| 2024-04-19T01:26:35.434368 | https://example.com/article/4978 |
Dominic Raab and Andrea Leadsom have joined the race to become the next prime minister after Theresa May announced her resignation on Friday.
The former Brexit secretary and ex-Commons leader became the latest to announce their bids for the Tory leadership, joining foreign secretary Jeremy Hunt, international development secretary Rory Stewart, health secretary Matt Hancock, former foreign secretary Boris Johnson, and former work and pensions secretary Esther McVey.
Setting out their stalls, both Mr Raab and Ms Leadsom said they would be prepared to order a no-deal Brexit in October if necessary.
Their entry came as the battle for No 10 started to turn bitter as international development secretary Rory Stewart launched a strongly-worded attack on front-runner Boris Johnson, comparing the former foreign secretary to Pinocchio.
Meanwhile, Matt Hancock said he was running for leader because the party needed to look to the future and attract younger votes, while international trade secretary Liam Fox refused to rule himself out as a candidate.
Who could succeed Theresa May as Conservative leader? Show all 9 1 /9 Who could succeed Theresa May as Conservative leader? Who could succeed Theresa May as Conservative leader? Boris Johnson Former foreign secretary Boris Johnson has long been hopeful, he previously stood in the leadership contest that followed the Brexit vote and has at many times since been thought to be maneuvering himself towards the goal. He remains a darling of the party's right wing, particularly those in the ERG, and is the most popular choice among Tory voters but his leadership bid would be fiercely opposed by many MPs PA Who could succeed Theresa May as Conservative leader? Michael Gove Environment secretary Michael Gove is another member who has long wanted to be leader. He has lately been known for rousing his party in the commons, his recent speeches on the Brexit deal and Labour's no confidence motion have overshadowed the Prime Minister's. He has been loyal to the Prime Minister, partly to shed his reputation as a backstabber who abandoned Boris Johnson to stand against him in the 2016 leadership election Getty Who could succeed Theresa May as Conservative leader? Dominic Raab Former Brexit secretary Dominic Raab has emerged as a favourite to be the Brexiteer candidate in a contest to succeed to Ms May. He displayed a grip on detail in his role as Brexit secretary. When asked recently if he would like to become prime minister he replied "never say never" Getty Who could succeed Theresa May as Conservative leader? Rory Stewart International development secretary Rory Stewart is pitching himself as the sensible candidate, promising to rule out both a second referendum and a no-deal Brexit. He was only recently promoted to the cabinet, previously serving as prisons minister, where he caught headlines with a pledge to resign if he could not reduce levels of violence within a year PA Who could succeed Theresa May as Conservative leader? Esther McVey The former work and pensions secretary announced that she will be standing for the leadership when May leaves. McVey is the first to explicitly state that she intends to stand. She resigned from the cabinet in protest over May's Brexit deal AFP/Getty Who could succeed Theresa May as Conservative leader? Sajid Javid Home secretary Sajid Javid is said to have a plan in place for a leadership race. He made headlines over Christmas when he declared that people smuggling over the English channel was a "major incident" and more recently when he revoked the citizenship of ISIS bride Shamima Begum. Son of a bus driver, he wants the Conservatives to be seen as the party of social mobility PA Who could succeed Theresa May as Conservative leader? Jeremy Hunt Foreign secretary Jeremy Hunt was recently thought to be the favourite in the event of a leadership race as he could sell himself as the man to unite the party. Critics worry that his long stint as health secretary could return to haunt him at a general election. He has reportedly been holding meetings with Tory MPs over breakfast to promote his leadership PA Who could succeed Theresa May as Conservative leader? Andrea Leadsom Following the Prime Minister's second defeat over her Brexit deal, Leader of the house Andrea Leadsom hosted a dinner party at which "leadership was the only topic of conversation", The Times heard. Leadsom ran against Theresa May in the 2016 leadership election before dropping out, allowing May to become Prime Minister AFP/Getty Who could succeed Theresa May as Conservative leader? Priti Patel Former international development secretary Priti Patel is thought to be positioning herself as a contender. One MP told The Independent "she knows she's from the right of the party, the part which is going to choose the next leader, so she's reminding everyone she's there." Patel left the government late in 2017 after it emerged that she had held undisclosed meetings with Israeli officials PA
Mr Hunt told the Sunday Times: “If I was prime minister, I’d be the first prime minister in living memory who has been an entrepreneur by background.
“Doing deals is my bread and butter as someone who has set up their own business.”
Mr Hunt’s emphasis on his entrepreneurial past is being seen as swipe at Mr Johnson who reportedly once said “f*** business” in relation to Brexit.
In a reference to Brexit by way of mythical sea monsters, Mr Hunt said. “The real question is: who has got the experience to avoid the Scylla and Charybdis of no-deal or no Brexit. I’ve got very important experience in that respect.
“We can never take no-deal off the table but the best way of avoiding it is to make sure you have someone who is capable of negotiating a deal.”
Jeremy Corbyn talks about Theresa May's resignation and calls for a general election
Mr Raab told the Mail on Sunday he would prefer to leave the EU with a deal, but said the UK must “calmly demonstrate unflinching resolve to leave in October – at the latest”.
The MP for Esher and Walton, who resigned over Ms May’s Withdrawal Agreement, said: “The country now feels stuck in the mud, humiliated by Brussels and incapable of finding a way forward.
“The prime minister has announced her resignation. It’s time for a new direction.”
Michel Barnier's response to Theresa May's resignation
Ms Leadsom, whose resignation helped trigger Ms May’s dramatic resignation statement, told the Sunday Times if she was elected PM, the UK would quit the EU in October with or without a deal.
She said: “To succeed in a negotiation you have to be prepared to walk away.”
Ms Leadsom added that she would introduce a citizens’ rights bill to resolve uncertainty facing EU nationals, then seek agreement in other areas where consensus already exists, such as on reciprocal healthcare and Gibraltar.
David Cameron expresses sympathy for Theresa May
Environment secretary Michael Gove is also preparing to launch a leadership bid as a self-styled ‘unity candidate’, according to the Sunday Telegraph.
Mr Stewart, the international development secretary, launched a scathing attack on Mr Johnson’s no deal stance, insisting such a position was ”damaging and dishonest”.
He told the BBC: “I could not serve in a government whose policy was to push this country into a no-deal Brexit.
“I could not serve with Boris Johnson.”
Trump says he 'feels badly' for Theresa May following her resignation
In what is likely to be seen by many as a dig at Mr Johnson, the Mr Stewart tweeted: “The star name will not always be the best choice.
“There may be times when Jiminy Cricket would make a better leader than Pinocchio.”
Mr Hancock, the health secretary, said he would take a different approach to try and get Commons support for a Brexit deal than the one Theresa May used.
He said: “She didn’t start by levelling with people about the trade-offs.
“I think it is much, much easier to bring people together behind a proposal if you are straightforward in advance.”
Politicians reacts to Theresa May's resignation
Asked if Labour would force a Commons no confidence vote in the new prime minister when they take office, shadow chancellor John McDonnell told the Today programme: “Yes. Because we believe any incoming prime minister in these circumstance should go to the country anyway and seek a mandate.”
The new Tory leader will likely take over as prime minister at the end of July. | 2024-04-25T01:26:35.434368 | https://example.com/article/6991 |
Author: Birgitte Katerine Boye
Birgitte was born on March 7, 1742, in Gentofte, Denmark. She was the daughter of Jens Johansen. Boye married a supreme court judge in Copenhagen, Denmark. She found time to study German, French and English and translated hymns into Danish from these languages. As a hymnist, she was involved with Guldbergs og Harboes Psalmebog (Ove Guldberg’s and Ludvig Harboe’s Psalter), to which she contributed 146 hymns. She also produced "national dramatic writing." She died on October 17, 1824.
Sources: Julian, p. 1001 & Stulken, p. 145
Go to person page > | 2024-06-19T01:26:35.434368 | https://example.com/article/3168 |
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Aquarium Automation: The Theiling Rollermat and Other Web-Filtering Technologies
Home / Equipment / Aquarium Automation: The Theiling Rollermat and Other Web-Filtering Technologies
The problem: For the longest time, I have been trying to lengthen the maintenance interval for the filter socks on my 450-gallon system, which currently clog every two days. I tried eliminating filter socks completely for a period of time, but the sump got extremely messy and turned into a nitrate bank. The next option was to try 200-micron-mesh socks, which did help extend the replacement period, but they did not polish the water as well and eventually still clogged over a period of time. The solution: Following my mantra to automate my system as much as possible, I looked into the Theiling Rollermat. It works by collecting overflow water that is gravity fed into the chamber and forcing it through the fleece to exit the sump, which is located in the center of the rolling web cage. After reviewing the specifications and checking the experiences of others who adopted it a year earlier, I believed this was the next step. The Theiling Rollermat initially comes with a shorter roll than the normal replacement 6” wide x 147’ long filter fleece roll MORE
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Saltwater Smarts
Saltwater Smarts is a unique online resource created by long-time aquarists Chris Aldrich and Jeff Kurtz to inspire and entertain a new generation of marine aquarium hobbyists while helping them acquire the reliable, authoritative knowledge base they need to succeed with a saltwater system. By clarifying key concepts, techniques, and terminology, as well as sharing expert insights from fellow enthusiasts and industry professionals, Chris and Jeff hope to promote a more accessible, sustainable, and enjoyable marine aquarium hobby. Read more about our mission and the contributors who are part of our team. | 2024-02-13T01:26:35.434368 | https://example.com/article/9282 |
Just moments ago 8 in-game images of Maya surfaced. Thanks to All Games Beta for acquiring these and posting them online!
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“Michele Leonhart, the head of the Drug Enforcement Administration, has a message for those considering legalizing marijuana: Please, think of Fido.
Testifying on the DEA budget during a House Appropriations subcommittee hearing on Wednesday, Leonhart said she expected a number of things to happen after Washington and Colorado were allowed to go forward with the legalization of marijuana last year. What she didn’t anticipate was the impact on man’s best friend.
“There was just an article last week, and it was on pets. It was about the unanticipated or unexpected consequences of this, and how veterinarians now are seeing dogs come in, their pets come in, and being treated because they’ve been exposed to marijuana,” Leonhart said.”
Read more: http://www.huffingtonpost.com/2014/04/02/dogs-marijuana-pets_n_5078556.html
Cenk Uygur, Michael Shure, Ana Kasparian and John Iadarola of The Young Turks discuss the DEA head’s insane comments. | 2023-09-23T01:26:35.434368 | https://example.com/article/2978 |
Earlier this week the reviews started coming in and they were middling at best. Empire gave it three stars and IGN gave it 6.8. I didn’t actually read those reviews, but my own predictions were that the film was going to be polarising. I thought that Affleck was going to be good as Batman but Superman was going to be mishandled again, that the film was going to be way too cluttered and it was ultimately going to make loads of money but it wasn’t going to be that good. Well, I can tell you here folks that those critics were wrong!
Yes, they were being too generous with three stars. Batman v Superman: Dawn of Justice is an abysmal film. And it disappoints me because I wanted it to be good, I wanted to believe that Snyder could improve on Man of Steel and deliver with this epic. But the sad thing is I’m not even surprised. It was two and a half hours of empty moralising, pretentious speeches, and ultimately felt like a child playing with toys. So there’s lots to talk about here.
It begins in the most unoriginal way possible with the death of Batman’s parents. Oh yes, that again. Then there’s a hamfisted dream sequence (not the last one of the film), then the basic theme of the film is introduced. Can Superman be trusted? Should he be allowed to act unilaterally? Bruce Wayne saw the destruction of Metropolis firsthand and believes that he needs to take action to stop him, because, if he wanted, Superman could destroy the world easily. Once he finds out that Lexcorp has found some Kryptonite, he gets an idea. But the whole notion that people still mistrust Superman…the film is set 18-24 months after Man of Steel, didn’t this come up in that time? Superman is once again brooding, I mean, from what I can recall he maybe smiled once in the whole film? It just shows a fundamental misunderstanding of the character. Snyder shoots his scenes in a way that depicts Superman as a being so far away from humanity, and it reflects the way Luthor thinks of Superman. People always say that Superman is difficult to write because he’s too powerful but that just shows a lack of imagination. They’re forgetting the man.
The bit that got me most mad was when Superman uttered the line, “No man stays good in this world,” and if you’re reading this and you don’t have a problem with that then that’s fine, you might actually get some enjoyment out of the film. I get that some people think that Superman should reflect the state of our culture now, and the sad fact of the matter is that the world is cynical and ridden with angst, but I dismiss the notion that Superman should be a reflection of us. Superman should represent the best of us. The kindness, the compassion, the striving to always do what’s good, to be truthful, to be a hero. Contrast this film’s Superman with the current Supergirl on the tv show of the same name. In a recent episode there was a scene where a little girl, wearing a Supergirl costume, was being picked on by some older kids. Supergirl heard this, swooped down, and acted like she was this girl’s friend. I just can’t see Cavill’s Superman doing that.
Affleck makes a good Batman I think his solo film is going to be really good, especially if he’s directing it. But even Batman isn’t handled perfectly. There are vague dream sequences/ hallucinations that are crammed into the film to set up the sequel, but feel shoehorned in, much like the Thor cave scenes in Age of Ultron, and it simply makes the film more of a mess. Batman though, it was an okay depiction of the character until he flies in the Batplane and kills a load of people in a hail of bullets. By that point I was just laughing at how stupid this all was. And it feels vacuous as well, everything in the film happens so quickly and so arbitrarily that it lacks any kind of emotional impact. The much-vaunted fight between the two titular characters is okay. I liked how Batman made up some traps, but again is was basically ‘Batman is amazing. Superman…ehh’ and the switch to when they form a truce is absolutely ridiculous. There was no organic flow, it was just people doing things because the plot demanded it.
Oh yes, Lex Luthor is a perfect example of this. He’s basically a plot device. And you know how people were saying that there’s more to the character than what we saw in the trailer? Nope. I was hoping that the kinda-crazy was all going to be an act, that it was going to be the mask he wore in front of everyone but no he was just insane. Lois wasn’t much better either. And this is what makes me really mad, the film trades on Superman’s history. In the film his relationship and love for Lois is said to be important but we hardly see them together. It trades on this history but it doesn’t respect it and Snyder doesn’t understand why Superman is such an enduring figure. Could they not have got some Superman writer to consult on the film?
Wonder Woman is probably the best thing about the film (either her or Perry White) and that’s most likely because she’s not in it enough for her character to be ruined. The conflict with Doomsday is empty, again, there’s no emotion to the battle. In Avengers the heroes were fighting a CGI army but at least there was Loki to give some context to the battle. This was, again, just a kid playing with action figures. But I get the feeling that Snyder probably thinks he’s made a grand, deep, profound film when instead the philosophy presented is shallow.
There are a couple of iconic shots lifted from comics that were kinda cool to see on the big screen, but the few things this film does right are let down by the rest of it. I mentioned Superman’s brooding earlier and I get that sometimes people are filled with a bit of doubt, but his brooding is never contrasted with him being optimistic or hopeful. We never get to see Superman actually look like he’s enjoying what he’s doing, like being the hero to earth is a burden. And the most damning fact of all for the film is this. A Civil War trailer played before this, the first one, the one I’ve seen probably 5 or 6 times now. Yet in those few seconds where Cap says “Bucky’s my friend,” and Tony replies with, “So was I,” I felt more emotion than I did in the entirety of the two and a half hours of Batman v Superman.
The film strives for an emotional ending but it feels unearned due to a misunderstanding of the characters and a rushed story. Disappointing, not surprising.
…Yeah I’m not going to give my usual plot overview. I’m going to keep this as spoiler-free as possible.
Obviously The Force Awakens has a lot of hype and a lot of weight surrounding it. So many things could have gone wrong. It has to introduce new characters while including the old, and try to recapture the magic of the original trilogy without seeming clichéd. I was concerned that it would be derivative and that it would basically be a highlights reel of ‘things we loved in Star Wars,’ and while it’s not a flawless film it is a fun film, and the energy of the original trilogy is back.
The main strength of the film lies with the characters. Rey (Ridley) and Finn (Boyega) are a good team, and Rey especially is a badass. I liked both their arcs, and both were sympathetic characters. The opening scene that introduces us to Finn and gets the plot moving is engaging and instantly creates a bond to the character. Rey’s introduction is more sedate, but through the film she shows herself to be a strong-willed character, and there are hints to her backstory that are intriguing. Po (Isaac) made an impact on me even though I was surprised at how little he was in the film. I look forward to seeing more of him.
With how good these new characters are, it meant that I wasn’t simply waiting for the cast of the original trilogy to show up. I of course wanted to see them and was excited when they finally appeared, but I was never getting bored of Finn and Rey (or BB-8, who was a completely endearing character). Kylo Ren is a menacing bad guy, and the film manages to give him a compelling and tragic backstory in about 10 seconds, and the prequels couldn’t do that with Anakin in three movies!
However, not all the character work is good, and here I must mention Christie as Captain Phasma. There was literally no point to her character. She could have been any generic stormtrooper and it wouldn’t have changed the film at all.
Shall we get to some more negative things? Sure!
While The Force Awakens isn’t just a highlight reel, it does follow the same template as A New Hope so the plot beats are predictable, and while there were a couple of moments that surprised me it’s the kind of film where you can see how things are going to play out fairly early on. There’s some wonky science, which doesn’t bother me so much because I’ve always seen Star Wars as space fantasy, and I’m willing to give a lot of poetic license, but some people may be bothered by that. I was a little disappointed with Jakku because it was basically Tatooine by any other name, and I’d rather there be new environments (say what you will about the prequels but there were some cool planets in there).
Another little thing was a moment with R2 but that’s all I’ll say there…
And the big thing is that the film went bigger instead of going deeper, and yeah Star Wars is bombastic and over the top etc but it just feels like it has to top the other films instead of taking a different angle, and it verges on the ridiculous.
The other big disappointment were the lightsaber duels. They lacked the gravitas of the ones from the original trilogy, and the frenetic choreography of the prequels, so there’s definitely room for improvement there.
I was also hoping that the situation would be reversed and that the Republic would be the expansive galactic force, while the remains of the Empire were a small band trying to reclaim their glory, but there wasn’t much time given to developing the new state of the galaxy (which I can forgive to some extent because the prequels were bogged down by the political state of the Republic, but I’d still like to know how the First Order were allowed to become as powerful as they were).
I did like the exploration of the force and how the light side and dark side oppose each other, and there’s always a tug of war between the two, and the Awakens aspect of the film was done well. There are also seeds planted for the next film in this new trilogy and the other thing I really really REALLY hate about the film is the ending because I just want to see the next one right now!
While I have my complaints (some of which I didn’t go into here because of spoilers) The Force Awakens is a really fun movie. It retains the visual appeal and includes frenetic space battles, but it also has great character work, on a par with that seen in The Empire Strikes Back. It would have been easy for the film to be underwhelming, or to not strike the right balance between the old and the new, but it manages to pull it off and for the most part I was sitting there with a big grin on my face. It was always going to be one of the biggest films of the year, but it’s also one of the best. | 2023-08-31T01:26:35.434368 | https://example.com/article/4253 |
Q:
Do most Wordpress users have output_buffering On?
My question is in relation to the answer to my other question seen here - now most developers and designers who work with the php back end and the guts of the code will have this turned on or should....I think
But does the average user, using my theme, or any other theme on WordPress have this turned on? do most private or shared hosting services have this turned on?
A:
It is. its set to a value, and because of that - it means its on. with out it I think there would be issues
| 2024-07-23T01:26:35.434368 | https://example.com/article/1973 |
Luminescent properties and characterization of Gd2O3:Eu(3+)@SiO2 and Gd2Ti2O7:Eu(3+)@SiO2 core-shell phosphors prepared by a sol-gel process.
Gd2O3:Eu(3+) and Gd2Ti2O7:Eu(3+) films 10 nm in thickness were individually coated onto silica spheres (particle size of 150-170 nm) using the sol-gel method. The synthesized materials were addressed as Gd2O3:Eu(3+)@SiO2 and Gd2Ti2O7:Eu(3+)@SiO2 phosphors. An x-ray powder diffractometer (XRD), field emission scanning electron microscope (FE-SEM), high-resolution transmission electron microscope (HR-TEM), and photoluminescence spectrophotometer (PL) were employed to characterize the core-shell phosphors. Uniform core-shell phosphor particles were observed using FE-SEM. The XRD and HR-TEM results indicated that the coated-shell layer was well crystallized after sintering at 1000 °C. The Gd2O3:Eu(3+)@SiO2 PL measurement showed a red emission at the main 615 nm wavelength. The Gd2Ti2O7:Eu(3+)@SiO2 phosphor showed an orange-red emission at the 588 and 615 nm wavelengths. In comparison with the Gd2O3:Eu(3+) and Gd2Ti2O7:Eu(3+) bulk material results, the core-shell phosphors maintained the same emission ability as the bulk materials and the novel core-shell phosphors possessed great potential in quantum phosphor applications. | 2024-06-23T01:26:35.434368 | https://example.com/article/8022 |
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Lawyer: Emma Newman
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Introduction {#Sec1}
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Myofibrillar myopathies (MFMs) are a heterogeneous group of inherited or sporadic neuromuscular disorders with clinical and genetic heterogeneity, characterized by the disintegration of Z disks and myofibrils, followed by the accumulation of myofibrillar degradation products and the ectopic accumulation of multiple proteins in the abnormal fiber regions.
The clinical phenotypes include limb-girdle muscular dystrophy, distal myopathy, scapuloperoneal syndrome or rigid spine syndrome. The diagnosis of MFM is based on clinical findings, electromyography (EMG), nerve conduction studies and, most importantly, muscle histology. Most patients with MFM present progressive muscle weakness but in some patients cardiomyopathy may precede muscle weakness. MFMs follow an autosomal dominant inheritance pattern although X-linked or autosomal recessive inheritance patterns can be occasionally observed.
These disorders have been associated with mutations in genes encoding sarcomeric Z-disk or Z-disk-related proteins, such as desmin (Clemen et al. [@CR8]), alpha crystallin B chain (Vicart et al. [@CR60]), myotilin (Selcen and Engel [@CR51]), Z-band alternatively spliced PDZ motif-containing protein (Selcen and Engel [@CR52]), filamin C (Vorgerd et al. [@CR61]), four and a half LIM domain 1 (Schessl et al. [@CR46]), titin (Pfeffer et al. [@CR42]), Bcl-2-associated athanogene-3 (BAG3) (Selcen et al. [@CR53]). The involvement of BAG3 in MFM has been described in a very limited number of MFM patients who carry the heterozygous mutation c.626 C \> T (p.P209L) (Selcen et al. [@CR53]; Odgerel et al. [@CR41]; Jaffer et al. [@CR25]; Lee et al. [@CR30]; Kostera-Pruszczyk et al. [@CR27]). In most of the cases, this mutation has occurred *de novo*. The clinical phenotype includes early age of onset, rapid evolution of the disease, respiratory insufficiency, neuropathy, limb and axial muscle weakness, cardiomyopathy. Rigid spine is present only in a few BAG3 MFM patients. The BAG3 protein belongs to the BAG co-chaperon family and it is involved in major biological processes such as apoptosis, protein quality control, autophagy and cytoskeleton organization (Rosati et al. [@CR44]). Moreover, the BAG3 protein appears to be important for the maintenance of mature skeletal muscle (Homma et al. [@CR24]), although a direct role for BAG3 in muscle function has not yet been fully elucidated (Hishiya et al. [@CR23]).
In this paper, we used whole exome sequencing (WES) to study an Italian female MFM patient who had been previously specifically investigated for mutations in the BAG3 gene and characterized as a carrier of the c.626C \> T mutation (Selcen et al. [@CR53]), in order to identify possible other genes involved in the patient's severe phenotype.
The WES analysis has been extended to her unaffected, non-consanguineous parents and brother. In the patient we identified variants in the NRAP and FHL1 genes that encode muscle-specific, LIM domain containing proteins and investigated their effect at mRNA and protein level in her skeletal muscle. NRAP is a 197 kDa multi-domain scaffolding protein with a N-terminal LIM domain, a C-terminal domain composed of five nebulin-related super-repeats (SR) and a linker region with nebulin-related single repeats (IB) (Mohiddin et al. [@CR39]). We identified three non-synonymous variants in the NRAP gene. Two of them lead to amino acid substitutions in the protein's SR region, involved in the binding with actin, vinculin (Luo et al. [@CR36]) and filamin C (Lu et al. [@CR33]). The third causes an amino acid change in the IB region, which binds a-actinin (Lu et al. [@CR33]) and MLP (Ehler et al. [@CR14]). FHL1 is a 32 kDa protein characterized by a N-terminal half LIM domain followed by four complete LIM domains. In the FHL1 gene we identified a non-synonymous variant that causes the substitution of an aspartic acid with an asparagine in the fourth LIM domain.
To our knowledge, this is the first study linking variants in the NRAP gene to a MFM phenotype. We also describe the simultaneous occurrence in the same patient of BAG3 and FHL1 gene variants already independently associated to MFMs, and suggest the involvement of BAG3 and FHL1 in the same signaling pathway.
Materials and methods {#Sec2}
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Ethical issue {#Sec3}
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This study was performed according to the guidelines of the Committee on the Use of Human Subjects in Research of the Policlinico Hospital of Milan (Milan, Italy). Informed consent was obtained from all family members.
Immunohistochemistry analysis on muscle biopsy {#Sec4}
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*Triceps surae* muscle biopsies were obtained from healthy subjects and from the patient. Normal subjects were age and sex matched: females aged between 18 and 30 years old. Biopsies were frozen in liquid nitrogen-cooled isopentane and sectioned on a cryostat. Serial sections of 10 µm thickness were stained with Hematoxylin & Eosin, Gomori's Trichrome, Oil Red O, Acid phosphatase, reduced nicotinamide adenine dinucleotide (NADH), Succinic dehydrogenase (SDH), Cytochrome oxidase, Myofibrillar ATPase and GPD staining. Images were captured using a Leica DM6000B microscope at ×20 and ×40 magnification (Leica, Germany). For immunohistochemical staining, sections were incubated at room temperature for 30 min with a solution of methanol containing 0.03 % H~2~O~2~, for 30 min with 2 % horse serum and then for 1 h with anti-NRAP (1:50, Santa Cruz Biotechnology Inc., Dallas, Texas, USA), anti-FHL1 (1:50, Millipore, Darmstadt, Germany) and anti-BAG3 (1:50, Abcam, Cambridge, UK) antibodies. After rinses with PBS 1X, sections were incubated with biotinylated secondary antibodies (1:100; Vector Laboratories, Burlingame, CA, USA), washed and incubated with the avidin--biotinylated peroxidase complex (avidin-biotin complex method kit, Vector Laboratories, Burlingame, CA, USA). Sections were counterstained with hematoxylin. For all immunostaining, negative controls did not contain the primary antibody, which was replaced with non-immune serum. Images were captured using a Leica DM6000B microscope at 10x and 40x magnification (Leica, Germany).
Whole exome sequencing (WES) {#Sec5}
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Genomic DNA was extracted from peripheral venous blood from all family members following standard procedures. For DNA library construction and exome capture, the Agilent SureSelectXT HumanAll Exon 50 Mb kit (Agilent Technologies, Santa Clara, CA, USA) was used starting from 3 µg of genomic DNA. Sequencing was performed as 72 bp paired-end reads on Illumina Genome Analyzer IIx.
The quality check of raw reads was performed using FASTQC (<http://www.bioinformatics.babraham.ac.uk/projects/fastqc>) and Prinseq (Schmieder and Edwards [@CR49]). Reads were aligned using Burrows-Wheeler Aligner BWA (Li and Durbin [@CR31]) with default parameters and using Hg19 as reference genome. We performed duplicate marking, local-realignment around INDELs and base quality score recalibration using Picard Tools (<http://picard.sourceforge.net>) and the GATK suite (DePristo et al. [@CR11]). We used the GATK Haplotype caller to call single nucleotide variants (SNVs). Annotations were performed using Annovar (Wang et al. [@CR62]) with complete database signatures updated to March 2014. We filtered out variants with low genotype quality (GQ \< 50) and coverage lower than 7x. High quality variants underwent a custom prioritization procedure aimed at identifying rare variants at population level in the patient compared to family members: we discarded variants in which the genotype of the patient was homozygous for the reference allele or was identical to the brother or to both parents. We focused on rare non-synonymous and stop-codon variants that followed classical patterns of inheritance (recessive, dominant, compound heterozygous and X-linked). Rarity was set as minor allele frequency (MAF) lower than 1 % in the 1000 Genomes Project. With regard to variants that support a heterozygous compound model of inheritance, rarity was applied when at least one of them followed such rule. Finally, we selected variants mapping in genes mainly expressed in skeletal and cardiac muscle. SIFT (Kumar et al. [@CR29]), CONDEL (González-Pérez and López-Bigas [@CR20]) and PROVEAN (Choi et al. [@CR7]) software were used for the prediction of the pathogenicity of top variants. The genotypes for the variants in the NRAP gene were confirmed in all family members by pyrosequencing using Pyromark Q24 (Qiagen, Valencia, CA, USA). The variant in the FHL1 gene was validated by Sanger sequencing in all family members. All PCR and sequencing primers are listed in Table [1](#Tab1){ref-type="table"}. The genotypes for all the four variants were confirmed in the patient and in her relatives.Table 1Primer sequences (5′--3′) used for variant validationGeneVariationValidation techniqueForward PCR primer sequenceReverse PCR primer sequenceSequencing primer sequenceNRAPrs200747403PyrosequencingTCCCCACTCATTCAAGTACACAGCACTTGGAAAGCAAGACTACATTATCTGGTTGCTGAATTNRAPrs2270182PyrosequencingAAGTACAGGCTGCCTTGTAAAATGTCCCCACATTGCTCTCTTACCTCCGTGCTGACTATGAGAANRAPrs2275799PyirosequencingCTGTGCATGGGAGTCAAATTCATATTGGTCTGCACATTCCCTTGTCTCAAGATGCCCTCAGFHL1rs151315725Sanger SequencingGTTTCCTCACCTGTATTCATTCAGCAAATGGGAGAAAAGACGGAAGGAGAACGAGAAAAGACGGAAGGAGAAC
Quantitative PCR analysis (qPCR) {#Sec6}
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Total RNA was extracted from the biopsy of the patient and of three age and sex matched controls using Trizol Reagent according to the manufacturer's instructions (Invitrogen Life Technologies, Grand Island, New York, USA). The samples were treated with RNase-Free DNase (Promega, Madison, WI, USA). First strand cDNA was prepared using SuperScript First-Strand III Synthesis System for RT-PCR (Invitrogen Life Technologies), starting from 2 µg total RNA with oligo(dT)~12--18~ primer. Absolute Real-Time PCR (qPCR) was used to have an absolute quantification of human NRAP, FHL1 and BAG3 expression. We also determined the expression of the human-specific GAPDH housekeeping gene for each sample. Primer sequences are shown in Table [2](#Tab2){ref-type="table"}. Target gene levels were measured in real-time with the SYBR GREEN technique using GoTaq MasterMix SyberGreen (Promega, Madison, WI, USA). Each sample was evaluated in triplicate and three independent experiments were performed. Statistical analysis was conducted comparing the average of all experiments by unpaired *T* test (p \< 0.05).Table 2Primer sequences (5′--3′) used in qPCR analysisGeneForward primer sequenceReverse primer sequenceGAPDHGTGGCAAAGTGGAGATTGTTGCCGTAGATGACCCGTTTGGCTCCBAG3GCTCCGACCAGGCTACATTGATAGACATGGAAAGGGTGCNRAPGCTGCAGAGTGATGTCAAGTATCCGAGCCATTTCCACTTTGTAFHL1AAAGGACTGTGTCAAGAGTGAGAAACAGGGTGAGAGGCAAG
Western blot analysis {#Sec7}
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Human muscle biopsies isolated from *Triceps Surae* of three healthy subjects and from the patient were homogenized in a lysis buffer containing 20 mM Tris--HCl (pH 7.8), 140 mM NaCl, 1 mM EDTA, 0.5 % NP40, 1 mM phenylmethylsulfonil fluoride, and complete protease inhibitor mixture (Roche Diagnostics, Rotkreuz, Schweiz), with a POTTER S Homogenizer (B.Braun Biotech International-Sartorius group). Samples were pulsed 5 times for 5 s each at a speed of 1000 rpm. Samples were then passed 5 times through a 30.5-gauge needle to disrupt the nuclei, then incubated at 4 °C for 15 min and finally centrifuged at 13,000 rpm for 15 min at 4 °C. Total protein concentration was determined according to Lowry's method. Samples were resolved on 8 % polyacrylamide gel for NRAP, 12 % for FHL1 and BAG3 and transferred to nitrocellulose membranes (Bio-Rad Laboratories, Hercules, CA, USA). The following antibodies were used for the assays: anti-NRAP (1:50) (Santa Cruz Biotechnology, Dallas, Texas, USA), anti-FHL1 (1:500) (Millipore, Darmstadt, Germany) and anti-BAG3 (1:1000) (Abcam, Cambridge, UK). The BAG3 antibody recognizes the C terminal part of the protein (196 amino acids). The FHL1 antibody recognizes the amino acid sequence CRDPLQGKKYVQKDGRH (amino acid 10--26).The NRAP antibody recognizes an internal sequence amino 1309--1393 (UniProt ID: Q86VF7). We also determined the expression for each sample of the anti-β-Tubulin III (1:500) (SIGMA, Saint Louis, MO, USA) housekeeping protein. Detection was performed with horseradish peroxidase (HRP)-conjugated secondary antibodies (DakoCytomation, Carpinteria, CA, USA), followed by enhanced chemiluminescence (ECL) development (Amersham Biosciences, Piscataway, NJ, USA). Bands were visualized by autoradiography using Amersham Hyperfilm™ (Amersham Biosciences, Piscataway, NJ, USA). Densitometric analysis was performed using ImageJ software (<http://rsbweb.nih.gov/ij/>). Each sample was evaluated in three independent experiments.
Molecular dynamics (MD) simulation and electrostatic potential studies of FHL1 fourth LIM domain {#Sec8}
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The NMR structure of the fourth LIM domain in FHL1 (PDB ID: 2egq) was obtained from the protein databank (PDB, <http://www.rcsb.org/pdb/>). Starting from the 3D structure of the fourth LIM domain, the D275N mutant was modeled using SCWRL4 (Krivov et al. [@CR28]). MD simulations of the wild type and D275N mutant were carried out by producing runs of 30 ns using AMBER12. In order to assess the impact of the amino acid substitution on protein folding and on the protein's ability to bind target proteins, we performed (for the wild type and mutant proteins) a structural statistical analysis of all conformations obtained during molecular dynamics and an electrostatic potential surface analysis using the Adaptive Poisson-Boltzmann Solver program (Baker et al. [@CR2]).
In vitro wild type and mutated BAG3 transfection experiments {#Sec9}
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Immortalized human healthy myoblasts (CHQRb) and myoblasts isolated from the patient were expanded and cultured on uncoated standard tissue culture plastic at 37 °C in 5 % CO~2~ 95 % air. Cells were plated onto six-well plastic tissue culture plates in DMEM (Euroclone, Italy), supplemented with 15 % fetal bovine serum (Euroclone, Italy) and 0.1 % penicillin/streptavidin antibiotic. CHQRb cells and the patient's myoblasts were then seeded at 2.0 × 10^5^ cells per well in a 6-well plate, grown for 24 h and transfected in different experiments with wild type pCIneoHisBag3 or mutated pCIneoHisBag3 c.626C \> T. The transfection mixtures for each sample contained 5 µl of Lipofectamine (Invitrogen Life Technologies, Carlsbad, CA, USA) and 3.5 µg plasmid in a 1.4 ml total volume of DMEM (Invitrogen Life Technologies, Carlsbad, CA, USA) without antibiotics and fetal bovine serum. Western blot analysis was performed 48 h after transfection to verify the expression of BAG3, NRAP and FHL1 proteins as described in Materials and Methods. For immunofluorescence analysis, CHQRb transfected cells and the patient's myoblasts were incubated with primary antibody against FHL1 (1:50) (Millipore, Darmstadt, Germany). Images were captured using the Leica TCS SP2 confocal system (Leica, Germany).
Results {#Sec10}
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Case description {#Sec11}
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We studied an Italian family with a 26-year-old female patient suffering from a BAG3 myopathy, her non-consanguineous asymptomatic healthy parents and her asymptomatic healthy brother (Fig. [1](#Fig1){ref-type="fig"}). The age of onset of symptoms in the patient ranged between 11 and 14 years. Creatine kinase (CK) levels ranged from normal to 1.500 U/L. The progression of the disease started with early spinal contractures causing spinal rigidity, scapular winging and later postural muscle atrophy as well as the development of an additional proximal weakness in a limb-girdle distribution pattern with loss of deambulation. Muscle biopsy at age of 13 years showed Z disk aggregates and atrophic type I fibers whereas type II fibers were hypertrophic. Electromyography showed axonal neuropathy. In the last 5 years the patient developed respiratory insufficiency, thus requiring ventilatory support on a continuous basis or overnight. Impaired conduction, arrhythmia and cardiac hypertrophy were reported.Fig. 1Family pedigree. The patient is marked with an *arrow* and is indicated with a *filled circle*. The unaffected relatives are marked with *open circle*/*square*
Characterization of muscle tissue {#Sec12}
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For this study *Triceps Surae* muscle biopsy was performed on the patient (Fig. [2](#Fig2){ref-type="fig"}). All experiments were conducted on the only available dystrophic muscle biopsy. Muscle biopsies from the patient's parents and brother were not available. The patient's muscle biopsy showed myofibrillar breakdown and Z-line streaming. Hematoxylin & Eosin staining revealed variability in the diameter of muscle fibers (from 10 to 100 µm), some of them divided by splitting and several muscle fibers in necrosis (Fig. [2](#Fig2){ref-type="fig"}a, a'). Some muscle fibers displayed vacuoles. Gomori's trichrome (Fig. [2](#Fig2){ref-type="fig"}i, i') staining showed increased collagen deposition while Oil Red O staining evidenced the formation of lipid droplets (Fig. [2](#Fig2){ref-type="fig"}j, j'). NADH (Fig. [2](#Fig2){ref-type="fig"}e, e'), SDH (Fig. [2](#Fig2){ref-type="fig"}h, h') and COX (Fig. [2](#Fig2){ref-type="fig"}d, d') staining showed normal mitochondrial or oxidative metabolism even in the presence of amorphous deposits. Trichrome staining showed small dense granules or amorphous masses in several muscle fibers (data not shown). Conversely, the αGPD enzyme permitted to visualize cytoplasmic glycolytic bodies (Fig. [2](#Fig2){ref-type="fig"}c, c'). No difference in the number of fast (Fig. [2](#Fig2){ref-type="fig"}f, f') and slow myofiber staining was observed (Fig. [2](#Fig2){ref-type="fig"}g, g'). Increased acid phosphatase activity was evidenced by many cytoplasmic inclusions (Fig. [2](#Fig2){ref-type="fig"}b, b').Fig. 2Immunohistochemistry analysis on the patient's muscle biopsy**. a, a'** Histological characterization of the patient's muscle tissue by Hematoxylin & Eosin. **b, b'** Acid phosphatase activity showed many cytoplasmic inclusions. **c, c'** Cytoplasmic glycolytic bodies were visualized by αGPD enzyme. Sections were stained for COX (**d, d'**) NADH (**e, e'**), SDH (**h, h'**), showing the presence of amorphous deposits. Fast (**f, f'**) and slow (**g, g'**) myofiber staining was performed. Gomori's trichrome (**i, i'**) and Oil Red O (**j, j'**) staining. Note the variability in fiber areas, collagen and oil droplets deposition
Whole exome sequencing and variant calling {#Sec13}
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On average 144 million raw 72 bp paired-end reads were generated among the samples, with a mean of 121 million reads after PCR duplicate removal. The mean coverage over the targeted exome across all samples was 46X. After quality filtering and removal of intergenic, intronic and synonymous variants, we identified 3663 SNPs. We confirmed the heterozygous c.626 C \> T (p.P209L) mutation in BAG3 in the patient and its absence in her relatives, as previously reported (Selcen et al. [@CR53]). Moreover, both the patient and her relatives were found to be negative for variants in all the already known MFM-related genes such as DES, CRYAB, MYOT, ZASP, FLNC and TTN, except for the FHL1 gene. We identified the non-synonymous variant rs151315725 located in exon 8 (c.823G \> A, p.D275N) in the heterozygous FHL1 gene in the patient. The FHL1 gene maps on chromosome X and the patient inherited this variant from her heterozygous mother, in accordance with an X-linked model of inheritance. Neither her father nor her brother carry this variant. Rs151315725 is very rare with a MAF = 0.0048 in the 1000 Genomes Project and is predicted to be deleterious by most prediction tools. After applying all prioritization filters, we also identified three non-synonymous variants in the NRAP gene on chromosome 10: rs200747403 in exon 32 (c.3674G \> A, p.A1225 V), rs2270182 in exon 16 (c.1556T \> A, p.N519I) and rs2275799 in exon 9 (c.844C \> T, p.A282T). Rs200747403 has been annotated in the 1000 Genomes Project with a MAF of the derivative A allele equal to 0.0004. The patient inherited the A allele from her father. At protein level, this variant falls in super domain 4 (SR4) and is predicted to be damaging by most prediction tools. Conversely, the derivative alleles A at rs2270182 and T at rs2275799 are frequent in the 1000 Genomes Project (MAF = 0.25 and 0.27 respectively) and are both inherited from the mother. Rs2270182 falls in SR1 and rs2275799 localizes in the single repeat region (IB). We validated the FHL1 variant in Sanger sequencing and NRAP variants in pyrosequencing. The genotypes for all the four variants were confirmed in the patient and in her relatives.
BAG3, NRAP and FHL1 expression in muscle biopsies {#Sec14}
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All experiments were conducted on the only available dystrophic muscle biopsy from the patient and on three healthy muscle tissues. Muscle biopsies from the healthy patient's parents and brother were not available. Real time PCR results showed a non-statistically significant reduction of BAG3 (Fig. [3](#Fig3){ref-type="fig"}a) and a statistically significant reduction of NRAP mRNA expression in the patient (p \< 0.05) (Fig. [4](#Fig4){ref-type="fig"}a), while FHL1 mRNA tended to be lower in the patient though the difference was not statistically significant (Fig. [4](#Fig4){ref-type="fig"}d). Western Blot analysis confirmed that the levels of BAG3 (Fig. [3](#Fig3){ref-type="fig"}b, c) and NRAP (Fig. [4](#Fig4){ref-type="fig"}b, c) proteins in the patient's muscle were respectively reduced and absent compared to the healthy muscle. Moreover, we demonstrated an increased expression of FHL1 protein isoform A (Fig. [4](#Fig4){ref-type="fig"}e, f) and the absence of the other isoforms compared to the control muscle specimens (data not shown). Immunohistochemistry (IHC) analysis was performed in the patient's and control muscle to evaluate BAG3, NRAP and FHL1 localization. In the patient, BAG3 (Fig. [3](#Fig3){ref-type="fig"}d) was present in abnormal cytoplasmic accumulations in some myofibers, whereas NRAP (Fig. [4](#Fig4){ref-type="fig"}g) was totally absent. On the contrary, subsarcolemmal and intra-cytoplasmic immunoreactivity of FHL1 was observed in several muscle fibers suggesting the presence of FHL1 in aggregates (Fig. [4](#Fig4){ref-type="fig"}g).Fig. 3Analysis of BAG3 expression, content and localization in the patient's muscle biopsy. **a** RT-qPCR analysis of BAG3 mRNA revealed a non-statistically significant downregulation of BAG3 expression in the patient's muscle compared with healthy controls. **b** WB analysis of BAG3 performed on the patient's and control muscles showed a downregulation of BAG3 expression in the patient's muscle. Images of bands were obtained using the CanoScan LiDE60 Scanner (Canon) and the Canon ScanGear Software. **c** Densitometric analysis of the protein levels was performed using ImageJ software (<http://rsbweb.nih.gov/ij/>). **d** Immunohistochemical analysis of BAG3 in the patient's and control muscles. In the controls BAG3 localized with sarcolemma, while in the patient it accumulated in the cytoplasm of some muscle fibersFig. 4Analysis of NRAP and FHL1 expression, content and localization in the patient's muscle biopsy. **a** RT-qPCR analysis showed a statistically significant downregulation of NRAP expression in the patient's muscle compared with healthy controls (unpaired *t* test, p \< 0.05). **b** WB analysis of NRAP in the patient's and control muscle. The analysis showed the absence of NRAP expression in the patient. **c** Densitometric analysis of the protein levels was performed using ImageJ software (<http://rsbweb.nih.gov/ij/>). **d** RT-qPCR analysis showed a non-statistically significant downregulation of FHL1 in the patient's muscle compared to healthy controls. **e** WB analysis revealed an overexpression of FHL1 in the patient's muscle compared to the healthy controls. **f** Densitometric analysis of the protein levels was performed using ImageJ software (<http://rsbweb.nih.gov/ij/>). **g** Immunohistochemical analysis of NRAP was performed on the patient's and control muscles. In the control NRAP localized with myofibrils, while in the patient it was not detectable. Immunohistochemical analysis of FHL1 demonstrated an intracytoplasmatic myofiber association of the protein in the controls while in the patient it was detectable in intracytoplasmatic aggregates
Molecular dynamics (MD) simulation and electrostatic potential studies of fourth LIM domain of FHL1 {#Sec15}
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MD simulations of the fourth LIM domain were carried out to investigate the relationship between structure and function in the D275N mutant. A statistical analysis (clustering) of the structures was performed to obtain the most representative of both wild type and mutant for their comparison. NMR data (pdb ID:2egq) showed that the FHL1 wild type adopted a well-defined structure (residues 217--276) and a highly flexible region (residues 200--216). Wild type and mutant protein showed very similar representative structures in the well-defined region (residues 217--276), suggesting conservation of the overall tertiary structure of the fourth LIM domain in the presence of the amino acid substitution (Fig. [5](#Fig5){ref-type="fig"}a). The structural analysis of the second Zinc atom involved in the C-terminal binding site conserved the coordination status during the simulation in spite of the proximity with the mutated residue (275N). On the other hand, the mutated 275N residue located on the surface of the domain modified the local charge of the surface compared to the wild type. To evaluate the effect of charge modification on protein function due to the D275N change, the electrostatic potential on the fourth LIM domain surface was calculated. It was observed that the D275N change was responsible for a modification of the surface charge distribution in the C-terminal Zinc binding site. The replacement of aspartic acid with an asparagine results in a generalized positivization of the surface area (Fig. [5](#Fig5){ref-type="fig"}b).Fig. 5Molecular dynamics simulation and electrostatic potential study of FHL1 fourth LIM domain. **a** Structure of fourth LIM domain from MD simulation of wild-type FHL1 and the D275N FHL1 mutant. Each structure was the most representative frame obtained from the cluster analysis of the simulations. A ribbon representation of the wild-type protein is shown in *green* with the mutant structure superimposed in cyan. Asp275, Asn275 mutant and the zinc ion coordination residues are shown in rod and *colored* by atom type, while the zinc ions are shown in space-filling (van der Waals) representations. The D275N mutant remained folded in native conformation, with zinc sites almost fully intact. **b** Surface electrostatic potential distribution of D275N mutant compared to the wild type LIM domain. Green circles indicate the position of Asp275 and Asn275 in wild type and mutant, respectively. The potential scale ranges from −1 kT/e to 1 kT/e from *red* to *blue*
In vitro evaluation of NRAP and FHL1 expression in human normal myoblasts and in the patient's myoblasts {#Sec16}
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In order to evaluate the influence of the c.626C \> T BAG3 mutation on NRAP and FHL1 expression, we performed transfection experiments in immortalized human healthy myoblasts (CHQRb) and in the patient's myoblasts. CHQRb cells were transfected with wild type BAG3 (pCIneoHisBag3) or the mutated form of BAG3 (pCIneoHisBag3 c.626C \> T) (BAG3^P209L^), and NRAP and FHL1 expression was evaluated by Western blot. No differences in NRAP expression were detected in CHQRb cells transfected with wild type BAG3 or BAG3^P209L^ (Fig. [6](#Fig6){ref-type="fig"}a, b). These results suggest that the absence of mRNA (Fig. [4](#Fig4){ref-type="fig"}a) and protein (Fig. [4](#Fig4){ref-type="fig"}b, c) found in the patient's muscle was not influenced by mutated BAG3. On the contrary, FHL1 expression was reduced in CHQRb overexpressing wild type BAG3, and it was increased in CHQRb overexpressing BAG3^P209L^ (Fig. [6](#Fig6){ref-type="fig"}a, b) compared to the control. The patient's myoblasts were transfected only with wild type BAG3 and no difference in NRAP expression was detected compared to non-transfected patient myoblasts (Fig. [6](#Fig6){ref-type="fig"}c, d). On the contrary, FHL1 expression was reduced in the patient's myoblasts transfected with wild type BAG3 compared to non-transfected patient myoblasts (Fig. [6](#Fig6){ref-type="fig"}c, d), similarly to what we observed in CHQRb transfected with wild type BAG3 (Fig. [6](#Fig6){ref-type="fig"}a, b).Fig. 6In vitro evaluation of NRAP and FHL1 expression after transfection with wild type and mutated BAG3. **a** Evaluation of the expression of BAG3, NRAP and FHL1 expression in CHQRb cells before and after transfection with wild-type pCIneoHisBag3 (BAG3) and mutated pCIneoHisBag3 c626C \> T (BAG3\*) by WB analysis. **b** Densitometric analysis of BAG3, NRAP and FHL1 levels in CHQRb cells performed using ImageJ software (<http://rsbweb.nih.gov/ij/>). **c** WB analysis for BAG3, NRAP and FHL1 expression in patient's myoblasts before and after transfection with wild-type pCIneoHisBag3 (BAG3). **d** Densitometric analysis of BAG3, NRAP and FHL1 levels in patient's myoblasts performed using ImageJ software (<http://rsbweb.nih.gov/ij/>). **e--h** Evaluation of the expression of FHL1 in patient's myoblasts before (**e**) and after (**f**) transfection with wild type pCIneoHisBag3 (BAG3) and in normal myoblasts treated with wild type (**g**) and mutated (**h**) BAG3 by immunofluorescence analysis. Images were captured using the Leica TCS SP2 confocal system (Leica, Germany), ×20 magnification, scale bar 100 μm
Since these data suggest that BAG3 influences FHL1 expression both in CHQRb and in the patient's myoblasts, we investigated whether BAG3^P209L^ affects FHL1 aggregation in these cell types. When wild type BAG3 was expressed in CHQRb cells, FHL1 had a diffuse cytosolic localization (Fig. [6](#Fig6){ref-type="fig"}g). In contrast, CHQRb cells expressing BAG3^P209L^ showed a fine granular FHL1 positive pattern with significant perinuclear aggregation (Fig. [6](#Fig6){ref-type="fig"}h). Moreover, FHL1 expression was reduced in the patient's myoblasts transfected with wild type BAG3 (Fig. [6](#Fig6){ref-type="fig"}f) compared with the patient's non-transfected myoblasts (Fig. [6](#Fig6){ref-type="fig"}e).
Discussion {#Sec17}
==========
In this work we provide data showing the co-presence of genetic variants in the NRAP and FHL1 genes in a patient with phenotypic features of MFM and who carries the BAG3 c.626C \> T mutation. The MFM BAG3 phenotype is very rare and accounts for twelve patients described worldwide. In this paper we focused on the only known Italian case of Bag3Opathy and examined the patient and her unaffected relatives with WES. WES received widespread consideration for the discovery of novel causative variants also in small pedigrees (Glazov et al. [@CR18]). The genetic variants identified in the patient map in the NRAP and FHL1 genes, which are specifically expressed in muscles and both encode LIM domain containing proteins. LIM domain containing proteins have been reported as important for normal skeletal and cardiac structure and function. Mutations in MLP (muscle LIM protein) and in Cipher/ZASP have been found in patients affected by both dilated and hypertrophic cardiomyopathy (Knöll et al. [@CR26]; Geier et al. [@CR17]; Sheikh et al. [@CR55]) and Cypher/ZASP mutations were also identified in zaspopathies, a subtype of MFM (Selcen and Engel [@CR52]; Griggs et al. [@CR21]).
NRAP is an actin-binding LIM protein encoded by a gene mapping on chromosome 10q25 (Luo et al. [@CR34], [@CR35]) and specifically expressed in skeletal and cardiac muscle tissues (Mohiddin et al. [@CR39]; Luo et al. [@CR34], [@CR35]). In the patient, we identified three non-synonymous variants in the NRAP gene: rs200747403 (inherited from her father and predicted as deleterious), rs2270182 and rs2275799, inherited from her mother and predicted as benign. Rs200747403 and rs2270182 localize in the SR region, which contains the binding sites for actin, vinculin (Luo et al. [@CR36]) and filamin C (Lu et al. [@CR33]). Rs2275799 falls in the IB region that binds a-actinin (Lu et al. [@CR33]) and MLP (Ehler et al. [@CR14]). In the patient, both alleles of the NRAP gene are affected by variants that cause the substitution of highly conserved amino acids and NRAP was completely absent at mRNA and protein level in the patient's muscle. The absence of NRAP mRNA in the patient's muscle suggests that both the very rare rs200747403 inherited from the father and the variants rs2270182 and rs2275799 inherited from the mother may have a deleterious effect on the messenger's stability by affecting both NRAP alleles. Though mRNA instability has been linked to the presence of non-sense and frame-shift variants in previous papers (Gong et al. [@CR19]; Zarraga et al. [@CR65]), Vasilopoulos et al. have also reported a decreased mRNA stability caused by a non-synonymous substitution (Vasilopoulos et al. [@CR59]). Our transfection experiments suggest that the absence of NRAP in the patient's muscle may be due to the three variants and not to the BAG3 mutated allele. NRAP mRNA and protein levels in the patient's relatives were not evaluated because no biopsies were available. To our knowledge, this is the first study describing variants in the NRAP gene in a MFM phenotype. The absence of NRAP protein in the patient's muscle could contribute to the disorganized myofibril assembly (Manisastry et al. [@CR37]; Carroll et al. [@CR5]). Dhume et al. were able to demonstrate that NRAP knockdown in cultured embryonic mouse cardiomyocytes resulted in disorganized myofibril assembly and led to a decrease in non-muscle myosin (NMHC) IIB by post-transcriptional mechanisms (Dhume et al. [@CR12]). Moreover, there are reports of a direct interaction of NRAP with NMHC IIB and a decrease of NRAP protein levels in mouse cardiomyocytes by NMHC IIB knockdown (Lu and Horowits [@CR32]). The Authors assigned two separate but tightly linked functional roles in cardiomyocyte biology to NMHC IIB and NRAP, with NMHC IIB involved in cardiomyocyte spreading and NRAP in myofibril assembly. However, the role of NMHC IIB in the assembly of pre-myofibrils is still questioned and to be elucidated (Lu and Horowits [@CR32]; Tullio et al. [@CR57]). No variant in the NMHC IIB (MYH10) gene was found either in the patient or in her relatives.
We also identified the c823G \> A transition (rs151315725) in the FHL1 gene, already reported in the 1000 Genomes Project, although extremely rare (MAF = 0.0048), leading to D275N amino acid substitution in one of the three splicing isoforms of the FHL1 protein, i.e. FHL1A, which is the full-length protein (rewieved in Cowling et al. [@CR10]). Rs151315725 has been already reported as a variant in a German family with the characteristic XMPMA phenotype and the Authors hypothesized a negative effect of the D275N amino acid change on FHL1 function when inherited together with the V280 M amino acid substitution caused by the c.838G \> A missense mutation (Schoser et al. [@CR50]). Moreover, rs151315725 was also identified in three unrelated European families with hypertrophic cardiomyopathy (HCM), and FHL1^D275N^ was found to activate a fetal hypertrophic gene program in rat-engineered heart tissue, suggesting that it could cause hypertrophic cardiomyopathy (HCM) in these patients (Friedrich et al. [@CR16]). Mutations in the FHL1 gene have been also associated with arrhythmias, HCM and dilated cardiomyopathy in several patients affected by skeletal muscle disorders as well (reviewed in Cowling et al. [@CR10]). Rs151315725 could play a role in the patient's compromised cardiac phenotype, which includes arrhythmias and cardiac hypertrophy. Additionally, rs151315725 has been reported as deleterious in the NHLBI Exome Sequencing Project (ESP) (<https://esp.gs.washington.edu/drupal/>) (MAF = 0.011) and in the Exome Aggregation Consortium (ExAC) (<http://exac.broadinstitute.org/>) (MAF = 0.013) databases, both including individuals affected by heart diseases. This could explain the difference in MAF reported in these databases compared to the 1000 Genomes Project. In addition to XMPMA (Windpassinger et al. [@CR64]), mutations in the FHL1 gene have been associated with other four clinically distinct human myopathies, including reducing body myopathy (RBM) (Schessl et al. [@CR46], [@CR47]), X-linked dominant scapuloperoneal myopathy (SPM) (Quinzii et al. [@CR43]; Chen et al. [@CR6]), Emery-Dreifuss muscular dystrophy (EDMD) (Gueneau et al. [@CR22]), and rigid spine syndrome (RSS) (Shalaby et al. [@CR54]). Spinal rigidity is the most common clinical feature associated with FHL1 mutations and has been reported in patients with RBM (Schessl et al. [@CR48]), XMPMA (Schoser et al. [@CR50]) and EDMD (Gueneau et al. [@CR22]). In our patient rs151315725 in the FHL1 gene is associated with a BAG3 MFM phenotype that also presents the rigid spine feature.
Rs151315725 in FHL1 is present in the patient's asymptomatic mother and this could be explained by X chromosome inactivation and by the mosaic for X-linked gene expression in heterozygous women. As previously reported for members of a German family affected by a familiar reducing body myopathy, females carrying the C150R amino acid change in the FHL1 LIM2 domain showed various clinical manifestations and may be asymptomatic, reflecting different degrees of X-inactivation (Schessl et al. [@CR48]). We did not perform any X-inactivation study in this family. We further investigated mRNA and protein expression in the patient's muscle biopsy and found a slight (though not statistically significant) reduction in mRNA and a weak increase in FHL1 isoform expression, which could be linked to FHL1 accumulation in the deposits observed in the patient's muscle fibers. Additionally, in the patient's myoblasts we observed a threefold increase in FHL1 protein expression compared to normal myoblasts (data not shown).
In order to assess the effect of the D275N change on FHL1 function, MD simulation and electrostatic potential analysis were performed on the fourth LIM domain of the protein. MD simulations showed that the wild type and the mutant had the same structural regions and that the second zinc binding site remained largely intact in the mutant. These findings suggest that protein function is not impaired by structural distortions that could generate unfolded protein. In line with these data, gene transfer experiments showed that the FHL1^D275N^ protein was stable in cardiac myocytes and the protein levels were not affected by proteasome inhibition (Friedrich et al. [@CR16]). Electrostatic potential studies showed the loss of negative potential on the fourth LIM domain surface that might create an unfavorable environment for the recognition of FHL1 target proteins. These data are supported by the observation that the FHL1^D275N^ protein had a lower binding specificity for proteins localized at the I-band (Friedrich et al. [@CR16]; Sheikh et al. [@CR56]). Indeed, FHL1A localizes to the sarcomeric I-band and to focal adhesions (Brown et al. [@CR3]; Ng et al. [@CR40]). Little is known about FHL1 function, but the available data suggest that it participates in muscle growth and differentiation, as well as in the assembly of the sarcomere, and that it is a regulator of skeletal muscle mass through the interaction with transcription factors and myosin-binding protein C (Cowling et al. [@CR9]; McGrath et al. [@CR38]). Domenighetti et al. demonstrated that FHL1-null mice develop an age-dependent myopathy associated with myofibrillar and intermyofibrillar disorganization (Domenighetti et al. [@CR13]). FHL1 was recently found as part of a complex which binds gamma-actin and NMHC IIB in vivo and in vitro (Wang et al. [@CR63]). Both NRAP and FHL1 are partners of NMHC IIB (Lu and Horowits [@CR32]; Wang et al. [@CR63]) and the patient's variants in these genes could affect their interactions with NMHC IIB, with possible implications in myofibrillar assembly.
Our study started from the identification in the patient of the P209L mutation in the BAG3 gene (Selcen et al. [@CR53]). In the original paper by Selcen, the authors described a subtype of MFM sharing common clinical features such as progressive limb and axial muscle weakness, contractures, respiratory insufficiency and hypertrophic cardiomyopathy (Selcen et al. [@CR53]). A characteristic of the disease is the association with peripheral neuropathy that may in some patients be the initial clinical manifestation (Jaffer et al. [@CR25]). The morphological analysis performed in the patient confirmed the feature of MFM.
BAG3 is co-chaperone for other heat shock proteins and has anti-apoptotic properties. It localizes to and co-chaperones the Z disk in skeletal and cardiac muscles. BAG3 protein deficiency determines fulminant myopathy and early mortality in mice (Homma et al. [@CR24]) and BAG3^P209L^ tends to aggregate into small granules, probably as a result of its altered folding and function (Selcen et al. [@CR53]). The results of our study demonstrated a lower muscular expression of BAG3 compared to the healthy controls, both at mRNA and protein level. In the patient, BAG3 IHC showed cytoplasmic accumulation in some muscle fibers. This data could be explained by a mechanism of wild type BAG3 sequestration into BAG3^P209L^ mediated aggregates (Ruparelia et al. [@CR45]), leading to a different localization or rapid degradation of this protein. In particular, the replacement of the 209 leucine caused by the BAG3 mutation in the patient could affect the binding properties of the wild type BAG3 domains.
Our transfection experiments show that BAG3 influences FHL1 protein content both in CHQRb and in the patient's myoblasts, suggesting the involvement of these two proteins in the same signaling pathway. To address this, Feldkirchner et al. used a quantitative proteomic approach to explore the plaque content in a MFM patient carrying the C224W amino acid substitution in FHL1 and found the accumulation of a series of 15 proteins including FHL1, BAG3 and NRAP (Feldkirchner et al. [@CR15]).
The effect of wild type BAG3 transfected in the patient's myoblasts suggests a role for wild type BAG3 in the control of FHL1 protein turnover, while this does not occur with the mutated BAG3 form.
Immunofluorescence analysis shows that wild type BAG3 expression in CHQRb and in the patient's myoblasts gives rise to a diffuse cytosolic immuno-localization of FHL1, whereas both BAG3^P209L^ expressed in CHQRb and the endogenous BAG3^P209L^ in the patient's myoblasts caused a prevalently perinuclear immuno-localization of FHL1. These data suggest that the different localization and level of aggregation of FHL1 depend on wild type BAG3 form.
In conclusion, this is the first study linking variants in the NRAP gene to a MFM phenotype and reporting, in the same patient, the simultaneous occurrence of BAG3 and FHL1 gene variants that have already been independently associated with MFMs. Moreover, our data suggest that BAG3 and FHL1 could be involved in the same signaling pathway. These data could also suggest that few genes might modulate this MFM phenotype. Examples are present in the literature revealing that for some diseases the phenotype cannot be completely explained by mutations at a single locus. This also applies to some neuromuscular disorders (Badano and Katsanis [@CR1]; Cady et al. [@CR4]; Van Blitterswijk et al. [@CR58]). The aetiology of these diseases could then require the combined action of mutant alleles at a small set of genes.
D'Avila F. and Meregalli M. are joint first Authors.
The Italian Ministry of Education and Research through the Flagship InterOmics (PB05) to DC and LM and HIRMA (RBAP11YS7 K) projects and the European MIMOmics (305280) project to LM. This work was supported by the Fondazione Roby ONLUS. MM was founded by the Associazione La Nostra Famiglia Fondo DMD Gli Amici di Emanuele.
Authors' contributions {#FPar1}
======================
FD, MM, DC, CB, YT: participated in design of the study. FD, MM, FDS, DB, AF, CS, SE: performed the experiments. MB, SL, FD: performed the analysis of sequencing data. AO, PD, LM: performed molecular dynamics analysis. FD, MM, CB, YT: wrote the manuscript.
Conflict of interest {#FPar2}
====================
The authors declare that they have no competing interests.
| 2023-09-10T01:26:35.434368 | https://example.com/article/4732 |
Sutherland, Tennessee
Sutherland is an unincorporated community in Johnson County, Tennessee, United States. Sutherland is located south of the border with Virginia on Tennessee State Route 133.
References
Category:Unincorporated communities in Johnson County, Tennessee
Category:Unincorporated communities in Tennessee | 2024-02-17T01:26:35.434368 | https://example.com/article/1602 |
thats an awesome one..... so you are accepting the fact that the universe is a bit of a cosmic community,, with "intent" or purpose of
life/intelligent life.... interaction, growth ( physically, mentally, spiritually, any way, everyway) relationships,,,, you think that beings having
individual selves is the best thing that can happen, and for these beings to live on planets together, and figure things out,, suffer together or
alone, achieve greatness together or alone etc.
how would you know you were you..... how would you know.... if you were not a consolidated "something" able to process these concepts? or you do not
wish to be anything? its interesting that in order to have that wish you first would have to know what it is to be something.....
something like an immortal Emperor of a galactic civilization, to create a just and peaceful utopia where people can travel the stars for free and
live the fullest lives imaginable. I would manage ways for people to eat the finest delicacies, drink the purest water, everything environmentally
friendly, cohabitation with animals and nature etc...
The point of this thread, and what im asking you guys...... is if nothing existed..... only your awareness.... nothing has ever happened or been
made....... and you are able to create whatever you want,,, and you are able to become whatever you want.... what would you create.... and what would
you become?
I would want to be immortal, forever the age I am now, and massively powerful politically. Then I could stay around for thousands of years, fighting
the PTB and improving the treatment of humanity. No more food for oil. It would be food for the people who are hungry. No more billionaires living in
mansions that cost 10 million, while a child on the other side of the world hunts through a garbage dump for rotten food, cause that's all there is
to eat. I would spend the rest of eternity making sure the type of scum who run the world now, would never have the chance to do so again.
Originally posted by yourmaker
something like an immortal Emperor of a galactic civilization, to create a just and peaceful utopia where people can travel the stars for free and
live the fullest lives imaginable. I would manage ways for people to eat the finest delicacies, drink the purest water, everything environmentally
friendly, cohabitation with animals and nature etc...
cool!! in the model of the current universe all that willed movement takes energy,,, its is why our society is ran the way it is,, using our energy to
gain goods to replenish our energy and this multiplied by the number of people in the society doing this same "working" many jobs and goods and
available,, and we have culture and technological progression....... how would you care for the complete needs of ever person and every animal?
somehow grant every wish they desiree "magically"?
Yes, that,s it more or less, for better or worse. But as I said, maybe with the possibility of going back to " rectify " what might be
mistakes...I.e. if you had had the power to enable Neanderthal man to begin the journey to become what we are today, might you think " Damn ! I
misjudged that one, I need to do something about it... " ( ? )
Originally posted by DAVID64
I would want to be immortal, forever the age I am now, and massively powerful politically. Then I could stay around for thousands of years, fighting
the PTB and improving the treatment of humanity. No more food for oil. It would be food for the people who are hungry. No more billionaires living in
mansions that cost 10 million, while a child on the other side of the world hunts through a garbage dump for rotten food, cause that's all there is
to eat. I would spend the rest of eternity making sure the type of scum who run the world now, would never have the chance to do so again.
cool! forever is a mighty long time... you are convinced what you are is a prime thing to be,, one of the best if you would be satisfied being in
your form committed to this world forever.... I commend you for your righteous aspirations.... so you would get society together and everyone would be
taken care of... and the purpose of your planet and duty would be making sure every person is able to eat and be healthy? would there be any long term
goals or desired achievements for technological/scientific advancement?
Yes, that,s it more or less, for better or worse. But as I said, maybe with the possibility of going back to " rectify " what might be
mistakes...I.e. if you had had the power to enable Neanderthal man to begin the journey to become what we are today, might you think " Damn ! I
misjudged that one, I need to do something about it... " ( ? )
so is it something about the technical capabilities of modern man that objectively sets him apart from other animal? sort of like other animals are
stone wheels and wooden carts, and modern man is an ipad in a ferrari.... the wiring of man, his self driven passion and longing for perfection, and
progression, is something rare and special in and of itself......... thats pretty much what its about and what i think your saying, man is a greatly
different "model" Neanderthal if able to become sentient and intelligent would never be able to be as elegant and intelligent and sophisticated and
novel and creative as mankind? same with cats.... because of the wiring of their brains, and their physical body, even if they did become
intelligent they would still be crawling on all fours, and it would be hard to build a rocket with paws?
questions
1st= i would be human
2nd= i would be flesh and bone
3rd= i would be born and live in england
4th= nothing is imposible.........ish!
5th= to procreate and advance for the better of the species.
Originally posted by yourmaker
something like an immortal Emperor of a galactic civilization, to create a just and peaceful utopia where people can travel the stars for free and
live the fullest lives imaginable. I would manage ways for people to eat the finest delicacies, drink the purest water, everything environmentally
friendly, cohabitation with animals and nature etc...
cool!! in the model of the current universe all that willed movement takes energy,,, its is why our society is ran the way it is,, using our energy to
gain goods to replenish our energy and this multiplied by the number of people in the society doing this same "working" many jobs and goods and
available,, and we have culture and technological progression....... how would you care for the complete needs of ever person and every animal?
somehow grant every wish they desiree "magically"?
if the social environment changed, and people were brought up with a sense of morals mixed with a love for science, a self-creating system of happy
geniuses on a mass scale would want to produce the essentials for their fellow humans and would find the way to bring everyone, everything they need.
our society has told us to get everything we don't need, and to spend, and consume more then produce.
change the environment that people are raised in and they will seek out these changes for all themselves.
the crackhead, at some point could have been an astronaut, eliminate the social validation within that environment he foudn himself in and you change
the future.
Yes..I think so, perhaps we have evolved too quickly, trying to run before we can walk properly, in that we,re using our technological advances mostly
for the wrong reasons. However, I suspect we,re not going much further, technologically, before we destroy ourselves, one way or another, a sort of "
Built in " fail safe to prevent civilisations like ours leaving this planet and possibly tainting other civilisations around the cosmos with our dark
primitive, side...?
Why would you choose to be human? if you had infinite time,,, and lets say you lived a mortal life of a human,,, after each mortal life would you
choose to be a human again? what im trying to ask is do you think there can be anything greater then a human,,,, what would/could be better then being
human? what would it be made of, how would it interact with its environment? what would be its purpose?
how surprising is it that this dumb universe created the best possible things to be, a human,, and all of us are one of them,,, and we cant think of
anything greater to be or do?
Yes..I think so, perhaps we have evolved too quickly, trying to run before we can walk properly, in that we,re using our technological advances mostly
for the wrong reasons. However, I suspect we,re not going much further, technologically, before we destroy ourselves, one way or another, a sort of "
Built in " fail safe to prevent civilisations like ours leaving this planet and possibly tainting other civilisations around the cosmos with our dark
primitive, side...?
but isnt it a sort of ashamed and bashful feeling to think you are not the greatest, you do not know a lot, you are not capable of doing something,,,
and is it not these feelings which propel us forward into that run... if we stopped for a moment and were satisfied with our selves we would be little
more then silly monkeys,,, but if we diligently and with haste evolve and learn, and attempt to advance and progress, we can view ourselves as
something worthy, we can have pride, and satisfaction, we can have hope that we now are creating a better future for our collective offspring,... this
isnt necessarily how i think,, but i think this is how a lot of people think in slightly different ways and slightly subconsciously,, because the
world has missed the point of being able to stop and communicate and solve problems, and ask questions, and trust each other, and work
together,,....
i dont think our species will destroy itself,,, i dont think you should think this either,,, it is a nice cautious thought if you are really scared
they will,, perhaps you are willing to warn everyone and make sure they dont,,,, but if you are not going to do that,,, i think you may hope or wish
they destroy themselves, to rub their unwarranted smugness in their ruined faces,,, theres a part of you that hopes the world doesnt go on, because
eventually it will be going on without you,,, i think this is a side effect of being mortal.... i could be totally wrong,, but there is no benefit of
believing the species is going to destroy itself, except making yourself look haughty and superior in that you know this and you look down upon the
entire species,,,, there is technology,,, there are underground bases,,,, 6.9 billion people can die and the species will not have destroyed
itself,,,,, as fragile as life can be it can also be resilient,,, if the species does get completely wiped out maybe in a few billion years itll be
back, no worries....... we should analyze the now though,, and prevent bad from happening and promote good..... hope i dont offend you but just
spewing my analysis.
No offence taken. And I,m not worried for the future of mankind, what will be, will be. BUT I don,t think our technological advances will get the
better of our essentially primitive, self destructive nature ?
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92 Ga. App. 616 (1955)
89 S.E.2d 585
KING
v.
THE STATE.
35831.
Court of Appeals of Georgia.
Decided September 22, 1955.
*617 Murphy & Murphy, Claude V. Driver, for plaintiff in error.
Robert J. Noland, Solicitor-General, contra.
TOWNSEND, J.
Any remarks to the jury by the trial judge or other officer of the court not relevant to any issue in the cause which would have a tendency to coerce them into reaching their verdict constitutes reversible error. Campbell v. State, 81 Ga. App. 834 (60 S. E. 2d 169). That the statement here complained of was made by the bailiff to the jury and falsely attributed to the judge, and that its falsity was not known until after the verdict, is admitted. In Shaw v. State, 83 Ga. 92, 101 (9 S. E. 768), the jury, while deliberating their verdict, were taken to a prayer meeting where the solicitor-general presided, seated them, and in his sermon made reference to the court and the trial. Headnote 1 of this case states: "Where misconduct of a juror or of the jury is shown, the presumption is that the defendant has been injured, and the onus is upon the State to remove such presumption by proper proof. While reviewing courts are loath to interfere with the decision of the trial judge that the presumption has been removed, such decision is in this State subject to review. The misconduct of the jury and of the officer in charge *618 of them in this case was of such a character as to require a new trial." At page 99 it is held as follows: "There are other things, however, which if done by an individual member of the jury, or by the whole jury, are so contrary to the public policy of the State in the procurement of fair and impartial trials for the citizens of the State as to require that a verdict rendered by such jury be set aside, whether the defendant has been injured thereby or not; and in our opinion, the case under consideration belongs to this class. The State is jealous of the rights and liberties of its people. When one of its citizens is accused of crime, it throws around him all the safeguards that are possible, in order to procure him a fair and impartial trial. It requires the officer who has charge of that particular jury, to swear, in substance, in open court to take them to the jury-room and there keep them safely, and not to communicate with them himself or suffer anyone else to communicate with them, unless by leave of the court. The law contemplates that when a jury are selected and sworn to try a citizen for felony, they shall be entirely separated from the world, and that no communication whatever shall be had with them, from the beginning of the trial until the verdict is rendered, unless by leave of the court. It contemplates that no outside influence shall be brought to bear on the minds of the jury, and that nothing shall occur outside of the trial which shall disturb their minds in any way; that the minds of the jury shall be entirely occupied with the consideration of the case which they are sworn to try."
In the Shaw case the jurors made affidavits, as in this case, that they were not influenced. In that case, at page 101, the Supreme Court stated: "It is true that the jury say in their affidavits that these things did not influence their minds; but how can they tell how can any man tell what particular facts and circumstances influence his judgment? Woolfolk v. State, 81 Ga. 551; Smith v. Lovejoy, 62 Ga. 373; Thompson on Trials, 962." Harris v. State, 150 Ga. 680 (104 S. E. 902), like this case, came on an extraordinary motion for new trial, and like this, was a felony case. As in this case, the bailiff stated to the jury that "the judge would keep them locked up until they did make a verdict." In that case the court, at page 683, stated: "We cannot be assured that the agreement [verdict of guilty] subsequently made, but unattainable *619 before, was not effected by this communication. The communication itself was clearly illegal; it was calculated to influence the jury, or some of them, and therefore the verdict is not free from taint." (quoted from Gholston v. Gholston, 31 Ga. 625, 639).
Code § 110-109, codified from Fulton County v. Phillips, 91 Ga. 65 (2) (16 S. E. 260), provides that "The affidavits of jurors may be taken to sustain but not to impeach their verdict"; and this rule of law is recognized, regardless of the fairness or unfairness thereof. Its effect of course is that jurors who contend they were not influenced by the improper remarks may swear to that effect. If the truth is to the contrary, their lips are sealed. Its further effect is that jurors who are asked the question are called upon either to refuse to answer, which means they were influenced in violation of their oaths, or to swear that they were not influenced. The temptation must be strong for a juror to uphold the integrity of his oath, given on entering the jury box, to "a true verdict give according to the evidence," rather than admit, also under oath and after the trial, that in violation thereof he allowed matters other than the evidence in the case to influence his decision. Of course, if he was influenced by how long he might be in the jury box, he was influenced by a matter other than the evidence in the case. Be that as it may, the authorities herein cited require the reversal of this case, notwithstanding affidavits of the jurors that they were not influenced.
On the other hand, the record here shows that after deliberating 24 hours, 3 of the jurors had consistently voted for acquittal; that, within 30 minutes after the statement herein complained of was made by the bailiff to the jury, these 3 jurors capitulated and voted for a verdict of guilty. Eleven of the jurors, being authorized to do so under Code § 110-109, testified the statement had no influence on them. This included 2 of the jurors who had previously voted for acquittal. The remaining juror first made an affidavit that he was influenced, which affidavit cannot be considered because it is in violation of Code § 110-109. He later made an affidavit for the State, in which he undertook to limit the amount of influence the statement had upon him. This affidavit fails, however, to show total lack of influence. Under any rule the onus is upon the State to remove the presumption of harm. *620 That burden could only be carried by affidavits of 12 jurors. If there was no affidavit at all, therefore, on the part of the 12th juror, the State would have failed to carry the burden. As herein pointed out, the 12th juror made 2 affidavits, neither of which can be considered because they both show influence and consequently tend to impeach the verdict. The second affidavit by this juror for the use of the State shows that he made the verdict sooner than he would have but for the statement. This shows some influence for bad and thus tends to impeach the verdict and cannot be considered. Since the 12th juror failed to make an affidavit that would uphold the verdict, the State failed to carry the burden of showing that this error in trial procedure had no harmful effect.
However, the well established rule in this State enunciated in Shaw v. State, supra, and Harris v. State, supra, applies to this case and requires its reversal regardless of whether or not it is made to appear that the error was prejudicial and harmful, it being conclusively presumed that it was so.
The trial court erred in denying the motion for a new trial.
Judgment reversed. Gardner, P. J., and Carlisle, J., concur.
| 2024-04-08T01:26:35.434368 | https://example.com/article/7248 |
The U.S. Department of the Interior will offer offshore Texas, Louisiana, Mississippi, Alabama and Florida for oil and gas exploration and development //snipp// This will be the largest such lease sale in the country's history, it will include almost 77 million acres of federal waters in the Gulf. The lease sale will be live streamed online from New Orleans.
PARKER COUNTY - It's been a tumultuous 24 hours for a young Chihuahua mix named Pumpkin. "She would like to take a nap," said Parker County Animal Control Supervisor Karen Kessler, whose arms Pumpkin was nuzzling into. The tiny pup was found Thursday, roaming a lot in rural Weatherford. A woman named Vanessa was the one who discovered her. "It was very skittish at first," Vanessa said of the dog. "It didn't want [to go] anywhere near me." Vanessa's family has had trouble with people illegally dumping on their property, so they set up game cameras. She went to check...
The security guard wounded in a 2015 ISIS-inspired terrorist attack at the "Draw Muhammad" event in Garland, Texas, is suing the FBI, and argues the bureau is liable for his damages because an agent "solicited, encouraged, directed and aided members of ISIS in planning and carrying out the May 3 attack," according to court documents filed Monday.
The Houston school district is under fire after a student without legal status ended up in immigration detention following his arrest by a school police officer for an altercation with a female student. A lawyer for Dennis Rivera Sarmiento, 19, said his client was bullied by the 15-year-old girl and retaliated only after she taunted him with racial slurs, threw a full bottle of Gatorade at him and confronted him. "He's very fearful of being deported to Honduras," said Rivera's attorney, Brandon Roché. On Wednesday, students at Stephen F. Austin High School in Houston staged a lunch hour walkout to...
Federal immigration agents are escalating efforts to crack down on businesses hiring undocumented workers. New data released Friday morning shows Immigration and Customs Enforcement visited 122 businesses over the past five days, mostly in Southern California. Mike Poindexter is CEO of his family business the Poindexter Nut Company near Fresno, California. He says most Americans don't want these labor-intensive jobs. "We hire people all the time. They show up, they work two days and they leave," Poindexter said. His company is now being audited by ICE. "We've had somewhere between 5 to 10 percent of our workforce quit voluntarily just...
President Trump on Wednesday called on lawmakers to oppose a series of bipartisan efforts to address immigration and resolve the fate of the so-called “Dreamers,” demanding fealty to his hard-line approach even as more moderate senators converged on a narrower approach. Senators in both parties are racing against a self-imposed, end-of-the-week deadline to write legislation that could win broad support by increasing border security while at the same time offering a path to citizenship for immigrants brought to the United States as children. Members of a bipartisan group calling itself the Common Sense Coalition said they have reached a deal...
DALLAS (CBSDFW.COM) – Missing since Friday, former Dallas Cowboys running back Lincoln Coleman was found safe on Tuesday morning, according to Dallas Police. Investigators were worried about his diminished mental capacity and his need for medical help. Coleman’s agent and friend of 15 years, Christopher Randolph, said Coleman had parked his car at a church three blocks from his house. He said Coleman could not figure out where he left his car or how to get home. Randolph said on Tuesday at about 4 a.m., Coleman returned home but was confused about what happened. “We were worried about him freezing....
DALLAS - If you can’t win big, go small. That’s the strategy gaining momentum among criminal justice reformers in the age of Trump, as the federal government hardens its approach to law enforcement. Instead of pouring money and energy into squeezing change out of Washington, national civil rights organizations are teaming with local groups to push their agendas in county-level district attorney races, where a few thousand votes can determine who asserts the most influence over the local justice system. Picking their targets carefully, and crunching election data to influence pivotal voter blocs - and benefiting from the largesse of...
Imagine going to sleep and waking up sounding British. It's a real thing, and it happened to a Valley woman who has never even left the country. "Everybody only sees or hears Mary Poppins," said Michelle Myers, a mom of seven who lives in Buckeye. Myers is a former Texas beauty queen who has never even left the United States. Three times in the past seven years, Myers has gone to sleep with blinding headaches only to wake up with a different accent. The first time it was Irish. The second time was Australian. Both incidents lasted about a week....
Myers says she has been diagnosed with Foreign Accent Syndrome. The disorder typically occurs after strokes or traumatic brain injuries damage the language center of a person's brain — to the degree that their native language sounds like it is tinged with a foreign accent, according to the Center for Communication Disorders at the University of Texas at Dallas.
"The parents of special needs children are especially vulnerable to state intervention."This mom's story in The Washington Post will kick anyone in the gut. Texas writer May Cobb was out for a day with her mom, her husband, and their autistic 5-year-old who, miraculously, was doing great. By great, Cobb explained, she meant he had not had a single meltdown during the hour they were at a park and on the boardwalk near Lady Bird Lake in Austin. He hadn't stripped off all his clothes, and he wasn't banging his head over and over again. Sure, his hair was messy—his...
The Austin Justice Coalition is asking community members to donate copies from a specific list of fiction and nonfiction titles to the Carver Branch of the library system. The city came up with the list of 126 works at the group’s request, and the donations will expand Carver’s collection. “For me, even if we get two books, it’s better than nothing,” said Ishia Lynette, AJC’s social media and community service director. She’s organizing the Black Literature Matters donation event Monday as part of the organization’s Black Unity Week. Carver already has a piece of its collection dedicated to African American...
Years after the former rodeo roper turned country singer lost his voice, LarryCallies stumbled into his past. Records from plantation days revealed connections between his slave ancestors and a white east Texas minister who had kids with slaves, uncovering hidden history became his passion.Larry Callies owns history with a collection of boots, buckles, stirrups, photos and more on display at the Black Cowboy Museum in Rosenberg. “I just don’t like to lose my heritage,” he said. “I don’t like to lose things that we used to have. I brought a lot of stuff from me just picking stuff up.” Years...
Texas Rep. Louis Gohmert appeared on Judge Jeanine Pirro’s show on Fox News to discuss the fallout of the FISA memos, which brought to light potential abuse of government surveillance to spy on the Trump campaign. “You and I believe in due process,” Gohmert said. “We would never send somebody to jail without due process, but one thing — and this is a good segue, I think — when a lawyer provides something to the court that is not true, and especially to a FISA secret court where there is nobody there for the other side. The other said —...
With McLennan County District Attorney Abel Reyna desperately dumping Twin Peaks biker cases right and left in recent days, the astonished taxpayer must demand honesty of himself if not of Reyna: Does anyone really believe Reyna has suddenly been struck by an epiphany that has stubbornly eluded him in the three years since the May 17, 2015, biker shootout that left nine dead and 20 wounded? -this epiphany has to do with political odds, not any interest in justice. And it must have been some epiphany. Reyna is credited with hijacking a Waco police murder investigation in 2015 and throwing...
An Austin mother is upset that Four Points Middle School sent her daughter home this week with an assignment to “Draw a picture of yourself as a slave…” “This is a learning tool that is not acceptable under any circumstances,” stated Tonya Jennings. The assignment is in reference to discussions of “slave life in Texas in the 1850’s”, according to a picture of the assignment sent to CBS Austin by Jennings. Upon learning of the assignment, Jennings husband went to the school Friday to discuss the issue with administrators. A Leander ISD spokesperson sent a statement to CBS Austin Saturday...
Heather Holland, a second-grade teacher at Ikard Elementary School with the Weatherford Independent School District died over the weekend, the Weatherford Democrat reports. Holland got sick about a week ago and took medication, but delayed picking up the prescription due to the $116 copay, according to the newspaper. By Friday night, Holland's condition worsened and she was taken to the hospital. Her husband Frank Holland told the Weatherford Democrat that she died Sunday morning. "She loved helping people, helping the kids, and the kids loved her," Holland's husband told the Weatherford Democrat. Charlotte LaGrone, a spokeswoman for Weatherford ISD, told...
Bush is overseeing a $450 million plan to redevelop and improve the site, featuring things like a new museum housed in nearby state-owned buildings and additional historic programming. A mix of public money and private donations is meant to cover the cost. But the report obtained by the newspaper, dated Sept. 8, notes that "the current situation obscures the control of the funds. It also has created a situation where GLO is responsible for state laws over the use of funds, but with limited control since the expenditures are prior to approval by the GLO." GLO spokeswoman Brittany Eck said...
WASHINGTON — Sen. Ted Cruz signaled a bruising fight Thursday if the White House pushes ahead with the nominee for a coveted Caribbean diplomatic post who spread unfounded conspiracy theories about him during the 2016 campaign. As an ardent cheerleader for Donald Trump, beauty supply executive Leandro Rizzuto Jr. used Twitter to promote an unsubstantiated allegation that Cruz cheated on his wife, and other claims that Heidi Cruz herself was part of a cabal seeking to unite North America under one government. "I don't know the fellow. He seems to have unusual views," Cruz said Thursday through an aide. "I...
The motions for dismissal approved by 54th Criminal District Judge Matt Johnson offer defendants no possible avenue for expunction of their record, nor does the language of the order hold any hope to recover damages in a civil rights case. Notice that the reason ticked off in the form is “other,” and adds the missive, and for cause would show the Court the following: While probable cause for the Defendant’s arrest and prosecution remains, based on continued investigation, the State is exercising its prosecutorial discretion in dismissing this matter in order to focus its efforts and resources on co-defendants with... | 2023-12-28T01:26:35.434368 | https://example.com/article/8841 |
Barnabas McDonald
Brother Barnabas McDonald F.S.C.(1865April 24, 1929), was a Brother of the Christian Schools involved with youth work, especially among delinquents and orphans in the United States. He is remembered as founder of the Columbian Squires of the Knights of Columbus and as a driving force in establishing the early relationship between the Boy Scouts of America and the American Catholic Church.
Boy Scouts of America
Brother Barnabas was a leader during the early years of Catholic Youth ministry. Together with Victor F. Ridder and with the cooperation of James E. West, he is credited with founding one of the earliest Catholic Boy Scout troops at St. Patrick's Cathedral in 1912, having received formal approval of John Murphy Farley, Cardinal Archbishop of New York.
In 1924 Brother Barnabas and Victor Ridder organized a Catholic Committee on Scouting under the honorary chairmanship of Patrick Hayes, Cardinal Archbishop of New York. Bishop Joseph H. Conroy of Ogdensburg was named chairman of this Committee. Reverend Matthew J. Walsh, president of Notre Dame University was selected as national Chaplain.
Brother Barnabas was selected by the Boy Scouts of America in 1925 to be the Education Director of their "Catholic Bureau" for Scout extension under Catholic leadership, replacing Fr. John F. White. who had served in that capacity since 1919. In 1927 Brother Barnabas was recognized with the Silver Buffalo Award for his service.
Brother Barnabas remained active as Director of the National Catholic Committee on Scouting until his death.
Knights of Columbus
In 1923, at the prompting of Brother Barnabas, the Knights of Columbus established a "Boy Life Bureau". Brother Barnabas was appointed the bureau's first Executive Secretary. The Boy Movement Committee of the Supreme Council of the Knights of Columbus had sent questionnaires to each Grand Knight and after receiving the responses met with Brother Barnabas.
Though Knights of Columbus councils were involved in the Boy Scouts America and other youth programs, it was decided to establish a youth section within the Order. Under the guidance of Brother Barnabas together with Supreme Director Daniel A. Tobin of Brooklyn, the first Columbian Squires circle was instituted on August 4, 1925.
According to Brother Barnabas, "The supreme purpose of the Columbian Squires is character building." Squires have fun and share their Catholic faith, help people in need, and enjoy the company of friends in social, family, athletic, cultural, civic and spiritual activities. Through their local circle, Squires work and socialize as a group of friends, elect their own officers, and develop into Catholic leaders.
Death
He died in Albuquerque, New Mexico on April 24, 1929.
See also
Columbian Squires
Lincolndale Agricultural School
Institute of the Brothers of the Christian Schools
References
Category:1865 births
Category:1929 deaths
Category:Recipients of the Silver Buffalo Award
Category:American people of Irish descent
Category:De La Salle Brothers
Category:People from Ogdensburg, New York | 2023-10-30T01:26:35.434368 | https://example.com/article/6228 |
Why you should care
By the time Richard Nixon nominated G. Harrold Carswell for the Supreme Court in January 1970, the seat vacated by Abe Fortas had been open for nine months, and the president was getting frustrated. Two months earlier, the Senate had rejected Nixon’s first nominee for the seat, South Carolina judge Clement F. Haynsworth (a little too pro-segregation for comfort), but Nixon had gone back once more to the well of conservative Southern judges to pluck out Carswell, 50, a judge on the U.S. Court of Appeals for the 5th Circuit.
Carswell had been a federal judge for more than a decade — at age 38, he had become the youngest one in the country — and his nomination looked promising. But sometimes, as has recently been proved again with the rocky nomination of Brett Kavanaugh, things can go unexpectedly sideways during the Supreme Court confirmation process. For Carswell, that was thanks in no small part to some outspoken female activists willing to call him out for his behavior toward women.
The knives were out for Carswell.
The Carswell nomination got off to an inauspicious start. It took reporters less than two days to unearth a speech he had given as a young office-seeker in which he had declared his belief “that segregation of the races is proper and the only practical and correct way of life in our states.” Oh, and he had also been involved in a plan to turn a public golf course in Florida into a whites-only country club. But, as is still true today, what were considered a few minor strikes against Carswell were not enough to scupper a nomination that the White House and Republicans in Congress were behind. “The killing of a Supreme Court nominee is rarely death by a thousand cuts,” says Daniel Urman, a law and politics expert at Northeastern University. “Usually it requires death by four or five stabbings.”
And the knives were out for Carswell, who managed to weather the opposition from civil rights activists during the initial days of the hearing, when he declared before the judiciary committee that “I am not a racist” and that his prior remarks were “something out of the disembodied past.” Then, two women came before the all-male committee to discuss the latest nominee to a court that at the time had never had a female justice — and to raise an issue nobody had ever raised before that body: sexism.
The first witness that January morning was Rep. Patsy Takemoto Mink, D-Hawaii, the first woman of color elected to the House of Representatives and only one of about a dozen women in Congress at the time. Mink told the committee that Carswell’s nomination was “an affront to the women of America,” before connecting the allegations of racism to those of sexism. “Male supremacy, like white supremacy,” Mink said, “is equally repugnant to those who really believe in equality.”
Mink then cited Carswell’s recent refusal to review a case in which a woman had been denied an assembly line job because she was the mother of preschool-age children (a company policy that, of course, did not apply to similarly situated fathers). When the Republican senator from Kentucky, Marlow Cook, challenged Mink by pointing out that 10 judges on Carswell’s court had denied a hearing for the case, she responded: “Yes, I am well aware of that, Mr. Senator. But the other nine are not up for appointment to the Supreme Court.” (If only confirmation hearings had been televised at the time.) Mink was followed by Betty Friedan, president of the National Organization for Women, who labeled Carswell “a sexually backward judge” who would be unsympathetic to cases coming before the court involving the legal rights of women.
National Organization for Women Chairperson Kathryn F. Clarenbach (left) and President Betty Friedan.
Thanks to Mink and Friedan, momentum began to build against Carswell, who was nonetheless endorsed by the committee for a full Senate vote. In the wake of the allegations of racism and sexism came a charge that proved to be far more deleterious (and a more palatable excuse for some senators to oppose Carswell): his mediocre career as a jurist. More than 450 lawyers, including the deans of Harvard and Yale law schools, signed a letter noting Carswell’s lack of distinction. Opponents pointed out that 40 percent of Carswell’s rulings had been overturned on appeal (a large percentage for a federal judge) and that his rulings cited fewer authorities than those of other judges. Some senators rallied to his defense but in a rather unhelpful way. “Even if he is mediocre,” Republican Sen. Roman Hruska of Nebraska famously argued, “there are a lot of mediocre judges and people and lawyers, and they are entitled to a little representation, aren’t they?”
Ultimately, Carswell went down in a narrow Senate vote of 51-45, with 38 Democrats and 13 Republicans voting against him. After being rejected, Carswell resigned from the federal appeals court, and six years later was charged with making homosexual advances to an undercover Tallahassee police officer in a mall restroom. So it goes.
It didn’t go much better for Nixon and his plan to put a Southern conservative on the court. “If they vote [Carswell] down, we’ll send them somebody from Mississippi,” Nixon boasted to fellow Republicans during the latter days of the fight. But when the time came for a third nominee, Nixon played it safe with Harry A. Blackmun of Minnesota, a justice who would prove to be more liberal than anticipated and pen the court’s opinion in Roe v. Wade just three years later — a landmark decision hailed by Mink, Friedan and women’s rights advocates everywhere. | 2023-08-30T01:26:35.434368 | https://example.com/article/7000 |
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| 2024-06-09T01:26:35.434368 | https://example.com/article/4275 |
Have you ever wanted to dump all the SSIS packages stored in msdb out to files? Of course you have, who wouldn’t? Right? Well, at least one person does because this was the subject of a thread (save all ssis packages to file) on the SSIS forum earlier today.
Some of you may have already figured out a way of doing this but for those that haven’t ...
Earlier today I was doing a little work using datadude/DBPro/Visual Studio Database Tools/pick your name and had a need to write a Powershell script that I think might be useful to other folks so I’m sharing it here.
Often when you’re putting together database projects you will have a need for multiple .sqlcmdvars files – one for each environment ...
This is a very simple script - but it's one I run each morning. It searches the Windows System Event Log for an error condition. You can replace ''System'' here with ''Application'' or ''Security'', or any of the other logs that are created on your Windows Server. This is run at the server, since I have each server check itself and make a file of ...
Intro
Of late I have been getting down and dirty with the Database Development tools in Visual Studio 2010. You may know this feature set by one of the plethora of other names it has had over recent years such as:
Visual Studio Team System for Database Professionals
DBPro
Datadude
For the rest of this post I’ll stick with the colloquial ...
I use Extended Properties on databases and their objects all the time. They are a great way to include information about the object – I use them for versioning the database, detailing what a column is used for and so on. They can be a little tricky to set, but it’s really not bad once you learn how. Ken Simmons, a SQL Server MVP ...
I ran into an issue the other day where I couldn't set up some features in SQL Server 2008 because they ddon't support the use of Rules or Defaults. Let me explain a little more about that. In older versions of SQL Server, you could decalre a ''Rule'' or ''Default'' just like you do with a Table Constraint today. You would then ''bind'' these ...
The other day I blogged that the version of the SQL Server PowerShell provider (sqlps) follows the version of PowerShell. That’s all goodness, but it has appeared to cause an issue for PowerShell 2.0. the Get-Command PowerShell command-let returns an error (Object reference not set to an instance of an object) if you are using PowerShell 2.0 and ...
There may be some misunderstanding on how the PowerShell Provider for SQL Server works. I’ve written an article or two explaining that you can use PowerShell with SQL Server, without having the SQL Server 2008 (or higher) provider around. After all, PowerShell just uses .NET, and SQL Server “Server Management Objects” or SMO listen to that ...
SQL Server used to have cool little tool that would let you track your licenses. Microsoft didn’t use it to limit your system or anything, it was just a place on the server where you could put that this system used this license key. I miss those days – we don’t track that any more, and I want to make sure I’m up to date on my licensing, so I ...
I read Jeffery Hicks’ article in this month’s Redmond Magazine on a new add-in for Windows PowerShell 2.0. It’s called the PowerShell Pack and it has a some great new features that I plan to put into place on my production systems as soon as I finished learning and testing them.
You can download the pack here if you have PowerShell 2.0. I’m ... | 2023-12-04T01:26:35.434368 | https://example.com/article/6071 |
/*
* EPSG PCS Codes - GeoTIFF Rev 0.2
*/
/* C database for Geotiff include files. */
/* the macro ValuePair() must be defined */
/* by the enclosing include file */
#ifdef INCLUDE_OLD_CODES
#include old_pcs.inc
#endif /* OLD Codes */
/* Newer PCS */
ValuePair(PCS_Hjorsey_1955_Lambert, 3053)
ValuePair(PCS_ISN93_Lambert_1993, 3057)
ValuePair(PCS_ETRS89_Poland_CS2000_zone_5,2176)
ValuePair(PCS_ETRS89_Poland_CS2000_zone_6,2177)
ValuePair(PCS_ETRS89_Poland_CS2000_zone_7,2177)
ValuePair(PCS_ETRS89_Poland_CS2000_zone_8,2178)
ValuePair(PCS_ETRS89_Poland_CS92,2180)
/* New PCS */
ValuePair(PCS_GGRS87_Greek_Grid,2100)
ValuePair(PCS_KKJ_Finland_zone_1,2391)
ValuePair(PCS_KKJ_Finland_zone_2,2392)
ValuePair(PCS_KKJ_Finland_zone_3,2393)
ValuePair(PCS_KKJ_Finland_zone_4,2394)
ValuePair(PCS_RT90_2_5_gon_W,2400)
ValuePair(PCS_Lietuvos_Koordinoei_Sistema_1994,2600)
ValuePair(PCS_Estonian_Coordinate_System_of_1992,3300)
ValuePair(PCS_HD72_EOV,23700)
ValuePair(PCS_Dealul_Piscului_1970_Stereo_70,31700)
ValuePair(PCS_Adindan_UTM_zone_37N, 20137)
ValuePair(PCS_Adindan_UTM_zone_38N, 20138)
ValuePair(PCS_AGD66_AMG_zone_48, 20248)
ValuePair(PCS_AGD66_AMG_zone_49, 20249)
ValuePair(PCS_AGD66_AMG_zone_50, 20250)
ValuePair(PCS_AGD66_AMG_zone_51, 20251)
ValuePair(PCS_AGD66_AMG_zone_52, 20252)
ValuePair(PCS_AGD66_AMG_zone_53, 20253)
ValuePair(PCS_AGD66_AMG_zone_54, 20254)
ValuePair(PCS_AGD66_AMG_zone_55, 20255)
ValuePair(PCS_AGD66_AMG_zone_56, 20256)
ValuePair(PCS_AGD66_AMG_zone_57, 20257)
ValuePair(PCS_AGD66_AMG_zone_58, 20258)
ValuePair(PCS_AGD84_AMG_zone_48, 20348)
ValuePair(PCS_AGD84_AMG_zone_49, 20349)
ValuePair(PCS_AGD84_AMG_zone_50, 20350)
ValuePair(PCS_AGD84_AMG_zone_51, 20351)
ValuePair(PCS_AGD84_AMG_zone_52, 20352)
ValuePair(PCS_AGD84_AMG_zone_53, 20353)
ValuePair(PCS_AGD84_AMG_zone_54, 20354)
ValuePair(PCS_AGD84_AMG_zone_55, 20355)
ValuePair(PCS_AGD84_AMG_zone_56, 20356)
ValuePair(PCS_AGD84_AMG_zone_57, 20357)
ValuePair(PCS_AGD84_AMG_zone_58, 20358)
ValuePair(PCS_Ain_el_Abd_UTM_zone_37N, 20437)
ValuePair(PCS_Ain_el_Abd_UTM_zone_38N, 20438)
ValuePair(PCS_Ain_el_Abd_UTM_zone_39N, 20439)
ValuePair(PCS_Ain_el_Abd_Bahrain_Grid, 20499)
ValuePair(PCS_Afgooye_UTM_zone_38N, 20538)
ValuePair(PCS_Afgooye_UTM_zone_39N, 20539)
ValuePair(PCS_Lisbon_Portugese_Grid, 20700)
ValuePair(PCS_Aratu_UTM_zone_22S, 20822)
ValuePair(PCS_Aratu_UTM_zone_23S, 20823)
ValuePair(PCS_Aratu_UTM_zone_24S, 20824)
ValuePair(PCS_Arc_1950_Lo13, 20973)
ValuePair(PCS_Arc_1950_Lo15, 20975)
ValuePair(PCS_Arc_1950_Lo17, 20977)
ValuePair(PCS_Arc_1950_Lo19, 20979)
ValuePair(PCS_Arc_1950_Lo21, 20981)
ValuePair(PCS_Arc_1950_Lo23, 20983)
ValuePair(PCS_Arc_1950_Lo25, 20985)
ValuePair(PCS_Arc_1950_Lo27, 20987)
ValuePair(PCS_Arc_1950_Lo29, 20989)
ValuePair(PCS_Arc_1950_Lo31, 20991)
ValuePair(PCS_Arc_1950_Lo33, 20993)
ValuePair(PCS_Arc_1950_Lo35, 20995)
ValuePair(PCS_Batavia_NEIEZ, 21100)
ValuePair(PCS_Batavia_UTM_zone_48S, 21148)
ValuePair(PCS_Batavia_UTM_zone_49S, 21149)
ValuePair(PCS_Batavia_UTM_zone_50S, 21150)
ValuePair(PCS_Beijing_Gauss_zone_13, 21413)
ValuePair(PCS_Beijing_Gauss_zone_14, 21414)
ValuePair(PCS_Beijing_Gauss_zone_15, 21415)
ValuePair(PCS_Beijing_Gauss_zone_16, 21416)
ValuePair(PCS_Beijing_Gauss_zone_17, 21417)
ValuePair(PCS_Beijing_Gauss_zone_18, 21418)
ValuePair(PCS_Beijing_Gauss_zone_19, 21419)
ValuePair(PCS_Beijing_Gauss_zone_20, 21420)
ValuePair(PCS_Beijing_Gauss_zone_21, 21421)
ValuePair(PCS_Beijing_Gauss_zone_22, 21422)
ValuePair(PCS_Beijing_Gauss_zone_23, 21423)
ValuePair(PCS_Beijing_Gauss_13N, 21473)
ValuePair(PCS_Beijing_Gauss_14N, 21474)
ValuePair(PCS_Beijing_Gauss_15N, 21475)
ValuePair(PCS_Beijing_Gauss_16N, 21476)
ValuePair(PCS_Beijing_Gauss_17N, 21477)
ValuePair(PCS_Beijing_Gauss_18N, 21478)
ValuePair(PCS_Beijing_Gauss_19N, 21479)
ValuePair(PCS_Beijing_Gauss_20N, 21480)
ValuePair(PCS_Beijing_Gauss_21N, 21481)
ValuePair(PCS_Beijing_Gauss_22N, 21482)
ValuePair(PCS_Beijing_Gauss_23N, 21483)
ValuePair(PCS_Belge_Lambert_50, 21500)
ValuePair(PCS_Bern_1898_Swiss_Old, 21790)
ValuePair(PCS_Bogota_UTM_zone_17N, 21817)
ValuePair(PCS_Bogota_UTM_zone_18N, 21818)
ValuePair(PCS_Bogota_Colombia_3W, 21891)
ValuePair(PCS_Bogota_Colombia_Bogota, 21892)
ValuePair(PCS_Bogota_Colombia_3E, 21893)
ValuePair(PCS_Bogota_Colombia_6E, 21894)
ValuePair(PCS_Camacupa_UTM_32S, 22032)
ValuePair(PCS_Camacupa_UTM_33S, 22033)
ValuePair(PCS_C_Inchauspe_Argentina_1, 22191)
ValuePair(PCS_C_Inchauspe_Argentina_2, 22192)
ValuePair(PCS_C_Inchauspe_Argentina_3, 22193)
ValuePair(PCS_C_Inchauspe_Argentina_4, 22194)
ValuePair(PCS_C_Inchauspe_Argentina_5, 22195)
ValuePair(PCS_C_Inchauspe_Argentina_6, 22196)
ValuePair(PCS_C_Inchauspe_Argentina_7, 22197)
ValuePair(PCS_Carthage_UTM_zone_32N, 22332)
ValuePair(PCS_Carthage_Nord_Tunisie, 22391)
ValuePair(PCS_Carthage_Sud_Tunisie, 22392)
ValuePair(PCS_Corrego_Alegre_UTM_23S, 22523)
ValuePair(PCS_Corrego_Alegre_UTM_24S, 22524)
ValuePair(PCS_Douala_UTM_zone_32N, 22832)
ValuePair(PCS_Egypt_1907_Red_Belt, 22992)
ValuePair(PCS_Egypt_1907_Purple_Belt, 22993)
ValuePair(PCS_Egypt_1907_Ext_Purple, 22994)
ValuePair(PCS_ED50_UTM_zone_28N, 23028)
ValuePair(PCS_ED50_UTM_zone_29N, 23029)
ValuePair(PCS_ED50_UTM_zone_30N, 23030)
ValuePair(PCS_ED50_UTM_zone_31N, 23031)
ValuePair(PCS_ED50_UTM_zone_32N, 23032)
ValuePair(PCS_ED50_UTM_zone_33N, 23033)
ValuePair(PCS_ED50_UTM_zone_34N, 23034)
ValuePair(PCS_ED50_UTM_zone_35N, 23035)
ValuePair(PCS_ED50_UTM_zone_36N, 23036)
ValuePair(PCS_ED50_UTM_zone_37N, 23037)
ValuePair(PCS_ED50_UTM_zone_38N, 23038)
ValuePair(PCS_Fahud_UTM_zone_39N, 23239)
ValuePair(PCS_Fahud_UTM_zone_40N, 23240)
ValuePair(PCS_Garoua_UTM_zone_33N, 23433)
ValuePair(PCS_ID74_UTM_zone_46N, 23846)
ValuePair(PCS_ID74_UTM_zone_47N, 23847)
ValuePair(PCS_ID74_UTM_zone_48N, 23848)
ValuePair(PCS_ID74_UTM_zone_49N, 23849)
ValuePair(PCS_ID74_UTM_zone_50N, 23850)
ValuePair(PCS_ID74_UTM_zone_51N, 23851)
ValuePair(PCS_ID74_UTM_zone_52N, 23852)
ValuePair(PCS_ID74_UTM_zone_53N, 23853)
ValuePair(PCS_ID74_UTM_zone_46S, 23886)
ValuePair(PCS_ID74_UTM_zone_47S, 23887)
ValuePair(PCS_ID74_UTM_zone_48S, 23888)
ValuePair(PCS_ID74_UTM_zone_49S, 23889)
ValuePair(PCS_ID74_UTM_zone_50S, 23890)
ValuePair(PCS_ID74_UTM_zone_51S, 23891)
ValuePair(PCS_ID74_UTM_zone_52S, 23892)
ValuePair(PCS_ID74_UTM_zone_53S, 23893)
ValuePair(PCS_ID74_UTM_zone_54S, 23894)
ValuePair(PCS_Indian_1954_UTM_47N, 23947)
ValuePair(PCS_Indian_1954_UTM_48N, 23948)
ValuePair(PCS_Indian_1975_UTM_47N, 24047)
ValuePair(PCS_Indian_1975_UTM_48N, 24048)
ValuePair(PCS_Jamaica_1875_Old_Grid, 24100)
ValuePair(PCS_JAD69_Jamaica_Grid, 24200)
ValuePair(PCS_Kalianpur_India_0, 24370)
ValuePair(PCS_Kalianpur_India_I, 24371)
ValuePair(PCS_Kalianpur_India_IIa, 24372)
ValuePair(PCS_Kalianpur_India_IIIa, 24373)
ValuePair(PCS_Kalianpur_India_IVa, 24374)
ValuePair(PCS_Kalianpur_India_IIb, 24382)
ValuePair(PCS_Kalianpur_India_IIIb, 24383)
ValuePair(PCS_Kalianpur_India_IVb, 24384)
ValuePair(PCS_Kertau_Singapore_Grid, 24500)
ValuePair(PCS_Kertau_UTM_zone_47N, 24547)
ValuePair(PCS_Kertau_UTM_zone_48N, 24548)
ValuePair(PCS_La_Canoa_UTM_zone_20N, 24720)
ValuePair(PCS_La_Canoa_UTM_zone_21N, 24721)
ValuePair(PCS_PSAD56_UTM_zone_18N, 24818)
ValuePair(PCS_PSAD56_UTM_zone_19N, 24819)
ValuePair(PCS_PSAD56_UTM_zone_20N, 24820)
ValuePair(PCS_PSAD56_UTM_zone_21N, 24821)
ValuePair(PCS_PSAD56_UTM_zone_17S, 24877)
ValuePair(PCS_PSAD56_UTM_zone_18S, 24878)
ValuePair(PCS_PSAD56_UTM_zone_19S, 24879)
ValuePair(PCS_PSAD56_UTM_zone_20S, 24880)
ValuePair(PCS_PSAD56_Peru_west_zone, 24891)
ValuePair(PCS_PSAD56_Peru_central, 24892)
ValuePair(PCS_PSAD56_Peru_east_zone, 24893)
ValuePair(PCS_Leigon_Ghana_Grid, 25000)
ValuePair(PCS_Lome_UTM_zone_31N, 25231)
ValuePair(PCS_Luzon_Philippines_I, 25391)
ValuePair(PCS_Luzon_Philippines_II, 25392)
ValuePair(PCS_Luzon_Philippines_III, 25393)
ValuePair(PCS_Luzon_Philippines_IV, 25394)
ValuePair(PCS_Luzon_Philippines_V, 25395)
ValuePair(PCS_Makassar_NEIEZ, 25700)
ValuePair(PCS_Malongo_1987_UTM_32S, 25932)
ValuePair(PCS_Merchich_Nord_Maroc, 26191)
ValuePair(PCS_Merchich_Sud_Maroc, 26192)
ValuePair(PCS_Merchich_Sahara, 26193)
ValuePair(PCS_Massawa_UTM_zone_37N, 26237)
ValuePair(PCS_Minna_UTM_zone_31N, 26331)
ValuePair(PCS_Minna_UTM_zone_32N, 26332)
ValuePair(PCS_Minna_Nigeria_West, 26391)
ValuePair(PCS_Minna_Nigeria_Mid_Belt, 26392)
ValuePair(PCS_Minna_Nigeria_East, 26393)
ValuePair(PCS_Mhast_UTM_zone_32S, 26432)
ValuePair(PCS_Monte_Mario_Italy_1, 26591)
ValuePair(PCS_Monte_Mario_Italy_2, 26592)
ValuePair(PCS_M_poraloko_UTM_32N, 26632)
ValuePair(PCS_M_poraloko_UTM_32S, 26692)
ValuePair(PCS_NAD27_UTM_zone_3N, 26703)
ValuePair(PCS_NAD27_UTM_zone_4N, 26704)
ValuePair(PCS_NAD27_UTM_zone_5N, 26705)
ValuePair(PCS_NAD27_UTM_zone_6N, 26706)
ValuePair(PCS_NAD27_UTM_zone_7N, 26707)
ValuePair(PCS_NAD27_UTM_zone_8N, 26708)
ValuePair(PCS_NAD27_UTM_zone_9N, 26709)
ValuePair(PCS_NAD27_UTM_zone_10N, 26710)
ValuePair(PCS_NAD27_UTM_zone_11N, 26711)
ValuePair(PCS_NAD27_UTM_zone_12N, 26712)
ValuePair(PCS_NAD27_UTM_zone_13N, 26713)
ValuePair(PCS_NAD27_UTM_zone_14N, 26714)
ValuePair(PCS_NAD27_UTM_zone_15N, 26715)
ValuePair(PCS_NAD27_UTM_zone_16N, 26716)
ValuePair(PCS_NAD27_UTM_zone_17N, 26717)
ValuePair(PCS_NAD27_UTM_zone_18N, 26718)
ValuePair(PCS_NAD27_UTM_zone_19N, 26719)
ValuePair(PCS_NAD27_UTM_zone_20N, 26720)
ValuePair(PCS_NAD27_UTM_zone_21N, 26721)
ValuePair(PCS_NAD27_UTM_zone_22N, 26722)
ValuePair(PCS_NAD27_Alabama_East, 26729)
ValuePair(PCS_NAD27_Alabama_West, 26730)
ValuePair(PCS_NAD27_Alaska_zone_1, 26731)
ValuePair(PCS_NAD27_Alaska_zone_2, 26732)
ValuePair(PCS_NAD27_Alaska_zone_3, 26733)
ValuePair(PCS_NAD27_Alaska_zone_4, 26734)
ValuePair(PCS_NAD27_Alaska_zone_5, 26735)
ValuePair(PCS_NAD27_Alaska_zone_6, 26736)
ValuePair(PCS_NAD27_Alaska_zone_7, 26737)
ValuePair(PCS_NAD27_Alaska_zone_8, 26738)
ValuePair(PCS_NAD27_Alaska_zone_9, 26739)
ValuePair(PCS_NAD27_Alaska_zone_10, 26740)
ValuePair(PCS_NAD27_California_I, 26741)
ValuePair(PCS_NAD27_California_II, 26742)
ValuePair(PCS_NAD27_California_III, 26743)
ValuePair(PCS_NAD27_California_IV, 26744)
ValuePair(PCS_NAD27_California_V, 26745)
ValuePair(PCS_NAD27_California_VI, 26746)
ValuePair(PCS_NAD27_California_VII, 26747)
ValuePair(PCS_NAD27_Arizona_East, 26748)
ValuePair(PCS_NAD27_Arizona_Central, 26749)
ValuePair(PCS_NAD27_Arizona_West, 26750)
ValuePair(PCS_NAD27_Arkansas_North, 26751)
ValuePair(PCS_NAD27_Arkansas_South, 26752)
ValuePair(PCS_NAD27_Colorado_North, 26753)
ValuePair(PCS_NAD27_Colorado_Central, 26754)
ValuePair(PCS_NAD27_Colorado_South, 26755)
ValuePair(PCS_NAD27_Connecticut, 26756)
ValuePair(PCS_NAD27_Delaware, 26757)
ValuePair(PCS_NAD27_Florida_East, 26758)
ValuePair(PCS_NAD27_Florida_West, 26759)
ValuePair(PCS_NAD27_Florida_North, 26760)
ValuePair(PCS_NAD27_Hawaii_zone_1, 26761)
ValuePair(PCS_NAD27_Hawaii_zone_2, 26762)
ValuePair(PCS_NAD27_Hawaii_zone_3, 26763)
ValuePair(PCS_NAD27_Hawaii_zone_4, 26764)
ValuePair(PCS_NAD27_Hawaii_zone_5, 26765)
ValuePair(PCS_NAD27_Georgia_East, 26766)
ValuePair(PCS_NAD27_Georgia_West, 26767)
ValuePair(PCS_NAD27_Idaho_East, 26768)
ValuePair(PCS_NAD27_Idaho_Central, 26769)
ValuePair(PCS_NAD27_Idaho_West, 26770)
ValuePair(PCS_NAD27_Illinois_East, 26771)
ValuePair(PCS_NAD27_Illinois_West, 26772)
ValuePair(PCS_NAD27_Indiana_East, 26773)
ValuePair(PCS_NAD27_BLM_14N_feet, 26774)
ValuePair(PCS_NAD27_Indiana_West, 26774)
ValuePair(PCS_NAD27_BLM_15N_feet, 26775)
ValuePair(PCS_NAD27_Iowa_North, 26775)
ValuePair(PCS_NAD27_BLM_16N_feet, 26776)
ValuePair(PCS_NAD27_Iowa_South, 26776)
ValuePair(PCS_NAD27_BLM_17N_feet, 26777)
ValuePair(PCS_NAD27_Kansas_North, 26777)
ValuePair(PCS_NAD27_Kansas_South, 26778)
ValuePair(PCS_NAD27_Kentucky_North, 26779)
ValuePair(PCS_NAD27_Kentucky_South, 26780)
ValuePair(PCS_NAD27_Louisiana_North, 26781)
ValuePair(PCS_NAD27_Louisiana_South, 26782)
ValuePair(PCS_NAD27_Maine_East, 26783)
ValuePair(PCS_NAD27_Maine_West, 26784)
ValuePair(PCS_NAD27_Maryland, 26785)
ValuePair(PCS_NAD27_Massachusetts, 26786)
ValuePair(PCS_NAD27_Massachusetts_Is, 26787)
ValuePair(PCS_NAD27_Michigan_North, 26788)
ValuePair(PCS_NAD27_Michigan_Central, 26789)
ValuePair(PCS_NAD27_Michigan_South, 26790)
ValuePair(PCS_NAD27_Minnesota_North, 26791)
ValuePair(PCS_NAD27_Minnesota_Cent, 26792)
ValuePair(PCS_NAD27_Minnesota_South, 26793)
ValuePair(PCS_NAD27_Mississippi_East, 26794)
ValuePair(PCS_NAD27_Mississippi_West, 26795)
ValuePair(PCS_NAD27_Missouri_East, 26796)
ValuePair(PCS_NAD27_Missouri_Central, 26797)
ValuePair(PCS_NAD27_Missouri_West, 26798)
ValuePair(PCS_NAD_Michigan_Michigan_East, 26801)
ValuePair(PCS_NAD_Michigan_Michigan_Old_Central, 26802)
ValuePair(PCS_NAD_Michigan_Michigan_West, 26803)
ValuePair(PCS_NAD83_UTM_zone_3N, 26903)
ValuePair(PCS_NAD83_UTM_zone_4N, 26904)
ValuePair(PCS_NAD83_UTM_zone_5N, 26905)
ValuePair(PCS_NAD83_UTM_zone_6N, 26906)
ValuePair(PCS_NAD83_UTM_zone_7N, 26907)
ValuePair(PCS_NAD83_UTM_zone_8N, 26908)
ValuePair(PCS_NAD83_UTM_zone_9N, 26909)
ValuePair(PCS_NAD83_UTM_zone_10N, 26910)
ValuePair(PCS_NAD83_UTM_zone_11N, 26911)
ValuePair(PCS_NAD83_UTM_zone_12N, 26912)
ValuePair(PCS_NAD83_UTM_zone_13N, 26913)
ValuePair(PCS_NAD83_UTM_zone_14N, 26914)
ValuePair(PCS_NAD83_UTM_zone_15N, 26915)
ValuePair(PCS_NAD83_UTM_zone_16N, 26916)
ValuePair(PCS_NAD83_UTM_zone_17N, 26917)
ValuePair(PCS_NAD83_UTM_zone_18N, 26918)
ValuePair(PCS_NAD83_UTM_zone_19N, 26919)
ValuePair(PCS_NAD83_UTM_zone_20N, 26920)
ValuePair(PCS_NAD83_UTM_zone_21N, 26921)
ValuePair(PCS_NAD83_UTM_zone_22N, 26922)
ValuePair(PCS_NAD83_UTM_zone_23N, 26923)
ValuePair(PCS_NAD83_Alabama_East, 26929)
ValuePair(PCS_NAD83_Alabama_West, 26930)
ValuePair(PCS_NAD83_Alaska_zone_1, 26931)
ValuePair(PCS_NAD83_Alaska_zone_2, 26932)
ValuePair(PCS_NAD83_Alaska_zone_3, 26933)
ValuePair(PCS_NAD83_Alaska_zone_4, 26934)
ValuePair(PCS_NAD83_Alaska_zone_5, 26935)
ValuePair(PCS_NAD83_Alaska_zone_6, 26936)
ValuePair(PCS_NAD83_Alaska_zone_7, 26937)
ValuePair(PCS_NAD83_Alaska_zone_8, 26938)
ValuePair(PCS_NAD83_Alaska_zone_9, 26939)
ValuePair(PCS_NAD83_Alaska_zone_10, 26940)
ValuePair(PCS_NAD83_California_1, 26941)
ValuePair(PCS_NAD83_California_2, 26942)
ValuePair(PCS_NAD83_California_3, 26943)
ValuePair(PCS_NAD83_California_4, 26944)
ValuePair(PCS_NAD83_California_5, 26945)
ValuePair(PCS_NAD83_California_6, 26946)
ValuePair(PCS_NAD83_Arizona_East, 26948)
ValuePair(PCS_NAD83_Arizona_Central, 26949)
ValuePair(PCS_NAD83_Arizona_West, 26950)
ValuePair(PCS_NAD83_Arkansas_North, 26951)
ValuePair(PCS_NAD83_Arkansas_South, 26952)
ValuePair(PCS_NAD83_Colorado_North, 26953)
ValuePair(PCS_NAD83_Colorado_Central, 26954)
ValuePair(PCS_NAD83_Colorado_South, 26955)
ValuePair(PCS_NAD83_Connecticut, 26956)
ValuePair(PCS_NAD83_Delaware, 26957)
ValuePair(PCS_NAD83_Florida_East, 26958)
ValuePair(PCS_NAD83_Florida_West, 26959)
ValuePair(PCS_NAD83_Florida_North, 26960)
ValuePair(PCS_NAD83_Hawaii_zone_1, 26961)
ValuePair(PCS_NAD83_Hawaii_zone_2, 26962)
ValuePair(PCS_NAD83_Hawaii_zone_3, 26963)
ValuePair(PCS_NAD83_Hawaii_zone_4, 26964)
ValuePair(PCS_NAD83_Hawaii_zone_5, 26965)
ValuePair(PCS_NAD83_Georgia_East, 26966)
ValuePair(PCS_NAD83_Georgia_West, 26967)
ValuePair(PCS_NAD83_Idaho_East, 26968)
ValuePair(PCS_NAD83_Idaho_Central, 26969)
ValuePair(PCS_NAD83_Idaho_West, 26970)
ValuePair(PCS_NAD83_Illinois_East, 26971)
ValuePair(PCS_NAD83_Illinois_West, 26972)
ValuePair(PCS_NAD83_Indiana_East, 26973)
ValuePair(PCS_NAD83_Indiana_West, 26974)
ValuePair(PCS_NAD83_Iowa_North, 26975)
ValuePair(PCS_NAD83_Iowa_South, 26976)
ValuePair(PCS_NAD83_Kansas_North, 26977)
ValuePair(PCS_NAD83_Kansas_South, 26978)
ValuePair(PCS_NAD83_Kentucky_North, 2205)
ValuePair(PCS_NAD83_Kentucky_South, 26980)
ValuePair(PCS_NAD83_Louisiana_North, 26981)
ValuePair(PCS_NAD83_Louisiana_South, 26982)
ValuePair(PCS_NAD83_Maine_East, 26983)
ValuePair(PCS_NAD83_Maine_West, 26984)
ValuePair(PCS_NAD83_Maryland, 26985)
ValuePair(PCS_NAD83_Massachusetts, 26986)
ValuePair(PCS_NAD83_Massachusetts_Is, 26987)
ValuePair(PCS_NAD83_Michigan_North, 26988)
ValuePair(PCS_NAD83_Michigan_Central, 26989)
ValuePair(PCS_NAD83_Michigan_South, 26990)
ValuePair(PCS_NAD83_Minnesota_North, 26991)
ValuePair(PCS_NAD83_Minnesota_Cent, 26992)
ValuePair(PCS_NAD83_Minnesota_South, 26993)
ValuePair(PCS_NAD83_Mississippi_East, 26994)
ValuePair(PCS_NAD83_Mississippi_West, 26995)
ValuePair(PCS_NAD83_Missouri_East, 26996)
ValuePair(PCS_NAD83_Missouri_Central, 26997)
ValuePair(PCS_NAD83_Missouri_West, 26998)
ValuePair(PCS_Nahrwan_1967_UTM_38N, 27038)
ValuePair(PCS_Nahrwan_1967_UTM_39N, 27039)
ValuePair(PCS_Nahrwan_1967_UTM_40N, 27040)
ValuePair(PCS_Naparima_UTM_20N, 27120)
ValuePair(PCS_GD49_NZ_Map_Grid, 27200)
ValuePair(PCS_GD49_North_Island_Grid, 27291)
ValuePair(PCS_GD49_South_Island_Grid, 27292)
ValuePair(PCS_Datum_73_UTM_zone_29N, 27429)
ValuePair(PCS_ATF_Nord_de_Guerre, 27500)
ValuePair(PCS_NTF_France_I, 27581)
ValuePair(PCS_NTF_France_II, 27582)
ValuePair(PCS_NTF_France_III, 27583)
ValuePair(PCS_NTF_Nord_France, 27591)
ValuePair(PCS_NTF_Centre_France, 27592)
ValuePair(PCS_NTF_Sud_France, 27593)
ValuePair(PCS_British_National_Grid, 27700)
ValuePair(PCS_Point_Noire_UTM_32S, 28232)
ValuePair(PCS_GDA94_MGA_zone_48, 28348)
ValuePair(PCS_GDA94_MGA_zone_49, 28349)
ValuePair(PCS_GDA94_MGA_zone_50, 28350)
ValuePair(PCS_GDA94_MGA_zone_51, 28351)
ValuePair(PCS_GDA94_MGA_zone_52, 28352)
ValuePair(PCS_GDA94_MGA_zone_53, 28353)
ValuePair(PCS_GDA94_MGA_zone_54, 28354)
ValuePair(PCS_GDA94_MGA_zone_55, 28355)
ValuePair(PCS_GDA94_MGA_zone_56, 28356)
ValuePair(PCS_GDA94_MGA_zone_57, 28357)
ValuePair(PCS_GDA94_MGA_zone_58, 28358)
ValuePair(PCS_Pulkovo_Gauss_zone_4, 28404)
ValuePair(PCS_Pulkovo_Gauss_zone_5, 28405)
ValuePair(PCS_Pulkovo_Gauss_zone_6, 28406)
ValuePair(PCS_Pulkovo_Gauss_zone_7, 28407)
ValuePair(PCS_Pulkovo_Gauss_zone_8, 28408)
ValuePair(PCS_Pulkovo_Gauss_zone_9, 28409)
ValuePair(PCS_Pulkovo_Gauss_zone_10, 28410)
ValuePair(PCS_Pulkovo_Gauss_zone_11, 28411)
ValuePair(PCS_Pulkovo_Gauss_zone_12, 28412)
ValuePair(PCS_Pulkovo_Gauss_zone_13, 28413)
ValuePair(PCS_Pulkovo_Gauss_zone_14, 28414)
ValuePair(PCS_Pulkovo_Gauss_zone_15, 28415)
ValuePair(PCS_Pulkovo_Gauss_zone_16, 28416)
ValuePair(PCS_Pulkovo_Gauss_zone_17, 28417)
ValuePair(PCS_Pulkovo_Gauss_zone_18, 28418)
ValuePair(PCS_Pulkovo_Gauss_zone_19, 28419)
ValuePair(PCS_Pulkovo_Gauss_zone_20, 28420)
ValuePair(PCS_Pulkovo_Gauss_zone_21, 28421)
ValuePair(PCS_Pulkovo_Gauss_zone_22, 28422)
ValuePair(PCS_Pulkovo_Gauss_zone_23, 28423)
ValuePair(PCS_Pulkovo_Gauss_zone_24, 28424)
ValuePair(PCS_Pulkovo_Gauss_zone_25, 28425)
ValuePair(PCS_Pulkovo_Gauss_zone_26, 28426)
ValuePair(PCS_Pulkovo_Gauss_zone_27, 28427)
ValuePair(PCS_Pulkovo_Gauss_zone_28, 28428)
ValuePair(PCS_Pulkovo_Gauss_zone_29, 28429)
ValuePair(PCS_Pulkovo_Gauss_zone_30, 28430)
ValuePair(PCS_Pulkovo_Gauss_zone_31, 28431)
ValuePair(PCS_Pulkovo_Gauss_zone_32, 28432)
ValuePair(PCS_Pulkovo_Gauss_4N, 28464)
ValuePair(PCS_Pulkovo_Gauss_5N, 28465)
ValuePair(PCS_Pulkovo_Gauss_6N, 28466)
ValuePair(PCS_Pulkovo_Gauss_7N, 28467)
ValuePair(PCS_Pulkovo_Gauss_8N, 28468)
ValuePair(PCS_Pulkovo_Gauss_9N, 28469)
ValuePair(PCS_Pulkovo_Gauss_10N, 28470)
ValuePair(PCS_Pulkovo_Gauss_11N, 28471)
ValuePair(PCS_Pulkovo_Gauss_12N, 28472)
ValuePair(PCS_Pulkovo_Gauss_13N, 28473)
ValuePair(PCS_Pulkovo_Gauss_14N, 28474)
ValuePair(PCS_Pulkovo_Gauss_15N, 28475)
ValuePair(PCS_Pulkovo_Gauss_16N, 28476)
ValuePair(PCS_Pulkovo_Gauss_17N, 28477)
ValuePair(PCS_Pulkovo_Gauss_18N, 28478)
ValuePair(PCS_Pulkovo_Gauss_19N, 28479)
ValuePair(PCS_Pulkovo_Gauss_20N, 28480)
ValuePair(PCS_Pulkovo_Gauss_21N, 28481)
ValuePair(PCS_Pulkovo_Gauss_22N, 28482)
ValuePair(PCS_Pulkovo_Gauss_23N, 28483)
ValuePair(PCS_Pulkovo_Gauss_24N, 28484)
ValuePair(PCS_Pulkovo_Gauss_25N, 28485)
ValuePair(PCS_Pulkovo_Gauss_26N, 28486)
ValuePair(PCS_Pulkovo_Gauss_27N, 28487)
ValuePair(PCS_Pulkovo_Gauss_28N, 28488)
ValuePair(PCS_Pulkovo_Gauss_29N, 28489)
ValuePair(PCS_Pulkovo_Gauss_30N, 28490)
ValuePair(PCS_Pulkovo_Gauss_31N, 28491)
ValuePair(PCS_Pulkovo_Gauss_32N, 28492)
ValuePair(PCS_Qatar_National_Grid, 28600)
ValuePair(PCS_RD_Netherlands_Old, 28991)
ValuePair(PCS_RD_Netherlands_New, 28992)
ValuePair(PCS_SAD69_UTM_zone_18N, 29118)
ValuePair(PCS_SAD69_UTM_zone_19N, 29119)
ValuePair(PCS_SAD69_UTM_zone_20N, 29120)
ValuePair(PCS_SAD69_UTM_zone_21N, 29121)
ValuePair(PCS_SAD69_UTM_zone_22N, 29122)
ValuePair(PCS_SAD69_UTM_zone_17S, 29177)
ValuePair(PCS_SAD69_UTM_zone_18S, 29178)
ValuePair(PCS_SAD69_UTM_zone_19S, 29179)
ValuePair(PCS_SAD69_UTM_zone_20S, 29180)
ValuePair(PCS_SAD69_UTM_zone_21S, 29181)
ValuePair(PCS_SAD69_UTM_zone_22S, 29182)
ValuePair(PCS_SAD69_UTM_zone_23S, 29183)
ValuePair(PCS_SAD69_UTM_zone_24S, 29184)
ValuePair(PCS_SAD69_UTM_zone_25S, 29185)
ValuePair(PCS_Sapper_Hill_UTM_20S, 29220)
ValuePair(PCS_Sapper_Hill_UTM_21S, 29221)
ValuePair(PCS_Schwarzeck_UTM_33S, 29333)
ValuePair(PCS_Sudan_UTM_zone_35N, 29635)
ValuePair(PCS_Sudan_UTM_zone_36N, 29636)
ValuePair(PCS_Tananarive_Laborde, 29700)
ValuePair(PCS_Tananarive_UTM_38S, 29738)
ValuePair(PCS_Tananarive_UTM_39S, 29739)
ValuePair(PCS_Timbalai_1948_Borneo, 29800)
ValuePair(PCS_Timbalai_1948_UTM_49N, 29849)
ValuePair(PCS_Timbalai_1948_UTM_50N, 29850)
ValuePair(PCS_TM65_Irish_Nat_Grid, 29900)
ValuePair(PCS_Trinidad_1903_Trinidad, 30200)
ValuePair(PCS_TC_1948_UTM_zone_39N, 30339)
ValuePair(PCS_TC_1948_UTM_zone_40N, 30340)
ValuePair(PCS_Voirol_N_Algerie_ancien, 30491)
ValuePair(PCS_Voirol_S_Algerie_ancien, 30492)
ValuePair(PCS_Voirol_Unifie_N_Algerie, 30591)
ValuePair(PCS_Voirol_Unifie_S_Algerie, 30592)
ValuePair(PCS_Bern_1938_Swiss_New, 30600)
ValuePair(PCS_Nord_Sahara_UTM_29N, 30729)
ValuePair(PCS_Nord_Sahara_UTM_30N, 30730)
ValuePair(PCS_Nord_Sahara_UTM_31N, 30731)
ValuePair(PCS_Nord_Sahara_UTM_32N, 30732)
ValuePair(PCS_Yoff_UTM_zone_28N, 31028)
ValuePair(PCS_Zanderij_UTM_zone_21N, 31121)
ValuePair(PCS_MGI_Austria_West, 31291)
ValuePair(PCS_MGI_Austria_Central, 31292)
ValuePair(PCS_MGI_Austria_East, 31293)
ValuePair(PCS_Belge_Lambert_72, 31300)
ValuePair(PCS_DHDN_Germany_zone_1, 31491)
ValuePair(PCS_DHDN_Germany_zone_2, 31492)
ValuePair(PCS_DHDN_Germany_zone_3, 31493)
ValuePair(PCS_DHDN_Germany_zone_4, 31494)
ValuePair(PCS_DHDN_Germany_zone_5, 31495)
ValuePair(PCS_NAD27_Montana_North, 32001)
ValuePair(PCS_NAD27_Montana_Central, 32002)
ValuePair(PCS_NAD27_Montana_South, 32003)
ValuePair(PCS_NAD27_Nebraska_North, 32005)
ValuePair(PCS_NAD27_Nebraska_South, 32006)
ValuePair(PCS_NAD27_Nevada_East, 32007)
ValuePair(PCS_NAD27_Nevada_Central, 32008)
ValuePair(PCS_NAD27_Nevada_West, 32009)
ValuePair(PCS_NAD27_New_Hampshire, 32010)
ValuePair(PCS_NAD27_New_Jersey, 32011)
ValuePair(PCS_NAD27_New_Mexico_East, 32012)
ValuePair(PCS_NAD27_New_Mexico_Cent, 32013)
ValuePair(PCS_NAD27_New_Mexico_West, 32014)
ValuePair(PCS_NAD27_New_York_East, 32015)
ValuePair(PCS_NAD27_New_York_Central, 32016)
ValuePair(PCS_NAD27_New_York_West, 32017)
ValuePair(PCS_NAD27_New_York_Long_Is, 32018)
ValuePair(PCS_NAD27_North_Carolina, 32019)
ValuePair(PCS_NAD27_North_Dakota_N, 32020)
ValuePair(PCS_NAD27_North_Dakota_S, 32021)
ValuePair(PCS_NAD27_Ohio_North, 32022)
ValuePair(PCS_NAD27_Ohio_South, 32023)
ValuePair(PCS_NAD27_Oklahoma_North, 32024)
ValuePair(PCS_NAD27_Oklahoma_South, 32025)
ValuePair(PCS_NAD27_Oregon_North, 32026)
ValuePair(PCS_NAD27_Oregon_South, 32027)
ValuePair(PCS_NAD27_Pennsylvania_N, 32028)
ValuePair(PCS_NAD27_Pennsylvania_S, 32029)
ValuePair(PCS_NAD27_Rhode_Island, 32030)
ValuePair(PCS_NAD27_South_Carolina_N, 32031)
ValuePair(PCS_NAD27_South_Carolina_S, 32033)
ValuePair(PCS_NAD27_South_Dakota_N, 32034)
ValuePair(PCS_NAD27_South_Dakota_S, 32035)
ValuePair(PCS_NAD27_Tennessee, 2204)
ValuePair(PCS_NAD27_Texas_North, 32037)
ValuePair(PCS_NAD27_Texas_North_Cen, 32038)
ValuePair(PCS_NAD27_Texas_Central, 32039)
ValuePair(PCS_NAD27_Texas_South_Cen, 32040)
ValuePair(PCS_NAD27_Texas_South, 32041)
ValuePair(PCS_NAD27_Utah_North, 32042)
ValuePair(PCS_NAD27_Utah_Central, 32043)
ValuePair(PCS_NAD27_Utah_South, 32044)
ValuePair(PCS_NAD27_Vermont, 32045)
ValuePair(PCS_NAD27_Virginia_North, 32046)
ValuePair(PCS_NAD27_Virginia_South, 32047)
ValuePair(PCS_NAD27_Washington_North, 32048)
ValuePair(PCS_NAD27_Washington_South, 32049)
ValuePair(PCS_NAD27_West_Virginia_N, 32050)
ValuePair(PCS_NAD27_West_Virginia_S, 32051)
ValuePair(PCS_NAD27_Wisconsin_North, 32052)
ValuePair(PCS_NAD27_Wisconsin_Cen, 32053)
ValuePair(PCS_NAD27_Wisconsin_South, 32054)
ValuePair(PCS_NAD27_Wyoming_East, 32055)
ValuePair(PCS_NAD27_Wyoming_E_Cen, 32056)
ValuePair(PCS_NAD27_Wyoming_W_Cen, 32057)
ValuePair(PCS_NAD27_Wyoming_West, 32058)
ValuePair(PCS_NAD27_Puerto_Rico, 32059)
ValuePair(PCS_NAD27_St_Croix, 32060)
ValuePair(PCS_NAD83_Montana, 32100)
ValuePair(PCS_NAD83_Nebraska, 32104)
ValuePair(PCS_NAD83_Nevada_East, 32107)
ValuePair(PCS_NAD83_Nevada_Central, 32108)
ValuePair(PCS_NAD83_Nevada_West, 32109)
ValuePair(PCS_NAD83_New_Hampshire, 32110)
ValuePair(PCS_NAD83_New_Jersey, 32111)
ValuePair(PCS_NAD83_New_Mexico_East, 32112)
ValuePair(PCS_NAD83_New_Mexico_Cent, 32113)
ValuePair(PCS_NAD83_New_Mexico_West, 32114)
ValuePair(PCS_NAD83_New_York_East, 32115)
ValuePair(PCS_NAD83_New_York_Central, 32116)
ValuePair(PCS_NAD83_New_York_West, 32117)
ValuePair(PCS_NAD83_New_York_Long_Is, 32118)
ValuePair(PCS_NAD83_North_Carolina, 32119)
ValuePair(PCS_NAD83_North_Dakota_N, 32120)
ValuePair(PCS_NAD83_North_Dakota_S, 32121)
ValuePair(PCS_NAD83_Ohio_North, 32122)
ValuePair(PCS_NAD83_Ohio_South, 32123)
ValuePair(PCS_NAD83_Oklahoma_North, 32124)
ValuePair(PCS_NAD83_Oklahoma_South, 32125)
ValuePair(PCS_NAD83_Oregon_North, 32126)
ValuePair(PCS_NAD83_Oregon_South, 32127)
ValuePair(PCS_NAD83_Pennsylvania_N, 32128)
ValuePair(PCS_NAD83_Pennsylvania_S, 32129)
ValuePair(PCS_NAD83_Rhode_Island, 32130)
ValuePair(PCS_NAD83_South_Carolina, 32133)
ValuePair(PCS_NAD83_South_Dakota_N, 32134)
ValuePair(PCS_NAD83_South_Dakota_S, 32135)
ValuePair(PCS_NAD83_Tennessee, 32136)
ValuePair(PCS_NAD83_Texas_North, 32137)
ValuePair(PCS_NAD83_Texas_North_Cen, 32138)
ValuePair(PCS_NAD83_Texas_Central, 32139)
ValuePair(PCS_NAD83_Texas_South_Cen, 32140)
ValuePair(PCS_NAD83_Texas_South, 32141)
ValuePair(PCS_NAD83_Utah_North, 32142)
ValuePair(PCS_NAD83_Utah_Central, 32143)
ValuePair(PCS_NAD83_Utah_South, 32144)
ValuePair(PCS_NAD83_Vermont, 32145)
ValuePair(PCS_NAD83_Virginia_North, 32146)
ValuePair(PCS_NAD83_Virginia_South, 32147)
ValuePair(PCS_NAD83_Washington_North, 32148)
ValuePair(PCS_NAD83_Washington_South, 32149)
ValuePair(PCS_NAD83_West_Virginia_N, 32150)
ValuePair(PCS_NAD83_West_Virginia_S, 32151)
ValuePair(PCS_NAD83_Wisconsin_North, 32152)
ValuePair(PCS_NAD83_Wisconsin_Cen, 32153)
ValuePair(PCS_NAD83_Wisconsin_South, 32154)
ValuePair(PCS_NAD83_Wyoming_East, 32155)
ValuePair(PCS_NAD83_Wyoming_E_Cen, 32156)
ValuePair(PCS_NAD83_Wyoming_W_Cen, 32157)
ValuePair(PCS_NAD83_Wyoming_West, 32158)
ValuePair(PCS_NAD83_Puerto_Rico_Virgin_Is, 32161)
ValuePair(PCS_WGS72_UTM_zone_1N, 32201)
ValuePair(PCS_WGS72_UTM_zone_2N, 32202)
ValuePair(PCS_WGS72_UTM_zone_3N, 32203)
ValuePair(PCS_WGS72_UTM_zone_4N, 32204)
ValuePair(PCS_WGS72_UTM_zone_5N, 32205)
ValuePair(PCS_WGS72_UTM_zone_6N, 32206)
ValuePair(PCS_WGS72_UTM_zone_7N, 32207)
ValuePair(PCS_WGS72_UTM_zone_8N, 32208)
ValuePair(PCS_WGS72_UTM_zone_9N, 32209)
ValuePair(PCS_WGS72_UTM_zone_10N, 32210)
ValuePair(PCS_WGS72_UTM_zone_11N, 32211)
ValuePair(PCS_WGS72_UTM_zone_12N, 32212)
ValuePair(PCS_WGS72_UTM_zone_13N, 32213)
ValuePair(PCS_WGS72_UTM_zone_14N, 32214)
ValuePair(PCS_WGS72_UTM_zone_15N, 32215)
ValuePair(PCS_WGS72_UTM_zone_16N, 32216)
ValuePair(PCS_WGS72_UTM_zone_17N, 32217)
ValuePair(PCS_WGS72_UTM_zone_18N, 32218)
ValuePair(PCS_WGS72_UTM_zone_19N, 32219)
ValuePair(PCS_WGS72_UTM_zone_20N, 32220)
ValuePair(PCS_WGS72_UTM_zone_21N, 32221)
ValuePair(PCS_WGS72_UTM_zone_22N, 32222)
ValuePair(PCS_WGS72_UTM_zone_23N, 32223)
ValuePair(PCS_WGS72_UTM_zone_24N, 32224)
ValuePair(PCS_WGS72_UTM_zone_25N, 32225)
ValuePair(PCS_WGS72_UTM_zone_26N, 32226)
ValuePair(PCS_WGS72_UTM_zone_27N, 32227)
ValuePair(PCS_WGS72_UTM_zone_28N, 32228)
ValuePair(PCS_WGS72_UTM_zone_29N, 32229)
ValuePair(PCS_WGS72_UTM_zone_30N, 32230)
ValuePair(PCS_WGS72_UTM_zone_31N, 32231)
ValuePair(PCS_WGS72_UTM_zone_32N, 32232)
ValuePair(PCS_WGS72_UTM_zone_33N, 32233)
ValuePair(PCS_WGS72_UTM_zone_34N, 32234)
ValuePair(PCS_WGS72_UTM_zone_35N, 32235)
ValuePair(PCS_WGS72_UTM_zone_36N, 32236)
ValuePair(PCS_WGS72_UTM_zone_37N, 32237)
ValuePair(PCS_WGS72_UTM_zone_38N, 32238)
ValuePair(PCS_WGS72_UTM_zone_39N, 32239)
ValuePair(PCS_WGS72_UTM_zone_40N, 32240)
ValuePair(PCS_WGS72_UTM_zone_41N, 32241)
ValuePair(PCS_WGS72_UTM_zone_42N, 32242)
ValuePair(PCS_WGS72_UTM_zone_43N, 32243)
ValuePair(PCS_WGS72_UTM_zone_44N, 32244)
ValuePair(PCS_WGS72_UTM_zone_45N, 32245)
ValuePair(PCS_WGS72_UTM_zone_46N, 32246)
ValuePair(PCS_WGS72_UTM_zone_47N, 32247)
ValuePair(PCS_WGS72_UTM_zone_48N, 32248)
ValuePair(PCS_WGS72_UTM_zone_49N, 32249)
ValuePair(PCS_WGS72_UTM_zone_50N, 32250)
ValuePair(PCS_WGS72_UTM_zone_51N, 32251)
ValuePair(PCS_WGS72_UTM_zone_52N, 32252)
ValuePair(PCS_WGS72_UTM_zone_53N, 32253)
ValuePair(PCS_WGS72_UTM_zone_54N, 32254)
ValuePair(PCS_WGS72_UTM_zone_55N, 32255)
ValuePair(PCS_WGS72_UTM_zone_56N, 32256)
ValuePair(PCS_WGS72_UTM_zone_57N, 32257)
ValuePair(PCS_WGS72_UTM_zone_58N, 32258)
ValuePair(PCS_WGS72_UTM_zone_59N, 32259)
ValuePair(PCS_WGS72_UTM_zone_60N, 32260)
ValuePair(PCS_WGS72_UTM_zone_1S, 32301)
ValuePair(PCS_WGS72_UTM_zone_2S, 32302)
ValuePair(PCS_WGS72_UTM_zone_3S, 32303)
ValuePair(PCS_WGS72_UTM_zone_4S, 32304)
ValuePair(PCS_WGS72_UTM_zone_5S, 32305)
ValuePair(PCS_WGS72_UTM_zone_6S, 32306)
ValuePair(PCS_WGS72_UTM_zone_7S, 32307)
ValuePair(PCS_WGS72_UTM_zone_8S, 32308)
ValuePair(PCS_WGS72_UTM_zone_9S, 32309)
ValuePair(PCS_WGS72_UTM_zone_10S, 32310)
ValuePair(PCS_WGS72_UTM_zone_11S, 32311)
ValuePair(PCS_WGS72_UTM_zone_12S, 32312)
ValuePair(PCS_WGS72_UTM_zone_13S, 32313)
ValuePair(PCS_WGS72_UTM_zone_14S, 32314)
ValuePair(PCS_WGS72_UTM_zone_15S, 32315)
ValuePair(PCS_WGS72_UTM_zone_16S, 32316)
ValuePair(PCS_WGS72_UTM_zone_17S, 32317)
ValuePair(PCS_WGS72_UTM_zone_18S, 32318)
ValuePair(PCS_WGS72_UTM_zone_19S, 32319)
ValuePair(PCS_WGS72_UTM_zone_20S, 32320)
ValuePair(PCS_WGS72_UTM_zone_21S, 32321)
ValuePair(PCS_WGS72_UTM_zone_22S, 32322)
ValuePair(PCS_WGS72_UTM_zone_23S, 32323)
ValuePair(PCS_WGS72_UTM_zone_24S, 32324)
ValuePair(PCS_WGS72_UTM_zone_25S, 32325)
ValuePair(PCS_WGS72_UTM_zone_26S, 32326)
ValuePair(PCS_WGS72_UTM_zone_27S, 32327)
ValuePair(PCS_WGS72_UTM_zone_28S, 32328)
ValuePair(PCS_WGS72_UTM_zone_29S, 32329)
ValuePair(PCS_WGS72_UTM_zone_30S, 32330)
ValuePair(PCS_WGS72_UTM_zone_31S, 32331)
ValuePair(PCS_WGS72_UTM_zone_32S, 32332)
ValuePair(PCS_WGS72_UTM_zone_33S, 32333)
ValuePair(PCS_WGS72_UTM_zone_34S, 32334)
ValuePair(PCS_WGS72_UTM_zone_35S, 32335)
ValuePair(PCS_WGS72_UTM_zone_36S, 32336)
ValuePair(PCS_WGS72_UTM_zone_37S, 32337)
ValuePair(PCS_WGS72_UTM_zone_38S, 32338)
ValuePair(PCS_WGS72_UTM_zone_39S, 32339)
ValuePair(PCS_WGS72_UTM_zone_40S, 32340)
ValuePair(PCS_WGS72_UTM_zone_41S, 32341)
ValuePair(PCS_WGS72_UTM_zone_42S, 32342)
ValuePair(PCS_WGS72_UTM_zone_43S, 32343)
ValuePair(PCS_WGS72_UTM_zone_44S, 32344)
ValuePair(PCS_WGS72_UTM_zone_45S, 32345)
ValuePair(PCS_WGS72_UTM_zone_46S, 32346)
ValuePair(PCS_WGS72_UTM_zone_47S, 32347)
ValuePair(PCS_WGS72_UTM_zone_48S, 32348)
ValuePair(PCS_WGS72_UTM_zone_49S, 32349)
ValuePair(PCS_WGS72_UTM_zone_50S, 32350)
ValuePair(PCS_WGS72_UTM_zone_51S, 32351)
ValuePair(PCS_WGS72_UTM_zone_52S, 32352)
ValuePair(PCS_WGS72_UTM_zone_53S, 32353)
ValuePair(PCS_WGS72_UTM_zone_54S, 32354)
ValuePair(PCS_WGS72_UTM_zone_55S, 32355)
ValuePair(PCS_WGS72_UTM_zone_56S, 32356)
ValuePair(PCS_WGS72_UTM_zone_57S, 32357)
ValuePair(PCS_WGS72_UTM_zone_58S, 32358)
ValuePair(PCS_WGS72_UTM_zone_59S, 32359)
ValuePair(PCS_WGS72_UTM_zone_60S, 32360)
ValuePair(PCS_WGS72BE_UTM_zone_1N, 32401)
ValuePair(PCS_WGS72BE_UTM_zone_2N, 32402)
ValuePair(PCS_WGS72BE_UTM_zone_3N, 32403)
ValuePair(PCS_WGS72BE_UTM_zone_4N, 32404)
ValuePair(PCS_WGS72BE_UTM_zone_5N, 32405)
ValuePair(PCS_WGS72BE_UTM_zone_6N, 32406)
ValuePair(PCS_WGS72BE_UTM_zone_7N, 32407)
ValuePair(PCS_WGS72BE_UTM_zone_8N, 32408)
ValuePair(PCS_WGS72BE_UTM_zone_9N, 32409)
ValuePair(PCS_WGS72BE_UTM_zone_10N, 32410)
ValuePair(PCS_WGS72BE_UTM_zone_11N, 32411)
ValuePair(PCS_WGS72BE_UTM_zone_12N, 32412)
ValuePair(PCS_WGS72BE_UTM_zone_13N, 32413)
ValuePair(PCS_WGS72BE_UTM_zone_14N, 32414)
ValuePair(PCS_WGS72BE_UTM_zone_15N, 32415)
ValuePair(PCS_WGS72BE_UTM_zone_16N, 32416)
ValuePair(PCS_WGS72BE_UTM_zone_17N, 32417)
ValuePair(PCS_WGS72BE_UTM_zone_18N, 32418)
ValuePair(PCS_WGS72BE_UTM_zone_19N, 32419)
ValuePair(PCS_WGS72BE_UTM_zone_20N, 32420)
ValuePair(PCS_WGS72BE_UTM_zone_21N, 32421)
ValuePair(PCS_WGS72BE_UTM_zone_22N, 32422)
ValuePair(PCS_WGS72BE_UTM_zone_23N, 32423)
ValuePair(PCS_WGS72BE_UTM_zone_24N, 32424)
ValuePair(PCS_WGS72BE_UTM_zone_25N, 32425)
ValuePair(PCS_WGS72BE_UTM_zone_26N, 32426)
ValuePair(PCS_WGS72BE_UTM_zone_27N, 32427)
ValuePair(PCS_WGS72BE_UTM_zone_28N, 32428)
ValuePair(PCS_WGS72BE_UTM_zone_29N, 32429)
ValuePair(PCS_WGS72BE_UTM_zone_30N, 32430)
ValuePair(PCS_WGS72BE_UTM_zone_31N, 32431)
ValuePair(PCS_WGS72BE_UTM_zone_32N, 32432)
ValuePair(PCS_WGS72BE_UTM_zone_33N, 32433)
ValuePair(PCS_WGS72BE_UTM_zone_34N, 32434)
ValuePair(PCS_WGS72BE_UTM_zone_35N, 32435)
ValuePair(PCS_WGS72BE_UTM_zone_36N, 32436)
ValuePair(PCS_WGS72BE_UTM_zone_37N, 32437)
ValuePair(PCS_WGS72BE_UTM_zone_38N, 32438)
ValuePair(PCS_WGS72BE_UTM_zone_39N, 32439)
ValuePair(PCS_WGS72BE_UTM_zone_40N, 32440)
ValuePair(PCS_WGS72BE_UTM_zone_41N, 32441)
ValuePair(PCS_WGS72BE_UTM_zone_42N, 32442)
ValuePair(PCS_WGS72BE_UTM_zone_43N, 32443)
ValuePair(PCS_WGS72BE_UTM_zone_44N, 32444)
ValuePair(PCS_WGS72BE_UTM_zone_45N, 32445)
ValuePair(PCS_WGS72BE_UTM_zone_46N, 32446)
ValuePair(PCS_WGS72BE_UTM_zone_47N, 32447)
ValuePair(PCS_WGS72BE_UTM_zone_48N, 32448)
ValuePair(PCS_WGS72BE_UTM_zone_49N, 32449)
ValuePair(PCS_WGS72BE_UTM_zone_50N, 32450)
ValuePair(PCS_WGS72BE_UTM_zone_51N, 32451)
ValuePair(PCS_WGS72BE_UTM_zone_52N, 32452)
ValuePair(PCS_WGS72BE_UTM_zone_53N, 32453)
ValuePair(PCS_WGS72BE_UTM_zone_54N, 32454)
ValuePair(PCS_WGS72BE_UTM_zone_55N, 32455)
ValuePair(PCS_WGS72BE_UTM_zone_56N, 32456)
ValuePair(PCS_WGS72BE_UTM_zone_57N, 32457)
ValuePair(PCS_WGS72BE_UTM_zone_58N, 32458)
ValuePair(PCS_WGS72BE_UTM_zone_59N, 32459)
ValuePair(PCS_WGS72BE_UTM_zone_60N, 32460)
ValuePair(PCS_WGS72BE_UTM_zone_1S, 32501)
ValuePair(PCS_WGS72BE_UTM_zone_2S, 32502)
ValuePair(PCS_WGS72BE_UTM_zone_3S, 32503)
ValuePair(PCS_WGS72BE_UTM_zone_4S, 32504)
ValuePair(PCS_WGS72BE_UTM_zone_5S, 32505)
ValuePair(PCS_WGS72BE_UTM_zone_6S, 32506)
ValuePair(PCS_WGS72BE_UTM_zone_7S, 32507)
ValuePair(PCS_WGS72BE_UTM_zone_8S, 32508)
ValuePair(PCS_WGS72BE_UTM_zone_9S, 32509)
ValuePair(PCS_WGS72BE_UTM_zone_10S, 32510)
ValuePair(PCS_WGS72BE_UTM_zone_11S, 32511)
ValuePair(PCS_WGS72BE_UTM_zone_12S, 32512)
ValuePair(PCS_WGS72BE_UTM_zone_13S, 32513)
ValuePair(PCS_WGS72BE_UTM_zone_14S, 32514)
ValuePair(PCS_WGS72BE_UTM_zone_15S, 32515)
ValuePair(PCS_WGS72BE_UTM_zone_16S, 32516)
ValuePair(PCS_WGS72BE_UTM_zone_17S, 32517)
ValuePair(PCS_WGS72BE_UTM_zone_18S, 32518)
ValuePair(PCS_WGS72BE_UTM_zone_19S, 32519)
ValuePair(PCS_WGS72BE_UTM_zone_20S, 32520)
ValuePair(PCS_WGS72BE_UTM_zone_21S, 32521)
ValuePair(PCS_WGS72BE_UTM_zone_22S, 32522)
ValuePair(PCS_WGS72BE_UTM_zone_23S, 32523)
ValuePair(PCS_WGS72BE_UTM_zone_24S, 32524)
ValuePair(PCS_WGS72BE_UTM_zone_25S, 32525)
ValuePair(PCS_WGS72BE_UTM_zone_26S, 32526)
ValuePair(PCS_WGS72BE_UTM_zone_27S, 32527)
ValuePair(PCS_WGS72BE_UTM_zone_28S, 32528)
ValuePair(PCS_WGS72BE_UTM_zone_29S, 32529)
ValuePair(PCS_WGS72BE_UTM_zone_30S, 32530)
ValuePair(PCS_WGS72BE_UTM_zone_31S, 32531)
ValuePair(PCS_WGS72BE_UTM_zone_32S, 32532)
ValuePair(PCS_WGS72BE_UTM_zone_33S, 32533)
ValuePair(PCS_WGS72BE_UTM_zone_34S, 32534)
ValuePair(PCS_WGS72BE_UTM_zone_35S, 32535)
ValuePair(PCS_WGS72BE_UTM_zone_36S, 32536)
ValuePair(PCS_WGS72BE_UTM_zone_37S, 32537)
ValuePair(PCS_WGS72BE_UTM_zone_38S, 32538)
ValuePair(PCS_WGS72BE_UTM_zone_39S, 32539)
ValuePair(PCS_WGS72BE_UTM_zone_40S, 32540)
ValuePair(PCS_WGS72BE_UTM_zone_41S, 32541)
ValuePair(PCS_WGS72BE_UTM_zone_42S, 32542)
ValuePair(PCS_WGS72BE_UTM_zone_43S, 32543)
ValuePair(PCS_WGS72BE_UTM_zone_44S, 32544)
ValuePair(PCS_WGS72BE_UTM_zone_45S, 32545)
ValuePair(PCS_WGS72BE_UTM_zone_46S, 32546)
ValuePair(PCS_WGS72BE_UTM_zone_47S, 32547)
ValuePair(PCS_WGS72BE_UTM_zone_48S, 32548)
ValuePair(PCS_WGS72BE_UTM_zone_49S, 32549)
ValuePair(PCS_WGS72BE_UTM_zone_50S, 32550)
ValuePair(PCS_WGS72BE_UTM_zone_51S, 32551)
ValuePair(PCS_WGS72BE_UTM_zone_52S, 32552)
ValuePair(PCS_WGS72BE_UTM_zone_53S, 32553)
ValuePair(PCS_WGS72BE_UTM_zone_54S, 32554)
ValuePair(PCS_WGS72BE_UTM_zone_55S, 32555)
ValuePair(PCS_WGS72BE_UTM_zone_56S, 32556)
ValuePair(PCS_WGS72BE_UTM_zone_57S, 32557)
ValuePair(PCS_WGS72BE_UTM_zone_58S, 32558)
ValuePair(PCS_WGS72BE_UTM_zone_59S, 32559)
ValuePair(PCS_WGS72BE_UTM_zone_60S, 32560)
ValuePair(PCS_WGS84_UTM_zone_1N, 32601)
ValuePair(PCS_WGS84_UTM_zone_2N, 32602)
ValuePair(PCS_WGS84_UTM_zone_3N, 32603)
ValuePair(PCS_WGS84_UTM_zone_4N, 32604)
ValuePair(PCS_WGS84_UTM_zone_5N, 32605)
ValuePair(PCS_WGS84_UTM_zone_6N, 32606)
ValuePair(PCS_WGS84_UTM_zone_7N, 32607)
ValuePair(PCS_WGS84_UTM_zone_8N, 32608)
ValuePair(PCS_WGS84_UTM_zone_9N, 32609)
ValuePair(PCS_WGS84_UTM_zone_10N, 32610)
ValuePair(PCS_WGS84_UTM_zone_11N, 32611)
ValuePair(PCS_WGS84_UTM_zone_12N, 32612)
ValuePair(PCS_WGS84_UTM_zone_13N, 32613)
ValuePair(PCS_WGS84_UTM_zone_14N, 32614)
ValuePair(PCS_WGS84_UTM_zone_15N, 32615)
ValuePair(PCS_WGS84_UTM_zone_16N, 32616)
ValuePair(PCS_WGS84_UTM_zone_17N, 32617)
ValuePair(PCS_WGS84_UTM_zone_18N, 32618)
ValuePair(PCS_WGS84_UTM_zone_19N, 32619)
ValuePair(PCS_WGS84_UTM_zone_20N, 32620)
ValuePair(PCS_WGS84_UTM_zone_21N, 32621)
ValuePair(PCS_WGS84_UTM_zone_22N, 32622)
ValuePair(PCS_WGS84_UTM_zone_23N, 32623)
ValuePair(PCS_WGS84_UTM_zone_24N, 32624)
ValuePair(PCS_WGS84_UTM_zone_25N, 32625)
ValuePair(PCS_WGS84_UTM_zone_26N, 32626)
ValuePair(PCS_WGS84_UTM_zone_27N, 32627)
ValuePair(PCS_WGS84_UTM_zone_28N, 32628)
ValuePair(PCS_WGS84_UTM_zone_29N, 32629)
ValuePair(PCS_WGS84_UTM_zone_30N, 32630)
ValuePair(PCS_WGS84_UTM_zone_31N, 32631)
ValuePair(PCS_WGS84_UTM_zone_32N, 32632)
ValuePair(PCS_WGS84_UTM_zone_33N, 32633)
ValuePair(PCS_WGS84_UTM_zone_34N, 32634)
ValuePair(PCS_WGS84_UTM_zone_35N, 32635)
ValuePair(PCS_WGS84_UTM_zone_36N, 32636)
ValuePair(PCS_WGS84_UTM_zone_37N, 32637)
ValuePair(PCS_WGS84_UTM_zone_38N, 32638)
ValuePair(PCS_WGS84_UTM_zone_39N, 32639)
ValuePair(PCS_WGS84_UTM_zone_40N, 32640)
ValuePair(PCS_WGS84_UTM_zone_41N, 32641)
ValuePair(PCS_WGS84_UTM_zone_42N, 32642)
ValuePair(PCS_WGS84_UTM_zone_43N, 32643)
ValuePair(PCS_WGS84_UTM_zone_44N, 32644)
ValuePair(PCS_WGS84_UTM_zone_45N, 32645)
ValuePair(PCS_WGS84_UTM_zone_46N, 32646)
ValuePair(PCS_WGS84_UTM_zone_47N, 32647)
ValuePair(PCS_WGS84_UTM_zone_48N, 32648)
ValuePair(PCS_WGS84_UTM_zone_49N, 32649)
ValuePair(PCS_WGS84_UTM_zone_50N, 32650)
ValuePair(PCS_WGS84_UTM_zone_51N, 32651)
ValuePair(PCS_WGS84_UTM_zone_52N, 32652)
ValuePair(PCS_WGS84_UTM_zone_53N, 32653)
ValuePair(PCS_WGS84_UTM_zone_54N, 32654)
ValuePair(PCS_WGS84_UTM_zone_55N, 32655)
ValuePair(PCS_WGS84_UTM_zone_56N, 32656)
ValuePair(PCS_WGS84_UTM_zone_57N, 32657)
ValuePair(PCS_WGS84_UTM_zone_58N, 32658)
ValuePair(PCS_WGS84_UTM_zone_59N, 32659)
ValuePair(PCS_WGS84_UTM_zone_60N, 32660)
ValuePair(PCS_WGS84_UTM_zone_1S, 32701)
ValuePair(PCS_WGS84_UTM_zone_2S, 32702)
ValuePair(PCS_WGS84_UTM_zone_3S, 32703)
ValuePair(PCS_WGS84_UTM_zone_4S, 32704)
ValuePair(PCS_WGS84_UTM_zone_5S, 32705)
ValuePair(PCS_WGS84_UTM_zone_6S, 32706)
ValuePair(PCS_WGS84_UTM_zone_7S, 32707)
ValuePair(PCS_WGS84_UTM_zone_8S, 32708)
ValuePair(PCS_WGS84_UTM_zone_9S, 32709)
ValuePair(PCS_WGS84_UTM_zone_10S, 32710)
ValuePair(PCS_WGS84_UTM_zone_11S, 32711)
ValuePair(PCS_WGS84_UTM_zone_12S, 32712)
ValuePair(PCS_WGS84_UTM_zone_13S, 32713)
ValuePair(PCS_WGS84_UTM_zone_14S, 32714)
ValuePair(PCS_WGS84_UTM_zone_15S, 32715)
ValuePair(PCS_WGS84_UTM_zone_16S, 32716)
ValuePair(PCS_WGS84_UTM_zone_17S, 32717)
ValuePair(PCS_WGS84_UTM_zone_18S, 32718)
ValuePair(PCS_WGS84_UTM_zone_19S, 32719)
ValuePair(PCS_WGS84_UTM_zone_20S, 32720)
ValuePair(PCS_WGS84_UTM_zone_21S, 32721)
ValuePair(PCS_WGS84_UTM_zone_22S, 32722)
ValuePair(PCS_WGS84_UTM_zone_23S, 32723)
ValuePair(PCS_WGS84_UTM_zone_24S, 32724)
ValuePair(PCS_WGS84_UTM_zone_25S, 32725)
ValuePair(PCS_WGS84_UTM_zone_26S, 32726)
ValuePair(PCS_WGS84_UTM_zone_27S, 32727)
ValuePair(PCS_WGS84_UTM_zone_28S, 32728)
ValuePair(PCS_WGS84_UTM_zone_29S, 32729)
ValuePair(PCS_WGS84_UTM_zone_30S, 32730)
ValuePair(PCS_WGS84_UTM_zone_31S, 32731)
ValuePair(PCS_WGS84_UTM_zone_32S, 32732)
ValuePair(PCS_WGS84_UTM_zone_33S, 32733)
ValuePair(PCS_WGS84_UTM_zone_34S, 32734)
ValuePair(PCS_WGS84_UTM_zone_35S, 32735)
ValuePair(PCS_WGS84_UTM_zone_36S, 32736)
ValuePair(PCS_WGS84_UTM_zone_37S, 32737)
ValuePair(PCS_WGS84_UTM_zone_38S, 32738)
ValuePair(PCS_WGS84_UTM_zone_39S, 32739)
ValuePair(PCS_WGS84_UTM_zone_40S, 32740)
ValuePair(PCS_WGS84_UTM_zone_41S, 32741)
ValuePair(PCS_WGS84_UTM_zone_42S, 32742)
ValuePair(PCS_WGS84_UTM_zone_43S, 32743)
ValuePair(PCS_WGS84_UTM_zone_44S, 32744)
ValuePair(PCS_WGS84_UTM_zone_45S, 32745)
ValuePair(PCS_WGS84_UTM_zone_46S, 32746)
ValuePair(PCS_WGS84_UTM_zone_47S, 32747)
ValuePair(PCS_WGS84_UTM_zone_48S, 32748)
ValuePair(PCS_WGS84_UTM_zone_49S, 32749)
ValuePair(PCS_WGS84_UTM_zone_50S, 32750)
ValuePair(PCS_WGS84_UTM_zone_51S, 32751)
ValuePair(PCS_WGS84_UTM_zone_52S, 32752)
ValuePair(PCS_WGS84_UTM_zone_53S, 32753)
ValuePair(PCS_WGS84_UTM_zone_54S, 32754)
ValuePair(PCS_WGS84_UTM_zone_55S, 32755)
ValuePair(PCS_WGS84_UTM_zone_56S, 32756)
ValuePair(PCS_WGS84_UTM_zone_57S, 32757)
ValuePair(PCS_WGS84_UTM_zone_58S, 32758)
ValuePair(PCS_WGS84_UTM_zone_59S, 32759)
ValuePair(PCS_WGS84_UTM_zone_60S, 32760)
/* end of list */
| 2024-01-02T01:26:35.434368 | https://example.com/article/5244 |
Levetiracetam for the treatment of idiopathic generalized epilepsy with myoclonic seizures.
Currently, there are no published randomized controlled trials evaluating the efficacy and safety of adjunctive antiepileptic therapy in idiopathic generalized epilepsy with myoclonic seizures. This randomized, double-blind, placebo-controlled multicenter trial assessed the efficacy and tolerability of adjunctive treatment with levetiracetam 3,000 mg/day in adolescents (>or=12 years) and adults (<or=65 years) with idiopathic generalized epilepsy, who experienced myoclonic seizures on >or=8 days during a prospective 8-week baseline period, despite antiepileptic monotherapy. The 8-week baseline period was followed by 4-week up-titration, 12-week evaluation, and 6-week down-titration/conversion periods. Of 122 patients randomized, 120 (levetiracetam, n = 60; placebo, n = 60) were evaluable. Diagnoses were either juvenile myoclonic epilepsy (93.4%) or juvenile absence epilepsy (6.6%). A reduction of >or=50% in the number of days/week with myoclonic seizures was seen in 58.3% of patients in the levetiracetam group and in 23.3% of patients in the placebo group (p < 0.001) during the treatment period. Levetiracetam-treated patients were more likely to respond to treatment than patients receiving placebo (OR = 4.77; 95% CI, 2.12 to 10.77; p < 0.001). Levetiracetam-treated patients had higher freedom from myoclonic seizures (25.0% vs 5.0%; p = 0.004) and all seizure types (21.7% vs 1.7%; p < 0.001) during the evaluation period. The only adverse events more frequent with levetiracetam were somnolence and neck pain. These results suggest that levetiracetam is an effective and well-tolerated adjunctive treatment for patients with previously uncontrolled idiopathic generalized epilepsy with myoclonic seizures. | 2023-08-15T01:26:35.434368 | https://example.com/article/2369 |
Legendary Royalty Combo
Legendary Royalty Combo
Present the new King and Queen with this dazzling Legendary Royalty Combo that can be used for Homecoming or Prom.
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$55.99
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Product Code: CWCLEG
This amazing Legendary Royalty Combo features a Royal Velvet King's Crown in your choice of color for the King and a sparkling Gold Sophie Tiara to dazzle the Queen.
Crown is made of fabric and tiara is made of metal and rhinestones
1 - Royal Velvet King's Crown (choose your color) - measures 6" high
1 - Gold Sophie Tiara - measures 3 3/4" high
WARNING:
This product can expose you to chemicals including DEHP, which is known to the State of California to cause cancer and birth defects or other reproductive harm. For more information go to
www.P65Warnings.ca.gov.
Please allow ample time for delivery. The delivery date for this product is noted above for US shipping only. Please refer to checkout for delivery dates outside of the Contiguous 48 States.
Shipping charges are based on the value of the merchandise and not the number of shipments. For additional shipping information, please contact our Customer Service Department at 800-348-5084. | 2024-06-09T01:26:35.434368 | https://example.com/article/4288 |
End Time News In The Light Of Bible Prophecy
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EU on brink: Trump trade war to wipe £255BILLION off GDP ‘Warning lights are flashing’
THE world is on the brink of a financial meltdown if Donald Trump’s import tariffs descend into a full-blown trade war – with the European Union wiping £255billion from its GDP, the World Trade Organisation has warned. In an apocalyptic notice, WTO director general Roberto Azevedo said “warning lights are flashing” and the world must axt immediately. The European Union faces seeing 1.7 percent wiped from its GDP growth, he said. That equals £255bn ($335bn) of the EU’s £15trillion ($19.7trn) GDP. The colossal figure roughly equates to the entire economic output of EU countries the size of Austria, Ireland, and Denmark and far exceeds the GDP of Portugal, Hungary, and Romania……Read More | 2024-04-18T01:26:35.434368 | https://example.com/article/3426 |
version: 1
dn: dicomDeviceName=dcm4chee-arc,cn=Devices,cn=DICOM Configuration,dc=dcm4che,dc=org
changetype: modify
replace: dicomSoftwareVersion
dicomSoftwareVersion: 5.15.1
-
replace: dcmBulkDataDescriptorID
dcmBulkDataDescriptorID: default
dn: dcmBulkDataDescriptorID=default,dicomDeviceName=dcm4chee-arc,cn=Devices,cn=DICOM Configuration,dc=dcm4che,dc=org
changetype: add
dcmBulkDataVRLengthThreshold: DS,FD,FL,IS,LT,OB,OD,OF,OL,OW,UC,UN,UR,UT=1024
dcmBulkDataDescriptorID: default
objectClass: dcmBulkDataDescriptor
dn: dcmAttributeSetID=study+dcmAttributeSetType=QIDO_RS,dicomDeviceName=dcm4chee-arc,cn=Devices,cn=DICOM Configuration,dc=dcm4che,dc=org
changetype: add
dcmAttributeSetTitle: Sample Study Attribute Set
dcmTag: 00080020
dcmTag: 00080030
dcmTag: 00080050
dcmTag: 00080061
dcmTag: 00080090
dcmTag: 00081030
dcmTag: 00100010
dcmTag: 00100020
dcmTag: 00100030
dcmTag: 00100040
dcmTag: 0020000D
dcmTag: 00200010
dcmTag: 00201206
dcmTag: 00201208
dcmAttributeSetType: QIDO_RS
dcmAttributeSetID: study
objectClass: dcmAttributeSet
dn: dicomDeviceName=keycloak,cn=Devices,cn=DICOM Configuration,dc=dcm4che,dc=org
changetype: modify
add: dcmTrustStoreURL
dcmTrustStoreURL: ${jboss.server.config.url}/dcm4chee-arc/cacerts.jks
-
add: dcmTrustStoreType
dcmTrustStoreType: JKS
-
add: dcmTrustStorePin
dcmTrustStorePin: secret
-
add: dcmKeyStoreURL
dcmKeyStoreURL: ${jboss.server.config.url}/dcm4chee-arc/key.jks
-
add: dcmKeyStoreType
dcmKeyStoreType: JKS
-
add: dcmKeyStorePin
dcmKeyStorePin: secret
dn: dicomDeviceName=dcm4chee-arc,cn=Devices,cn=DICOM Configuration,dc=dcm4che,dc=org
changetype: modify
add: dcmTrustStoreURL
dcmTrustStoreURL: ${jboss.server.config.url}/dcm4chee-arc/cacerts.jks
-
add: dcmTrustStoreType
dcmTrustStoreType: JKS
-
add: dcmTrustStorePin
dcmTrustStorePin: secret
-
delete: dicomAuthorizedNodeCertificateReference
-
delete: userCertificate;binary
-
delete: objectClass
objectClass: pkiUser
dn: dcmuiConfigName=default,dicomDeviceName=dcm4chee-arc,cn=Devices,cn=DICOM Configuration,dc=dcm4che,dc=org
changetype: modify
add: dcmuiModalities
dcmuiModalities: CR
dcmuiModalities: CT
dcmuiModalities: DX
dcmuiModalities: KO
dcmuiModalities: MR
dcmuiModalities: MG
dcmuiModalities: NM
dcmuiModalities: OT
dcmuiModalities: PT
dcmuiModalities: PR
dcmuiModalities: US
dcmuiModalities: XA
| 2023-10-12T01:26:35.434368 | https://example.com/article/8989 |
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See What Customers Have To Say About Autohaus Arizona
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with imports. Thx again!!!!!! : ) | 2024-02-11T01:26:35.434368 | https://example.com/article/2112 |
<?xml version="1.0" encoding="UTF-8"?>
<g:element xmlns:g="http://www.esri.com/geoportal/gxe"
xmlns:h="http://www.esri.com/geoportal/gxe/html"
g:targetName="gml:ReferenceType"
g:extends="$base/xtn/ui/UI_Wrapped_Element.xml">
<g:body>
<g:import g:src="$base/schema/gml/gmlBase/OwnershipAttributeGroup.xml"/>
<g:import g:src="$base/schema/gml/gmlBase/AssociationAttributeGroup.xml"/>
</g:body>
</g:element>
| 2023-12-21T01:26:35.434368 | https://example.com/article/7092 |
Canada advances to the Fed Cup World Group II playoffs
After finishing atop Group A at the Fed Cup by BNP Paribas Americas Zone Group I event, Canada contested the final against Chile on Saturday in Metepec, Mexico.
Canada remained undefeated in the competition and were crowned champions following a 2-0 triumph over Chile. Fed Cup rookie Katherine Sebov (Toronto, ON) won her third straight singles match of the week 6-2, 6-2 over Barbara Galtican in 59 minutes to give her country a 1-0 lead. Bianca Vanessa Andreescu (Mississauga, ON) sealed the deal for Canada thanks to a 6-3, 6-1 victory over Daniela Seguel 6-1, 6-3. This week, Andreescu went undefeated in her Fed Cup debut, winning four singles matches and two more in doubles.
“The risk to go with a young team paid off,” said Sylvain Bruneau, captain of the Canadian Fed Cup team. “The girls really outdid themselves and honestly, they played even better than I expected. They were impeccable all week.”
On Friday, sixteen-year-old Andreescu was named the first recipient of the Rene Simpson-Collins Excellence Award, given to an outstanding female junior player that exhibits the same important values and traits of the award’s namesake. The annual honour, named in memory of the former player, coach, and Fed Cup captain, will present Andreescu with a $2,000 scholarship to help offset costs related to her training and development.
By winning the Americas Zone Group I event, Canada advances to the World Group II playoffs in April. The team will find out its opponent and the location of the tie on Tuesday when the official draw takes place. | 2023-08-31T01:26:35.434368 | https://example.com/article/9274 |
Andriy Ralyuchenko
Andriy Ralyuchenko (; born 8 June 1995) is a professional Ukrainian football midfielder.
Career
Ralyuchenko is a product of the FC Metalist School System.
He spent his career in the Ukrainian Premier League Reserves club FC Metalist. In 2015 Ralyuchenko was promoted to the Ukrainian Premier League's squad. He made his debut for Metalist Kharkiv in the Ukrainian Premier League in the match against FC Volyn Lutsk on 6 March 2016.
In July 2016 he was signed by Veres Rivne. In December 2016 contract was terminated.
He is son of Serhiy Ralyuchenko.
References
External links
Statistics at FFU website (Ukr)
Category:1995 births
Category:Living people
Category:Sportspeople from Kharkiv
Category:Ukrainian footballers
Category:FC Metalist Kharkiv players
Category:Ukrainian Premier League players
Category:Association football midfielders
Category:NK Veres Rivne players
Category:FC Metalist 1925 Kharkiv players
Category:FC Hirnyk-Sport Horishni Plavni players
Category:Ukrainian First League players | 2024-05-18T01:26:35.434368 | https://example.com/article/1202 |
<!DOCTYPE html><html lang=en><head>
<meta content="text/html; charset=utf-8" http-equiv=Content-Type>
<title>Mixed Content</title>
<link href=./default.css rel=stylesheet type=text/css>
<link href=https://www.w3.org/StyleSheets/TR/W3C-WD rel=stylesheet type=text/css>
</head>
<body class=h-entry>
<div class=head>
<p data-fill-with=logo><a class=logo href=http://www.w3.org/>
<img alt=W3C height=48 src=https://www.w3.org/Icons/w3c_home width=72>
</a>
</p>
<h1 class="p-name no-ref" id=title>Mixed Content</h1>
<h2 class="no-num no-toc no-ref heading settled" id=subtitle><span class=content>W3C Last Call Working Draft,
<span class=dt-updated><span class=value-title title=20141113>13 November 2014</span></span></span></h2>
<div data-fill-with=spec-metadata><dl><dt>This version:<dd><a class=u-url href=http://www.w3.org/TR/2014/WD-mixed-content-20141113/>http://www.w3.org/TR/2014/WD-mixed-content-20141113/</a><dt>Latest version:<dd><a href=http://www.w3c.org/TR/mixed-content/>http://www.w3c.org/TR/mixed-content/</a><dt>Editor's Draft:<dd><a href=https://w3c.github.io/webappsec/specs/mixedcontent/>https://w3c.github.io/webappsec/specs/mixedcontent/</a><dt>Previous Versions:<dd><a href=http://www.w3.org/TR/2014/WD-mixed-content-20140722/ rel=previous>http://www.w3.org/TR/2014/WD-mixed-content-20140722/</a><dt>Version History:<dd><a href=https://github.com/w3c/webappsec/commits/master/specs/mixedcontent/index.src.html>https://github.com/w3c/webappsec/commits/master/specs/mixedcontent/index.src.html</a><dt>Feedback:<dd><span><a href="mailto:public-webappsec@w3.org?subject=%5BMIX%5D%20feedback">public-webappsec@w3.org</a> with subject line “<kbd>[MIX] <var>… message topic …</var></kbd>” (<a href=http://lists.w3.org/Archives/Public/public-webappsec/ rel=discussion>archives</a>)</span><dt class=editor>Editor:<dd class=editor><div class="p-author h-card vcard"><a class="p-name fn u-email email" href=mailto:mkwst@google.com>Mike West</a> (<span class="p-org org">Google Inc.</span>)</div></dl></div>
<div data-fill-with=warning></div>
<p class=copyright data-fill-with=copyright><a href=http://www.w3.org/Consortium/Legal/ipr-notice#Copyright>Copyright</a> © 2014
<a href=http://www.w3.org/><abbr title="World Wide Web Consortium">W3C</abbr></a><sup>®</sup>
(<a href=http://www.csail.mit.edu/><abbr title="Massachusetts Institute of Technology">MIT</abbr></a>,
<a href=http://www.ercim.eu/><abbr title="European Research Consortium for Informatics and Mathematics">ERCIM</abbr></a>,
<a href=http://www.keio.ac.jp/>Keio</a>, <a href=http://ev.buaa.edu.cn/>Beihang</a>),
All Rights Reserved.
<abbr title="World Wide Web Consortium">W3C</abbr> <a href=http://www.w3.org/Consortium/Legal/ipr-notice#Legal_Disclaimer>liability</a>,
<a href=http://www.w3.org/Consortium/Legal/ipr-notice#W3C_Trademarks>trademark</a> and
<a href=http://www.w3.org/Consortium/Legal/copyright-documents>document use</a>
rules apply.
</p>
<hr title="Separator for header">
</div>
<h2 class="no-num no-toc no-ref heading settled" id=abstract><span class=content>Abstract</span></h2>
<div class=p-summary data-fill-with=abstract><p>This specification describes how user agents should handle rendering and execution of content loaded over unencrypted or unauthenticated connections in the context of an encrypted and authenticated document.</p>
</div>
<h2 class="no-num no-toc no-ref heading settled" id=status><span class=content>Status of this document</span></h2>
<div data-fill-with=status>
<em>This section describes the status of this document at the time of
its publication. Other documents may supersede this document. A list of
current W3C publications and the latest revision of this technical report
can be found in the <a href=http://www.w3.org/TR/>W3C technical reports
index at http://www.w3.org/TR/.</a></em>
<p>
This document was published by the
<a href=http://www.w3.org/2011/webappsec/>Web Application Security Working Group</a>
as a Working Draft. This document is intended to become a W3C Recommendation.
<p>
The (<a href=http://lists.w3.org/Archives/Public/public-webappsec/>archived</a>) public mailing list
<a href="mailto:public-webappsec@w3.org?Subject=%5BMIX%5D%20PUT%20SUBJECT%20HERE">public-webappsec@w3.org</a>
(see <a href=http://www.w3.org/Mail/Request>instructions</a>)
is preferred for discussion of this specification.
When sending e-mail,
please put the text “MIX” in the subject,
preferably like this:
“[MIX] <em>…summary of comment…</em>”
<p>
Publication as a Last Call Working Draft does not imply endorsement by the W3C
Membership. This is a draft document and may be updated, replaced or
obsoleted by other documents at any time. It is inappropriate to cite this
document as other than work in progress.
<p>
This document was produced by the
<a href=http://www.w3.org/2011/webappsec/>Web Application Security Working Group</a>.
<p>
This document was produced by a group operating under
the <a href=http://www.w3.org/Consortium/Patent-Policy-20040205/>5 February 2004 W3C Patent Policy</a>.
W3C maintains a <a href=http://www.w3.org/2004/01/pp-impl/49309/status rel=disclosure>public list of any patent disclosures</a>
made in connection with the deliverables of the group;
that page also includes instructions for disclosing a patent.
An individual who has actual knowledge of a patent which the individual believes contains <a href=http://www.w3.org/Consortium/Patent-Policy-20040205/#def-essential>Essential Claim(s)</a>
must disclose the information in accordance with <a href=http://www.w3.org/Consortium/Patent-Policy-20040205/#sec-Disclosure>section 6 of the W3C Patent Policy</a>.
<p>
This specification is a <strong>Last Call Working Draft</strong>. All
persons are encouraged to review this document and <strong>send comments
to the <a href=http://lists.w3.org/Archives/Public/public-webappsec/>public-webappsec</a>
mailing list</strong> as described above. The <strong>deadline for
comments</strong> is <strong>11 December 2014</strong>.
<p>
This document is governed by the <a href=http://www.w3.org/2014/Process-20140801/ id=w3c_process_revision>1 August 2014 W3C Process Document</a>.
</div>
<div data-fill-with=at-risk></div>
<h2 class="no-num no-toc no-ref heading settled" id=contents><span class=content>Table of Contents</span></h2>
<div data-fill-with=table-of-contents role=navigation><ul class=toc role=directory><li><a href=#intro><span class=secno>1</span> <span class=content>Introduction</span></a><li><a href=#terms><span class=secno>2</span> <span class=content>Key Concepts and Terminology</span></a><ul class=toc><li><a href=#terms-defined-here><span class=secno>2.1</span> <span class=content>Terms defined by this specification</span></a><li><a href=#terms-defined-by-reference><span class=secno>2.2</span> <span class=content>Terms defined by reference</span></a></ul><li><a href=#categories><span class=secno>3</span> <span class=content>Content Categories</span></a><ul class=toc><li><a href=#category-optionally-blockable><span class=secno>3.1</span> <span class=content>Optionally-blockable Content</span></a><li><a href=#category-blockable><span class=secno>3.2</span> <span class=content>Blockable Content</span></a><li><a href=#categories-unknown-content><span class=secno>3.3</span> <span class=content>Future Contexts</span></a></ul><li><a href=#requirements><span class=secno>4</span> <span class=content>User Agent Requirements</span></a><ul class=toc><li><a href=#requirements-fetching><span class=secno>4.1</span> <span class=content>Resource Fetching</span></a><li><a href=#requirements-script><span class=secno>4.2</span> <span class=content>Script APIs</span></a><li><a href=#requirements-forms><span class=secno>4.3</span> <span class=content>Form Submission</span></a><li><a href=#requirements-ux><span class=secno>4.4</span> <span class=content>UI Requirements</span></a><li><a href=#requirements-user-controls><span class=secno>4.5</span> <span class=content>User Controls</span></a></ul><li><a href=#algorithms><span class=secno>5</span> <span class=content>Insecure Content in Secure Contexts</span></a><ul class=toc><li><a href=#categorize-settings-object><span class=secno>5.1</span> <span class=content>
Does <var>settings object</var> restrict mixed content?
</span></a><li><a href=#should-block-fetch><span class=secno>5.2</span> <span class=content>
Should fetching <var>request</var> be blocked as mixed content?
</span></a><li><a href=#should-block-response><span class=secno>5.3</span> <span class=content>
Should <var>response</var> to <var>request</var> be blocked as mixed
content?
</span></a></ul><li><a href=#powerful-features><span class=secno>6</span> <span class=content>
Secure Contexts for Powerful Features
</span></a><ul class=toc><li><a href=#may-document-use-powerful-features><span class=secno>6.1</span> <span class=content>
May <var>Document</var> use powerful features?
</span></a><li><a href=#settings-powerful-features><span class=secno>6.2</span> <span class=content>
May <var>environment settings object</var> use powerful features?
</span></a><li><a href=#is-origin-trusted><span class=secno>6.3</span> <span class=content>
Is <var>origin</var> potentially trusted?
</span></a></ul><li><a href=#fetch-integration><span class=secno>7</span> <span class=content>Integration with Fetch</span></a><li><a href=#websockets-integration><span class=secno>8</span> <span class=content>Modifications to WebSockets</span></a><li><a href=#acknowledgements><span class=secno>9</span> <span class=content>Acknowledgements</span></a><li><a href=#conformance><span class=secno></span> <span class=content>Conformance</span></a><ul class=toc><li><a href=#conventions><span class=secno></span> <span class=content>Document conventions</span></a><li><a href=#conformant-algorithms><span class=secno></span> <span class=content>Conformant Algorithms</span></a><li><a href=#conformance-classes><span class=secno></span> <span class=content>Conformance Classes</span></a></ul><li><a href=#references><span class=secno></span> <span class=content>References</span></a><ul class=toc><li><a href=#normative><span class=secno></span> <span class=content>Normative References</span></a><li><a href=#informative><span class=secno></span> <span class=content>Informative References</span></a></ul><li><a href=#index><span class=secno></span> <span class=content>Index</span></a></ul></div>
<main>
<section>
<h2 class="heading settled" data-level=1 id=intro><span class=secno>1. </span><span class=content>Introduction</span><a class=self-link href=#intro></a></h2>
<p><em>This section is not normative.</em></p>
<p>When a user successfully loads a resource from example.com over a secure
channel (HTTPS, for example), the user agent is able to make three assertions
critical to the user’s security and privacy:</p>
<ul>
<li>
The user is communicating with a server that is allowed to claim to be
<code>example.com</code>, and not one of the many, many servers through
which her request has hopped. The connection can be
<strong>authenticated</strong>.
</li>
<li>
The user’s communications with <code>example.com</code> cannot be
trivially eavesdropped upon by middlemen, because the requests she makes
and the responses she receives are <strong>encrypted</strong>.
</li>
<li>
The user’s communications with <code>example.com</code> cannot be
trivially modified by middlemen, the encryption and authentication
provide a guarantee of <strong>data integrity</strong>.
</li>
</ul>
<p>Together, these assertions give the user some assurance that
<code>example.com</code> is the only entity that can read and respond to her
requests (caveat: without shocking amounts of work) and that the bits she’s
receiving are indeed those that <code>example.com</code> actually sent.</p>
<p>The strength of these assertions is substantially weakened, however, when
the encrypted and authenticated resource requests subresources (scripts,
images, etc) over an insecure channel. Those resource requests result in a
resource whose status is mixed, as insecure requests are wide open for
man-in-the-middle attacks. This scenario is unfortunately quite common.</p>
<p>This specification details how user agents can mitigate these risks to
security and privacy by limiting a resource’s ability to inadvertently
communicate in the clear.</p>
<p class=note role=note>Note: Nothing described in this document is really new; everything covered
here has appeared in one or more user agents over the years: Internet Explorer
led the way, alerting users to mixed content since at least version 4.</p>
</section>
<section>
<h2 class="heading settled" data-level=2 id=terms><span class=secno>2. </span><span class=content>Key Concepts and Terminology</span><a class=self-link href=#terms></a></h2>
<h3 class="heading settled" data-level=2.1 id=terms-defined-here><span class=secno>2.1. </span><span class=content>Terms defined by this specification</span><a class=self-link href=#terms-defined-here></a></h3>
<dl>
<dt>
<dfn data-dfn-type=dfn data-export="" data-local-title=mixed id=mixed-content>mixed content<a class=self-link href=#mixed-content></a></dfn>
</dt>
<dd>
A resource is said to be <strong>mixed content</strong> if the resource’s
<a data-link-type=dfn href=#origin title=origin>origin</a> is <a data-link-type=dfn href=#insecure-origin title=insecure>insecure</a>, <strong>and</strong> the the context
responsible for loading it <a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts mixed content</a>.
<div class=example>
The image <code>http://example.com/image.png</code> is <strong>mixed
content</strong> when loaded by
<code>https://not.example.com/</code>.
<p>The image <code>http://127.0.0.1/image.png</code> is <strong>mixed
content</strong> when loaded by <code>http://example.com/</code>.</p>
</div>
</dd>
<dt>
<dfn data-dfn-type=dfn data-export="" data-local-title="potentially secure" id=potentially-secure-origin>
potentially secure origin
<a class=self-link href=#potentially-secure-origin></a></dfn>
</dt>
<dt>
<dfn data-dfn-type=dfn data-export="" id=potentially-secure-url>
potentially secure URL
<a class=self-link href=#potentially-secure-url></a></dfn>
</dt>
<dd>
An <a data-link-type=dfn href=#origin title=origin>origin</a> is said to be <strong>potentially secure</strong>
if the origin’s scheme component is <code>HTTPS</code>, <code>WSS</code>,
or <code>about</code>.
<p>A URL whose <a data-link-type=dfn href=#origin title=origin>origin</a> is potentially secure is itself considered to
be potentially secure.</p>
</dd>
<dt>
<dfn data-dfn-type=dfn data-export="" data-local-title="a priori insecure" id=a-priori-insecure-origin>
<em>a priori</em> insecure origin
<a class=self-link href=#a-priori-insecure-origin></a></dfn>
</dt>
<dt>
<dfn data-dfn-type=dfn data-export="" id=a-priori-insecure-url>
<em>a priori</em> insecure URL
<a class=self-link href=#a-priori-insecure-url></a></dfn>
</dt>
<dd>
Any <a data-link-type=dfn href=#origin title=origin>origin</a> which is not <a data-link-type=dfn href=#potentially-secure-origin title="potentially secure">potentially secure</a> is said to
be <strong><em>a priori</em> insecure</strong>. We know, for example, that
<code>http://example.com/</code> is insecure just by looking at its scheme
component.
<p>A URL whose <a data-link-type=dfn href=#origin title=origin>origin</a> is <em>a priori</em> insecure is itself
considered to be <em>a priori</em> insecure.</p>
</dd>
<dt>
<dfn data-dfn-type=dfn data-export="" data-local-title=insecure id=insecure-origin>
insecure origin
<a class=self-link href=#insecure-origin></a></dfn>
</dt>
<dt>
<dfn data-dfn-type=dfn data-export="" id=insecure-url>
insecure URL
<a class=self-link href=#insecure-url></a></dfn>
</dt>
<dd>
An resource’s origin is said to be <strong>insecure</strong> if it is
either <a data-link-type=dfn href=#a-priori-insecure-origin title="a priori insecure"><em>a priori</em> insecure</a>, or the user agent discovers
only after performing a TLS-handshake that the TLS-protection offered
is either <a data-link-type=dfn href=#weakly-tls-protected title=weak>weak</a> or <a data-link-type=dfn href=#deprecated-tls-protection title=deprecated>deprecated</a>.
<p>A URL whose <a data-link-type=dfn href=#origin title=origin>origin</a> is insecure is itself considered to be insecure.</p>
</dd>
<dt>
<dfn data-dfn-type=dfn data-export="" data-local-title=deprecated id=deprecated-tls-protection>
deprecated TLS-protection
<a class=self-link href=#deprecated-tls-protection></a></dfn>
</dt>
<dd>
A resource’s TLS-protection is said to be <strong>deprecated</strong>
if it is not <a data-link-type=dfn href=#weakly-tls-protected title="weakly TLS-protected">weakly TLS-protected</a>, but the user agent chooses to
refuse it anyway. This determination is vendor-specific.
<p>For example, a user agent may choose to reject resources for which the
server presented a publicly-trusted certificate for an "Internal
Name" (e.g. <code>https://intranet/</code>), a certificate with an
overly-long validity period, a certificate signed with SHA-1, or a
certificate which otherwise fails to meet the
<a href=https://cabforum.org/baseline-requirements-documents/>
CA/Browser Forum’s Baseline Requirements</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-cab title=CAB>[CAB]</a></p>
<p class=note role=note>Note: We recommend that user agents return network errors rather than
fetching resources whose TLS-protection is deprecated.</p>
</dd>
</dl>
<h3 class="heading settled" data-level=2.2 id=terms-defined-by-reference><span class=secno>2.2. </span><span class=content>Terms defined by reference</span><a class=self-link href=#terms-defined-by-reference></a></h3>
<dl>
<dt><dfn data-dfn-type=dfn data-noexport="" id=tls-protected>TLS-protected<a class=self-link href=#tls-protected></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-local-title=weak data-noexport="" id=weakly-tls-protected>weakly TLS-protected<a class=self-link href=#weakly-tls-protected></a></dfn></dt>
<dd>
These terms are defined in
<a href=http://www.w3.org/TR/2010/REC-wsc-ui-20100812/#typesoftls>§5.2
of "Web Security Context: User Interface Guidelines"</a> <a data-biblio-type=normative data-link-type=biblio href=#biblio-wsc-ui title=WSC-UI>[WSC-UI]</a>.
A resource is <strong>TLS-protected</strong> when it is delivered over an
encrypted channel. <strong>Weakly TLS-protected</strong> refers to a
subset of those resources delivered over a channel that doesn’t offer
strong protection of the content.
<p>For example, resources would be considered weakly TLS-protected when
delivered by a server presenting a self-signed certificate which does not
chain to a root certificate in the user agent’s local trust store, as
such a certificate only weakly authenticates the server. Similarly, a
server which negotiates down to a weak cipher suite (such as
<code>TLS_RSA_WITH_NULL_MD5</code>) would only weakly protect resources
it serves.</p>
<p class=note role=note>Note: We recommend that user agents return network errors rather than
fetching resources whose TLS-protection is weak.</p>
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=origin>origin<a class=self-link href=#origin></a></dfn></dt>
<dd>
An origin defines the scope of authority or privilege under which a
resource operates. It is defined in detail in the Origin specification.
<a data-biblio-type=normative data-link-type=biblio href=#biblio-rfc6454 title=RFC6454>[RFC6454]</a>
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=globally-unique-identifier>globally unique identifier<a class=self-link href=#globally-unique-identifier></a></dfn></dt>
<dd>
This term is defined in
<a href=http://tools.ietf.org/html/rfc6454#section-4>Section 4 of
RFC6454</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-rfc6454 title=RFC6454>[RFC6454]</a>
<p class=note role=note>Note: URLs that do not use
<a href=http://tools.ietf.org/html/rfc3986#section-3.2>hierarchical
elements</a> as naming authorities (for example: <code>blob:</code>, and
<code>data:</code>) have origins which are globally unique identifiers.
<a data-biblio-type=informative data-link-type=biblio href=#biblio-uri title=URI>[URI]</a></p>
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=fetch>fetch<a class=self-link href=#fetch></a></dfn></dt>
<dd>
"fetching" is the process by which a user agent requests resources, and
delivers responses. It is defined in detail in the Fetch living standard.
<a data-biblio-type=normative data-link-type=biblio href=#biblio-fetch title=FETCH>[FETCH]</a>
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=request>request<a class=self-link href=#request></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-local-title=client data-noexport="" id=request-client>request client<a class=self-link href=#request-client></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-local-title=context data-noexport="" id=request-context>request context<a class=self-link href=#request-context></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-local-title="frame type" data-noexport="" id=request-context-frame-type>request context frame type<a class=self-link href=#request-context-frame-type></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-local-title="tls state" data-noexport="" id=request-client-tls-state>request client TLS state<a class=self-link href=#request-client-tls-state></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-noexport="" id=response-tls-state>response TLS state<a class=self-link href=#response-tls-state></a></dfn></dt>
<dd>
These terms are defined in
<a href=http://fetch.spec.whatwg.org/#requests>Section 2.2</a> of the
Fetch living standard. <a data-biblio-type=normative data-link-type=biblio href=#biblio-fetch title=FETCH>[FETCH]</a>
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=response>response<a class=self-link href=#response></a></dfn></dt>
<dt><dfn data-dfn-type=dfn data-noexport="" id=network-error>network error<a class=self-link href=#network-error></a></dfn></dt>
<dd>
These terms are defined in detail in
<a href=http://fetch.spec.whatwg.org/#responses>Section 2.3</a> of the
Fetch living standard. <a data-biblio-type=normative data-link-type=biblio href=#biblio-fetch title=FETCH>[FETCH]</a>
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=environment-settings-object>environment settings object<a class=self-link href=#environment-settings-object></a></dfn></dt>
<dd>
Defined in <a data-biblio-type=normative data-link-type=biblio href=#biblio-html5 title=HTML5>[HTML5]</a>.
</dd>
<dt><dfn data-dfn-type=dfn data-noexport="" id=embedding-document>embedding document<a class=self-link href=#embedding-document></a></dfn></dt>
<dd>
Given a <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code> <var>A</var>, the <strong>embedding
document</strong> of <var>A</var> is the <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code>
<a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#browsing-context-nested-through title="nested through">through which</a> <var>A</var>’s <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#browsing-context title="browsing context">browsing
context</a> is nested.
</dd>
</dl>
</section>
<section>
<h2 class="heading settled" data-level=3 id=categories><span class=secno>3. </span><span class=content>Content Categories</span><a class=self-link href=#categories></a></h2>
<p>In a perfect world, user agents would be required to block all <a data-link-type=dfn href=#mixed-content title="mixed content">mixed
content</a> without exception. Unfortunately, that is impractical on today’s
internet. For instance, a survey in 2013 notes that blocking mixed content
would break around ~43% of secure websites in one way or another
<a data-biblio-type=informative data-link-type=biblio href=#biblio-dangerous-mix title=DANGEROUS-MIX>[DANGEROUS-MIX]</a>. Draconian blocking policies applied to some types of mixed
content are (for the moment) infeasible. User agents need to be more nuanced
in their restrictions.</p>
<p>With that in mind, we here split mixed content into two categories defined in
the following two sections: <a data-section="" href=#category-blockable>§3.2 Blockable Content</a> and
<a data-section="" href=#category-optionally-blockable>§3.1 Optionally-blockable Content</a>.</p>
<p>Future versions of this specification will update these categories with
the intent of moving towards a world where all <a data-link-type=dfn href=#mixed-content title=mixed>mixed</a> content is
blocked; that is the end goal, but this is the best we can do for now.</p>
<section>
<h3 class="heading settled" data-level=3.1 id=category-optionally-blockable><span class=secno>3.1. </span><span class=content>Optionally-blockable Content</span><a class=self-link href=#category-optionally-blockable></a></h3>
<p>A resource is considered
<dfn data-dfn-type=dfn data-local-title=optionally-blockable data-noexport="" id=optionally-blockable-content>optionally-blockable content<a class=self-link href=#optionally-blockable-content></a></dfn>
when the risk of allowing its usage as <a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a> is outweighed by
the risk of breaking significant portions of the web. This could be because
mixed usage of the resource type is sufficiently high, or because the resource
is very clearly low-risk in and of itself. This category of content includes:</p>
<ul>
<li>
Images loaded via <a data-link-type=element href=https://html.spec.whatwg.org/#the-img-element title=img>img</a>
<p class=note role=note>Note: This includes SVG documents loaded as images.</p>
</li>
<li>
Video loaded via <a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-video-element title=video>video</a> and <a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-source-element title=source>source</a>
</li>
<li>
Audio loaded via <a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-audio-element title=audio>audio</a> and <a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-source-element title=source>source</a>
</li>
<li>
<a href=http://www.w3.org/TR/html5/links.html#link-type-prefetch>Prefetched</a>
content <a data-biblio-type=normative data-link-type=biblio href=#biblio-html5 title=HTML5>[HTML5]</a>
</li>
</ul>
<p>These resource types map to the following Fetch <a data-link-type=dfn href=#request-context title="request contexts">request contexts</a>:
<code>audio</code>, <code>image</code>, <code>prefetch</code>, and
<code>video</code>. These contexts are <dfn data-dfn-type=dfn data-noexport="" id=optionally-blockable-request-contexts>optionally-blockable request
contexts<a class=self-link href=#optionally-blockable-request-contexts></a></dfn>.</p>
<p class=note role=note>Note: The fact that these resource types are optionally-blockable does not
mean that they are <em>safe</em>, simply that they’re less catastrophically
dangerous than other resource types. For example, images and icons are often
the central UI elements in an application’s interface. If an attacker
reversed the "Delete email" and "Reply" icons, there would be real impact on
users.</p>
<p class=note role=note>Note: We further limit this category in <a data-section="" href=#should-block-fetch>§5.2
Should fetching request be blocked as mixed content?
</a> by
force-failing any CORS-enabled request. This means that mixed content images
loaded via <code><img crossorigin ...></code> will be blocked. This is
a good example of the general principle that a category of content falls
into this category <em>only</em> when it is too widely used to be blocked
outright. The working group intends to find more blockable subsets of an
otherwise <a data-link-type=dfn href=#optionally-blockable-request-contexts title="optionally-blockable request context">optionally-blockable request context</a>.</p>
</section>
<section>
<h3 class="heading settled" data-level=3.2 id=category-blockable><span class=secno>3.2. </span><span class=content>Blockable Content</span><a class=self-link href=#category-blockable></a></h3>
<p>Any resource that isn’t <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a> is considered
<dfn data-dfn-type=dfn data-local-title=blockable data-noexport="" id=blockable-content>blockable content<a class=self-link href=#blockable-content></a></dfn>.
A non-exhaustive sample of content that falls into this category includes:</p>
<ul>
<li>
Scripts (loaded, for example, via <a data-link-type=element href=http://www.w3.org/TR/html5/scripting-1.html#the-script-element title=script>script</a> elements, as
well as scripts loaded as Workers and SharedWorkers <a data-biblio-type=informative data-link-type=biblio href=#biblio-workers title=WORKERS>[WORKERS]</a>, or
ServiceWorkers <a data-biblio-type=informative data-link-type=biblio href=#biblio-serviceworkers title=SERVICEWORKERS>[SERVICEWORKERS]</a>) <a data-biblio-type=informative data-link-type=biblio href=#biblio-ecma-262 title=ECMA-262>[ECMA-262]</a>
</li>
<li>Stylesheets <a data-biblio-type=informative data-link-type=biblio href=#biblio-css21 title=CSS21>[CSS21]</a></li>
<li>
<a data-link-type=dfn href=http://www.w3.org/TR/html5/infrastructure.html#plugin title=Plugin>Plugin</a> data (loaded, for example, through
<a data-link-type=element href=https://html.spec.whatwg.org/#the-applet-element title=applet>applet</a>, <a data-link-type=element href=https://html.spec.whatwg.org/#the-embed-element title=embed>embed</a>, or <a data-link-type=element href=https://html.spec.whatwg.org/#the-object-element title=object>object</a>
elements; or through a <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#plugin-document title="plugin document">plugin document</a> loaded into an
<a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-iframe-element title=iframe>iframe</a> or <a data-link-type=element href=http://www.w3.org/TR/html5/obsolete.html#frame title=frame>frame</a> element) <a data-biblio-type=informative data-link-type=biblio href=#biblio-html5 title=HTML5>[HTML5]</a>
</li>
<li>SVG Documents <a data-biblio-type=informative data-link-type=biblio href=#biblio-svg2 title=SVG2>[SVG2]</a></li>
<li>XSL Transformations <a data-biblio-type=informative data-link-type=biblio href=#biblio-xslt title=XSLT>[XSLT]</a></li>
<li>HTML Imports <a data-biblio-type=informative data-link-type=biblio href=#biblio-html-imports title=HTML-IMPORTS>[HTML-IMPORTS]</a></li>
<li>HTML Manifests <a data-biblio-type=informative data-link-type=biblio href=#biblio-manifest title=MANIFEST>[MANIFEST]</a></li>
<li>Documents rendered in <a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-iframe-element title=iframe>iframe</a> elements</li>
<li>Beacon <a data-biblio-type=informative data-link-type=biblio href=#biblio-beacon title=BEACON>[BEACON]</a></li>
<li>Custom Filters <a data-biblio-type=informative data-link-type=biblio href=#biblio-filter-effects title=FILTER-EFFECTS>[FILTER-EFFECTS]</a></li>
<li>
Data (loaded, for example, via XMLHttpRequest <a data-biblio-type=informative data-link-type=biblio href=#biblio-xmlhttprequest title=XMLHTTPREQUEST>[XMLHTTPREQUEST]</a>,
EventSource <a data-biblio-type=informative data-link-type=biblio href=#biblio-eventsource title=EVENTSOURCE>[EVENTSOURCE]</a>, or WebSockets <a data-biblio-type=informative data-link-type=biblio href=#biblio-websockets title=WEBSOCKETS>[WEBSOCKETS]</a>)
</li>
<li>
<a href=http://www.whatwg.org/specs/web-apps/current-work/multipage/semantics.html#hyperlink-auditing>hyperlink auditing pings</a> <a data-biblio-type=informative data-link-type=biblio href=#biblio-html title=HTML>[HTML]</a>
</li>
<li>
Subtitles and captions loaded via <a data-link-type=element href=http://www.w3.org/TR/html5/embedded-content-0.html#the-track-element title=track>track</a> elements
</li>
<li>Web Fonts <a data-biblio-type=informative data-link-type=biblio href=#biblio-css3-webfonts title=CSS3-WEBFONTS>[CSS3-WEBFONTS]</a></li>
<li>Images loaded via <code><picture></code></li>
<li>
Resources which are not rendered directly in the browser, but
downloaded to a user’s storage device (either as a result of a
<a data-link-type=element-attr href=https://html.spec.whatwg.org/#attr-hyperlink-download title=download>download</a> attribute, or
<code>Content-Disposition</code> headers)
</li>
</ul>
<p>These resource types map to the following Fetch <a data-link-type=dfn href=#request-context title="request contexts">request contexts</a>:
<code>beacon</code>, <code>cspreport</code>, <code>download</code>,
<code>embed</code>, <code>eventsource</code>, <code>favicon</code>,
<code>fetch</code>, <code>font</code>, <code>form</code>,
<code>frame</code>, <code>hyperlink</code>, <code>iframe</code>,
<code>imageset</code>, <code>location</code>, <code>manifest</code>,
<code>object</code>, <code>ping</code>, <code>plugin</code>,
<code>script</code>, <code>serviceworker</code>, <code>sharedworker</code>,
<code>subresource</code>, <code>style</code>, <code>track</code>,
<code>worker</code>, <code>xmlhttprequest</code>, and <code>xslt</code>.
These contexts are the <dfn data-dfn-type=dfn data-noexport="" id=blockable-request-contexts>blockable request contexts<a class=self-link href=#blockable-request-contexts></a></dfn>.</p>
<p class=note role=note>Note: The request contexts <code>form</code>, <code>hyperlink</code>, and
<code>location</code> might refer to <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#top-level-browsing-context title="top-level browsing context">top-level browsing context</a>
<a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#navigate title=navigated>navigations</a>, which are not considered mixed
content. See the treatment of <a data-link-type=dfn href=#request-context-frame-type title="request context frame type">request context frame type</a> in
<a data-section="" href=#should-block-fetch>§5.2
Should fetching request be blocked as mixed content?
</a> for details.</p>
</section>
<section>
<h3 class="heading settled" data-level=3.3 id=categories-unknown-content><span class=secno>3.3. </span><span class=content>Future Contexts</span><a class=self-link href=#categories-unknown-content></a></h3>
<p>This document exhaustively categorizes the <a data-link-type=dfn href=#request-context title="request contexts">request contexts</a> currently
defined in the Fetch specification. It is the intention of the Working Group
that any new content types defined in the future be prevented from loading
as <a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a>. To that end, any <a data-link-type=dfn href=#request-context title="request context">request context</a> which is
not explicitly listed in the preceeding content categories MUST be
considered a <a data-link-type=dfn href=#blockable-request-contexts title="blockable request context">blockable request context</a>.</p>
</section>
</section>
<section>
<h2 class="heading settled" data-level=4 id=requirements><span class=secno>4. </span><span class=content>User Agent Requirements</span><a class=self-link href=#requirements></a></h2>
<section>
<h3 class="heading settled" data-level=4.1 id=requirements-fetching><span class=secno>4.1. </span><span class=content>Resource Fetching</span><a class=self-link href=#requirements-fetching></a></h3>
<p>User agents SHOULD reject <a data-link-type=dfn href=#weakly-tls-protected title="weakly TLS-protected">weakly TLS-protected</a> resources entirely
by failing the TLS handshake, or by requiring explicit user acceptance
of the risk (for instance, presenting the user with a confirmation screen
she must click through).</p>
<p>If a <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code>'s <a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#incumbent-settings-object title="incumbent settings object">incumbent settings object</a> <a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts
mixed content</a>, or the <a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#relevant-settings-object-for-a-script title="relevant settings object for a script">relevant settings object for a script</a>
<a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts mixed content</a>, then <a data-link-type=dfn href=#fetch title=fetching>fetching</a> resource in response
to requests (including not only requests for a <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code>'s subresources,
but also requests made from (Workers, SharedWorkers, Service Workers, and
so on) will exhibit the following behavior:</p>
<ol>
<li>
<a data-link-type=dfn href=#request title=Requests>Requests</a> for <a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> resources from an
<a data-link-type=dfn href=#a-priori-insecure-origin title="a priori insecure origin"><em>a priori</em> insecure origin</a> will not generate network
traffic, but will instead return a synthetically generated <a data-link-type=dfn href=#network-error title="network error">network
error</a> response.
</li>
<li>
<a data-link-type=dfn href=#response title=Responses>Responses</a> to <a data-link-type=dfn href=#request title=requests>requests</a> for <a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> resources from
an <a data-link-type=dfn href=#insecure-origin title="insecure origin">insecure origin</a> will not be delivered to the <a data-link-type=dfn href=#request-client title="request client">request
client</a>, but instead will return a synthetically generated <a data-link-type=dfn href=#network-error title="network error">network
error</a> response.
</li>
</ol>
<p><a data-section="" href=#fetch-integration>§7 Integration with Fetch</a> and <a data-section="" href=#algorithms>§5 Insecure Content in Secure Contexts</a> detail how these fetching
requirements could be implemented.</p>
<p>User agents MAY take further action:</p>
<ol>
<li>
<a data-link-type=dfn href=#request title=Requests>Requests</a> for <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a> resources which
are <a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a> SHOULD be treated as <a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> (and
therefore returned as a <a data-link-type=dfn href=#network-error title="network error">network error</a> as described above), but
user agents MAY allow them to load normally.
<p class=note role=note>Note: For instance, a user agent could interpret the presence of a
<code>Strict-Transport-Security</code> header field as forcing all
content into the <a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> category. <a data-biblio-type=informative data-link-type=biblio href=#biblio-rfc6797 title=RFC6797>[RFC6797]</a></p>
</li>
<li>
<a data-link-type=dfn href=#request title=Requests>Requests</a> for <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a> resources which
are <a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a> MAY be modified to reduce the risk to users.
For example, cookies and other authentication tokens could be stripped
from the requests, or the user agent could automatically change the
protocol of the requested URL to <code>HTTPS</code> in certain cases.
</li>
</ol>
</section>
<section>
<h3 class="heading settled" data-level=4.2 id=requirements-script><span class=secno>4.2. </span><span class=content>Script APIs</span><a class=self-link href=#requirements-script></a></h3>
<p>If the <a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#relevant-settings-object-for-a-script title="relevant settings object for a script">relevant settings object for a script</a> <var>script</var>
<a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts mixed content</a>, then user agents will model a mixed content
failure as a network error. This means that:</p>
<ol>
<li>
An XMLHttpRequest rejected as mixed content will run the steps for a
network error during execution of the
<a href=http://www.w3.org/TR/XMLHttpRequest2/#the-send-method><code>send()</code>
method</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-xmlhttprequest title=XMLHTTPREQUEST>[XMLHTTPREQUEST]</a>
</li>
<li>
An EventSource connection rejected as mixed content will cause the user agent to
<a href=http://www.w3.org/TR/eventsource/#fail-the-connection>fail the
connection</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-eventsource title=EVENTSOURCE>[EVENTSOURCE]</a>
</li>
<li>
When processing WebSocket’s
<a href=http://www.w3.org/TR/websockets/#the-websocket-interface>constructor</a>,
for an <a data-link-type=dfn href=#a-priori-insecure-origin title="a priori insecure origin">a priori insecure origin</a>, a <code>SecurityError</code> exception will
be thrown. <a data-biblio-type=normative data-link-type=biblio href=#biblio-websockets title=WEBSOCKETS>[WEBSOCKETS]</a>
</li>
</ol>
</section>
<section>
<h3 class="heading settled" data-level=4.3 id=requirements-forms><span class=secno>4.3. </span><span class=content>Form Submission</span><a class=self-link href=#requirements-forms></a></h3>
<p>If a <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code>'s <a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#incumbent-settings-object title="incumbent settings object">incumbent settings object</a> <a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts mixed
content</a>, then user agents MAY choose to warn users of the presence of
one or more <a data-link-type=element href=https://html.spec.whatwg.org/#the-form-element title=form>form</a> elements with <a data-link-type=element-attr href=https://html.spec.whatwg.org/#attr-fs-action title=action>action</a>
attributes whose values are <a data-link-type=dfn href=#insecure-url title="insecure URLs">insecure URLs</a>.</p>
<p class=note role=note>Note: Chrome, for example, currently gives the same UI treatment to a page
with an insecure form action as it does for a page that displays an insecure
image.</p>
<p>Further, user agents MAY <strong>optionally</strong> treat form submissions
in the <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#top-level-browsing-context title="top-level browsing context">top-level browsing context</a> from a <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code> whose
<a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#incumbent-settings-object title="incumbent settings object">incumbent settings object</a> <a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts mixed content</a> as a
request for <a data-link-type=dfn href=#blockable-content title="blockable content">blockable content</a> to protect users from accidental data
leakage.</p>
</section>
</section>
<section>
<h3 class="heading settled" data-level=4.4 id=requirements-ux><span class=secno>4.4. </span><span class=content>UI Requirements</span><a class=self-link href=#requirements-ux></a></h3>
<p>If a <a data-link-type=dfn href=#request title=request>request</a> for an <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a> resource which is
<a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a> is <strong>not</strong> treated as <a data-link-type=dfn href=#blockable-content title=blockable>blockable</a>,
then the user agent MUST NOT provide the user with a visible indication that
the <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#top-level-browsing-context title="top-level browsing context">top-level browsing context</a> which loaded that resource is secure
(for instance, via a green lock icon). The user agent SHOULD instead display
a visible indication that <a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a> is present.</p>
<p>This requirement explicitly includes any visible indication of the
<a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#top-level-browsing-context title="top-level browsing context">top-level browsing context</a>’s
<a href=https://cabforum.org/about-ev-ssl/>EV status</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-cab title=CAB>[CAB]</a></p>
</section>
<section>
<h3 class="heading settled" data-level=4.5 id=requirements-user-controls><span class=secno>4.5. </span><span class=content>User Controls</span><a class=self-link href=#requirements-user-controls></a></h3>
<p>User agents MAY offer users the ability to directly decide whether or not to
treat <strong>all</strong> <a data-link-type=dfn href=#mixed-content title="mixed content">mixed content</a> as <a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> (meaning
that even <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a> would be blocked in a
mixed context).</p>
<p class=note role=note>Note: It is <em>strongly recommended</em> that users take advantage of such
an option if provided.</p>
<p>User agents MAY offer users the ability to override its decision to block
<a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> mixed content on a particular page.</p>
<p class=note role=note>Note: Practically, user agents probably can’t get away with not offering
such a back door. That said, allowing mixed script is in particular a very
dangerous option, and user agents
<a href=http://tools.ietf.org/html/rfc6919#section-3>REALLY SHOULD NOT</a>
<a data-biblio-type=informative data-link-type=biblio href=#biblio-rfc6919 title=RFC6919>[RFC6919]</a> present such a choice to users without careful consideration and
communication of the risk involved.</p>
</section>
<section>
<h2 class="heading settled" data-level=5 id=algorithms><span class=secno>5. </span><span class=content>Insecure Content in Secure Contexts</span><a class=self-link href=#algorithms></a></h2>
<section>
<h3 class="heading settled" data-level=5.1 id=categorize-settings-object><span class=secno>5.1. </span><span class=content>
Does <var>settings object</var> restrict mixed content?
</span><a class=self-link href=#categorize-settings-object></a></h3>
<p>Both documents and workers have <a data-link-type=dfn href=#environment-settings-object title="environment settings objects">environment settings objects</a> which
may be examined according to the following algorithm in order to determine
whether they <dfn data-dfn-type=dfn data-export="" data-local-title="restricts mixed content" id=restrict-mixed-content>restrict
mixed content<a class=self-link href=#restrict-mixed-content></a></dfn>. This algorithm returns <code>Restricts Mixed
Content</code> or <code>Does Not Restrict Mixed Content</code>, as
appropriate.</p>
<p>Given an <a data-link-type=dfn href=#environment-settings-object title="environment settings object">environment settings object</a> <var>settings</var>:</p>
<ol>
<li>
If <var>settings</var>' <a data-link-type=dfn href=#request-client-tls-state title="TLS state">TLS state</a> is not
<code>unauthenticated</code>, then return <strong>Restricts Mixed
Content</strong>.
</li>
<li>
If <var>settings</var> has a <a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#responsible-document title="responsible document">responsible document</a>
<var>document</var>, then:
<ol>
<li>
While <var>document</var> has an <a data-link-type=dfn href=#embedding-document title="embedding document">embedding document</a>:
<ol>
<li>
Let <var>document</var> be <var>document</var>’s <a data-link-type=dfn href=#embedding-document title="embedding document">embedding
document</a>.
</li>
<li>
Let <var>embedder settings</var> be <var>document</var>’s
<var>incumbent settings object</var>.
</li>
<li>
If <var>embedder settings</var>' <a data-link-type=dfn href=#request-client-tls-state title="TLS state">TLS state</a> is not
<code>unauthenticated</code>, then return <strong>Restricts
mixed content</strong>.
</li>
</ol>
</li>
</ol>
</li>
<li>Return <strong>Does Not Restrict Mixed Content</strong>.</li>
</ol>
<div class=note role=note>
If a document has an <a data-link-type=dfn href=#embedding-document title="embedding document">embedding document</a>, user agents need to
check not only the document itself, but also the <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#top-level-browsing-context title="top-level browsing context">top-level browsing
context</a> in which the document is nested, as that is the context
which controls the user’s expectations regarding the security status of
the resource she’s loaded. For example:
<div class=example>
<code>http://a.com</code> loads <code>http://evil.com</code>. The
insecure request will be allowed, as <code>a.com</code> was not loaded
over a secure connection.
</div>
<div class=example>
<code>https://a.com</code> loads <code>http://evil.com</code>. The
insecure request will be blocked, as <code>a.com</code> was loaded over
a secure connection.
</div>
<div class=example>
<code>http://a.com</code> frames <code>https://b.com</code>, which
loads <code>http://evil.com</code>. In this case, the insecure request
to <code>evil.com</code> will be blocked, as <code>b.com</code> was
loaded over a secure connection, even though <code>a.com</code> was not.
</div>
<div class=example>
<code>https://a.com</code> frames a <code>data:</code> URL, which loads
<code>http://evil.com</code>. In this case, the insecure request to
<code>evil.com</code> will be blocked, as <code>a.com</code> was loaded
over a secure connection, even though the framed data URL was not.
</div>
</div>
</section>
<section>
<h3 class="heading settled" data-level=5.2 id=should-block-fetch><span class=secno>5.2. </span><span class=content>
Should fetching <var>request</var> be blocked as mixed content?
</span><a class=self-link href=#should-block-fetch></a></h3>
<p class=note role=note>Note: The Fetch specification hooks into this algorithm to determine whether
a request should be entirely blocked (e.g. because the request is for
<a data-link-type=dfn href=#blockable-content title=blockable>blockable</a> content, and we can <em>assume</em> that it won’t be
loaded over a secure connection).</p>
<p>Given a <a data-link-type=dfn href=#request title=request>request</a> <var>request</var>, a user agent determines
whether the <a data-link-type=dfn href=#request title=Request>Request</a> <var>request</var> should proceed or not via the
following algorithm:</p>
<ol>
<li>
Let <var>context</var> be <var>request</var>’s <code>context</code>.
</li>
<li>
Let <var>frame type</var> be <var>request</var>’s <code>context frame
type</code>.
</li>
<li>
Let <var>origin</var> be the <a data-link-type=dfn href=#origin title=origin>origin</a> of <var>request</var>’s
<strong>URL</strong>.
</li>
<li>
If <var>request</var>’s <a data-link-type=dfn href=#request-client title=client>client</a> does not <a data-link-type=dfn href=#restrict-mixed-content title="restrict mixed content">restrict mixed
content</a>, return <strong>allowed</strong>.
</li>
<li>
If <var>request</var>’s <code>context frame type</code> is
<code>top-level</code>, return <strong>allowed</strong>.
</li>
<li>
If <var>origin</var> is <a data-link-type=dfn href=#a-priori-insecure-origin title="a priori insecure"><em>a priori</em> insecure</a>:
<ol>
<li>
If <var>request</var>’s <code>mode</code> is <code>CORS</code> or
<code>CORS-with-forced-preflight</code>, return
<strong>blocked</strong>.
</li>
<li>
If <var>context</var> is a <a data-link-type=dfn href=#blockable-request-contexts title="blockable request context">blockable request context</a>, return
<strong>blocked</strong>.
</li>
<li>
If the user agent is configured to block <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a>
mixed content, return <strong>blocked</strong>.
</li>
</ol>
</li>
<li>
Otherwise, <var>origin</var> is <a data-link-type=dfn href=#potentially-secure-origin title="potentially secure">potentially secure</a>, so
return <strong>allowed</strong>.
</li>
</ol>
</section>
<section>
<h3 class="heading settled" data-level=5.3 id=should-block-response><span class=secno>5.3. </span><span class=content>
Should <var>response</var> to <var>request</var> be blocked as mixed
content?
</span><a class=self-link href=#should-block-response></a></h3>
<p class=note role=note>Note: <a href=#should-block-fetch>If a request proceeds</a>, we still
might want to block the response based on the state of the connection
that generated the response (e.g. because the response is for <a data-link-type=dfn href=#blockable-content title="blockable content">blockable
content</a>, but the server is <a data-link-type=dfn href=#insecure-origin title=insecure>insecure</a>). This algorithm is used to
make that determination.</p>
<p>Given a <a data-link-type=dfn href=#request title=request>request</a> <var>request</var> and <a data-link-type=dfn href=#response title=response>response</a>
<var>response</var>, the user agent determines what response should be
returned via the following algorithm:</p>
<ol>
<li>
If <var>request</var>’s <a data-link-type=dfn href=#request-client title=client>client</a> does not <a data-link-type=dfn href=#restrict-mixed-content title="restrict mixed content">restrict mixed
content</a>, return <strong>allowed</strong>.
</li>
<li>
Let <var>context</var> be the <a data-link-type=dfn href=#request-context title="request context">request context</a> of
<var>request</var>.
</li>
<li>
If <var>context</var> is an <a data-link-type=dfn href=#blockable-request-contexts title="blockable request context">blockable request context</a> or the
user agent is configured to block <a data-link-type=dfn href=#optionally-blockable-content title=optionally-blockable>optionally-blockable</a> mixed
content:
<ol>
<li>
If <var>response</var>’s <a data-link-type=dfn href=#request-client-tls-state title="TLS state">TLS state</a> is not
<code>authenticated</code>, return <strong>blocked</strong>.
<p class=note role=note>Note: This covers both cases in which unauthenticated resources are
requested, as well as cases in which the TLS handshake succeeds, and
the resource exceeds the definition of <a data-link-type=dfn href=#weakly-tls-protected title="weakly TLS-protected">weakly TLS-protected</a>,
but the user agent chooses to hold it to a higher standard. The
definition of <a data-link-type=dfn href=#deprecated-tls-protection title="deprecated TLS-protection">deprecated TLS-protection</a> has some examples of
these kinds of scenarios.</p>
</li>
</ol>
</li>
<li>Return <strong>allowed</strong>.</li>
</ol>
</section>
</section>
<section>
<h2 class="heading settled" data-level=6 id=powerful-features><span class=secno>6. </span><span class=content>
Secure Contexts for Powerful Features
</span><a class=self-link href=#powerful-features></a></h2>
<p>Tangentially related to a user agent’s handling of insecure resources in
secure contexts, certain web platform features that have distinct impact
on a user’s security or privacy wish to restrict themselves for use only
in sufficiently secure contexts. Service Workers, for instance, may only
be registered when the user agent is satisfied that doing so doesn’t put
the user at risk.</p>
<p>Here, we define algorithms for such determination.</p>
<section>
<h3 class="heading settled" data-level=6.1 id=may-document-use-powerful-features><span class=secno>6.1. </span><span class=content>
May <var>Document</var> use powerful features?
</span><a class=self-link href=#may-document-use-powerful-features></a></h3>
<p>Given a <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code> <var>document</var>, this algorithm returns
<code>Allowed</code> or <code>Not Allowed</code> as appropriate.</p>
<ol>
<li>
While <var>document</var> corresponds to <a data-link-type=dfn href=http://www.w3.org/TR/html5/embedded-content-0.html#an-iframe-srcdoc-document title="an iframe srcdoc Document">an iframe srcdoc
Document</a>, let <var>document</var> be that Document’s <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#browsing-context title="browsing context">browsing
context</a>’s <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#browsing-context-container title="browsing context container">browsing context container</a>’s <code class=idl><a data-link-type=idl href=http://www.w3.org/TR/html5/dom.html#the-document-object title=Document>Document</a></code>.
</li>
<li>
If <var>document</var>’s active <a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#sandboxing-flag-set title="sandboxing flag set">sandboxing flag set</a> has its
<a data-link-type=dfn href=http://www.w3.org/TR/html5/browsers.html#sandboxed-origin-browsing-context-flag title="sandboxed origin browsing context flag">sandboxed origin browsing context flag</a> set:
<ol>
<li>
Set <var>origin</var> to the <a data-link-type=dfn href=#origin title=origin>origin</a> of
<var>document</var>’s address.
</li>
</ol>
</li>
<li>
If the result of executing the <a data-section="" href=#is-origin-trusted>§6.3
Is origin potentially trusted?
</a> algorithm
on <var>origin</var> is <code>Potentially Trusted</code>, return
<code>Allowed</code>.
</li>
<li>
Return the result of executing the <a data-section="" href=#settings-powerful-features>§6.2
May environment settings object use powerful features?
</a>
algorithm on <var>browsing context</var>’s <a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#incumbent-settings-object title="incumbent settings object">incumbent settings
object</a>.
</li>
</ol>
<p class=note role=note>Note: Sandboxed documents will have a unique origin. This algorithm uses the
location of a sandboxed document to determine whether it should be considered
authenticated. That is, the document inside
<code><iframe src="https://example.com/" sandbox="allow-script"></code>
would be considered to allow powerful features.</p>
</section>
<section>
<h3 class="heading settled" data-level=6.2 id=settings-powerful-features><span class=secno>6.2. </span><span class=content>
May <var>environment settings object</var> use powerful features?
</span><a class=self-link href=#settings-powerful-features></a></h3>
<p>Given an <a data-link-type=dfn href=#environment-settings-object title="environment settings object">environment settings object</a> <var>settings</var>, this
algorithm returns <code>Allowed</code> if powerful features may be used
in the object’s context, and <code>Not Allowed</code> otherwise.</p>
<ol>
<li>
If <var>settings</var>' <a data-link-type=dfn href=#request-client-tls-state title="TLS state">TLS state</a> is
<code>authenticated</code>, return <code>Allowed</code>.
</li>
<li>
Otherwise:
<ol>
<li>
Let <var>origin</var> be <var>settings</var>' <a data-link-type=dfn href=#origin title=origin>origin</a>.
</li>
<li>
If the result of executing the <a data-section="" href=#is-origin-trusted>§6.3
Is origin potentially trusted?
</a> algorithm
on <var>origin</var> is <code>Potentially Trusted</code>, return
<code>Allowed</code>.
</li>
</ol>
</li>
<li>
Return <code>Not Allowed</code>.
</li>
</ol>
</section>
<section>
<h3 class="heading settled" data-level=6.3 id=is-origin-trusted><span class=secno>6.3. </span><span class=content>
Is <var>origin</var> potentially trusted?
</span><a class=self-link href=#is-origin-trusted></a></h3>
<p>Certain origins are impossible for a user agent not to place trust in. In
particular, <code>file:</code> URLs and the loopback interface both expose
aspects of the machine on which the user agent is running. The user agent
has no choice but to trust these origins.</p>
<p>Certain user agents extend this trust to other, vendor-specific URL schemes
like <code>app:</code> or <code>chrome-extension:</code>.</p>
<p>Given an <a data-link-type=dfn href=#origin title=origin>origin</a> <var>origin</var>, the following algorithm returns
<code>Potentially Trusted</code> or <code>Not Trusted</code> as appropriate.</p>
<ol>
<li>
If <var>origin</var> is a <a data-link-type=dfn href=#potentially-secure-origin title="potentially secure origin">potentially secure origin</a>,
return <code>Potentially Trusted</code>.
<p class=note role=note>Note: The origin of <code>blob:</code> and <code>filesystem:</code> URLs
is the origin of the context in which they were created. Therefore,
blobs created in an potentially secure origin will themselves be
potentially secure. The origin of <code>data:</code> and
<code>javascript:</code> URLs is an opaque identifier, which will not
be considered potentially secure.</p>
</li>
<li>
If <var>origin</var>’s <code>host</code> component is
<code>localhost</code>, return <code>Potentially Trusted</code>.
</li>
<li>
If <var>origin</var>’s <code>host</code> component matches one of
the CIDR notations <code>127.0.0.0/8</code> or <code>::1/128</code>
<a data-biblio-type=normative data-link-type=biblio href=#biblio-rfc4632 title=RFC4632>[RFC4632]</a>, return <code>Potentially Trusted</code>.
</li>
<li>
If <var>origin</var>’s <code>scheme</code> component is
<code>file</code>, return <code>Potentially Trusted</code>.
</li>
<li>
If <var>origin</var>’s <code>scheme</code> component is one which
the user agent considers to be authenticated, return
<code>Potentially Trusted</code>.
<p class=note role=note>Note: This is meant to cover vendor-specific URL schemes whose
contents are authenticated by the user agent. For example, FirefoxOS
application resources are referred to with an URL whose
<code>scheme</code> component is <code>app:</code>. Likewise, Chrome’s
extensions and apps live on <code>chrome-extension:</code> schemes.
These could reasonably be considered trusted origins.</p>
</li>
<li>
Return <code>Not Trusted</code>.
</li>
</ol>
</section>
</section>
<section>
<h2 class="heading settled" data-level=7 id=fetch-integration><span class=secno>7. </span><span class=content>Integration with Fetch</span><a class=self-link href=#fetch-integration></a></h2>
<p>When fetching resources, the mixed content checks described in the algorithms
above should be inserted at the top of the Fetch algorithm to block network
traffic to <a data-link-type=dfn href=#a-priori-insecure-origin title="a priori insecure origins"><em>a priori</em> insecure origins</a>, and at the bottom of
the algorithm, to block responses from <a data-link-type=dfn href=#insecure-origin title="insecure origins">insecure origins</a>.</p>
<p>Fetch calls the algorithm defined in
<a data-section="" href=#should-block-fetch>§5.2
Should fetching request be blocked as mixed content?
</a> during
<a href=http://fetch.spec.whatwg.org/#fetching>Step 4 of the Fetching
algorithm</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-fetch title=FETCH>[FETCH]</a></p>
<p class=note role=note>Note: Hooking into Fetch here ensures that we catch not only the initial
request, but all redirects as well. That is certainly the intent.</p>
<p>Further, Fetch calls the algorithm defined in
<a data-section="" href=#should-block-response>§5.3
Should response to request be blocked as mixed
content?
</a> during
<a href=http://fetch.spec.whatwg.org/#fetching>Step 7 of the Fetching
algorithm</a>. <a data-biblio-type=normative data-link-type=biblio href=#biblio-fetch title=FETCH>[FETCH]</a></p>
<p class=note role=note>Note: This hook is necessary to detect resources modified or
synthesized by a ServiceWorker, as well as to determine whether a
resource is <a data-link-type=dfn href=#insecure-origin title=insecure>insecure</a> once the TLS-handshake has finished. See
steps 4.1 and 4.2 of the algorithm defined in <a data-section="" href=#should-block-response>§5.3
Should response to request be blocked as mixed
content?
</a> for
detail.</p>
</section>
<section>
<h2 class="heading settled" data-level=8 id=websockets-integration><span class=secno>8. </span><span class=content>Modifications to WebSockets</span><a class=self-link href=#websockets-integration></a></h2>
<p>The <a href=http://www.w3.org/TR/2012/CR-websockets-20120920/#the-websocket-interface><code>WebSocket()</code>
constructor algorithm</a> <a data-biblio-type=normative data-link-type=biblio href=#biblio-websockets title=WEBSOCKETS>[WEBSOCKETS]</a> is modified as follows:</p>
<ul>
<li>
Replace Step 2 with the following steps:
<ol>
<li>
If <var>secure</var> is <strong>false</strong>, but <var>entry
script</var>’s
<a data-link-type=dfn href=http://www.w3.org/TR/html5/webappapis.html#relevant-settings-object-for-a-script title="relevant settings object for a script">relevant settings
object</a>’s <a data-link-type=dfn href=#restrict-mixed-content title="restricts mixed content">restricts mixed content</a>, then throw a
<code>SecurityError</code> exception.
</li>
</ol>
</li>
</ul>
<p>The <a href=http://tools.ietf.org/html/rfc6455#section-4.1>Establish a
WebSocket Connection algorithm</a> <a data-biblio-type=normative data-link-type=biblio href=#biblio-rfc6455 title=RFC6455>[RFC6455]</a> is modified as follows:</p>
<ul>
<li>
After step 5, perform the following step:
<ol>
<li>
If secure is <strong>true</strong>, and the TLS handshake performed
in step 5 results in a <a data-link-type=dfn href=#weakly-tls-protected title="weakly TLS-protected">weakly TLS-protected</a> connection, or the
TLS-protection is <a data-link-type=dfn href=#deprecated-tls-protection title=deprecated>deprecated</a>,then the client MUST
<a href=http://tools.ietf.org/html/rfc6455#section-7.1.7>Fail the
WebSocket Connection</a> and abort the connection. <a data-biblio-type=normative data-link-type=biblio href=#biblio-rfc6455 title=RFC6455>[RFC6455]</a>
</li>
</ol>
</li>
</ul>
</section>
<section>
<h2 class="heading settled" data-level=9 id=acknowledgements><span class=secno>9. </span><span class=content>Acknowledgements</span><a class=self-link href=#acknowledgements></a></h2>
<p>In addition to the wonderful feedback gathered from the WebAppSec WG, the
Chrome security team was invaluable in preparing this specification. In
particular, Chris Palmer, Chris Evans, Ryan Sleevi, Michal Zalewski, Ken
Buchanan, and Tom Sepez gave lots of early feedback. Anne van Kesteren
explained Fetch and helped define the interface to this specification.</p>
</section>
</main>
<h2 class="no-ref no-num heading settled" id=conformance><span class=content>Conformance</span><a class=self-link href=#conformance></a></h2>
<h3 class="no-ref no-num heading settled" id=conventions><span class=content>Document conventions</span><a class=self-link href=#conventions></a></h3>
<p>Conformance requirements are expressed with a combination of
descriptive assertions and RFC 2119 terminology. The key words "MUST",
"MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT",
"RECOMMENDED", "MAY", and "OPTIONAL" in the normative parts of this
document are to be interpreted as described in RFC 2119.
However, for readability, these words do not appear in all uppercase
letters in this specification.
<p>All of the text of this specification is normative except sections
explicitly marked as non-normative, examples, and notes. <a data-biblio-type=normative data-link-type=biblio href=#biblio-rfc2119 title=RFC2119>[RFC2119]</a></p>
<p>Examples in this specification are introduced with the words "for example"
or are set apart from the normative text with <code>class="example"</code>,
like this:
<div class=example>
<p>This is an example of an informative example.</p>
</div>
<p>Informative notes begin with the word "Note" and are set apart from the
normative text with <code>class="note"</code>, like this:
<p class=note role=note>Note, this is an informative note.</p>
<h3 class="no-ref no-num heading settled" id=conformant-algorithms><span class=content>Conformant Algorithms</span><a class=self-link href=#conformant-algorithms></a></h3>
<p>Requirements phrased in the imperative as part of algorithms (such as
"strip any leading space characters" or "return false and abort these
steps") are to be interpreted with the meaning of the key word ("must",
"should", "may", etc) used in introducing the algorithm.</p>
<p>Conformance requirements phrased as algorithms or specific steps can be
implemented in any manner, so long as the end result is equivalent. In
particular, the algorithms defined in this specification are intended to
be easy to understand and are not intended to be performant. Implementers
are encouraged to optimize.</p>
<h3 class="no-ref no-num heading settled" id=conformance-classes><span class=content>Conformance Classes</span><a class=self-link href=#conformance-classes></a></h3>
<p>A <dfn data-dfn-type=dfn data-noexport="" id=conformant-user-agent>conformant user agent<a class=self-link href=#conformant-user-agent></a></dfn> must implement all the requirements
listed in this specification that are applicable to user agents.</p>
<p>A <dfn data-dfn-type=dfn data-noexport="" id=conformant-server>conformant server<a class=self-link href=#conformant-server></a></dfn> must implement all the requirements listed
in this specification that are applicable to servers.</p>
<h2 class="no-num heading settled" id=references><span class=content>References</span><a class=self-link href=#references></a></h2><h3 class="no-num heading settled" id=normative><span class=content>Normative References</span><a class=self-link href=#normative></a></h3><dl><dt id=biblio-cab title=CAB><a class=self-link href=#biblio-cab></a>[CAB]<dd>???. <a href=https://cabforum.org/baseline-requirements-documents/>CA/Browser Forum Baseline Requirements v1.1.8</a>. URL: <a href=https://cabforum.org/baseline-requirements-documents/>https://cabforum.org/baseline-requirements-documents/</a><dt id=biblio-fetch title=FETCH><a class=self-link href=#biblio-fetch></a>[FETCH]<dd>Anne van Kesteren. <a href=http://fetch.spec.whatwg.org/>Fetch</a>. Living Standard. URL: <a href=http://fetch.spec.whatwg.org/>http://fetch.spec.whatwg.org/</a><dt id=biblio-rfc4632 title=RFC4632><a class=self-link href=#biblio-rfc4632></a>[RFC4632]<dd>Vince Fuller; Tony Li. <a href=http://www.ietf.org/rfc/rfc4632.txt>Classless Inter-domain Routing (CIDR): The Internet Address Assignment and Aggregation Plan</a>. RFC. URL: <a href=http://www.ietf.org/rfc/rfc4632.txt>http://www.ietf.org/rfc/rfc4632.txt</a><dt id=biblio-rfc6454 title=RFC6454><a class=self-link href=#biblio-rfc6454></a>[RFC6454]<dd>Adam Barth. <a href=http://www.ietf.org/rfc/rfc6454.txt>The Web Origin Concept</a>. RFC. URL: <a href=http://www.ietf.org/rfc/rfc6454.txt>http://www.ietf.org/rfc/rfc6454.txt</a><dt id=biblio-rfc6455 title=RFC6455><a class=self-link href=#biblio-rfc6455></a>[RFC6455]<dd>Ian Fette; Alexey Melnikov. <a href=http://www.ietf.org/rfc/rfc6455.txt>The WebSocket Protocol</a>. RFC. URL: <a href=http://www.ietf.org/rfc/rfc6455.txt>http://www.ietf.org/rfc/rfc6455.txt</a><dt id=biblio-xmlhttprequest title=XMLHttpRequest><a class=self-link href=#biblio-xmlhttprequest></a>[XMLHttpRequest]<dd>Anne van Kesteren; et al. <a href=http://www.w3.org/TR/XMLHttpRequest/>XMLHttpRequest Level 1</a>. 30 January 2014. WD. URL: <a href=http://www.w3.org/TR/XMLHttpRequest/>http://www.w3.org/TR/XMLHttpRequest/</a><dt id=biblio-eventsource title=eventsource><a class=self-link href=#biblio-eventsource></a>[eventsource]<dd>Ian Hickson. <a href=http://www.w3.org/TR/eventsource/>Server-Sent Events</a>. 11 December 2012. CR. URL: <a href=http://www.w3.org/TR/eventsource/>http://www.w3.org/TR/eventsource/</a><dt id=biblio-html5 title=html5><a class=self-link href=#biblio-html5></a>[html5]<dd>Robin Berjon; et al. <a href=http://www.w3.org/TR/html5/>HTML5</a>. 28 October 2014. REC. URL: <a href=http://www.w3.org/TR/html5/>http://www.w3.org/TR/html5/</a><dt id=biblio-rfc2119 title=rfc2119><a class=self-link href=#biblio-rfc2119></a>[rfc2119]<dd>S. Bradner. <a href=http://www.ietf.org/rfc/rfc2119.txt>Key words for use in RFCs to Indicate Requirement Levels</a>. March 1997. Best Current Practice. URL: <a href=http://www.ietf.org/rfc/rfc2119.txt>http://www.ietf.org/rfc/rfc2119.txt</a><dt id=biblio-websockets title=websockets><a class=self-link href=#biblio-websockets></a>[websockets]<dd>Ian Hickson. <a href=http://www.w3.org/TR/websockets/>The WebSocket API</a>. 20 September 2012. CR. URL: <a href=http://www.w3.org/TR/websockets/>http://www.w3.org/TR/websockets/</a><dt id=biblio-wsc-ui title=wsc-ui><a class=self-link href=#biblio-wsc-ui></a>[wsc-ui]<dd>Thomas Roessler; Anil Saldhana. <a href=http://www.w3.org/TR/wsc-ui/>Web Security Context: User Interface Guidelines</a>. 12 August 2010. REC. URL: <a href=http://www.w3.org/TR/wsc-ui/>http://www.w3.org/TR/wsc-ui/</a></dl><h3 class="no-num heading settled" id=informative><span class=content>Informative References</span><a class=self-link href=#informative></a></h3><dl><dt id=biblio-beacon title=BEACON><a class=self-link href=#biblio-beacon></a>[BEACON]<dd>Jatinder Mann; Alois Reitbauer. <a href=http://www.w3.org/TR/beacon/>Beacon</a>. WD. URL: <a href=http://www.w3.org/TR/beacon/>http://www.w3.org/TR/beacon/</a><dt id=biblio-css21 title=CSS21><a class=self-link href=#biblio-css21></a>[CSS21]<dd>Bert Bos; et al. <a href=http://www.w3.org/TR/2011/REC-CSS2-20110607>Cascading Style Sheets Level 2 Revision 1 (CSS 2.1) Specification</a>. 7 June 2011. W3C Recommendation. URL: <a href=http://www.w3.org/TR/2011/REC-CSS2-20110607>http://www.w3.org/TR/2011/REC-CSS2-20110607</a><dt id=biblio-css3-webfonts title=CSS3-WEBFONTS><a class=self-link href=#biblio-css3-webfonts></a>[CSS3-WEBFONTS]<dd>Michel Suignard; Chris Lilley. <a href=http://www.w3.org/TR/2002/WD-css3-webfonts-20020802>CSS3 module: Web Fonts</a>. 2 August 2002. W3C Working Draft. (Work in progress.) URL: <a href=http://www.w3.org/TR/2002/WD-css3-webfonts-20020802>http://www.w3.org/TR/2002/WD-css3-webfonts-20020802</a><dt id=biblio-dangerous-mix title=DANGEROUS-MIX><a class=self-link href=#biblio-dangerous-mix></a>[DANGEROUS-MIX]<dd>Ping Chen; et al. <a href=http://www.securitee.org/files/mixedinc_isc2013.pdf>A Dangerous Mix: Large-scale analysis of mixed-content websites</a>. URL: <a href=http://www.securitee.org/files/mixedinc_isc2013.pdf>http://www.securitee.org/files/mixedinc_isc2013.pdf</a><dt id=biblio-ecma-262 title=ECMA-262><a class=self-link href=#biblio-ecma-262></a>[ECMA-262]<dd>???. <a href=http://www.ecma-international.org/publications/standards/Ecma-262.htm>ECMAScript Language Specification, Edition 5.1</a>. June 2011. URL: <a href=http://www.ecma-international.org/publications/standards/Ecma-262.htm>http://www.ecma-international.org/publications/standards/Ecma-262.htm</a><dt id=biblio-filter-effects title=FILTER-EFFECTS><a class=self-link href=#biblio-filter-effects></a>[FILTER-EFFECTS]<dd>Dean Jackson; Erik Dahlström; Dirk Schulze. <a href=http://www.w3.org/TR/2013/WD-filter-effects-20130523/>Filter Effects 1.0</a>. 23 May 2013. W3C Working Draft. (Work in progress.) URL: <a href=http://www.w3.org/TR/2013/WD-filter-effects-20130523/>http://www.w3.org/TR/2013/WD-filter-effects-20130523/</a><dt id=biblio-html title=HTML><a class=self-link href=#biblio-html></a>[HTML]<dd>Ian Hickson. <a href=https://html.spec.whatwg.org/>HTML</a>. Living Standard. URL: <a href=https://html.spec.whatwg.org/>https://html.spec.whatwg.org/</a><dt id=biblio-html-imports title=HTML-IMPORTS><a class=self-link href=#biblio-html-imports></a>[HTML-IMPORTS]<dd>Dmitri Glazkov; Hajime Morrita. <a href=http://www.w3.org/TR/html-imports/>HTML Imports</a>. WD. URL: <a href=http://www.w3.org/TR/html-imports/>http://www.w3.org/TR/html-imports/</a><dt id=biblio-manifest title=MANIFEST><a class=self-link href=#biblio-manifest></a>[MANIFEST]<dd>Marcos Caceres; Anssi Kostiainen; Kenneth Rohde Christiansen; et al. <a href=http://w3c.github.io/manifest/>Manifest for web application</a>. WD. URL: <a href=http://w3c.github.io/manifest/>http://w3c.github.io/manifest/</a><dt id=biblio-rfc6797 title=RFC6797><a class=self-link href=#biblio-rfc6797></a>[RFC6797]<dd>Jeff Hodges; Collin Jackson; Adam Barth. <a href=http://www.ietf.org/rfc/rfc6797.txt>HTTP Strict Transport Security (HSTS)</a>. RFC. URL: <a href=http://www.ietf.org/rfc/rfc6797.txt>http://www.ietf.org/rfc/rfc6797.txt</a><dt id=biblio-serviceworkers title=SERVICEWORKERS><a class=self-link href=#biblio-serviceworkers></a>[SERVICEWORKERS]<dd>Alex Russell; Jungkee Song. <a href=http://www.w3.org/TR/service-workers/>Service Workers</a>. WD. URL: <a href=http://www.w3.org/TR/service-workers/>http://www.w3.org/TR/service-workers/</a><dt id=biblio-svg2 title=SVG2><a class=self-link href=#biblio-svg2></a>[SVG2]<dd>Nikos Andronikos; et al. <a href=http://www.w3.org/TR/SVG2/>Scalable Vector Graphics (SVG) 2</a>. 11 February 2014. WD. URL: <a href=http://www.w3.org/TR/SVG2/>http://www.w3.org/TR/SVG2/</a><dt id=biblio-uri title=URI><a class=self-link href=#biblio-uri></a>[URI]<dd>T. Berners-Lee; R. Fielding; L. Masinter. <a href=http://www.ietf.org/rfc/rfc3986.txt>Uniform Resource Identifiers (URI): generic syntax</a>. January 2005. URL: <a href=http://www.ietf.org/rfc/rfc3986.txt>http://www.ietf.org/rfc/rfc3986.txt</a><dt id=biblio-rfc6919 title=rfc6919><a class=self-link href=#biblio-rfc6919></a>[rfc6919]<dd>R. Barnes; S. Kent; E. Rescorla. <a href=http://www.ietf.org/rfc/rfc6919.txt>Further Key Words for Use in RFCs to Indicate Requirement Levels</a>. 1 April 2013. Experimental. URL: <a href=http://www.ietf.org/rfc/rfc6919.txt>http://www.ietf.org/rfc/rfc6919.txt</a><dt id=biblio-workers title=workers><a class=self-link href=#biblio-workers></a>[workers]<dd>Ian Hickson. <a href=http://www.w3.org/TR/workers/>Web Workers</a>. 1 May 2012. CR. URL: <a href=http://www.w3.org/TR/workers/>http://www.w3.org/TR/workers/</a><dt id=biblio-xslt title=xslt><a class=self-link href=#biblio-xslt></a>[xslt]<dd>James Clark. <a href=http://www.w3.org/TR/xslt>XSL Transformations (XSLT) Version 1.0</a>. 16 November 1999. REC. URL: <a href=http://www.w3.org/TR/xslt>http://www.w3.org/TR/xslt</a></dl><h2 class="no-num heading settled" id=index><span class=content>Index</span><a class=self-link href=#index></a></h2><ul class=indexlist><li>a priori insecure, <a href=#a-priori-insecure-origin title="section 2.1">2.1</a><li>a priori insecure origin, <a href=#a-priori-insecure-origin title="section 2.1">2.1</a><li>a priori insecure URL, <a href=#a-priori-insecure-url title="section 2.1">2.1</a><li>blockable, <a href=#blockable-content title="section 3.2">3.2</a><li>blockable content, <a href=#blockable-content title="section 3.2">3.2</a><li>blockable request contexts, <a href=#blockable-request-contexts title="section 3.2">3.2</a><li>client, <a href=#request-client title="section 2.2">2.2</a><li>conformant server, <a href=#conformant-server title="section Unnumbered section">Unnumbered section</a><li>conformant user agent, <a href=#conformant-user-agent title="section Unnumbered section">Unnumbered section</a><li>context, <a href=#request-context title="section 2.2">2.2</a><li>deprecated, <a href=#deprecated-tls-protection title="section 2.1">2.1</a><li>deprecated TLS-protection, <a href=#deprecated-tls-protection title="section 2.1">2.1</a><li>embedding document, <a href=#embedding-document title="section 2.2">2.2</a><li>environment settings object, <a href=#environment-settings-object title="section 2.2">2.2</a><li>fetch, <a href=#fetch title="section 2.2">2.2</a><li>frame type, <a href=#request-context-frame-type title="section 2.2">2.2</a><li>globally unique identifier, <a href=#globally-unique-identifier title="section 2.2">2.2</a><li>insecure, <a href=#insecure-origin title="section 2.1">2.1</a><li>insecure origin, <a href=#insecure-origin title="section 2.1">2.1</a><li>insecure URL, <a href=#insecure-url title="section 2.1">2.1</a><li>mixed, <a href=#mixed-content title="section 2.1">2.1</a><li>mixed content, <a href=#mixed-content title="section 2.1">2.1</a><li>network error, <a href=#network-error title="section 2.2">2.2</a><li>optionally-blockable, <a href=#optionally-blockable-content title="section 3.1">3.1</a><li>optionally-blockable content, <a href=#optionally-blockable-content title="section 3.1">3.1</a><li>optionally-blockable request
contexts, <a href=#optionally-blockable-request-contexts title="section 3.1">3.1</a><li>origin, <a href=#origin title="section 2.2">2.2</a><li>potentially secure, <a href=#potentially-secure-origin title="section 2.1">2.1</a><li>potentially secure origin, <a href=#potentially-secure-origin title="section 2.1">2.1</a><li>potentially secure URL, <a href=#potentially-secure-url title="section 2.1">2.1</a><li>request, <a href=#request title="section 2.2">2.2</a><li>request client, <a href=#request-client title="section 2.2">2.2</a><li>request client TLS state, <a href=#request-client-tls-state title="section 2.2">2.2</a><li>request context, <a href=#request-context title="section 2.2">2.2</a><li>request context frame type, <a href=#request-context-frame-type title="section 2.2">2.2</a><li>response, <a href=#response title="section 2.2">2.2</a><li>response TLS state, <a href=#response-tls-state title="section 2.2">2.2</a><li>restrict
mixed content, <a href=#restrict-mixed-content title="section 5.1">5.1</a><li>restricts mixed content, <a href=#restrict-mixed-content title="section 5.1">5.1</a><li>TLS-protected, <a href=#tls-protected title="section 2.2">2.2</a><li>tls state, <a href=#request-client-tls-state title="section 2.2">2.2</a><li>weak, <a href=#weakly-tls-protected title="section 2.2">2.2</a><li>weakly TLS-protected, <a href=#weakly-tls-protected title="section 2.2">2.2</a></ul>
| 2023-11-15T01:26:35.434368 | https://example.com/article/1104 |
It is the love that dared not speak its name. I refer, of course, to the sudden passion for the Liberal Democrats that has apparently been beating in Labour hearts. Alastair Campbell and Charles Clarke are among the pro-European, centre-ground politicians who have come out as being among the record number of Lib Dem voters in the European elections.
They were joined by Conservative refuseniks like Michael Heseltine, while even Heidi Allen, interim leader of Change UK, wanted her supporters to back us — quite a change from a party who a month ago was suggesting the Lib Dems should “fold” into them.
So the Lib Dems are back, underlined by our earlier brilliant performance in the local elections. Very occasionally, an issue comes | 2024-07-19T01:26:35.434368 | https://example.com/article/6393 |
"I am Arthur Frayn, and I am Zardoz." "I have lived 300 years and I long to die, but death is no longer possible" "I am immortal." "I present now my story, full of mystery and intrigue, rich in irony and most satirical." "It is set deep in a possible future, so none of these events has been occurred" "But they may" "Be warned, lest you end as I" "In this tale I am a fake god by occupation and a magician by inclination." "Merlin is my hero" "I am the puppet master" "I manipulate many of the characters" "But I am invented too for your entertainment and amusement" "And you, poor creatures, who conjured you out of the clay?" "Is God in show business too?" "Zardoz." "Praise be to Zardoz!" "Praise be to Zardoz!" "Praise be to Zardoz!" "Zardoz speaks to you, his Chosen Ones." "We are the Chosen Ones!" "You have been raised up from brutality to kill the Brutals who multiply and are legion." "To this end, Zardoz, your god, gave you the gift of the gun." "The gun is good!" "The gun is good!" "The penis is evil." "The penis shoots seeds and makes new life to poison the Earth with the plague of men as once it was" "But the gun shoots death and purifies the Earth of the filth of Brutals." "Go forth and kill!" "Zardoz has spoken." "Guns!" "You" "foolish!" "I could've shown you!" "Without me, you are nothing!" "A bore!" "How pointless!" "How pointless!" "Attention." "Harvest produce report" "Attention." "Harvest produce report" "Attention." "Harvest produce report" "Submit surpluses and needs." "Submit surpluses and needs for inter-Vortex barter and exchange." "Year 2293." "Third harvest yield." "Vortex Four." "Needs: soap, apples, salt, leather." "Vortex Nine." "Surplus: soap, apples, leather." "Needs: oats, barley, carrots." "Here is a list of surpluses and needs remaining." "Here is a list of surpluses and needs remaining." "Here is a list of surpluses and needs remaining." "Food" "Meet" "Who lives here?" "I am Arthur Frayn." " No!" " Vortex Four." "I am Arthur..." "Vort..." "Four." "Arthur Frayn." "Vortex Four." "I am..." "Ar..." "Vortex Four." "I am Arthur Frayn." "Vortex Four." "Three from Vortex Eight." "Four from Vortex Five." "Did you ever see such mangled limbs?" " There was some kind of rock fall in their quarry." " There are 14 bodies for repair." " Liver malfunction." "Myopia, left eye." " This wheat is very good quality." " What is it?" " Flower." " For what?" " Decorative." " Do you know where you are?" " In the Vortex." "You come from the Outlands." "You were told about the Vortex?" " Zardoz says..." " What does Zardoz say?" "Zardoz says if you obey him, you'llgo toa Vortex when you die... and there you will live forever." " Happily?" " Yes." "So, you think you're dead?" "Am I?" " You're an Exterminator." " I kill for Zardoz." "You came here in the stone head." "I don't know." "It is the only path and passage into the Vortex." "You will show me how you come to be here." " You have a name?" " My name is Zed." "Zed for Zardoz." "I am an Exterminator." "The memories are simple heroics." "There are no abstractions, you will notice." "It is certainly very fragmented." "The shock of entering the Vortex could be responsible." "Zarday 3 12." "Twenty-five Brutals exterminated." "Took a woman in His name." "Zardoz." "The place... where the sea meets the land." "It's blacked again." "It seems to be able to control its memory." "Show us more of your work." "Zardoz made us grow wheat." "This is a more recent memory." "Cultivation has started." " Disturbed?" " A little." " The Outlands have to be controlled." " I've always voted against forced farming." "You eat the bread." "We have to shut ourselves off." "We have to." "This is the first direct visual contact..." "with the Outlands in years as opposed to data since Arthur was delegated to control them." " It is proper that we investigate." "It's better not to know." "These images will pollute us." "Quench it." "Quell it." "No Brutal has ever penetrated a Vortex." "It therefore requires study." "Perhaps it can tell us why Arthur has vanished so mysteriously." "May..." "Please." "Is Arthur Frayn's memory transmission still functioning?" "Arthur Frayn ceased transmission three days ago." "Replay his last memory moments." "No." "Play back the preceding images so we can discover how he suffered this fall." "It is permitted only to show the accident." "No other memory image may be shown... without the consent of the individual concerned." "But we need to determine the location in case he is injured and the body has to be recovered." "Arthur Frayn died." "Reconstruction has begun." "Ah, yes." "There." "That'san end to it." " Kill it, May." " No." " May, for our love." " Consuella..." " Don't." "I will invoke a community vote." " The community will follow my intuition." " Then I will go to the Vortex." " You're hurting me." " Consuella, this is an experiment!" "We must find out how it came here!" "Where is Arthur Frayn?" "How did you come into the stone?" "Zardoz..." "The stone." "Terribly exciting." " What of the suffering?" " Oh, you can't equate." "Their feelings with ours." "It's just entertainment." "Again, this is a key image." "My father was Chosen." "My mother was Chosen." "Only we could breed." "Only the Chosen." "Selective breeding, do you think?" "What has Arthur been doing out there all these years?" "Never discuss this in the Vortex." "You'll have to be thoroughly investigated." "No one else wanted to run the Outlands." "He's an artist!" "He does it with imagination." "I love to see them running." "I love the moment of their death when I am one with Zardoz" "Obscenely decaying flesh." "The sweet scent of put refaction already in the air." "He's a fine, strong beast." "Dear May," " What exactly do you want to do with him?" " A full genetic study." "Break its DNA code." "See if there are any structural or evolutional changes since ours were analyzed 200 years ago." "Discover any new hereditary disease factors that may have emerged... which might result in broadening our immunization spectrum." "Study its emotional and psychic elements in relation to its sociology." "That all sounds respectably scientific, but what is May's under-thought?" "Not long ago she was asking for new births, although we have no death." "We are perfectly stabilized." "We said no to May." "Now she wants to bring in this animal from the outside." "Think about equilibrium." "Remember the delicate balance we must maintain." "The presence will dismay our tranquility." "May is a great scientist, but she also has destructive tendencies." " We have adequate means of controlling it." " Surely, we are not so vulnerable!" "Look at it." "It knows its life is at stake." "Otherwise, it would rape and kill, as it always has." " I don't agree." " No, no!" " You can see the disrupting effect." " Let's keep it." " Yes!" " Anything to relieve the boredom." " I want to see more of its memories." " So do I!" "This is a psychic disturbance." "Avalow, what does it portend for the future?" "How did we conjure up a monster in our midst, and why?" "That is the question we must answer." "Well, you've set their fur flying, my friend." "I wonder what's going on inside your pea brain, hmm?" "I like you, you sly old monster." "Do you hear?" " Yes, vote." "Vote." " Let's vote." "Pro." "Against." "Verdict." "Congratulations." "You live... for three weeks." "Zed." "I'll examine him later in the dome." "Morning, monster." "Time for work." "All right, let's stop all the nonsense, shall we?" "Where's Arthur Frayn?" "Ever hear the expression 'lf looks could kill?" "' Well, here they can." "There's no need to pretend innocence with me." "I'm in Arthur Frayn's confiidence." "I know more than you think." "You're saying nothing." "All right, we'll wait and see." "Don't be sullen." "I'm going to look after you." "Whenever you're ready to, just ask me questions." "Anything at all." "This is where you'll be working for me each morning." "Just menial tasks, nothing too taxing." " Is this your god's house?" " Ah, it's God you're seeking, is it?" "Well, here we are." "Gods, goddesses, kings and queens." "Take your pick." " But they're all dead." " Dead?" "Died of boredom." "That's wrong." "It's wrong!" "It is cataloged according to your instructions." "I told you to analyze design growth across all makes of car, not just a chronological list from one manufacturer!" "A much more complex program." "Shall I seek Vortex consent for a longer program?" " Shall I seek Vortex consent..." " Yes!" " It will take time." "There is a stack-up on some circuits." "Well, I've got time, and plenty of it." "Three weeks." "Define three weeks." "Twenty-one days." "Five hundred and four hours." "Thirty thousand, two-hundred and forty minutes." "One million, eight-hundred..." "and fourteen thousand..." "Do you believe, he's never seen a clock before?" "Obviously not!" " Are you not taking food with us, May?" " No." "Come, Zed, this way." " She's taking her studies very seriously." " She only has three weeks." " Doy ou know yethow the Brutal came here?" " No conclusion." "Insuffiicient data received." "Go in." "Go on." " Look into the ring." " No retina abnormalities." "Fundus normal." "Disc and retinal vessels normal." "No hemorrhages or exudates." "Macula area clear." "Attention..." "Continuation of the trial of George Saden of Vortex Four." "George Saden, accused of transmitting a negative aura in Second Level." "This is not so." "I have studied our social, emotional substructures for 140 years." "These thoughts are constructive criticisms, pyramidical." "I am innocent of psychic violence." "As you examine my face and eyes, you will see that this is true." "He's lying." "Vortex Three." "You looking for the head, monster?" "It's gone." "Off on its endless journey from Vortex to Vortex, round and round like me and the bread, forever and ever." " Will he be punished for that?" " Of course." "But you have no police, no Exterminators." "Ah, but we discuss it endlessly!" "Every little sin and misdemeanor raked over and over." " So, what happens to him then?" " He'll get six months at least." " Prison?" " Aging." " Aging?" " Yes!" "I'm getting old myself." "Three months here, a year there." "These sentences add up." "So, if you're bad often enough, you'll die." "They make you old, but they don't let you die." " So, what's to stop you killing yourself?" " I do now and again, but the eternal Tabernacle simply rebuilds me." " Would you like to see immortality at work?" " Yes!" "Well, get a move on then!" "This is where they live, the Renegades." "They're condemned to an eternity of senility." "We provide them with food, but they are shunned." "They're malicious and vicious, so in and out fast." "I, myself, feel quite at home in there." "Hey!" "Look, I got it!" "I got it!" "I got..." "Loamer." "Gray." "I loved this girl once, monster." "You idle Apathetic!" "Melancholy sight." "Grayler." "Bones." " Whoa there, boy." "Whoa up." "You are asked to vote at the termination of the trial of George Saden." "Final statement from the accused begins." "I confess to the charges, but plead mitigation." "I tried to suppress these thoughts, but they leak out in Second Level." "through the head wound of my third death." "I was imperfectly repaired." "No." "That is not true." " I think what I think." " That's more like it." "I'm with you, George." "I hate you all." "I hate you all." "I hate you all." "especially me." "Vote, please." "Vote, please." "I'm voting for him, monster." "It won't do any good." "Nothing ever does." "Absolute acquittal." "Go on, monster, help your self." "Didn't Zardoz tell you about the Apathetics?" "It's a disease." "And it's slowly creeping through all the Vortexes." "That's why Zardoz made you grow crops... to feed these people." "We can't support them anymore." "Apathetic or Renegade, make your choice." "Yes." "A bit frightening, isn't it?" "Very good." "Now you're beginning to show yourself." "Final votes." "For, 9;" "Against, 586; undecided, 86." "Sentence." "George Saden will be aged five years." "Welcome to paradise." "Penile erection was one of the many unsolved evolutionary mysteries surrounding sexuality." "Every society had an elaborate subculture devoted to erotic stimulation." "But nobody could quite determine how this becomes this." "Of course, we all know the physical process involved, but not the link between stimulus and response." "There seems to be a correlation with violence, with fear." "Many hanged men died with an erection." "You are all more or less aware of our intensive researches into this subject." "Sexuality declined probably because we no longer needed to procreate." "Eternals soon discovered that erection was impossible to achieve." "And we are no longer victims of this violent, convulsive act... which so debased women and betrayed men." "This Brutal, like other primates living unselfconscious lives, is capable of spontaneous and reflexive erection." "As part of May's studies of this creature, we're trying to find, once again, the link between erotic stimulation and erection." "This experiment will measure autoerotic stimulation of the cortex, leading to erection." "Play." "The tracer indicates that this image is not erotically stimulating to the Brutal." "Change." "This doesn't seem to affect him either." "Consuella's done the trick herself." "The Brutal is now in fourth hour of unconscious sleep." "It's astonishing that Homo sapiens spend so much time in this vulnerable condition, at the mercy of its enemies." "Is there any data on the sleeping patterns of primitive people?" " Is that a priority request?" " Yes." "I'm now going to test its waking response to danger stimuli." "Does it please you to sleep?" " Yes." "Why?" "I have dreams." "Sleep was necessary fo rman... when his waking and unconscious lives were separated." "As Eternals achieved total consciousness, sleep became obsolete and Second Level meditation took its place." "Sleep was closely connected with death." "Look at it." "It's you." "Your genetic structure." "Your life chart." "Look!" "You are a Mutant." "Second, maybe third generation." "Therefore, genetically stable." "Enlarged brain." "Total recall." "Your potential is..." " Your breeding potential..." " Breeding?" "Frayn." "How did you get into the Vortex?" "What is your purpose?" "I'm just an Exterminator." "I know nothing" "You must know that you're mentally and physically vastly superior to me or anyone else here." "You could be anything." "Could do... anything." " You must be destroyed." " Why?" " Because you could destroy us." " As you've destroyed the rest of life?" "Can you un-know what you know now about me?" "For the sake of science, I will keep this knowledge from the others for the moment." "Keep you alive." "But you must follow me, obey me, be circumspect, make no disruption, quietly do whatever work is given you." "I will watch over you." "Get a move on, you silly beast." "Friend, put that thing outside!" "Anyone else disturbed?" "Then let's take yet another boringly democratic vote, shall we, Consuella?" "It's Friend's day to make the food." "He must do this without help as we all do." "It's fundamental to our society that we do everything for ourselves on a basis of absolute equality." " And Friend knows that perfectly well." " Yes or no?" "Potatoes, yes or no?" "I say get more Zeds to do the work." "We have eternal life, and yet we sentence ourselves to all this drudgery." "I tell you, I'm sick of 200 years of washing up." "And I'm sick of pitting my bare hands against the blind brute stupidity of nature!" " You'd better do something about this." " Consuella is right." "Zed is being kept here for scientific study." "It can earn its keep on the land, but it should not do the work of a servant." "Time enough has gone to finish your study, May." "Destroy it!" "No!" "No." "No." "See how it disrupts our community?" " It is almost over." " How can you speak such in front of Zed?" "It feels." "I sense that." " Vote!" " Yes, vote!" "Give your votes." "May has been given seven days to complete her study." "Then Zed will be terminated." "The monster is a mirror." "And when we look at him, we look into our own hidden faces." "Meditate on this at Second Level." "No." "No." "I will..." "I will not go to Second Level." "No!" "I will..." "I will not go to Second Level with you!" "I will..." "No!" "I will not be one mind with you!" "I know what..." "I know what May wants with Zed." "No!" "No." "The Vortex is an obscenity!" "I know..." "I know that I hate all women." "Birth." "Fertility." "Superstition." "Friend is beyond redemption." " Renegade." " Renegade." "Friend, he's a Renegade." "He must be cast out." "He is no longer one with us." "Renegade." "Cast him out!" "No!" "Renegade!" "Renegade!" "Caution." "You are approaching the periphery shield of Vortex Four." "Caution." "You are approaching the periphery shield of Vortex Four." "Have you seen Friend?" "Friend." "I seek Friend." "Friend." "I seek Friend." "Friend." "Old Friend." "This is your fault." "Now hear this, you old farts!" "Meet this creature from the outside world." " Huh?" "What?" " This man has the gift of death." " Death?" " He can mete it out, and he can die himself!" "He's mortal." " He can die!" " Die!" " Shall we give him back to death?" " Yes!" " Silent death?" " Yes!" " Glorious death?" " Yes!" "May, the scientist, wants him to spawn another generation to suffer our agonies!" "Come on back to death!" "Stop!" "Stop!" "What is it you want?" "Sweet death." "Oblivion." "For yourself, or for the whole Vortex?" "For everybody." "An end to the human race." "It has plagued this pretty planet for far too long." "You stink of despair." "Fight back!" "Fight for death, if that's what you want" "I thought at first you were the one to help." "But it's hopeless." "All my powers have gone." "Where is it, the Tabernacle?" "The Tabernacle is..." " I can't remember." " Who made it?" "Someone must know how to break it." "Yes." "You can meet him for yourself." "One of our founders." "One of the geniuses that discovered immortality." "But he found he didn't like it for himself." "He didn't conform." "So this is what his grateful people did to him." " We want to die!" " Hmm?" " What's the trick?" " Death." "Death." "Talk to May." "May?" "May, I want your help." "You want to destroy us." "The Tabernacle" "I want the truth." "You must give the truth..." "if you wish to receive it." "I'm ready." " It'll burn you." " Then burn me." " Tell me... everything." "Show me pictures." "Open your mind." "Your memory... go back to the beginning." " Open." " Zar..." " Open." " Zar..." " Open!" " Zardoz!" "Zardoz gave us the gun." "We were the Chosen Ones." "What was your task?" "To kill the Brutals, who multiply and are legion." "We rode out." "We roamed the Outlands." "We killed." "It was enough." "Man was born to hunt and kill." " And then?" " Then, one day..." " Yes?" " Something happened." "It changed everything." "I..." "lost my innocence." "A face in the window." " Who was he?" " I don't know." "He wore a mask." "He led me on like a game." "Why did you spare him?" "Something..." "Uh, I don't know." " Had you seen a book before?" " Never." " You learned to read." " Yes." " How long did it take?" " It came easy." "I read everything." "I learned all that had been hidden from me." "I learned what the world had been before the darkness fell." "Then, one day, I found the book." "The book called..." "Uh, called..." "What was the book?" "What was the name of the book?" " I don't remember!" " Tell me." " Show me." "You must tell me!" " No!" "No!" "Zardoz." "Tell me." "Show me." "You must tell me." " I can't!" " You saw him carved in stone." " Of course you know." " Can't remember!" " Yes you can!" " You knew that Arthur was Zardoz." " No!" " You killed Arthur, didn't you?" " No!" "Show me." "What are you doing?" "You murdered your own god by accident." "Or was it an accident?" "Now, show me that book." "What did you find in that book?" "Show it to me." "It's a trick!" "A trick!" "What was a trick?" "Tell me!" "Zardoz said, 'Stop. '" "Said, 'No more. '" " No more what?" " No more killing." " He told you to take prisoners?" " Yes." " To make slaves?" " Yes." " To cultivate instead of kill?" " Yes!" " To grow wheat?" " Yes!" " Did you need wheat?" " No." "We ate meat." "Zardoz betrayed us." "We were hunters, not farmers." "Show how you came into the stone." "Show." "It was easy." "Each season, Zardoz came down to take our harvest." "Zardoz." " Your friends were Mutants too." " Yes." " You had a plot." " Yes." " Revenge?" " The truth." "We wanted the truth!" " I told them about the book." " Show it." "What is 'the book'?" "No." "No." "No!" "Zardoz." "Zardoz is pleased." " So that was it." " The Wizard of Oz." "Zardoz." "The Wizard of Oz was a fairy story, about an old man who frightened people with a loud voice and a big mask." "It was Arthur Frayn's idea." "A simple way of controlling the Outlands." "But remember the end of the story." "They looked behind the mask and found the truth." "I looked behind the mask, and I saw the truth." " Zardoz." "So, that was your plan... to stow away in the head." "Yes." "What was your purpose?" "To kill Arthur?" "To penetrate the Vortex?" "To find a way in for your friends to destroy us?" " He made us killers." " Revenge!" "You wanted revenge." "The truth!" "The truth." "Truth or revenge?" "Revenge!" "Revenge." "Mm." "I remember feelings such as those." "They stir in me." "So this is your scientific investigation." "There's another word for it." "Bestiality." "For this, you will be aged 50 years, no less." "No man, woman or beast will ever desire you again." "He can't see." "He's blind." "We can no longer quell him." "He's out of control." "We must now become hunters and killers ourselves." "Come." "This will restore your sight, and you will see more and deeper than you ever saw before." "I've seen men rape an old crippled woman in a wet ditch." "I see now why you are here." "You are the One, the Liberator." "Death." "I will help you... if, when the time comes, you will set me free." "You have great strength, but there are times when that strength will fail you." "Eat this when the need arises." "This place is built on lies and suffering." "How could you do what you did to us?" "The world was dying.." "We took all that was good and made an oasis here." "We few, the rich, the powerful, the clever, cut ourselves off to guard the knowledge and treasures of civilization as the world plunged into a Dark Age." "To do this, we had to harden our hearts against the suffering outside." "We are custodians of the past for an unknown future." "You are the price we now pay for that isolation." "You have brought hate and anger into the Vortex... to infect us all." "Get him!" "Get him!" "Kill him!" " It's indestructible." " No!" "No!" "It can't be done!" "No!" "Caution." "You are approaching the periphery shield..." "Ride round." "Fast!" "He's somewhere in these buildings." "Smoke him out." "Cover the exits." "We've got him trapped." "There's no one in here." "We... take life from you." "Life flows out of you." "Flows into us." "Get him!" "Get him!" "Come on!" "Search the undergrowth!" "Come on!" "Look over here!" "He's no..." "He's not here." "It's getting dark." " It's him." "It's him!" " None of them could catch him!" "But he falls into the hands of the poor old Renegades." "Death." "Bring..." "Bring death to you all." "Find Friend..." "Take me to Friend." " What'd he say?" " Shut up." "It's a miracle!" "We're Apathetics." "Tell us how, please." "We want some too." "We started chasing the Brutal." "We got excited." "We saw someone." "We thought it was him." "It wasn't, but we killed him anyway." "And then we felt desire." "Look at the excitement you've caused." "You naughty girl." "Your task is to secure allarms, weapons and food supplies." "Work house to house, east to west down the valley." "If you find the Brutal, destroy immediately." "He's trapped." "It's only a matter of time." "Friend." "Friend!" "Kiss the bride, dear Friend." "Kiss the bride!" "You did well." "I will take the bride." "Death comes closer for us all." "Find May." "Tell her that Friend needs her." "Friend, I cannot sanction this violence and destruction." "It's too late, May." "There's no going back." "Don't destroy the Vortex!" "Let us renew it." "A better breed could prosper here." "Given time..." "Time?" "Wasn't eternity enough?" "This place is against life.." "It must die." "I have my followers." "Inseminate us all, and we'll teach you all we know." "Give you all we have." "Perhaps you can break the Tabernacle." "Or be broken." "An end to eternity." "A higher form." "Revenge." "Charge!" "in human society, or in man's thinking." " How much time do we have?" " We will not work in time." "You will take our knowledge..." "by osmosis... out of time." "We will touch teach you, and you will give us your seed." "...where it is assumed that E-75 equals R-and M-75." "Contradictions exist everywhere, but they differ in accordance with the different nature of different things." "...physical and geometrical assumptions." "And the two things..." "In any given phenomenon or thing, the unity of opposites is conditional, temporary..." "Giustizia mosse il mio alto Fattore Fecemi la divina Potestate La Somma Sapienza e il Primo Amore™" "...could have results in many different ways..." "by making compensative changes..." "Le ciel, pardessus le toit si bleu, si calme, là, pardessus le toit ...could twist the sinews of thy heart." "And when thy heart began to beat, oh, what dread hand and what dread feet." "* The invisible worm*." "* That flies in the night *l" "* Has found out thy bed of secret dreams *" "Through me you pass into the city of woe." "Through me you pass into eternal sorrow." "Through me you pass among the forgotten people." "Marxist philosophy held that the law of the unity of opposites is the fundamental law of the universe." "This law operates universally, whether in the natural world, in human society, or in man's thinking." "The central nervous system no longer occurs as a self-contained organism," "Now, you know all that we know." "It's a prison." "A prison." "No, it's an ark." "A ship." "A space ship." "All this technology was for travel to the distant stars." " Did you go?" " Yes." "Another dead end." "How did it come about?" "The Vortex." "How did it start?" "They did it." "They were the scientists, the best in the world." "But they were middle-aged, too conditioned to mortality." "They went Renegade." "We were their off spring, and we were born into Vortex life." "We seal ourselves..." "here with... into this place of learning." "Death is banished forever." "I direct that the Tabernacle erase from us all memories of its construction, so we can never destroy it if we should ever crave for death." "Here, man and the sum of his knowledge will never die, but go forward to perfection." "We applied ourselves to the unsolved mysteries of the universe, but even with infinite time and the help of the Tabernacle, our minds were not up to it." "We failed." "Two." "Four continuations of the same, two anomalous." "...is to be changeless, and matter..." "And now we're trapped by our own devices" "There is no exit." "Violence has the tendency to accelerate." "However, the concept of total violence..." "Destroy it!" "The Tabernacle!" "Kill the Tabernacle." "The Tabernacle is indestructible and everlasting." "This crystal shall join us each to each, and all to the Tabernacle." "A crystal joins them." "A crystal." "Now we have given you all that we are, one gift remains, which contains everything... and nothing." "Look into this." "You will see lines running into the future." "You will make insight jumps." "When you can see into this crystal, then you will be ready." "Only then." "I see nothing inside, except my own perplexity." "Knowledge is not enough." "I have come for you." "Overhere." " We've met before, I believe." " Arthur Frayn." "Come now." "My Brutal friends call me Zardoz." "Revenge!" "Now, we're even." "'Would it have been worth while... 'to have squeezed the universe into a ball... 'to roll it towards some overwhelming question?" "To say, 'I am Lazarus, come from the dead?" "'" "Do you know the next line?" "It's T.S. Eliot." "'I am Lazarus, come from the dead." "Come back to tell you all." "I shall tell you all. '" "Well done, well done." "You've learned your lessons well." "What will you tell me?" "What do you see in the ball?" " Nothing." " Nothing?" "Then I have nothing to tell you." "That way!" "There!" "What do you see in the ball?" "Consuella." "I've ached for this moment." "You cannot." "You will not." "The hunt is always better than the kill." "In hunting you, I have become you." "I have destroyed what I set out to defend." "'He that fights too long against dragons..." "becomes a dragon himself. ' Nietzsche." "I am not like the others." "I would fill you with life... and love." "You have given me what no other gave." "Love." "If I live, we will live together." "Go now." "The Brutal is not here." "I was mistaken." "Refraction of light." "Infinite." "Break the Tabernacle." "Or be broken." "What do you see in the crystal ball?" "When you see into the crystal, then you will be ready." "Now I see it." "I am ready." "Tabernacle?" "What are you?" "Not permitted." " Where are you?" " Not permitted." "Do you know me?" "I have your voice print, Zed, and your genetic code." "But only memory fragments." "Tell me about the crystal transmitter." "I cannot give information which may threaten my own security." "Brain emissions refract low-wavelength laser light, passing through the crystal in the brain." "They are a code sent to you for interpretation and storage." " Yes or no?" " Not permitted." "A receiver must be like a transmitter." "I think you're a crystal." "In fact, this one." "This diamond." "In here, there is infinite storage space for refracted light patterns." "Yes or no?" "You have me in the palm of your hand." "But you could be elsewhere." "Yet I choose to be here." " Why?" " To confront you." "Already you have learned to see my light wavelengths in the diamond." "Now, you will try to erase the refractions and destroy me." "Your aim is to destroy me, isn't it?" "Yes." "Would you kill God?" "Such vanity." "I am the sum of all these people and all their knowledge" "I am all-seeing." "I am everywhere and nowhere." "That has often served as a definition of God." "Would you destroy us and all that we are?" "Yes." "Would you not rather be part of us, joined to us, a light shining to the future?" "Love us!" "Cherish the truth!" "No!" "You have penetrated me." "There is no escape." "You are within me." "Come to my center." "Come into the center of the crystal." "Tabernacle!" "Tabernacle!" "Tabernacle!" "Tabernacle!" "No!" "No!" "No!" "You have destroyed us." "You found the flaw in the crystal." "We are gone." "You are alone." "Take him to the east door." "Oh, it's too late." "He's finished." " Consuella, no." "Stay close to me, inside my aura." "Where did they go?" "Where?" "They went up there." "Can you tell us how things stand?" "Wh-What next?" "An old man calls me." "'The voice of the turtle is heard in the land. '" "I..." "I remember now." "The way it was." "We challenged the natural order." "The Vortex is..." "an offense against nature." "She had to find a way to destroy us." "Battle of wills." "So... she made you!" "We..." "We forced the hand of evolution." "A good death." "You've done it!" "He's dead!" " Look!" " The stone head!" "Take this, and let your sons and daughters look into it." "Ride east." "There, you will pass through the wall." "What will become of you?" "Will you go back to your people?" "There is no going back for me." "Put 'em out of there!" "Get out!" "Stop!" "It's useless." "It's over." " The Renegades are all dying like flies!" " Dying?" " It's not Zed to blame." "We destroyed ourselves." " That's truer than you know, Consuella." "And here I would like to claim some credit." "You see, our death wish was devious and deep." "As Zardoz, Zed, I was able to choose your forefathers." "It was careful genetic breeding that produced this Mutant." "This slave who could free his masters." "And Friend was my accomplice!" "Don't you remember the man in the library, Zed?" "It was I who led you to The Wizard of Oz book." "It was I who gave you access to the stone." "It was I!" "I bred you." "I led you." "And I have looked into the face of the force that put the idea in your mind." "You are bred and led yourself." "Arthur!" "We've all been used." " And reused." " And abused!" " And amused!" "Death approaches." "We are all mortal again." "Now we can say yes to death, but never again no." "Now, we must make our farewells." "to each other, to the sun and moon, trees and sky, earth and rock." "The landscape of our long, waking dream." "Zed... the Liberator, liberate me now..." "according to your promise." "Do it." "Do it!" "All that I was is gone." "Kill me too!" " Let's kill each other, Friend." " Huh?" "What?" " Proper regard for irony." " Yes, yes." "One last trick?" "Success." "It was all a joke." "I want to die." "Please!" "Kill me, I..." "I want to die!" "Please!" "Zed!" "Zed!" "Zed!" "Zed!" "Zed!" "Zed!" "Eru" | 2023-09-03T01:26:35.434368 | https://example.com/article/8793 |
House Democrats are voicing their opposition to Republican Gov. Bill Haslam's administration's decision to withhold $3.4 million in state funding from Nashville because of a disputed charter school application. The lawmakers at a news conference outside the legislative office complex in Nashville on Tuesday afternoon argued that Haslam's decision was unfair to students at city schools.
House Democratic Caucus Chairman Mike Turner said the withheld funding could be subject to a legal challenge, while fellow Nashville Democrat Mike Stewart said lawmakers didn't envision the state holding the power to demand the approval of applications when they passed a law allowing more charter schools in Tennessee last year.
Opponents of the Great Hearts Academy charter school said its proposal lacked a plan for promoting diversity. | 2023-08-19T01:26:35.434368 | https://example.com/article/4158 |
Minerals miner K+S settles with conservationist group
FRANKFURT (Reuters) - German potash miner K+S has agreed to cut waste water discharge volumes by a million cubic metres over the next four years in a settlement deal with German conservationist group BUND, which dropped a lawsuit in return.
K+S has been trying to come to terms with local communities and environmentalists, who are fighting its practice of injecting salty waste water - a byproduct of processing potassium ore into fertiliser products - into porous layers of rock.
Limits imposed by regulators crimped output and earnings in 2016 but a landmark ruling last December allowed K+S to discharge up to 1.5 million cubic metres of waste water per year into layers of rock through 2021, ending months of uncertainty and production outages.
“K+S receives legal security for its existing injection permit,” the group said in a statement on Monday, adding it would seek closer dialogue with BUND to avoid further disputes.
K+S, whose shares were up 0.2 percent at 19.68 euros at 0940 GMT, also committed to not renewing a permit for deep-well injection that expires in 2021, thanks to a 180 million euro (£160.87 million) water treatment plant it plans to bring onstream next year.
“Judicial disputes are to be avoided as far as possible in the future,” the miner added.
The deal is contingent on a normal water level of the Werra river, which is an alternative discharge route for its waste water.
Negotiations are ongoing with another plaintiff, the municipality of Gerstungen, a company spokesman said. | 2024-06-06T01:26:35.434368 | https://example.com/article/5412 |
New Indievania game portal lets you buy direct from creators, takes no cut
The developers behind the indie hit Capsized have started their own game …
Game developers setting up their own distribution channels isn't a new phenomenon, with Valve's Steam service being the most prominent example. But even though the developers at Alientrap Games—the team behind Capsized—enjoyed working with Valve, they still wanted the freedom of selling a DRM-free game and handling their own promotions. What started as a way to sell games from the Alientrap site has since expanded into Indievania, a new distribution site for indie titles where no games get rejected—and all of the profits go to the developers.
The site isn't actually designed to be a money-making machine for the small, two-man studio behind it. In fact, Alientrap doesn't even take a commission from game sales. When someone purchases a game from Indievania, they are purchasing directly from that particular developer's PayPal account. It's like buying the game directly from the developer, but with the benefits and promotion potential of a game portal. The site itself is funded entirely by optional donations at the end of each checkout.
There's also a focus on ease of use, as there's no client to download, no DRM included in the games, and no platform limits. Currently, PC, Mac, and Linux games are all available, and the Alientrap team is working on adding Android titles to the store as well.
"We realized a site like this was needed to be an open alternative," Alientrap's Lee Vermeulen told Ars. "Players want to support independent developers, not game distributors. So we wanted to make a site where the focus was on connecting the developers and players directly and eliminating the middle man."
While Steam can be challenging for indie developers looking to be accepted, Indievania has no screening process. "It's important to give developers the option to sell unfinished games or games that were rejected from other services to help fund further development," explained Vermeulen.
That being said, more popular games will still benefit from additional promotion. Games that sell well or are highly rated will be featured on the service's front page and will be promoted through social networking sites like Facebook and Twitter. The site also plans to use bundles and other special deals to help attract consumers.
Though the service is still in open beta, it has already attracted a number of notable indie games, including Blocks That Matter and Cthulhu Saves the World, both of which are also for sale on Steam. According to Vermeulen, the response from the indie community has been positive.
"Developers have definitely loved the system. It was designed to make managing their game/sales/promotions as easy as possible," he told Ars. "We are trying to make the site basically the exact same as if a player was buying a game from the developer's website. And that's exactly what developers want—they want control over how their games are sold, but at the same time they need help with promoting their game and bundles that they can't do from just selling on their website."
Though he didn't go into details, Vermeulen explained that the team is currently in the process of adding additional features and games in order to get Indievania primed for its official launch in the near future.
"We definitely want to make sure the site is ready for a large audience," he said.
It's good to have options I guess, but I don't see how an un-curated portal is better than a developer owned website. If you aren't getting the benefits of Steam (payment processing, promotion, bundles, captive customers) then you might as well just do it yourself and have full control.
Zero cut gives me zero confidence this site will be around very long. The big draw of Steam is the online catalog it allows you keep. Without confidence the store will be around next year, I have little incentive to even look at the store.
It is nice to have an alternative out there, especially one that gathers indie devs. I might give it a shot, but as it has been said, there needs to be an insurance that this won't flop in a year or two so people don't lose their games.
Really?? They have a game called ^^^^^^ for purchase on their site? Does Terry Cavanagh know about this? I like the idea of another DRM-free site like GOG.com, but with games like that, they're asking for trouble.
Zero cut gives me zero confidence this site will be around very long. The big draw of Steam is the online catalog it allows you keep. Without confidence the store will be around next year, I have little incentive to even look at the store.
Given that these games are sold with no DRM, there is no concern that a failing business will result in shutting down activation servers (as is the case with Steam and Origin). Once you buy from Indievania (or GoG), it doesn't matter if they stay in business. Of course, you have to keep your downloaded installation files, but that doesn't sound unreasonable.
It's good to have options I guess, but I don't see how an un-curated portal is better than a developer owned website. If you aren't getting the benefits of Steam (payment processing, promotion, bundles, captive customers) then you might as well just do it yourself and have full control.
That means running your own website and managing your own payment processing. For a small team (especially if it's just a single developer), the ability to sell your game without having to invest time, energy or money in building and maintaining a site is pretty attractive. Also, selling your game through a marketplace like this puts your product directly in front of customers who are actively looking for indie games, which is pretty good marketing for free.
Zero cut gives me zero confidence this site will be around very long. The big draw of Steam is the online catalog it allows you keep. Without confidence the store will be around next year, I have little incentive to even look at the store.
Given that these games are sold with no DRM, there is no concern that a failing business will result in shutting down activation servers (as is the case with Steam and Origin). Once you buy from Indievania (or GoG), it doesn't matter if they stay in business. Of course, you have to keep your downloaded installation files, but that doesn't sound unreasonable.
Exactly this. Now it's like the old days where you have to keep up with your own discs or files.
Of course, you have to keep your downloaded installation files, but that doesn't sound unreasonable.
Again, that's the primary reason I buy games on Steam. The online persistent catalog is the 'killer app' for PC games. Without the catalog, then the game has to be truly astonishing for me to even bother with another distribution method.
Really?? They have a game called ^^^^^^ for purchase on their site? Does Terry Cavanagh know about this? I like the idea of another DRM-free site like GOG.com, but with games like that, they're asking for trouble.
No kidding, that looks like an outrageous ripoff!
Quote:
^^^^^^ is a retro platformer where you must flip gravity to traverse extremely hard levels. The goal is to collect all the energy bits located around the level to repair your space ship.
When you see the screenshots it cements the fact that it is a travesty.
The only thing I'm not so happy about is that it might take a lot of wading through shit before you find a decent title. It's not horrible at the moment but as time goes on there will likely be a number of copy cat titles and possibly complete knock offs plus the titles that just aren't worth a grain of salt.
That means running your own website and managing your own payment processing. For a small team (especially if it's just a single developer), the ability to sell your game without having to invest time, energy or money in building and maintaining a site is pretty attractive.
They are using paypal to do payments, anyone can do that. If you are serious enough that you are charging money for your game, then you need a website, it's not optional. It's also extremely cheap unless you have massive traffic, in which case you should be able to afford it. If you don't have a site full of screenshots and preferably a forum and maybe a wiki, you aren't even trying. That stuff is not hard in 2011.
Point still stands though. Name is just as ridiculous, and the graphics are just as "bad". Dunno what the actual game is like, of course, but if "Lol 8-bit" and "weird name" is the worst that commenters can come up with, I don't think Indievania has much to worry about.
Wow, this seems to be a bad deal for developers. It's good to get your game out there and get 100% of the proceeds, but it will only take one or two clones to bury you and your hopefully original idea. And there are TONS of assholes out there waiting to rip off a game and re-sell it with minor or even no changes.
Point still stands though. Name is just as ridiculous, and the graphics are just as "bad".
I'm honestly not sure what you're trying to say. I assume you're talking about VVVVVV, since the blatant ripoff game has no reviews that I saw, and it sounds like you're claiming that the former isn't worth your attention. It was arguably one of the best games to come out in 2010, though you're certainly entitled to your opinion (the throwback visuals and audio aren't for everyone, though they do add a considerable amount of charm to the puzzle/action game). But then you say this:
WolfintheSheep wrote:
Dunno what the actual game is like, of course, but if "Lol 8-bit" and "weird name" is the worst that commenters can come up with, I don't think Indievania has much to worry about.
and you seem to miss the original point that the game being published on this new site is a blatant ripoff, regardless of how you feel of the original version. Indievania has nothing to worry about?? They have plenty to worry about if they are going to allow lawsuit-bait like this on their site.
One of the strengths of Steam is it's easy updates and installations. Buying from this means handling updates and backups yourself, or relying on the developers to reinvent their own updating mechanism.
I think Desura makes a much better case but I don't know how much is their cut.
"Players want to support independent developers, not game distributors..."
Quote:
The site itself is funded entirely by optional donations at the end of each checkout.
Something metallic about that.
I wonder how their donations will work. It must be a separate transaction (right?). 2dboy said they didn't earn anything for $0.30 donations, so I assume that they'll need donations to be above that mark to make anything. Most people who donate will probably give them a dollar? But some games are a dollar... I imagine if it works out really well for some developers, they might have partnership programs for more promotion. Good luck to them.
Ignus Fast wrote:
Wow, this seems to be a bad deal for developers. It's good to get your game out there and get 100% of the proceeds, but it will only take one or two clones to bury you and your hopefully original idea. And there are TONS of assholes out there waiting to rip off a game and re-sell it with minor or even no changes.
Sounds like the Android marketplace (I imagine iOS too). But developers have the same problem on the internet. Marketing sells games and getting your game on the portals first so that the word gets out about your game is the best way to make money. Unless you're already a big company, then you just use lawyers
That made me think about someone from buying a game on the store and then selling it on the store as their own. But they are moderating games:
indievania wrote:
Registering as a developer will take you instantly to the game adding pages, where you can submit your game to our system. It'll be held in moderation until a moderator approves it and uploads the files to our storage.
Then again, Apple moderates their store and someone did that to Lugaru on the Mac App store.
They are using paypal to do payments, anyone can do that. If you are serious enough that you are charging money for your game, then you need a website, it's not optional. It's also extremely cheap unless you have massive traffic, in which case you should be able to afford it. If you don't have a site full of screenshots and preferably a forum and maybe a wiki, you aren't even trying. That stuff is not hard in 2011.
Oh, what I meant to say is that it costs more than no-money/no-time to do it right. The indie guys that do have a free phpBBDrupalFizzyCamlBOL server often end up with it turning into a pile of farmaceutical (what can you do when there's already a 'ph'?) spam. Second, you haven't heard of PCI, in the current year that we so happen to be situated in?
I have Defy Gravity Extended for sale on indievania for 3$. For every single purchase the paypal sale was split between me and indievania. It sent $0.27 per sale to alientrap games(ie. indievania). This is in addition to the paypal fee. The last transaction occurred on Aug 15th.
Oh, what I meant to say is that it costs more than no-money/no-time to do it right. The indie guys that do have a free phpBBDrupalFizzyCamlBOL server often end up with it turning into a pile of farmaceutical (what can you do when there's already a 'ph'?) spam. Second, you haven't heard of PCI, in the current year that we so happen to be situated in?
It's a cost of releasing a game, if you actually expect it to do well. There's no way around it. If you are selling anything on the web then you need a website, because people automatically are wary of things that don't have a website.
Of course, you have to keep your downloaded installation files, but that doesn't sound unreasonable.
Again, that's the primary reason I buy games on Steam. The online persistent catalog is the 'killer app' for PC games. Without the catalog, then the game has to be truly astonishing for me to even bother with another distribution method.
It's the reason I don't have a Steam account (aside from lack of a native Linux client for Steam). I don't want to rely on a third party for any purchased product. I want a one-time transaction, after which I don't have to care about the fate of the seller. Local storage isn't a problem. I bought a 1.5 TB NAS in 2008, and I still haven't managed to fill it up yet (though it's gradually getting closer) Since I already back up my own files regularly (because I don't want to lose them), it really isn't difficult or expensive to have a backup of the full NAS.
Online persistent catalog with free re-downloads is a nice bonus feature (GOG.com has it, eMusic used to have it), I certainly would never even consider relying on that as my primary storage (as in the case of eMusic, where the feature was removed, presumably at the request of the music labels). As far as I'm concerned, it's DRM-free downloads or nothing. Actually, I would consider disc-based physical media DRM for something I really wanted, but for marginal products or impulse buys even that would be a deal killer.
I trust my ability to keep a DVD in good condition more than I trust an online authentication server to remain running, but then again I'm careful with my discs, and I have plenty of games on DC and DVD going back to the mid 90's that still work fine (aside from non-media-related compatibility problems with DOSBox or Wine). Many of them are from developers or publishers that no longer exist, and I suspect that if they required online authentication, they probably would be unplayable (unless I repurchased them on GOG.com DRM-free) | 2024-03-18T01:26:35.434368 | https://example.com/article/5368 |
---
abstract: 'Canonical parametrisations of classical confocal coordinate systems are introduced and exploited to construct non-planar analogues of incircular (IC) nets on individual quadrics and systems of confocal quadrics. Intimate connections with classical deformations of quadrics which are isometric along asymptotic lines and circular cross-sections of quadrics are revealed. The existence of octahedral webs of surfaces of Blaschke type generated by asymptotic and characteristic lines which are diagonally related to lines of curvature is proven theoretically and established constructively. Appropriate samplings (grids) of these webs lead to three-dimensional extensions of non-planar IC nets. Three-dimensional octahedral grids composed of planes and spatially extending (checkerboard) IC-nets are shown to arise in connection with systems of confocal quadrics in Minkowski space. In this context, the Laguerre geometric notion of conical octahedral grids of planes is introduced. The latter generalise the octahedral grids derived from systems of confocal quadrics in Minkowski space. An explicit construction of conical octahedral grids is presented. The results are accompanied by various illustrations which are based on the explicit formulae provided by the theory.'
author:
- |
Arseniy V. Akopyan$^1$, Alexander I. Bobenko$^2$, Wolfgang K. Schief$^3$ and Jan Techter$^2$\
$^1$Institute of Science and Technology Austria (IST Austria),\
Am Campus 1, A–3400 Klosterneuburg, Austria\
$^2$Institut für Mathematik, TU Berlin,\
Str. des 17. Juni 136, 10623 Berlin, Germany\
$^3$School of Mathematics and Statistics,\
The University of New South Wales, Sydney, NSW 2052, Australia
---
| 2024-05-30T01:26:35.434368 | https://example.com/article/4749 |
1. Technical Field
The present invention is related to an add-in card fixing frame, especially to an add-in card fixing frame including an attached locking assembly and a limit switch.
2. Related Art
With the development of the industrial computer and cloud computing, in order to increase PC or Server performance, or to reduce the motherboard load, it is very common to add various cards, such as a sound card or display card. The add-in card(s) is usually assembled to the socket(s) on the motherboard and fixed to the outside of the case frame, so as to maintain firmly both mechanical strength and electrical connection. The traditional add-in card uses an L-shaped fixing structure and/or a screw nut to fix the card on the outside of the case frame. However, if the screw/screw nut falls out when being tightened, or due to being inadequately tightened during insertion, it may cause damage or short circuit to the components on the add-in card or on the motherboard. These effects may cause a PC or Server to crash. Additionally, the data stored in the PC or the Server may be rendered inaccessible, so the users of the PC or the Server may be inconvenienced.
Usually, the add-in card(s) is assembling to the outer frame while the PC or Server is powered off; power on the PC or Server after the add-in card is assembled to the outer frame. However, if the add-in card is inadequately tightened during insertion, it is necessary to disconnect the electric power from the PC or Server in order to remove and re-insert the add-in card. The computer component life may be reduced by repeatedly switching on and off of the electric power. Thus, there is a need for a structure or a method to solve the above problems of avoiding screws falling out, and avoiding powering the computer on and off repeatedly. | 2023-10-02T01:26:35.434368 | https://example.com/article/4240 |
Square-Enix Releasing a GOTY Edition for Final Fantasy XIV: A Realm Reborn
The re-release will come with all of the game’s updates as of its November 14th release date, along with a “Book of Diamonds” grimoire box, 90 days of subscription-free play time and five pieces of art postcards.
There’s currently no news as to whether or not the Game of the Year edition will come to PlayStation 4 like the original game.
After a poor initial launch in 2010, Final Fantasy XIV was re-released as A Realm Reborn last year. The game has been a huge success for Square-Enix since being relaunched. For more on A Realm Reborn, check out Gaming Trend’s review. | 2024-05-17T01:26:35.434368 | https://example.com/article/8234 |
1. Field of the Invention
The present invention relates generally to physiological function monitors and, more particularly, to a garment utilizing a small, lightweight module for use in conjunction with sensors embedded in clothing.
2. Description of the Related Art
The need for real-time continuous monitoring of human physiological functions is becoming increasingly important due to the rapidly increasing over 60 population and the desire of baby boomers to monitor their vital signs and stay fit and the general trend in younger generations for fitness training. Also both amateur and professional athletes are pushing their bodies to the limit so real-time monitoring of their health status is of paramount importance.
Real-time monitoring or recording for later reading of physiological function data especially of exercisers and athletes has to be done in a non-intrusive, non-motion inhibiting manner yet it must provide reliable sensing and signal processing to transmit or store relevant information for the individual, coach and/or the physician. Key to this monitoring is the development of electronics matched to an appropriate sensing system.
Clothing containing sensors to monitor bodily physiological functions is not new, however, the major problem to date with electronically active or smart clothing is that the monitoring control and powering electronics always require a relatively large box (electronics plus battery) attached to the clothing or, in some cases, attached to a wrist band or a belt. Wires typically run from the garment containing the sensors to these boxes. Other embodiments have actually embedded these boxes into the garment thus causing difficulties in laundering. In some cases the sensors have to be attached directly to the body, using adhesives or conducting gels, such as is the case with wearable heart monitors.
In light of the above, there is a need for a wearable garment having electronics and sensors that can be configured to provide reliable data while being unintrusive and non-motion inhibiting to the wearer especially during exercising and can be safe during or easily removed for garment cleaning cycles. | 2023-10-10T01:26:35.434368 | https://example.com/article/7906 |
THE JOURNAL
Heroes of Design: Patagonia
"The more you know, the less you need," said Patagonia founder Yvon Chouinard. As design heroes go, few others speak to Bellroy’s guiding principles quite as coherently as Patagonia. Chouinard captured our attention through the pages of his alternative management manifesto, 'Let My People Go Surfing'. As environmental pioneers, Patagonia push us to seek alternatives, to give back, to advocate for meaningful change, and to advance manufacturing methods.
GREAT DESIGN CONSIDERS THE CONTEXT
As a design house, they’ve shown us that making the best products involves deep consideration of a context far greater than just the product itself. They inspire us with their emphasis on thriving business as a key ingredient to social and environmental contributions. And, perhaps most importantly, they speak a language of solutions – from helping people navigate the day-to-day to responding to our greatest environmental challenges.
Yvon Chouinard began climbing in the 1950s, and made his own tools before founding Patagonia.
Chouinard in the shed where Patagonia began.
By following Patagonia’s lead, we’ve learned the earth need not wear the cost of our quest for superior gear.
The Patagonia journey began with an elemental design shift. In the 1960s, when Chouinard learned he could craft reusable rock-climbing anchor points from recycled steel, he took to backyard blacksmithery. His homemade ‘pitons’ were soon in hot demand, and in 1965 he joined forces with aeronautical engineer Tom Frost. Under the banner of Chouinard Equipment, the two went on to redesign almost every climbing tool – making them stronger, lighter, simpler, more functional, and accessible to the masses.
The ‘Patagonia’ moniker came soon afterwards, encompassing the burgeoning wilderness clothing arm of the business. Waterproof polypropylene underwear, heavy-duty rugby shirts for climbing, light-weight polyurethane parkas, boiled-wool gloves and bivouac sacks – from the outset, inherent in the Patagonia code was the concept of function always heavily influencing form. And this constant response to environmental input continues to drive design and innovation today.
As suggested in the blurb for Let My People Go Surfing, Chouinard’s story is that of “an iconoclastic entrepreneur who brought doing good to the heart of his business; challenging conventional wisdom, leading a simpler and more examined life, and making a living without losing your soul”. The examples Patagonia have set in terms of business responsibility and lasting, intelligent, utilitarian design have inspired a movement of likeminded operators – Bellroy included – to reach for greater things.
Here are three of Patagonia’s guiding principles that resound strongly:
THINK BEYOND THE PRODUCT
A critical realization came early in the Patagonia story. In the late 1960s, as rock-climbing’s popularity was growing, the environmental impacts of steel and hammers on natural rock faces became pronounced. Chouinard and Frost’s response was to look beyond the tools themselves and incorporate some broader context into a safe and eco-friendly solution.
Improving gear for rock climbers was Patagonia's earliest venture.
Their revolutionary hand-inserted, aluminium anchor points first appeared in Chouinard Equipment’s catalogue in 1972. The booklet opened with an essay spruiking the environmental benefits of ‘clean’ climbing. “Clean is climbing the rock without changing it; a step closer to organic climbing for the natural man,” they declared. For 1972, the concepts of clean, natural and organic signified radical thinking. Little did they know at the time, this synergy between function, form, innovation and ecological responsibility would underpin the Patagonia business and design practices for the decades ahead.
IT'S EQUALLY ABOUT WHAT YOU USE AND HOW YOU USE IT
For a long time, Patagonia have been considered at the forefront of environmentally conscious manufacturing. By donating one percent of sales (not just profits) to grassroots environmental organizations, they’re active in the fight to save wilderness areas. Since 1996, they’ve shifted away from pesticide-intensive cotton crops, using 100% organics. Recycled polyester, hemp and renewables, sulphide-free dyes – though pollution is an inevitable by-product of manufacturing, through research and innovation they work steadily to reduce harm.
Patagonia source their cotton from 100% organic crops.
But in many ways, product longevity trumps all of the eco-initiatives. The longer you can keep every item out of landfill, the less of a footprint your products are leaving behind. At Bellroy, we take quality and long-sightedness very seriously. This is why every design is considered... deeply. We give a great deal of consideration to the habits, technology and currency of a region; the environmental footprint of the materials and construction; the functionality over years to come; and how we can put a little quiet delight into the interactions our customers have with the things they carry through life. So our customers can hold onto their Bellroy for a very long time to come.
CONSIDER THE ENTIRE PRODUCT LIFE CYCLE
At Bellroy, we credit Patagonia with guiding us towards sustainable product life cycles worth replicating – or the ‘cradle-to-cradle’ approach. In cradle-to-cradle design, materials used in production are designated as either biological nutrients (materials that can be returned to the earth without harm) or technical nutrients (synthetic materials that can be recycled or reused well). It’s about constantly seeking out the ‘right’ materials, not just what’s available or popular. By choosing fabrics and components based on these measures, we’re working hard to create products that will live a long life, adapt to their environments and stay true to their purposes.
In many ways, product longevity trumps all of the eco-initiatives. The longer you can keep every item out of landfill, the less of a footprint your products are leaving behind.
Patagonia have a repair service to assist product longevity and keep gear out of landfill.
By following Patagonia’s lead, we’ve learned the earth need not wear the cost of our quest for superior gear. On the contrary, as thoughtful manufacturers working with high-quality, durable materials and enduring designs we can play a meaningful role in the reduction of harm to our environment. | 2023-09-07T01:26:35.434368 | https://example.com/article/8885 |
Needle detachment in a slim and physically active child with insulin pump treatment.
Insulin pump therapy (CSII) is well established in pediatric patients with type 1 diabetes. In childhood diabetes, insulin pump treatment shows considerable advantages such as fewer injections, increased flexibility, fewer hypoglycemic events and lower HbA1c levels. Side effects such as catheter obstruction, technical pump failure, and dermatological complications have been observed, but are rarely reported. The reported patient is a physically very active and slim 10-year-old boy with reduced subcutaneous fatty tissue. After strong muscular activity an accidental rupture of the infusion set and needle detachment occurred in October 2013. X-ray and ultrasound imaging localized the needle in the musculus rectus femoris dexter. The needle was kept in situ and oral antibiotic treatment to prevent inflammatory reaction was prescribed. Repeated ultrasound measurements documented that the needles position had remained unchanged. Steel needle catheters (Sure-T infusion set, 6 mm) positioned in a thin layer of subcutaneous fat tissue of the thigh, combined with intense sports activity can result in a needle rupture and penetration into the muscle. Careful monitoring provides an alternative to surgery and lowers the risk of muscular necrosis. Because of differences in the distribution of subcutaneous fat tissue, an individualized catheter selection is necessary in pump treatment for children and adolescents, requiring a variety of different catheter sets. | 2024-05-31T01:26:35.434368 | https://example.com/article/2279 |
Caring. Core value, currency, and commodity ... is it time to get tough about "soft"?
Consumers of health care expect caring behaviors and become satisfied and loyal customers when their health experience included caring. In today's health care environment, however, caring often takes a back seat to task completion and capital expenditures. Caregivers may feel caring, but they often provide care without regard for how patients prefer to experience caring. Caring theorists provide a framework of patient centered caring to guide professional practice. Stories of caring that occur in spite of diminished resources are inspirational and illustrate these theories. Chief nursing officers share a unique opportunity and imperative to assure that caring stories, the essence of our work, routinely inform decisions made in the executive suite and boardroom. | 2023-12-27T01:26:35.434368 | https://example.com/article/3570 |
The problem of electrical discharge and subsequent explosive detonation of the ullage inside chemical storage tanks containing methane-infused fluids is becoming more widespread as the use of new non-metallic storage tanks proliferates. Such tanks are typically made of non-corrosive but otherwise insulating materials (either fiberglass resin, PVC, or similar insulating plastics), have no continuous metallic grounding conductors within or outside of the tanks, and are exposed to the electrical environment in the vicinity of lightning-producing thunderstorms. They are often used to store fluids used in hydraulic fracturing. The gas inside the tank above the fluid level (the tank's ullage) can contain a stoichiometrically explosive mixture of oxygen and methane or other similarly volatile hydrocarbon gas. Such a mixture is amenable to explosive detonation upon either arc or strong corona discharge within the tank.
Conventional metallic tanks form a Faraday cage of conducting material around both the fluid and potentially explosive ullage, thus ensuring that electric fields never approach appreciable values within the tank. However, the lack of a continuous conducting boundary resulting from the use of non-metallic tank walls permits electric fields to approach breakdown strength in response to a nearby lightning discharge. Furthermore, depending on the specific conductor geometry, enhanced local electric fields that exceed breakdown strength can occur near either small metallic objects or even dielectric objects within the ullage region of the tank. Such conductors include small boltheads or other metallic fasteners, as well as other electrically good conduction materials within the tank (e.g., including droplets of the fluid itself and the fluid surface corners). Enhanced fields at sharp conductors can occur during either the incipient or active phase of a nearby lightning strike, but gaseous dielectric breakdown and subsequent ullage ignition will likely only occur during a nearby strike event.
Since the fluid inside the tank is often laden with salts, it can be expected to be of moderate to high ionic content. As such, its conductivity can range from a low value of ˜0.001 S/m to values for heavily brackish water that can easily exceed a few S/m. Such fluids have relaxation time constants of less than ˜1 nsec, but for low saline contents (i.e., spring water) this time constant can be as long as ˜1 usec. In either case, these fluid masses behave as good electrical conductors on the time scale of an atmospheric electrical transient. They redistribute a surface charge event and thus effectively shield the charges on the fluid surface so they don't manifest itself within the volume of fluid itself.
However, the transient can produce a strong field within the ullage. It is well known that high electric fields occur where conductive materials form sharp corners or points. For example, the electric field around a simple spherical metallic object immersed in an otherwise uniform electric field will be up to a factor of three times as large due to the electric polarizability of the object. If the object is needle-like (for example, a rivet or long bolt) this field amplification factor can be significantly higher, readily approaching a factor of ˜10× for many common fasteners. The field amplification effect occurs not only around good conductors but also at the ends of long dielectric objects, albeit to a slightly lesser extent that depends on the dielectric constant of the object. For example, for a sphere of fiberglass with a relative dielectric constant of 4.2 the amplification would be a factor of approximately two times that of the external field.
Origin of Tank Explosions: It is hypothesized that the cause of recent explosions of ullage in fracture fluid storage tanks is the result of the above field amplification near sharp ungrounded metallic objects or sharp dielectric protrusions. Rapid increases in the external field of order 2MV/m per millisecond will cause field amplification on many small dielectric and conducting objects within a non-metallic tank. The rapidity of this field change does not permit time for charge to bleed off through the insulating tank walls, and thus to null out the applied external field from the lightning transient. A rapidly increasing field that exceeds the local dielectric breakdown strength at a location in the vicinity of a lightning strike can readily produce additional localized corona or even arc discharge by exceeding the breakdown strength of the gas mixture. Note that the breakdown strength of ullage gases may also differ from that of air, as well. For example, carbon dioxide hydrogen, and helium all serve to lower the breakdown strength of air, and can contribute to a somewhat lower overall breakdown strength if present in the ullage. The presence of such sharp conductors is thus to be avoided in order to minimize field enhancement anywhere within the ullage. Alternately, the use of proper shielding can reduce the likelihood of the transient producing high fields within the ullage.
What is needed in the art is a grounding system that is highly corrosion resistant, can be secured to a roof in a non-metallic tank, and then rest on the bottom of the tank like an anchor. The present invention provides a stainless steel tripod type electrode that readily rests on the tank bottom and is connected to a roof of the tank with a cable. | 2023-10-28T01:26:35.434368 | https://example.com/article/1100 |
Ligament augmentation for prevention of proximal junctional kyphosis and proximal junctional failure in adult spinal deformity.
OBJECTIVE Proximal junctional kyphosis (PJK) is a well-recognized, yet incompletely defined, complication of adult spinal deformity surgery. There is no standardized definition for PJK, but most studies describe PJK as an increase in the proximal junctional angle (PJA) of greater than 10°-20°. Ligament augmentation is a novel strategy for PJK reduction that provides strength to the upper instrumented vertebra (UIV) and adjacent segments while also reducing junctional stress at those levels. METHODS In this study, ligament augmentation was used in a consecutive series of adult spinal deformity patients at a single institution. Patient demographics, including age; sex; indication for surgery; revision surgery; surgical approach; and use of 3-column osteotomies, vertebroplasty, or hook fixation at the UIV, were collected. The PJA was measured preoperatively and at last follow-up using 36-inch radiographs. Data on change in PJA and need for revision surgery were collected. Univariate and multivariate analyses were performed to identify factors associated with change in PJA and proximal junctional failure (PJF), defined as PJK requiring surgical correction. RESULTS A total of 200 consecutive patients were included: 100 patients before implementation of ligament augmentation and 100 patients after implementation of this technique. The mean age of the ligament augmentation cohort was 66 years, and 67% of patients were women. Over half of these cases (51%) were revision surgeries, with 38% involving a combined anterior or lateral and posterior approach. The mean change in PJA was 6° in the ligament augmentation group compared with 14° in the control group (p < 0.001). Eighty-four patients had a change in PJA of less than 10°. In a multivariate linear regression model, age (p = 0.016), use of hook fixation at the UIV (p = 0.045), and use of ligament augmentation (p < 0.001) were associated with a change in PJA. In a separate model, only ligament augmentation (OR 0.193, p = 0.012) showed a significant association with PJF. CONCLUSIONS Ligament augmentation represents a novel technique for the prevention of PJK and PJF. Compared with a well-matched historical cohort, ligament augmentation is associated with a significant decrease in PJK and PJF. These data support the implementation of ligament augmentation in surgery for adult spinal deformity, particularly in patients with a high risk of developing PJK and PJF. | 2024-05-05T01:26:35.434368 | https://example.com/article/5481 |
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Tucked away deep inside your body and even on your skin, is an invisible world of tiny little organisms – microorganisms – so tiny it takes a microscope to see them. This invisible world is called the human microbiome. Even…
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This simple recipe can replace your heavy duty and anti-bacterial household cleaners. It takes about two minutes to make. Many people find it difficult to use vinegar as a cleaner due to the strong odor. Adding essential oils…
Keeping a home fresh and clean is not about killing as many germs as possible. It is about removing dirt and grime, which will remove most of the germs that could cause us harm. Killing off all microbes is not…
Perfect Quotes
God knows what each one of us is dealing with. He knows our pressures. He knows our conflicts. And He has made a provision for each and every one of them. That provision is Himself in the person of the Holy Spirit, indwelling us and empowering us to respond rightly.
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Style and Fashion Featured Article
Flower Crowns are a super cute boho trend that has been going around lately. They are so versatile and cute, you can wear them with anything! I love to wear them as a whimsical addition to virtually any outfit and…
Featured Posts
Tucked away deep inside your body and even on your skin, is an invisible world of tiny little organisms – microorganisms – so tiny it takes a microscope to see them. This invisible world is called the human microbiome. Even… | 2024-02-12T01:26:35.434368 | https://example.com/article/3479 |
Cytoglobin is expressed in hepatic stellate cells, but not in myofibroblasts, in normal and fibrotic human liver.
Cytoglobin (CYGB) is ubiquitously expressed in the cytoplasm of fibroblastic cells in many organs, including hepatic stellate cells. As yet, there is no specific marker with which to distinguish stellate cells from myofibroblasts in the human liver. To investigate whether CYGB can be utilized to distinguish hepatic stellate cells from myofibroblasts in normal and fibrotic human liver, human liver tissues damaged by infection with hepatitis C virus (HCV) and at different stages of fibrosis were obtained by liver biopsy. Immunohistochemistry was performed on histological sections of liver tissues using antibodies against CYGB, cellular retinol-binding protein-1 (CRBP-1), α-smooth muscle actin (α-SMA), thymocyte differentiation antigen 1 (Thy-1), and fibulin-2 (FBLN2). CYGB- and CRBP-1-positive cells were counted around fibrotic portal tracts in histological sections of the samples. The expression of several of the proteins listed above was examined in cultured mouse stellate cells. Quiescent stellate cells, but not portal myofibroblasts, expressed both CYGB and CRBP-1 in normal livers. In fibrotic and cirrhotic livers, stellate cells expressed both CYGB and α-SMA, whereas myofibroblasts around the portal vein expressed α-SMA, Thy-1, and FBLN2, but not CYGB. Development of the fibrotic stage was positively correlated with increases in Sirius red-stained, α-SMA-positive, and Thy-1-positive areas, whereas the number of CYGB- and CRBP-1-positive cells decreased with fibrosis development. Primary cultured mouse stellate cells expressed cytoplasmic CYGB at day 1, whereas they began to express α-SMA at the cellular margins at day 4. Thy-1 was undetectable throughout the culture period. In human liver tissues, quiescent stellate cells are CYGB positive. When activated, they also become α-SMA positive; however, they are negative for Thy-1 and FBLN2. Thus, CYGB is a useful marker with which to distinguish stellate cells from portal myofibroblasts in the damaged human liver. | 2023-09-17T01:26:35.434368 | https://example.com/article/7114 |
---
abstract: 'This paper presents expressions for gamma values at rational points with the denominator dividing 24 or 60. These gamma values are expressed in terms of 10 distinct gamma values and rational powers of $\pi$ and a few real algebraic numbers. Our elementary list of formulas can be conveniently used to evaluate, for example, algebraic Gauss hypergeometric functions by the Gauss identity. Also, algebraic independence of gamma values and their relation to the elliptic [**K**]{} function are briefly discussed.'
author:
- |
Raimundas Vidūnas[^1]\
*Kyushu University*
title: Expressions for values of the gamma function
---
Introduction
============
The gamma function [@specfaar Chapter 1] satisfies the difference equation $$\label{differeq}
\Gamma(x+1) = x\,\Gamma(x),$$ the Euler reflection formula $$\label{reflection}
\Gamma(x)\,\Gamma(1-x)=\frac{\pi}{\sin(\pi x)},$$ and the Gauss multiplication formula $$\label{gmultiplic}
\Gamma(x)\,\Gamma\left(x+\frac1n\right)\ldots\Gamma\left(x+\frac{n\!-\!1}{n}\right)
= n^{\frac12-nx}\,(2\pi)^{\frac{n-1}2}\,\Gamma(nx).$$ In the last formula, $n$ is a positive integer. Its special case $n=2$ is known as Legendre’s duplication formula. We refer to these functional equations for the gamma function as the [*standard equations*]{}.
Values of the gamma function at rational points are of broad interest. By historical motivation, $\Gamma(n)=(n-1)!$ when $n$ is a positive integer. An easy consequence of the reflection formula is ${\Gamma\!\left(\frac{1}{2}\right)}=\sqrt{\pi}$. By using difference equation (\[differeq\]) one can evaluate $\Gamma(x)$ for rational $x$ with the denominator $2$. No explicit evaluations of other gamma values are known. Some gamma terms (i.e., quotients of products of gamma values) occur as values of hypergeometric functions at special points [@specfaar] and as period integrals [@periods], [@deligne]. In particular, this applies to values of the elliptic $\bf K$-function at so-called [*elliptic integral singular values*]{} [@zucker], [@selbergc], [@campbell]. Conversely, some gamma values at rational points can be expressed in terms of elliptic integrals; see [@borwzu], [@waldschmidt] and Section \[gammaelliptic\] in this paper.
The purpose of this paper is to present explicit relations between gamma values in the set $$\label{gammaset}
\left\{ \left. {\Gamma\!\left(\frac{k}{n}\right)} \;\right|\; k,n\in{\mbox{\bf Z}};\ 0<\frac{k}{n}<1;\
\mbox{$n$ divides 24 or 60} \right\}.$$ We show that standard formulas (\[reflection\])–(\[gmultiplic\]) imply that all these gamma values can be multiplicatively expressed in terms of rational powers of $\pi$, rational powers of few algebraic numbers, and the following 10 gamma values: $$\label{gammabasis}
\begin{array}{ccccc}
{\displaystyle}{\Gamma\!\left(\frac{1}{3}\right)}, & {\displaystyle}{\Gamma\!\left(\frac{1}{4}\right)},& {\displaystyle}{\Gamma\!\left(\frac{1}{5}\right)},
& {\displaystyle}{\Gamma\!\left(\frac{2}{5}\right)},& {\displaystyle}{\Gamma\!\left(\frac{1}{8}\right)}, \vspace{2pt}\\
{\displaystyle}{\Gamma\!\left(\frac{1}{15}\right)},& {\displaystyle}{\Gamma\!\left(\frac{1}{20}\right)}, & {\displaystyle}{\Gamma\!\left(\frac{1}{24}\right)},& {\displaystyle}{\Gamma\!\left(\frac{1}{60}\right)},
& {\displaystyle}{\Gamma\!\left(\frac{7}{60}\right)}.
\end{array}$$ In Section \[gammaevaluations\] we present explicit expressions for the gamma values in (\[gammaset\]) in these terms. By using difference equation (\[differeq\]) and our list of formulas, one can express any gamma value at a rational point with the denominator dividing 24 or 60 in the same fashion. In Section \[generalresults\] we indicate an elementary proof of our evaluations, and show that the standard formulas do not imply any relations between the distinguished values in (\[gammabasis\]). If Lang’s conjecture [@lang] is true, those 10 gamma values and the constant $\pi$ are algebraically independent over ${\mbox{\bf Q}}$.
Relations between gamma values at rational points with small denominators are widely known; see [@wolfram page GammaFunction.html] for example. Some tricky relations between gamma values from the set (\[gammaset\]) are derived in [@borwzu], [@kato] and probably by other authors. Of special interest are gamma terms with algebraic values [@koblitzo], [@pdas]. Our list of relations between gamma values may be useful for many purposes. For example, explicit evaluation of algebraic Gauss hypergeometric functions at $x=1$ requires gamma values at rational points with the denominators dividing 24 or 60; see Section \[application\]. Our formula list is precisely enough for this purpose. In Section 5 we present available expressions of gamma values in (\[gammabasis\]) in terms of the elliptic $\bf K$-function.
Explicit formulas {#gammaevaluations}
=================
Here we present a list of explicit expressions of gamma values in the set (\[gammaset\]) in terms of the gamma values in (\[gammabasis\]). A proof of these relations is indicated in the following Section. A comparable list of expressions for gamma values is available at [@webval].
To make formulas more compact, we introduce the following constants: $$\label{cconstants}
\begin{array}{ll}
\phi=5+\sqrt5, & \phi^\star=5-\sqrt5,\vspace{2pt}\\
\psi=\sqrt{5+2\sqrt5},\qquad & \psi^\star=\sqrt{5-2\sqrt5}.
\end{array}$$ Note that $$\phi\,\phi^\star=20,\qquad \psi\,\psi^\star=\sqrt{5},\qquad
\psi=\frac{\phi\,^{3/2}}{2^{3/2}\,\sqrt{5}},\qquad
\psi^\star=\frac{\phi^\star\,^{3/2}}{2^{3/2}\,\sqrt{5}}.$$ We express gamma values from (\[gammaset\]) in terms of the values in (\[gammabasis\]) and rational powers of the following constants: $$\label{algnumbers}
\begin{array}{c}
\pi,\quad 2,\quad 3,\quad 5,\quad \sqrt2\pm1,\quad \sqrt3\pm 1,\quad
\sqrt{3}\pm\sqrt2,\quad \sqrt5\pm\sqrt3,\\
\phi,\quad \phi^\star,\quad\sqrt{15}\pm\psi,\quad
\sqrt{15}\pm\psi^\star,\quad \sqrt{10}\pm\sqrt{\phi},\quad
\sqrt{10}\pm\sqrt{\phi^\star}.
\end{array}$$ When applying our formulas to gamma terms, it is easy to invert and simplify these algebraic numbers. Some useful expressions with these algebraic numbers are presented in Lemma \[algrelations\] in the next Section.
Here is our list of formulas: $$\begin{aligned}
{\Gamma\!\left(\frac{1}{2}\right)}{&\!\!=\!\!&}\sqrt{\pi}\,,\hspace{126pt}
{\Gamma\!\left(\frac{2}{3}\right)}{\;\,=\;\,}\frac{2\,\pi}{\sqrt3}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1},\\
{\Gamma\!\left(\frac{3}{4}\right)}{&\!\!=\!\!&}\pi\,\sqrt2\,\;{\Gamma\!\left(\frac{1}{4}\right)}^{-1},\hspace{76pt}
{\Gamma\!\left(\frac{1}{6}\right)}{\;\,=\;\,}\frac{\sqrt3}{\sqrt\pi\;2^{1/3}}\;{\Gamma\!\left(\frac{1}{3}\right)}^2,\\
{\Gamma\!\left(\frac{3}{5}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt2\,\sqrt{\phi^\star}}{\sqrt5}\;{\Gamma\!\left(\frac{2}{5}\right)}^{-1},\hspace{54pt}
{\Gamma\!\left(\frac{5}{6}\right)}{\;\,=\;\,}\frac{\pi^{3/2}\,2^{4/3}}{\sqrt3}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-2},\\
{\Gamma\!\left(\frac{4}{5}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt2\;\sqrt{\phi}}{\sqrt5}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1},\hspace{58pt}
{\Gamma\!\left(\frac{3}{8}\right)}{\;\,=\;\,}\sqrt{\pi}\,\sqrt{\sqrt2-1}\;{\Gamma\!\left(\frac{1}{4}\right)}^{-1}{\Gamma\!\left(\frac{1}{8}\right)},\\
{\Gamma\!\left(\frac{5}{8}\right)}{&\!\!=\!\!&}\sqrt{\pi}\,2^{3/4}\;{\Gamma\!\left(\frac{1}{4}\right)}{\Gamma\!\left(\frac{1}{8}\right)}^{-1},\hspace{35pt}
{\Gamma\!\left(\frac{7}{8}\right)}{\;\,=\;\,}\pi\,2^{3/4}\,\sqrt{\sqrt2+1}\;{\Gamma\!\left(\frac{1}{8}\right)}^{-1},\\
{\Gamma\!\left(\frac{1}{10}\right)}{&\!\!=\!\!&}\frac{\sqrt{\phi}}{\sqrt{\pi}\;2^{7/10}}\;{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{2}{5}\right)},\hspace{34pt}
{\Gamma\!\left(\frac{3}{10}\right)}{\;\,=\;\,}\frac{\sqrt{\pi}\;\phi^\star}{2^{3/5}\,\sqrt{5}}\;{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{2}{5}\right)}^{-1},\\
{\Gamma\!\left(\frac{7}{10}\right)} {&\!\!=\!\!&}\sqrt{\pi}\;2^{3/5}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}, \hspace{30pt}
{\Gamma\!\left(\frac{9}{10}\right)}{\;\,=\;\,}\frac{\pi^{3/2}\,2^{7/10}\,\sqrt{\phi}}{\sqrt{5}}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}^{-1},\\
{\Gamma\!\left(\frac{1}{12}\right)} {&\!\!=\!\!&}\frac{3^{3/8}\,\sqrt{\sqrt3+1}}{\sqrt{\pi}\;2^{1/4}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{4}\right)},\\
{\Gamma\!\left(\frac{5}{12}\right)} {&\!\!=\!\!&}\frac{\sqrt{\pi}\;2^{1/4}\,\sqrt{\sqrt3-1}}{3^{1/8}}\;{\Gamma\!\left(\frac{1}{4}\right)}{\Gamma\!\left(\frac{1}{3}\right)}^{-1},\\
{\Gamma\!\left(\frac{7}{12}\right)} {&\!\!=\!\!&}\sqrt{\pi}\;2^{1/4}\,3^{1/8}\,\sqrt{\sqrt3-1}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{4}\right)}^{-1},\\
{\Gamma\!\left(\frac{11}{12}\right)} {&\!\!=\!\!&}\frac{\pi^{3/2}\,2^{3/4}\,\sqrt{\sqrt3+1}}{3^{3/8}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{4}\right)}^{-1},\\
{\Gamma\!\left(\frac{2}{15}\right)}{&\!\!=\!\!&}\frac{\sqrt{\phi^\star}\,\sqrt{\sqrt{15}-\psi^\star}}
{2\cdot 3^{7/20}\,5^{1/3}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}{\Gamma\!\left(\frac{1}{15}\right)},\\
{\Gamma\!\left(\frac{4}{15}\right)}{&\!\!=\!\!&}\frac{\sqrt{\phi}\,\sqrt{\sqrt{15}-\psi}\,\sqrt{\sqrt{15}-\psi^\star}}
{2^{3/2}\,3^{3/10}\,\sqrt{5}}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}{\Gamma\!\left(\frac{1}{15}\right)},\\
{\Gamma\!\left(\frac{7}{15}\right)}{&\!\!=\!\!&}\frac{3^{9/20}\,\sqrt{\phi^\star}\,\sqrt{\sqrt{15}+\psi^\star}}
{2\cdot 5^{1/6}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{1}{15}\right)}^{-1},\\
{\Gamma\!\left(\frac{8}{15}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt2\,\sqrt{\sqrt{15}-\psi}}{3^{9/20}\,5^{1/3}}
\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{15}\right)},\\
{\Gamma\!\left(\frac{11}{15}\right)}{&\!\!=\!\!&}2\,\pi\cdot 3^{3/10}\;{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{15}\right)}^{-1},\\
{\Gamma\!\left(\frac{13}{15}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt2\;3^{7/20}\,\sqrt{\sqrt{15}+\psi}}{5^{1/6}}
\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{15}\right)}^{-1},\\
{\Gamma\!\left(\frac{14}{15}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt{\phi}\,\sqrt{\sqrt{15}+\psi}\,\sqrt{\sqrt{15}+\psi^\star}}
{\sqrt{2}\,\sqrt{5}}\;{\Gamma\!\left(\frac{1}{15}\right)}^{-1},\\
{\Gamma\!\left(\frac{3}{20}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\phi^\star\,\sqrt{\sqrt{10}-\sqrt{\phi^\star}}}
{2^{21/20}\,5^{7/8}}\;{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{20}\right)},\\
{\Gamma\!\left(\frac{7}{20}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\sqrt{10}-\sqrt{\phi}}}
{2^{3/20}\,5^{3/8}}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{20}\right)},\\
{\Gamma\!\left(\frac{9}{20}\right)}{&\!\!=\!\!&}\frac{\pi\sqrt{\sqrt{10}-\sqrt{\phi}}\;\sqrt{\sqrt{10}-\sqrt{\phi^\star}}}
{2^{1/5}\,\sqrt5}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{20}\right)},\\
{\Gamma\!\left(\frac{11}{20}\right)}{&\!\!=\!\!&}2^{1/5}\,\sqrt\phi\;{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{2}{5}\right)}{\Gamma\!\left(\frac{1}{20}\right)}^{-1},\\
{\Gamma\!\left(\frac{13}{20}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;2^{3/20}\,\sqrt{\phi^\star}\,
\sqrt{\sqrt{10}+\sqrt{\phi^\star}}}{5^{1/8}}\;{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{1}{20}\right)}^{-1},\\
{\Gamma\!\left(\frac{17}{20}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;2^{1/20}\,\sqrt{\phi}\,\sqrt{\sqrt{10}+\sqrt{\phi}}}
{5^{1/8}}\;{\Gamma\!\left(\frac{2}{5}\right)}{\Gamma\!\left(\frac{1}{20}\right)}^{-1},\\
{\Gamma\!\left(\frac{19}{20}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt\phi\,\sqrt{\sqrt{10}+\sqrt{\phi}}\;\sqrt{\sqrt{10}+\sqrt{\phi^\star}}}
{\sqrt5}\;{\Gamma\!\left(\frac{1}{20}\right)}^{-1},\\
{\Gamma\!\left(\frac{5}{24}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\sqrt2-1}\,\sqrt{\sqrt3-1}}{2^{1/6}\,\sqrt3}
\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{24}\right)},\\
{\Gamma\!\left(\frac{7}{24}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\,\sqrt{\sqrt3-1}\,\sqrt{\sqrt3-\sqrt2}}
{2^{1/4}\,3^{3/8}}\;{\Gamma\!\left(\frac{1}{4}\right)}^{-1}{\Gamma\!\left(\frac{1}{24}\right)},\\
{\Gamma\!\left(\frac{11}{24}\right)}{&\!\!=\!\!&}\frac{\pi\,2^{1/12}\,\sqrt{\sqrt2-1}\,\sqrt{\sqrt3-\sqrt2}}
{3^{3/8}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{4}\right)}^{-1}{\Gamma\!\left(\frac{1}{24}\right)},\\
{\Gamma\!\left(\frac{13}{24}\right)}{&\!\!=\!\!&}2^{2/3}\,3^{3/8}\,\sqrt{\sqrt3+1}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{4}\right)}{\Gamma\!\left(\frac{1}{24}\right)}^{-1},\\
{\Gamma\!\left(\frac{17}{24}\right)}{&\!\!=\!\!&}2\,\sqrt\pi\;3^{3/8}\,\sqrt{\sqrt2+1}\;{\Gamma\!\left(\frac{1}{4}\right)}{\Gamma\!\left(\frac{1}{24}\right)}^{-1},\\
{\Gamma\!\left(\frac{19}{24}\right)}{&\!\!=\!\!&}\sqrt\pi\;2^{11/12}\,\sqrt3\,\sqrt{\sqrt3+\sqrt2}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{24}\right)}^{-1},\\
{\Gamma\!\left(\frac{23}{24}\right)}{&\!\!=\!\!&}\pi\;2^{3/4}\,\sqrt{\sqrt2+1}\,\sqrt{\sqrt3+1}\,\sqrt{\sqrt3+\sqrt2}\;{\Gamma\!\left(\frac{1}{24}\right)}^{-1},\\
{\Gamma\!\left(\frac{1}{30}\right)}{&\!\!=\!\!&}\frac{3^{9/20}\,\sqrt{\phi}\,\sqrt{\sqrt{15}+\psi}}
{\sqrt\pi\;2^{16/15}\,5^{1/6}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{5}\right)},\\
{\Gamma\!\left(\frac{7}{30}\right)}{&\!\!=\!\!&}\frac{3^{3/20}\,\sqrt{\phi^\star}\,\sqrt{\sqrt{15}+\psi^\star}}
{\sqrt\pi\;2^{22/15}\,5^{1/6}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{2}{5}\right)},\\
{\Gamma\!\left(\frac{11}{30}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\,\sqrt{\phi}\,\sqrt{\sqrt{15}-\psi}}
{2^{11/15}\,3^{1/20}\,5^{1/3}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{5}\right)},\\
{\Gamma\!\left(\frac{13}{30}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;3^{7/20}\,\phi^\star\,\sqrt{\sqrt{15}-\psi^\star}}
{2^{41/30}\,5^{2/3}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{2}{5}\right)}^{-1},\\
{\Gamma\!\left(\frac{17}{30}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\phi^\star}\,\sqrt{\sqrt{15}-\psi^\star}}
{2^{2/15}\,3^{7/20}\,5^{1/3}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)},\\
{\Gamma\!\left(\frac{19}{30}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;3^{1/20}\,\phi\,\sqrt{\sqrt{15}-\psi}}
{2^{23/30}\,5^{2/3}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{5}\right)}^{-1},\\
{\Gamma\!\left(\frac{23}{30}\right)}{&\!\!=\!\!&}\frac{\pi^{3/2}\,\phi^\star\,\sqrt{\sqrt{15}+\psi^\star}}
{2^{1/30}\,3^{3/20}\,5^{5/6}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}^{-1},\\
{\Gamma\!\left(\frac{29}{30}\right)}{&\!\!=\!\!&}\frac{\pi^{3/2}\,\phi\,\sqrt{\sqrt{15}+\psi}}
{2^{13/30}\,3^{9/20}\,5^{5/6}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{5}\right)}^{-1},\\
{\Gamma\!\left(\frac{11}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\phi}\;\sqrt{\sqrt{15}-\psi}\,\sqrt{\sqrt{10}-\sqrt{\phi}}}
{2^{5/4}\,\sqrt3\;5^{17/24}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{60}\right)},\\
{\Gamma\!\left(\frac{13}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\phi^\star}\,\sqrt{\sqrt3+1}\,\sqrt{\sqrt5-\sqrt3}
\,\sqrt{\sqrt{15}-\psi^\star}}{2^{13/10}\,3^{3/20}\,5^{3/8}}\;{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{7}{60}\right)},\\
{\Gamma\!\left(\frac{17}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\phi^\star}\,\sqrt{\sqrt{15}-\psi^\star}\,
\sqrt{\sqrt{10}-\sqrt{\phi^\star}}}{2^{3/4}\,\sqrt3\;5^{11/24}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{7}{60}\right)},\\
{\Gamma\!\left(\frac{19}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;\sqrt{\phi}\;\sqrt{\sqrt3-1}\,\sqrt{\sqrt5-\sqrt3}\,
\sqrt{\sqrt{15}-\psi}}{2^{7/5}\,3^{9/20}\,5^{5/8}}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{60}\right)},\\
{\Gamma\!\left(\frac{23}{60}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt{\phi^\star}\,\sqrt{\sqrt3+1}\,\sqrt{\sqrt5-\sqrt3}\,
\sqrt{\sqrt{10}-\sqrt{\phi^\star}}}{2^{11/20}\,3^{3/20}\,5^{7/12}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{7}{60}\right)},\\
{\Gamma\!\left(\frac{29}{60}\right)}{&\!\!=\!\!&}\frac{\pi\,\sqrt{\phi}\;\sqrt{\sqrt3-1}\,\sqrt{\sqrt5-\sqrt3}\,
\sqrt{\sqrt{10}-\sqrt{\phi}}}{2^{23/20}\,3^{9/20}\,5^{7/12}}\;{\Gamma\!\left(\frac{1}{3}\right)}^{-1}{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{60}\right)},\\
{\Gamma\!\left(\frac{31}{60}\right)}{&\!\!=\!\!&}\frac{3^{9/20}\,\sqrt\phi\;\sqrt{\sqrt{15}+\psi}}{2^{1/10}\,5^{1/6}}
\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{5}\right)}{\Gamma\!\left(\frac{1}{60}\right)}^{-1},\\
{\Gamma\!\left(\frac{37}{60}\right)}{&\!\!=\!\!&}\frac{3^{3/20}\,\sqrt{\phi^\star}\,\sqrt{\sqrt{15}+\psi^\star}}
{2^{7/10}\,5^{1/6}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{2}{5}\right)}{\Gamma\!\left(\frac{7}{60}\right)}^{-1},\\
{\Gamma\!\left(\frac{41}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;2^{3/20}\,3^{9/20}\,\sqrt\phi\;\sqrt{\sqrt{10}+\sqrt\phi}}
{5^{1/8}}\;{\Gamma\!\left(\frac{1}{5}\right)}^{-1}{\Gamma\!\left(\frac{1}{60}\right)},\\
{\Gamma\!\left(\frac{43}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\,\sqrt3\;\sqrt{\phi^\star}\;\sqrt{\sqrt3-1}\,
\sqrt{\sqrt5+\sqrt3}}{\sqrt2\; 5^{7/24}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{7}{60}\right)}^{-1},\\
{\Gamma\!\left(\frac{47}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\;2^{1/20}\,3^{3/20}\,\sqrt{\phi^\star}\;
\sqrt{\sqrt{10}+\sqrt{\phi^\star}}}{5^{3/8}}\;{\Gamma\!\left(\frac{2}{5}\right)}^{-1}{\Gamma\!\left(\frac{7}{60}\right)},\\
{\Gamma\!\left(\frac{49}{60}\right)}{&\!\!=\!\!&}\frac{\sqrt\pi\,\sqrt3\;\sqrt\phi\;\sqrt{\sqrt3+1}\,
\sqrt{\sqrt5+\sqrt3}}{5^{1/24}}\;{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{1}{60}\right)}^{-1},\\
{\Gamma\!\left(\frac{53}{60}\right)}{&\!\!=\!\!&}\frac{\pi\,\phi^\star\sqrt{\sqrt3-1}\,\sqrt{\sqrt{5}+\sqrt{3}}\,
\sqrt{\sqrt{15}+\psi^\star}\,\sqrt{\sqrt{10}+\sqrt{\phi^\star}}}{2^{5/4}\,5^{3/4}}\;{\Gamma\!\left(\frac{7}{60}\right)}^{-1},\\
{\Gamma\!\left(\frac{59}{60}\right)}{&\!\!=\!\!&}\frac{\pi\,\phi\;\sqrt{\sqrt3+1}\,\sqrt{\sqrt{5}+\sqrt{3}}\;
\sqrt{\sqrt{15}+\psi}\;\sqrt{\sqrt{10}+\sqrt\phi}}{2^{5/4}\,5^{3/4}}\;{\Gamma\!\left(\frac{1}{60}\right)}^{-1}.\end{aligned}$$
Proof of the formulas {#generalresults}
=====================
Here we give an elementary proof of all identities in the previous Section. We do not reproduce detailed computations in our proofs; they are quite straightforward though tedious. Lemma \[algrelations\] gives compact expressions for some products of employed algebraic numbers (\[algnumbers\]). We also show that the standard equations do not imply any relations between gamma values in (\[gammabasis\]), and discuss briefly algebraic independence of those gamma values. Along the way, we give a set of 16 gamma values which are enough to express any gamma value at a rational point with the denominator dividing 120.
First we indicate relevant values of the sine function. To read off the sinus values, one has to compare formulas in Lemma \[cosecants\] with the following form of Euler’s identity: $${\exp\left(ix\right)}= \sin\left(\frac\pi2-x\right)+i\sin x. $$ For completeness, recall the well-known values ${\exp\left(\frac{i\pi}{3}\right)}=\frac{1+i\sqrt3}2$ and ${\exp\left(\frac{i\pi}{4}\right)}=\frac{1+i}{\sqrt2}$.
\[cosecants\] With the same notation as in $(\ref{cconstants})$, the following formulas hold: $$\begin{aligned}
{\exp\left(\frac{i\pi}{5}\right)}{&\!\!=\!\!&}\phi\;\frac{1+i\,\psi^\star}{4\,\sqrt5},\hspace{78pt}
{\exp\left(\frac{2i\pi}{5}\right)}{\;\,=\;\,}\phi^\star\,\frac{1+i\,\psi}{4\,\sqrt5},\\
{\exp\left(\frac{i\pi}{8}\right)}{&\!\!=\!\!&}\frac{\sqrt{\sqrt2+1}+i\sqrt{\sqrt2-1}}{2^{3/4}},\hspace{28pt}
{\exp\left(\frac{i\pi}{12}\right)}{\;\,=\;\,}\frac{\sqrt3+1+i\left(\sqrt3-1\right)}{2\,\sqrt2},\\
{\exp\left(\frac{i\pi}{15}\right)}{&\!\!=\!\!&}\phi^\star\;\frac{\sqrt3\,\psi+1+i\left(\psi-\sqrt3\right)}{8\,\sqrt5},\quad
{\exp\left(\frac{2i\pi}{15}\right)}{\;\,=\;\,}\phi\;\frac{\sqrt3\,\psi^\star+1+i\left(\psi^\star-\sqrt3\right)}{8\,\sqrt5},\\
{\exp\left(\frac{4i\pi}{15}\right)}{&\!\!=\!\!&}\phi^\star\;\frac{\sqrt3\,\psi-1+i\left(\psi+\sqrt3\right)}{8\,\sqrt5},\quad
{\exp\left(\frac{7i\pi}{15}\right)}{\;\,=\;\,}\phi\;\frac{\sqrt3\,\psi^\star-1+i\left(\sqrt3-\psi^\star\right)}{8\,\sqrt5},\\
{\exp\left(\frac{i\pi}{20}\right)}{&\!\!=\!\!&}\sqrt{\phi^\star}\;\frac{\psi+\sqrt5+i\left(\psi-\sqrt5\right)}{4\,\sqrt5},\quad
{\exp\left(\frac{3i\pi}{20}\right)}{\;\,=\;\,}\sqrt{\phi}\;\frac{\sqrt5+\psi^\star+i\left(\sqrt5-\psi^\star\right)}{4\,\sqrt5},\\
{\exp\left(\frac{i\pi}{24}\right)}{&\!\!=\!\!&}\frac{\sqrt{2\sqrt2+\sqrt3+1}+i\,\sqrt{2\sqrt2-\sqrt3-1}}{2^{5/4}},\\
{\exp\left(\frac{7i\pi}{24}\right)}{&\!\!=\!\!&}\frac{\sqrt{2\sqrt2-\sqrt3+1}+i\,\sqrt{2\sqrt2+\sqrt3-1}}{2^{5/4}},\\
{\exp\left(\frac{i\pi}{60}\right)}{&\!\!=\!\!&}\phi^\star\;\frac{\left(\sqrt3+1\right)\left(\psi-\sqrt3+2\right)+i
\left(\sqrt3-1\right)\left(\sqrt3-\psi+2\right)}{8\,\sqrt{10}},\\
{\exp\left(\frac{7i\pi}{60}\right)}{&\!\!=\!\!&}\phi\;\frac{\left(\sqrt3-1\right)\left(\psi^\star\!+\sqrt3+2\right)+i
\left(\sqrt3+1\right)\left(\sqrt3+\psi^\star\!-2\right)}{8\,\sqrt{10}},\\
{\exp\left(\frac{13i\pi}{60}\right)}{&\!\!=\!\!&}\phi\;\frac{\left(\sqrt3+1\right)\left(\psi^\star\!-\sqrt3+2\right)+i
\left(\sqrt3-1\right)\left(\sqrt3-\psi^\star\!+2\right)}{8\,\sqrt{10}},\\
{\exp\left(\frac{19i\pi}{60}\right)}{&\!\!=\!\!&}\phi^\star\;\frac{\left(\sqrt3-1\right)\left(\psi+\sqrt3+2\right)+i
\left(\sqrt3+1\right)\left(\sqrt3+\psi-2\right)}{8\,\sqrt{10}}.\\
$$
[[**Proof.** ]{}]{}One can deduce the first two formulas by checking the sign of real and imaginary parts on their right-hand sides, and checking the respective equations $x^5\pm 1=0$. The remaining formulas can be consequently deduced by inspecting the values of $$\begin{aligned}
{\exp\left(\frac{i\pi}{8}\right)}^2,\ {\exp\left(\frac{i\pi}{12}\right)}{\exp\left(\frac{i\pi}{4}\right)},\
{\exp\left(\frac{i\pi}{15}\right)}{\exp\left(\frac{i\pi}{3}\right)},\ {\exp\left(\frac{i\pi}{15}\right)}^2,\
{\exp\left(\frac{2i\pi}{15}\right)}^2,\\ {\exp\left(\frac{2i\pi}{15}\right)}{\exp\left(\frac{i\pi}{3}\right)},\quad
{\exp\left(\frac{i\pi}{20}\right)}{\exp\left(\frac{i\pi}{5}\right)},\quad
{\exp\left(\frac{3i\pi}{20}\right)}{\exp\left(\frac{i\pi}{4}\right)},\\
{\exp\left(\frac{i\pi}{24}\right)}^2,\quad{\exp\left(\frac{i\pi}{24}\right)}{\exp\left(\frac{i\pi}{4}\right)},\quad
{\exp\left(\frac{i\pi}{60}\right)}{\exp\left(\frac{i\pi}4\right)},\\
{\exp\left(\frac{i\pi}{12}\right)}{\exp\left(\frac{i\pi}{5}\right)},
\quad{\exp\left(\frac{i\pi}{60}\right)}{\exp\left(\frac{i\pi}5\right)},\quad{\exp\left(\frac{7i\pi}{60}\right)}{\exp\left(\frac{i\pi}5\right)}.\end{aligned}$$ Simplification of each exponential expression relates the respective exponent value to earlier concluded exponent values, so it is enough to check those relations with substituted algebraic expressions (and sometimes the sign of the new exponent value).[$\Box$\
]{}
Now we present some expressions with employed algebraic numbers. They can be used to simplify evaluated gamma terms and to transform the sinus values in the previous Lemma.
\[algrelations\] With the same notation as in $(\ref{cconstants})$, the following formulas hold: $$\begin{aligned}
\sqrt{\sqrt{15}+\psi}\,\sqrt{\sqrt{15}-\psi}{&\!\!=\!\!&}\sqrt2\;\sqrt{\phi^\star},\hspace{46pt}
\sqrt{\sqrt{10}+\sqrt{\phi}}\,\sqrt{\sqrt{10}-\sqrt{\phi}}{\;\,=\;\,}\sqrt{\phi^\star},\\
\sqrt{\sqrt{15}+\psi^\star}\,\sqrt{\sqrt{15}-\psi^\star}{&\!\!=\!\!&}\sqrt2\;\sqrt{\phi},\hspace{42pt}
\sqrt{\sqrt{10}+\sqrt{\phi^\star}}\,\sqrt{\sqrt{10}-\sqrt{\phi^\star}}{\;\,=\;\,}\sqrt{\phi},\\
\sqrt{\sqrt{15}\pm\psi}\,\sqrt{\sqrt{15}\pm\psi^\star}{&\!\!=\!\!&}\frac{\sqrt{\phi^\star}}{\sqrt{2}}
\left(\psi\pm\sqrt3\right),\quad
\sqrt{\sqrt{10}\pm\sqrt{\phi}}\,\sqrt{\sqrt{10}\pm\sqrt{\phi^\star}}{\;\,=\;\,}\psi\pm\sqrt5,\\
\sqrt{\sqrt{15}\pm\psi}\,\sqrt{\sqrt{15}\mp\psi^\star}{&\!\!=\!\!&}\frac{\sqrt{\phi}}{\sqrt{2}}
\left(\sqrt3\pm\psi^\star\right),\quad
\sqrt{\sqrt{10}\pm\sqrt{\phi}}\,\sqrt{\sqrt{10}\mp\sqrt{\phi^\star}}{\;\,=\;\,}\sqrt5\pm\psi^\star,\\
\frac{\psi}{\sqrt5}\left(\sqrt{15}\pm\psi^\star\right){&\!\!=\!\!&}\sqrt{3}\;\psi\pm1,\hspace{92pt}
\frac{\psi^\star}{\sqrt5}\left(\sqrt{15}\pm\psi\right){\;\,=\;\,}\sqrt{3}\;\psi^\star\pm1,\\
$$ $$\begin{aligned}
\hspace{10pt}
\sqrt{\sqrt{15}\pm\psi}\,\sqrt{\sqrt{10}\pm\sqrt{\phi}}{&\!\!=\!\!&}\frac{\phi^\star}{2^{7/4}\,5^{1/4}}\,\sqrt{\sqrt3-1}\,\sqrt{\sqrt5+\sqrt3}\,\left(\sqrt3+2\pm\psi\right),\\
\sqrt{\sqrt{15}\mp\psi}\,\sqrt{\sqrt{10}\pm\sqrt{\phi}}{&\!\!=\!\!&}\frac{\phi^\star}{2^{7/4}\,5^{1/4}}\,
\sqrt{\sqrt3+1}\,\sqrt{\sqrt5-\sqrt3}\,\left(\psi\mp\sqrt3\pm2\right),\\
\sqrt{\sqrt{15}\pm\psi^\star}\,\sqrt{\sqrt{10}\pm\sqrt{\phi^\star}}{&\!\!=\!\!&}\frac{\phi}{2^{7/4}\,5^{1/4}}\,
\sqrt{\sqrt3+1}\,\sqrt{\sqrt5+\sqrt3}\,\left(\psi^\star\mp\sqrt3\pm 2\right),\\
\sqrt{\sqrt{15}\mp\psi^\star}\,\sqrt{\sqrt{10}\pm\sqrt{\phi^\star}}{&\!\!=\!\!&}\frac{\phi}{2^{7/4}\,5^{1/4}}\,\sqrt{\sqrt3-1}\,\sqrt{\sqrt5-\sqrt3}\,\left(\sqrt3+2\pm\psi^\star\right),\\
2\sqrt2\pm\sqrt3+1{&\!\!=\!\!&}\left(\sqrt2+1\right)\left(\sqrt3\mp1\right)\left(\sqrt3\pm\sqrt2\right),\\
2\sqrt2\pm\sqrt3-1{&\!\!=\!\!&}\left(\sqrt2-1\right)\left(\sqrt3\pm1\right)\left(\sqrt3\mp\sqrt2\right),\\
2\sqrt3\pm\sqrt5\pm1{&\!\!=\!\!&}\frac{\phi^\star}{2\,\sqrt{5}}\;\left(\sqrt3\pm1\right)\left(\sqrt5\pm\sqrt3\right),\\
2\sqrt3\pm\sqrt5\mp1{&\!\!=\!\!&}\frac{\phi}{2\,\sqrt{5}}\;\left(\sqrt3\mp1\right)\left(\sqrt5\pm\sqrt3\right).\end{aligned}$$ Formulas with $\pm$, $\mp$ signs represent two identities, which can be read by taking the upper signs or the lower signs respectively.
[[**Proof.** ]{}]{}The identities can be proved by direct manipulation. [$\Box$\
]{} The following Lemma is important for proving independence of the gamma values in (\[gammabasis\]) with respect to the standard equations.
\[kubert\] Let $N$ denote an integer greater than 2, and let $\varphi(N)$ denote Euler’s totient value. Let $\Sigma$ be the set of gamma values at rational points with the denominator dividing $N$. Suppose that $\Sigma_0$ is a minimal subset of $\Sigma$ which determines all other gamma values in $\Sigma$ by the standard equations. Then $\Sigma_0$ has precisely $\varphi(N)/2$ elements.
[[**Proof.** ]{}]{}This is a reformulation of Kubert’s theorem in [@kubert]. See also [@lang Chapter 2]. [$\Box$\
]{}
In the setting of the last Lemma, the set $\left\{\left.{\Gamma\!\left(\frac{k}{N}\right)}\;\right|\; \gcd(k,N)=1,\ k<\frac{N}2\right\}$ looks like a natural candidate for $\Sigma_0$. This is a false impression in general. One can check the formulas in Section \[gammaevaluations\] and notice that for $N=20,24,30,60$ gamma values at rational points with the denominator $N$ depend on fewer gamma values of (\[gammabasis\]) than $\varphi(N)/2$. In these cases, gamma values in the mentioned set are dependent.
Here we prove our main results. Along the way, we complement the set in (\[gammabasis\]) to a generating set for gamma values at rational points with the denominator dividing 120. Note that $120$ is the lowest common multiple of 24 and 60.
\[mainresults\]
1. Formulas in Section $\ref{gammaevaluations}$ hold.
2. Standard equations $(\ref{differeq})$–$(\ref{gmultiplic})$ imply that any gamma value with the denominator dividing $120$ can be expressed in terms of $(\ref{gammabasis})$ and the following $6$ gamma values: $$\label{extravals}
{\Gamma\!\left(\frac{1}{40}\right)},\quad {\Gamma\!\left(\frac{3}{40}\right)},\quad {\Gamma\!\left(\frac{7}{40}\right)},\quad {\Gamma\!\left(\frac{1}{120}\right)},\quad
{\Gamma\!\left(\frac{7}{120}\right)},\quad {\Gamma\!\left(\frac{11}{120}\right)}.$$
3. Standard equations $(\ref{differeq})$–$(\ref{gmultiplic})$ do not imply any relations[^2] between gamma values in $(\ref{gammabasis})$.
[[**Proof.** ]{}]{}For $x\in{\mbox{\bf Q}}$, let $R(x)$ denote reflection formula (\[reflection\]), and let $M_n(x)$ denote multiplication formula (\[gmultiplic\]). Consider the following sequence of formulas: $$\begin{aligned}
\label{eqs1}
R\!\left(\frac12\right), R\!\left(\frac13\right), R\!\left(\frac14\right),
R\!\left(\frac15\right), R\!\left(\frac25\right), M_2\!\left(\frac16\right),
R\!\left(\frac16\right), M_2\!\left(\frac18\right), R\!\left(\frac18\right),
R\!\left(\frac38\right),\\
M_2\!\left(\frac15\right),\ M_2\!\left(\frac1{10}\right),\
R\!\left(\frac1{10}\right),\ R\!\left(\frac3{10}\right),\
M_3\!\left(\frac1{12}\right),\ M_2\!\left(\frac1{12}\right),\
R\!\left(\frac1{12}\right),\ R\!\left(\frac5{12}\right),\\
M_3\!\left(\frac1{15}\right),\ R\!\left(\frac1{15}\right),\
R\!\left(\frac4{15}\right),\ M_5\!\left(\frac1{15}\right),\
M_3\!\left(\frac2{15}\right),\ R\!\left(\frac2{15}\right),\
R\!\left(\frac7{15}\right),\\
M_2\!\left(\frac1{20}\right),\ R\!\left(\frac1{20}\right),\
R\!\left(\frac9{20}\right),\ M_5\!\left(\frac1{20}\right),\
M_2\!\left(\frac3{20}\right),\ R\!\left(\frac3{20}\right),\
R\!\left(\frac7{20}\right),\\
M_3\!\left(\frac1{24}\right),\ M_2\!\left(\frac1{24}\right),\
M_2\!\left(\frac5{24}\right),\ R\!\left(\frac1{24}\right),\
R\!\left(\frac5{24}\right),\ R\!\left(\frac7{24}\right),\
R\!\left(\frac{11}{24}\right),\\
M_2\!\left(\frac1{15}\right),\ M_2\!\left(\frac2{15}\right),\
M_2\!\left(\frac1{30}\right),\ M_2\!\left(\frac7{30}\right),\
R\!\left(\frac1{30}\right),\ R\!\left(\frac7{30}\right),\
R\!\left(\frac{11}{30}\right),\ R\!\left(\frac{13}{30}\right),\\
M_3\!\left(\frac1{60}\right),\ M_3\!\left(\frac7{60}\right),\
M_2\!\left(\frac1{60}\right),\ M_2\!\left(\frac7{60}\right),\
M_2\!\left(\frac{11}{60}\right),\ R\!\left(\frac{13}{60}\right),\
M_2\!\left(\frac{13}{60}\right),\\
R\!\left(\frac1{60}\right),\ R\!\left(\frac7{60}\right),\
R\!\left(\frac{11}{60}\right),\ R\!\left(\frac{17}{60}\right),\
R\!\left(\frac{19}{60}\right),\ R\!\left(\frac{23}{60}\right),\
R\!\left(\frac{29}{60}\right).\end{aligned}$$ We claim that these formulas, seen as equations in gamma values from the set (\[gammaset\]), have a unique solution if the gamma values in (\[gammabasis\]) are assumed to be known. To prove this claim, note that the first 14 formulas, up till $R\!\left(\frac3{10}\right)$, determine consequently the gamma values at $$\label{gamvals1}
\frac12,\ \frac23,\ \frac34,\ \frac45,\ \frac35,\ \frac16,\ \frac56,\
\frac58,\ \frac78,\ \frac38,\ \frac7{10},\ \frac1{10},\ \frac9{10},\
\frac3{10}.$$ Each of those 14 formulas relates the respective gamma value to earlier concluded gamma values and the gamma values in (\[gammabasis\]), like in the proof of Lemma \[cosecants\]. The next 4 formulas, up till $R\!\left(\frac5{12}\right)$, express the products ${\Gamma\!\left(\frac{1}{12}\right)}{\Gamma\!\left(\frac{5}{12}\right)}$, ${\Gamma\!\left(\frac{1}{12}\right)}{\Gamma\!\left(\frac{7}{12}\right)}$, ${\Gamma\!\left(\frac{1}{12}\right)}{\Gamma\!\left(\frac{11}{12}\right)}$, ${\Gamma\!\left(\frac{5}{12}\right)}{\Gamma\!\left(\frac{7}{12}\right)}$ in terms of gamma values in (\[gammabasis\]) and at the points in (\[gamvals1\]). Straightforward manipulation of those 4 formulas expresses the gamma values at $\frac1{12}, \frac5{12},
\frac7{12}, \frac{11}{12}$ in terms of (\[gammabasis\]) and the earlier values. Similarly, the next 3 formulas, up till $R\!\left(\frac4{15}\right)$, consequently determine ${\Gamma\!\left(\frac{11}{15}\right)}$, ${\Gamma\!\left(\frac{14}{15}\right)}$, ${\Gamma\!\left(\frac{4}{15}\right)}$; and then the subsequent 4 formulas all together determine ${\Gamma\!\left(\frac{2}{15}\right)}$, ${\Gamma\!\left(\frac{7}{15}\right)}$, ${\Gamma\!\left(\frac{8}{15}\right)}$, ${\Gamma\!\left(\frac{13}{15}\right)}$. In the same way, the next formulas $M_2\!\left(\frac1{20}\right)$, $R\!\left(\frac1{20}\right)$,$R\!\left(\frac9{20}\right)$ consequently determine ${\Gamma\!\left(\frac{11}{20}\right)}$, ${\Gamma\!\left(\frac{19}{20}\right)}$, ${\Gamma\!\left(\frac{9}{20}\right)}$; and then the following 4 formulas[^3] all together determine ${\Gamma\!\left(\frac{3}{20}\right)}$, ${\Gamma\!\left(\frac{7}{20}\right)}$, ${\Gamma\!\left(\frac{13}{20}\right)}$, ${\Gamma\!\left(\frac{17}{20}\right)}$. The remaining formulas, starting from $M_3\!\left(\frac1{24}\right)$, consequently determine gamma values at $$\begin{aligned}
&{\displaystyle}\frac{17}{24},\ \frac{13}{24},\ \frac5{24},\ \frac{23}{24},\
\frac{19}{24},\ \frac7{24},\ \frac{11}{24},\ \frac{17}{30},\ \frac{19}{30},\
\frac1{30},\ \frac7{30},\ \frac{29}{30},\ \frac{23}{30},\ \frac{11}{30},\ \frac{13}{30},\\
&{\displaystyle}\frac{41}{60},\ \frac{47}{60},\ \frac{31}{60},\ \frac{37}{60},\
\frac{11}{60},\ \frac{13}{60},\ \frac{43}{60},\ \frac{59}{60},\
\frac{53}{60},\ \frac{49}{60},\ \frac{17}{60},\ \frac{19}{60},\
\frac{23}{60},\ \frac{29}{60}.\end{aligned}$$ We see that formulas are independent, and that they unique determine the mentioned gamma values. Also, the gamma values in (\[gammabasis\]) and the consequently concluded gamma values exhaust all elements of the set in (\[gammaset\]). The claim follows.
To prove the first statement of the theorem, it is enough now to check that evaluations in Section \[gammaevaluations\] are compatible with the sequence of formulas introduced at the beginning of this proof. Identities in Lemmas \[cosecants\] and \[algrelations\] are very helpful in these computations.
Here we show the second statement of the Theorem. We need to check the gamma values at rational points with the denominators 40 and 120. The equations $$M_2\!\left(\frac1{40}\right),\ M_2\!\left(\frac3{40}\right),\
M_2\!\left(\frac7{40}\right),\ R\!\left(\frac{19}{40}\right),\
M_5\!\left(\frac3{40}\right),\ M_2\!\left(\frac{11}{40}\right)$$ determine consequently the gamma values at $\frac{21}{40}$, $\frac{23}{40}$, $\frac{27}{40}$, $\frac{19}{40}$, $\frac{11}{40}$, $\frac{31}{40}$ in terms of (\[gammabasis\]) and (\[extravals\]). After this, other gamma values at rational points with the denominator 40 are determined by reflection formulas. Similarly, the equations $$\begin{aligned}
M_3\!\left(\frac1{120}\right),\ M_3\!\left(\frac7{120}\right),\
M_3\!\left(\frac{11}{120}\right),\ M_2\!\left(\frac1{120}\right),\
M_2\!\left(\frac7{120}\right),\ M_2\!\left(\frac{11}{120}\right),\
M_2\!\left(\frac{31}{120}\right),\\
M_2\!\left(\frac{41}{120}\right),\ M_2\!\left(\frac{47}{120}\right),\
R\!\left(\frac{59}{120}\right),\ M_5\!\left(\frac{11}{120}\right),\
M_3\!\left(\frac1{40}\right),\ M_2\!\left(\frac{23}{120}\right),\
M_2\!\left(\frac{43}{120}\right)\end{aligned}$$ determine consequently the gamma values at $$\label{gamvals2}
\frac{41}{120},\ \frac{47}{120},\ \frac{91}{120},\ \frac{61}{120},\
\frac{67}{120},\ \frac{71}{120},\ \frac{31}{120},\ \frac{101}{120},\
\frac{107}{120},\ \frac{59}{120},\ \frac{83}{120},\ \frac{43}{120},\
\frac{23}{120},\ \frac{103}{120}.$$ After this, other gamma values at rational points with the denominator 120 are determined by reflection formulas.
Now we show the third statement of the Theorem. We apply Lemma \[kubert\] with $N=120$ and conclude that the generating set of 16 gamma values in (\[gammabasis\]) and (\[extravals\]) cannot be made smaller. Therefore the standard equations do not imply any relations between those 16 values. This certainly applies to the subset (\[gammabasis\]) of gamma values. [$\Box$\
]{}
Explicit expressions of Chapter \[gammaevaluations\] and of all gamma values at rational points with the denominator dividing 120, in terms of (\[gammabasis\]) and (\[extravals\]), are available as small [Mathematica]{} and [Maple]{} packages via webpage [@homepage]. In those packages, the list (\[algnumbers\]) of algebraic numbers for multiplicative expressions of the gamma values is extended by $$\sqrt6\pm\sqrt5,\quad \sqrt{10}\pm3,\quad \sqrt{\phi}\pm\sqrt5,\quad
\sqrt5\pm\sqrt{\phi^\star},\quad \sqrt{\phi}\pm\sqrt3,\quad
\sqrt3\pm\sqrt{\phi^\star}.$$
Here we discuss briefly algebraic independence of gamma values. Rohrlich’s conjecture [@diophantine Section 3.3] implies that all multiplicative relations between gamma values at rational points are implied by the standard equations. The stronger Lang’s conjecture [@lang Ch. 2] implies that all algebraic relations between gamma values at rational points are implied by the standard equations. If these conjectures are true, we have (respectively) multiplicative or algebraic independence of the distinguished gamma values in (\[gammabasis\]). Analogues of these conjectures are proved for the Thakur’s gamma function in positive characteristic [@gammap]. It is known that all $\overline{{\mbox{\bf Q}}}$-linear relations between the beta values ${\rm B}(a,b)$ with $a,b,a+b\in{\mbox{\bf Q}}\setminus{\mbox{\bf Z}}$ are implied by the standard equations [@wolfart]. Chudnovsky proved that ${\Gamma\!\left(\frac{1}{3}\right)}$ and ${\Gamma\!\left(\frac{1}{4}\right)}$ are transcendental over ${\mbox{\bf Q}}(\pi)$; see [@waldschmidt]. Algebraicity of gamma terms is determined, assuming Rohrlich’s conjecture, by Koblitz-Ogus criterion [@koblitzo].
Application to algebraic hypergeometric functions {#application}
=================================================
It is well-known that Gauss hypergeometric functions can be evaluated at some points in terms of the gamma function. The most important formula is the Gauss’ identity [@specfaar Theorem 2.2.2]: $$\label{gaussid}
{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{a,\;b\; \atop c}\right| \,1\, \right) }=\frac{\Gamma(c)\,\Gamma(c-a-b)}{\Gamma(c-a)\,\Gamma(c-b)},
\qquad \mbox{if Re}(c-a-b)>0.$$ Akin to this identity, linear relations between the 24 Kummer’s solutions of the hypergeometric differential equation (and analytic continuation formulas for the Gauss hypergeometric function) involve similar gamma terms. An example is [@specfaar Corollary 2.3.3]: $$\begin{aligned}
{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{a,\,b\, \atop c}\right| \,x \right) }&=&\frac{\Gamma(c)\,\Gamma(c-a-b)}{\Gamma(c-a)\,\Gamma(c-b)}
\;{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{a,\;b\, \atop a+b+1-c}\right| \,1-x \right) }\\
&&\!+\frac{\Gamma(c)\,\Gamma(a+b-c)}{\Gamma(a)\,\Gamma(b)}\,(1-x)^{c-a-b}
\;{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{c-a,\;c-b\, \atop c+1-a-b}\right| \,1-x \right) }.\end{aligned}$$
Our formulas in Section \[gammaevaluations\] can be used to evaluate widely used instances of the Gauss hypergeometric function most explicitly. In particular, evaluation of algebraic Gauss hypergeometric functions with (\[gaussid\]) requires gamma values at rational points with the denominator dividing 24 or 60; see [@schwartz], [@kato], [@alggauss]. The formulas in Section \[gammaevaluations\] are precisely sufficient to evaluate algebraic Gauss hypergeometric functions at $x=1$. Here are a few examples: $$\begin{aligned}
{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{\frac14,\,-\frac1{12}\, \atop \frac23}\right| \,1\, \right) }{&\!\!=\!\!&}\frac{{\Gamma\!\left(\frac{1}{2}\right)}{\Gamma\!\left(\frac{2}{3}\right)}}{{\Gamma\!\left(\frac{3}{4}\right)}{\Gamma\!\left(\frac{5}{12}\right)}}{\;\,=\;\,}\frac{\sqrt{\sqrt3+1}}{2^{1/4}\,3^{3/8}},\\
{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{\frac5{24},\,-\frac1{24}\, \atop \frac23}\right| \,1\, \right) }{&\!\!=\!\!&}\frac{{\Gamma\!\left(\frac{1}{2}\right)}{\Gamma\!\left(\frac{2}{3}\right)}}{{\Gamma\!\left(\frac{11}{24}\right)}{\Gamma\!\left(\frac{17}{24}\right)}}{\;\,=\;\,}\frac{\sqrt{\sqrt3+\sqrt2}}{2^{1/12}\,\sqrt3},\\
{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{\frac{11}{60},\,-\frac{1}{60}\, \atop \frac23}\right| \,1\, \right) }{&\!\!=\!\!&}\frac{{\Gamma\!\left(\frac{1}{2}\right)}{\Gamma\!\left(\frac{2}{3}\right)}}{{\Gamma\!\left(\frac{29}{60}\right)}{\Gamma\!\left(\frac{41}{60}\right)}}{\;\,=\;\,}\frac{\sqrt{\phi^\star}\,\sqrt{\sqrt3+1}
\,\sqrt{\sqrt5+\sqrt3}}{2\,\sqrt3\;5^{7/24}},\\
{{}_{2}\mbox{\rm F}_{\!1}\!
\left(\left.{\frac3{10},\,-\frac1{30}\, \atop \frac35}\right| \,1\, \right) }{&\!\!=\!\!&}\frac{{\Gamma\!\left(\frac{1}{3}\right)}{\Gamma\!\left(\frac{3}{5}\right)}}{{\Gamma\!\left(\frac{3}{10}\right)}{\Gamma\!\left(\frac{19}{30}\right)}}{\;\,=\;\,}\frac{\sqrt{\sqrt{15}+\psi}}{2^{19/30}\,3^{1/20}\,5^{1/3}}.\end{aligned}$$ More of these evaluations are independently presented in [@kato]. Explicit expressions for algebraic Gauss hypergeometric functions are given in [@alggauss].
Gamma values and (hyper)elliptic integrals {#gammaelliptic}
==========================================
As is known [@borwzu], some gamma values can be expressed in terms of special values of the elliptic $\bf K$-function (i.e., [*complete elliptic integral of the first kind*]{}). The advantage of doing this is that numerical values of the elliptic $\bf K$-function can be very effectively computed using the arithmetic-geometric mean; see [@specfaar Section 3.2] and [@borwbai pg. 137].
Here we present direct expressions for most of gamma values from (\[gammabasis\]) in terms of the elliptic $\bf K$-function. By combining the data in [@wolfram pages EllipticIntegralSingularValue.html, EllipticLambdaFunction.html] and our formulas in Section \[gammaevaluations\] we get the following evaluations: $$\begin{aligned}
{\Gamma\!\left(\frac{1}{3}\right)}{&\!\!=\!\!&}\frac{\pi^{1/3}\,2^{7/9}}{3^{1/12}}\;{\mbox{\bf K}\!\left(\frac{\sqrt{3}-1}{2\,\sqrt2}\right)}^{1/3},\\
{\Gamma\!\left(\frac{1}{4}\right)}{&\!\!=\!\!&}2\,\pi^{1/4}\;{\mbox{\bf K}\!\left(\frac{1}{\sqrt2}\right)}^{1/2},\\
{\Gamma\!\left(\frac{1}{8}\right)}{&\!\!=\!\!&}\pi^{1/8}\,2^{17/8}\;{\mbox{\bf K}\!\left(\frac{1}{\sqrt2}\right)}^{1/4}\,{\mbox{\bf K}\!\left(\sqrt2-1\right)}^{1/2},\\
{\Gamma\!\left(\frac{1}{15}\right)}{&\!\!=\!\!&}\frac{\pi^{1/6}\,3^{29/60}\,5^{1/24}\,\sqrt{\phi^\star}\,\sqrt{\psi+\sqrt3}}
{2^{1/9}}\;{\Gamma\!\left(\frac{1}{5}\right)}^{1/2}{\Gamma\!\left(\frac{2}{5}\right)}^{-1/2}{\mbox{\bf K}\!\left(\frac{\sqrt3-1}{2\,\sqrt2}\right)}^{1/6}\\
&&\times\;
{\mbox{\bf K}\!\left(\frac{\left(2-\sqrt3\right)\left(3-\sqrt5\right)\left(\sqrt5-\sqrt3\right)}{8\,\sqrt2}\right)}^{1/2},\\
{\Gamma\!\left(\frac{1}{20}\right)}{&\!\!=\!\!&}\frac{2^{9/40}\,5^{1/8}\,\phi^{5/8}\,\sqrt{\psi^\star+1}}{\pi^{1/4}}
\;{\Gamma\!\left(\frac{1}{5}\right)}^{1/2}{\Gamma\!\left(\frac{2}{5}\right)}^{1/2}{\mbox{\bf K}\!\left(\sqrt{\frac12-\sqrt{\sqrt5-2}}\right)}^{1/2},\\
{\Gamma\!\left(\frac{1}{24}\right)}{&\!\!=\!\!&}\pi^{1/24}\,2^{89/36}\,3^{25/48}\,\sqrt{\sqrt2+1}\left(\sqrt3-1\right)^{1/4}
\,{\mbox{\bf K}\!\left(\frac{1}{\sqrt2}\right)}^{1/4}{\mbox{\bf K}\!\left(\frac{\sqrt{3}-1}{2\,\sqrt2}\right)}^{1/3}\\
&&\times\;{\mbox{\bf K}\!\left((2-\sqrt3)(\sqrt3-\sqrt2)\right)}^{1/2}.
$$
Other gamma values in (\[gammabasis\]) can be expressed in terms of hyperelliptic integrals. For example, consider the integrals: $$H_1=\int_0^1\frac{dz}{\sqrt{1-z^5}},\qquad\qquad
H_2=\int_0^1\frac{z\,dz}{\sqrt{1-z^5}}.$$ Note that the two differentials under integration form a basis for the space of holomorphic differentials on the genus 2 curve $y^2=x^5-1$. We have ${\rm
B}\left(\frac15,\frac12\right)=5\,H_1$, ${\rm
B}\left(\frac25,\frac12\right)=5\,H_2$; this can be seen after the substitution $t\mapsto z^5$ in the standard definition [@specfaar Definition 1.1.3] of the beta integral. From the two beta values we conclude $${\Gamma\!\left(\frac{1}{5}\right)}=\pi^{1/5}\,2^{19/50}\,\sqrt5\,\phi^{1/10}\,H_1^{2/5}\,H_2^{1/5},\quad
{\Gamma\!\left(\frac{2}{5}\right)}=\pi^{2/5}\,2^{4/25}\,\phi^{1/5}\,H_1^{-1/5}\,H_2^{2/5}.$$
To get similar expressions for gamma values at rational points with the denominator 60, one may substitute $t\mapsto z^{30}$ into the beta integrals ${\rm B}\left(\frac1{60},\,\frac12\right)$ and ${\rm
B}\left(\frac7{60},\,\frac12\right)$ and get hyperelliptic integrals on the genus 15 curve $y^2=x^{31}-x$. Possibly, there are integrals on lower genus curves related to those gamma values.
[AAR]{} G.E. Andrews, R. Askey, R. Roy, [*Special Functions*]{}, Cambridge Univ. Press, Cambridge, 1999. G.W. Anderson, W.D. Brownawell, M.A. Papanikolas, [*Determination of the algebraic relations among special $\Gamma$-values in positive charateristic*]{}, accepted by Annals of Mathematics; available at [http://arxiv.org/abs/math.NT/0207168]{}. J.M. Borwein, D.H. Bailey, [*Mathematics by Experiment; Plausible Reasoning in the 21st Century*]{}, A.K. Peters, Natick Ma, 2003. J.M. Borwein, I.J. Zucker, [*Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind*]{}, IMA J. of Numer Analysis, 12(1992), pg. 519–526. R. Campbell, [*Les intégrales eulériennes et leurs applications*]{}, Dunod, Paris, 1966. P. Das, [*Algebraic gamma monomials and double coverings of cyclotomic fields*]{}, Trans. Amer. Math. Soc., Vol. 352, No. 8 (2000), pg. 3557–3594. P. Deligne, [*Valuers de fonctions $L$ et périodes d’intégrales*]{}, Proc. Sympos. Pure Math., 33 (1979), part 2, pg. 313-346. M. Kato, [*Connection formulas for algebraic hypergeometric functions*]{}, preprint of Ryukyus Univ., 2004; submitted to the Kyushu Journal of Mathematics. N. Koblitz, A. Ogus, [*Algebraicity of some products of values of the $\Gamma$ function*]{}, Appendix to the reference [@deligne], pg. 343-346. J. Kool, [*Gamma Values*]{}, website [http://www.jgk.org/math/gamma-values.html]{}. T. H. Koornwinder, N. Temme, R. Vidunas, [*Algorithmic Methods for Functions by Computer Algebra*]{}, NWO research project 613-06-565 website, [http://staff.science.uva.nl/\~thk/specfun/compalg.html]{}. D. Kubert, [*The universal ordinary distribution*]{}, Bull. Soc. Math. France, 107 (1979), pg. 179–202. M. Kontsevich, D. Zagier, [*Periods*]{}, in B. Engquist, W. Schmid (Ed.) [*Mathematics Unlimited–2001 and Beyond*]{}, Springer, Berlin, 2001, pg. 771–808. S. Lang, [*Cyclotomic Fields I and II*]{}, Graduate Texts in Mathematics, No 121, Springer-Verlag, New York 1990. A. Selberg, S. Chowla, [*On Epstein’s zeta function*]{}, J. Reine Angew. Math., 227 (1967), pg. 86–110. H. Schwarz, [*Ueber diejenigen [F]{}alle, in welchen die [G]{}aussische hypergeometrische [R]{}eihe eine algebraische [F]{}unktion ihres vierten [E]{}lements darstelt*]{}, J. Reine Angew. Math., 75 (1872), pg. 292–335. R. Vidunas, [*Darboux evaluations of algebraic Gauss hypergeometric functions*]{}, preprint, Kyushu university, 2004. M. Waldschmidt, [*Les travaux de G.V. Chudnovsky sur les nombres transcendants*]{}, in [*Séminaire Bourbaki, Vol. 1975/76, 28e année, Exp. No 488*]{}, pg. 274–292; Lecture Notes in Math., Vol. 567, Springer, Berlin, 1977. M. Waldschmidt, [*Open Diophantine Problems*]{}, to appear in Moscow Mathematical Journal Vol. 4 No. 1 (2004); available at [http://arxiv.org/math.NT/0312440]{}. Wolfram Research Mathworld website, [http://mathworld.wolfram.com]{}. J. Wolfart, G. Wüstholz, [*Der Überlagerungradius gewisser algerbaischer Kurven und die Werte de Betafunktion an rationalen Stellen*]{}, Math. Ann. 273 (1985), pg. 1–15. I.J. Zucker, [*The evaluation in terms of $\Gamma$-functions of the periods of elliptic curves admitting complex multiplication*]{}, Proc. Camb. Phil. Soc, 82 (1977), pg. 111–118.
[^1]: Supported by the 21 Century COE Programme “Development of Dynamic Mathematics with High Functionality” of the Ministry of Education, Culture, Sports, Science and Technology of Japan.
[^2]: This statement also holds for the total set of 16 gamma values in (\[gammabasis\]) and (\[extravals\]).
[^3]: Gamma values cannot be determined entirely consequently. As was noted in [@pdas], some relations between gamma values are implied by the standard equations up to taking square roots of both sides of an equality.
| 2023-09-16T01:26:35.434368 | https://example.com/article/3743 |
Present Perfect
2008-4-209:01 am
I’m sure smart people have worked on the xdg spec, but the naming of the xdg dirs illustrates one of my pet peeves – choosing directory names that aren’t well-thought-out.
Among others, I have Music, Videos, and Pictures.
Pictures is not the worst. I guess it’s a little quaint to not be talking about Images instead on a computer, but at least “picture” covers more or less the full range of items it wants to capture.
Videos is not too bad either. The pluralisation makes me puke, but I guess that’s a personal dislike.
But against these two, Music is just plain terrible. I’m pretty sure my Bill Hicks albums are in no way Music. Neither are my radio podcasts. Or the audio books that I luckily don’t have. Never mind that it’s a non-plural word and thus inconsistent with the others.
Elisa is now using the xdg dirs, it seems. It is neither better nor worse than what it had before. I think before it was labeling audio as Music as well, and video as Movies (forgetting the fact that there are also tv series, video clips, camera clips, …)
I’ve always done audio/video/image, which seems to me the most straightforward and concise. Some people argue that (while video is fine) audio is too technical. I guess I’m not a usability expert – I would expect any human being that understands the word video to understand the word audio as well, especially when presented in the exact same context.
I guess this is one spec that is going to keep me a grumpy old man for the rest of my Linux days :)
Cool, seems like I am not the only one who is obsessed by this stuff. I spend quite a lot of time figuring out the perfect way to organize my home directory and how to name the directories in it. I also use ‘audio’ and ‘video’ but I use ‘pictures’ to store pictures (photos). Images can be more then just pictures/photos so i store these in other places: icons and other images for specific projects belong to the projects themselves, wallpapers have their own directory (because a wallpaper is conceptually as distinct from a photograph then a photograph is from a song imo)
One more spec designed against Windows behaviour : My Documents, My Images, My Videos, My Music …
Again, they are hardcoded path location adn expect people to put the documents tehere, which is totally wrong !
When I’m writting an article for a magazine, I will put my screenshots in the same dir than the one which contains the OO document.
IMHO, theses directories ( Audio, Images, Videos ) should be virtual directories. They should be static beagle/tracker/strigi/nepomuk queries. And so when for example you enter in Videos directory, you will have all the videos files indexed in your home directory and others directories ( think about remote or removable storage were all you films are stored )
I don’t expect other people to be as anal as me though. I mean, honestly, will normal users actually create a music directory inside of audio? Normal users would probably be perfectly happy putting sermons in a Music directory. Remember, there are still people in the world that store all their photos on their desktop…
If it makes you feel better, think of how many times have you seen Windows users not use their “My Music” and “My Pictures” folders and use something like a “Music” folder instead (for me, that is the majority).
This “usability” spec isn’t for forcing a certain behavior on you, it’s for programs to actually be able to follow what your usage is. Instead of having an app that just stuffs music in ~/Music, they now have a sane way to find out that you actually keep your music in ~/audio_band_excitation or whatever. I think you’re missing the point of the spec completely.
Speaking of XDG, what about dot-{files,dirs}? Running a typical gnome session (and some fdo technology), I have tons of them in $HOME. What happened with ~/.config and ~/.local? Hardly anything uses it.
@Dan: I don’t think I miss the point of the spec. The point of the spec is for apps to know where to go look for some common kinds of files the user creates.
I do think you missed the point of my entry. To make it more clear – if I write a sound recorder, where should it record the sounds to by default ? Don’t tell me they should go in Music or XDG_MUSIC_DIR.
@Thomas. I use ardour for working on audio projects and i use eclipse for programming. so i structure it like this:
~/workspaces/ardour/*audio projects go here, each in it’s own directory*
~/workspaces/eclipse/*programming projects go here, each in it’s own directory*
(although obviously I can sometimes edit the eclipse projects with other editors such as vim or joe. but i still think it’s better to name these directories after the “environment” – eg eclipse – that defines how the directories are structured then more general names such as programming or audio-work. because different programs can expect different formats/directory layouts)
My own little dirty scripts or tools go in ~/scripts or ~/bin. These directories should not contain anything that can’t be generated from an eclipse project directory (or downloaded from the net). Likewise, after finishing an audio project (not that I ever get to that ;-) I could mix down music and then put it in my ~/audio directory, or hell for things like this I would even put symlinks in my audio folder pointing to the mixed down music in my audio project directory.
As for the standup comedy, I don’t see what could be wrong with a structure like this?
(of course you could have comedie movies. these still belong in movies) | 2024-01-17T01:26:35.434368 | https://example.com/article/9372 |
// This is a generated file from running the "createIcons" script. This file should not be updated manually.
import React, { forwardRef } from "react";
import { FontIcon, FontIconProps } from "@react-md/icon";
export const WrapTextFontIcon = forwardRef<HTMLElement, FontIconProps>(
function WrapTextFontIcon(props, ref) {
return (
<FontIcon {...props} ref={ref}>
wrap_text
</FontIcon>
);
}
);
| 2023-09-07T01:26:35.434368 | https://example.com/article/6281 |
Q:
How to determine if a table relationship is bidirectional or unidirectional in Doctrine 2?
I am in the process of upgrading from Doctrine 1.1.4 to Doctrine 2.0.6 in my Zend application.
Currently, I am working on mapping the associations between entities. In Doctrine 2's Documentation it says 'relationships maybe bidirectional or unidirectional. I am confused as to what these terms mean within the given context.
How do I determine if a relationship is unidirectional or bidirectional?
Appreciate the help.
A:
A relationship is bidirectional if both entities contain a reference to the other.
If you omit one of those references, it's unidirectional.
Consider a typical "posts" and "tags" schema. Typically, you'd implement a bidirectional association:
<?php
class Post {
// ...
/**
* @ManyToMany(targetEntity="Tag",inversedBy="posts")
*/
protected $tags;
// ...
}
class Tag {
// ...
/**
* @ManyToMany(targetEntity="Post",mappedBy="tags")
*/
protected $posts
// ...
}
Now, imagine you decided you never (or rarely) needed to answer questions like "Which posts have Tag 'foo'?". You could omit the $posts association in your Tag entity, converting it to a unidirectional association, and take some load off of the ORM.
You could still answer that kind of question, but you'd have to write code to do it.
In fact, it's probably a good way to go in Posts/Tags scenario, as you wouldn't typically be adding/removing Posts from Tags. Typically, you'd add/remove tags from posts only. You'd only ever go from Tags to Posts when looking for "all posts with tag 'x'", which could be trivially implemented in a service class of some sort.
| 2024-04-10T01:26:35.434368 | https://example.com/article/6872 |
Comparison of the effect of two types of whole mushroom (Agaricus bisporus) powders on intestinal fermentation in rats.
The effects of two types of mushroom (Agaricus bisporus; white, WM; brown, BM) powders on intestinal fermentation in rats were investigated in terms of the physical characteristics of animals and by bacterial and HPLC analyses of cecal contents. Short-chain fatty acid levels were found to be significantly higher in the WM group than in the BM and the control (CN) groups; coliform bacteria levels in the BM group were significantly lower than those in the CN group, with the WM group inducing an apparent but insignificant decrease in coliforms. Anaerobe levels in the WM group were significantly higher than those in the CN group and, compared with the CN group, the BM and WM groups exhibited significantly increased feces weight and cecum weight, respectively. These results indicate that the mushroom powders, and in particular the WM powder, have beneficial effects on the intestinal environment in rats. | 2023-08-12T01:26:35.434368 | https://example.com/article/8855 |
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