Frederick H. Evans (26 June 1853, London – 24 June 1943, London) was a British photographer, primarily of architectural subjects. He is best known for his images of English and French cathedrals. Evans began his career as a bookseller, but retired from that to become a full-time photographer in 1898, when he adopted the platinotype technique for his photography. Platinotype images, with extensive and subtle tonal range, non glossy-images, and better resistance to deterioration than other methods available at the time, suited Evans' subject matter. Almost as soon as he began, however, the cost of platinum – and consequently, the cost of platinum paper for his images – began to rise. Because of this cost, and because he was reluctant to adopt alternate methodologies, by 1915 Evans retired from photography altogether.
Evans' ideal of straightforward, "perfect" photographic rendering – unretouched or modified in any way – as an ideal was well-suited to the architectural foci of his work: the ancient, historic, ornate and often quite large cathedrals, cloisters and other buildings of the English and French countryside. This perfectionism, along with his tendency to exhibit and write about his work frequently, earned for him international respect and much imitation. He ultimately became regarded as perhaps the finest architectural photographer of his, or any, era – though some professionals privately felt that the Evans' philosophy favoring extremely literal images was restrictive of the creative expression rapidly becoming available within the growing technology of the photographic field.
Frederick H. Evans is best known for his breathtaking platinum prints of architectural interiors. Before devoting his time solely to the art of photography, Evans owned a small bookshop in London where many artists and writers, including George Bernard Shaw and Aubrey Beardsley, came together. Frederick H. Evans did take some portraits of these friends, but his photographic mastery can be found in his images of English and French cathedrals. Frederick Evans worked tirelessly to use the effects of light and shade to create images with harmonized values and he achieved these masterful works of art without manipulating the negative or the print.
He wrote several articles for publications including Amateur Photographer and Photogram and exhibited his work widely. He contributed many prints to Alfred Stieglitz's Camera Work and exhibited at Stieglitz's gallery "291". Frederick Evans was a member of The Linked Ring and was named an Honorary Fellow of the Royal Photographic Society. In the 1920s platinum paper became scarce and Frederick H. Evans found he could not achieve the same rich tonal quality using silver paper so he stopped making photographs. Today Frederick Evans is considered one of the masters of pictorial photography.
Beaumont Newhall, Frederick Evans Photography, Rochester, N.Y., George Eastman House ca. 1964.
Frederick H. Evans, The library of Frederick H. Evans of London, New York, 1919.
Frederick H. Evans, Drafting room series, Peoria, Illinois : The Manual Arts Press, ca. 1913.
Illustrations prepared for the memorial edition of the Works of George Meredith : 60 photogravures and 4 collotypes of reproductions of manuscripts, London : Constable, 1911.


text:
Province updates codes of practice after prominent farm animal abuse cases
CTV Vancouver
Published Thursday, February 28, 2019 3:51PM PST
A chicken is shown after being pulled from a pile of manure at an Abbotsford, B.C. farm in April 2018.
The provincial government is updating its codes of practice to better protect B.C. farm animals from abuse.
In a statement Thursday, the Ministry of Agriculture announced the NDP has opted to adopt standards outlined by the National Farm Care Council.
"By accepting these codes of practice in their animal management practices, farmers and ranchers are making it clear that animals in their care are being treated with the utmost care and respect," Minister Lana Popham said in the statement.
The codes apply to all farm owners and employees, and provide direction for animal handling, feed and water, housing, health and welfare and husbandry, the province said. They will come into effect for poultry, fur and meat livestock in June.
"It is important that industry, government, animal welfare organizations and consumers work together to ensure the highest levels of welfare for the millions of farm animals raised in our province each year," BC SPCA CEO Craig Daniell said.
The update comes about two months after two companies and a B.C. man were charged in connection with a hidden camera investigation into chicken abuse allegations in the Fraser Valley.
The Canadian Food Inspection Agency announced a total of 38 charges in December after animal rights activists released video allegedly showing farm workers mistreating chickens. Two years ago, the farm labour company at the centre of the allegations launched a new policy that staff would wear body cameras while inside the barns.
The company is also under investigation from the BC SPCA following a disturbing video allegedly captured at egg farms in Abbotsford last year, which activists say shows widespread mistreatment.
Undercover video was also used in a cattle cruelty case that resulted in a worker serving jail time in 2017.
Companies, B.C. man charged in alleged chicken abuse in Fraser Valley
Activists say new video suggests widespread mistreatment of chickens at Fraser Valley farms
Worker in cattle cruelty case given jail time, but able to work at other farm

redpajama_set_name: RedPajamaCommonCrawl


The vast majority of drug abuse deaths involving oxycodone (96.7%) are related to the ingestion of multiple drugs, not solely oxycodone (3.3%), according to an analysis of over 1000 deaths published in the March issue of Journal of Analytical Toxicology. The March issue of the Journal of Analytical Toxicology will be available on their web site, http://www.jatox.com/jan-june03.htm on February 27, 2003.
Further, in this study of deaths involving oxycodone, the specific pain medicine OxyContin® (oxycodone hydrochloride controlled-release) Tablets was the only drug found in 12 (1.3%) of the cases. Oxycodone is a morphine-like pain medication found in dozens of analgesics sold throughout the United States.
The investigators evaluated oxycodone related deaths solicited from Medical Examiner and Coroner offices in 23 states. The results showed that the vast majority of the 1014 cases (919 or 90.6%) involved drug abuse, with the remainder of deaths due to other causes, such as cancer.
Of the drug abuse cases, 30 deaths involved oxycodone only; the remaining cases (889 or 96.7%) had multiple drugs present at autopsy.
"While abuse of any medication is dangerous, abuse of multiple drugs may be a cause for even greater concern, as there is little recognition of the added risks of abusing opioids with other drugs, such as alcohol and depressants," said Dr. Bruce Goldberger, Director of Toxicology and Associate Professor, University of Florida College of Medicine and Editor-in-Chief, Journal of Analytical Toxicology.
The new system used to analyze drug abuse deaths built upon the federal Drug Abuse Warning Network (DAWN) system for reporting drug abuse mortality data in the United States, by instituting a more rigorous method of classifying and reviewing deaths thought to involve drugs. This system enabled objective grouping of cases into single drug and multiple drug categories, drug-induced and drug-related categories, as well as categories not involving drug abuse.
"The DAWN terminology employed by the authors is very useful and is to be recommended."
"This analysis sheds light on the nature and complexity of determining whether a specific product plays a role in a drug death," said Dr. Bruce Goldberger. "This new, enhanced method of classification, based on the DAWN system, should be implemented as a standard for analyzing deaths involving drugs."
Study Methodology An Oxycodone Postmortem Database containing 1243 cases was assembled that consisted of solicited submissions from Medical Examiner and Coroner offices in 23 states in the United States over the period from August 27, 1999, through January 17, 2002.
A system of categorization developed for this study was based on the federal DAWN system for reporting drug abuse mortality data in the United States. Only cases of death involving oxycodone were requested. Each case was evaluated to determine the role of oxycodone and the specific drug product OxyContin in the death. Oxycodone presence was based on toxicology testing; OxyContin identification was based on evidence found at the scene, credible witness reports, or identification of tablets or remnants in gastrointestinal contents.
A board-certified forensic pathologist and a board-certified forensic toxicologist reviewed each case file independently. In addition, following their assessments, two more reviewers performed independent assessments of each case based on a set of predetermined questions.
The study was funded by Purdue Pharma L.P. The principal investigators, who are not employed by Purdue Pharma, served as consultants and received compensation for their participation in this work.
The Journal of Analytical Toxicology (JAT) is the international source for practical, clinical/forensic applications for isolating, identifying, and quantitating potentially toxic substances.
Since its inception in 1977, JAT has striven to present state-of-the-art techniques to address current issues in toxicology.
Overdoses linked to OxyContin may have to do with combinations.
The prescription painkiller OxyContin may not be the sole culprit behind the hundreds of drug overdoses for which it's been blamed.
Researchers have found that most of the drug-abuse deaths associated with Oxycodone -- a morphine-like painkiller that is the active ingredient in OxyContin, Percocet and other medications -- are the result of mixing several drugs.
The overdoses have prompted increased regulatory scrutiny of prescriptions nationwide, making some doctors reluctant to prescribe the drug, even for patients in severe pain.
"We found that the oxycodone deaths were primarily related to mixing many different kinds of drugs with these opiates," says Edward J. Cone, lead author of the study and a forensic toxicologist. "These drugs often have a synergistic effect on each other, and in combination can be a deadly brew."
Researchers solicited the records of 1,243 oxycodone-related cases from medical examiners in 23 states from August 1999 through January 2002. OxyContin caused only 12 of these deaths, and another 18 were linked to Oxycodone. In the vast majority of cases (96.7%), victims had at least three other drugs in their system, such as benzodiazepines (Valium-like drugs), alcohol, cocaine, marijuana, antidepressants or other narcotics.
This finding is in stark contrast to the figures compiled last year by the U.S. Drug Enforcement Administration, which lists OxyContin as the cause of 146 deaths, and the "likely" cause of an additional 318 fatalities.
Purdue Pharma, the Stanford, Conn., maker of OxyContin, funded the study, which was in the March issue of the Journal of Analytical Toxicology.


Clever Endeavour Games is a game development studio from Montreal, Canada. Our goal is to bring meaningful and empowering gaming experiences to players to fulfill the basic human need to overcome challenges, to make meaningful decisions, and to connect with other people. We plan on pushing the boundaries of moral decisions and autonomy implied through gameplay and mechanics, and exploring new social interaction in games that bring people together, in person and online.
Clever Endeavour Games is a studio from Montreal, Canada, creating adventure games for PC (and soon for console).


If you missed a sermon or would like to listen again you can find them here.
Lazarus joins us to (amongst other things) share some stories from his work with 222 ministries.
Today we celebrated with baptisms and dedications!
Andrew concludes the series and talks about how we are called to actively anticipate the coming kingdom.
When Jesus ascended into heaven he sent the Spirit to his followers, to both indwell them and empower them for life. God the Holy Spirit brings the reality of the kingdom into and through our lives.
Raising the expectation of the kingdom of God breaking into our lives at anytime.
Andrew introduces our new series looking at Gods Kingdom, starting with a kingdom attitude to Compassion and Justice.
In this series we celebrated the welcoming culture we already have as a church and were challenged to become more actively invitational in our lives.
Andrew concludes the series, talking about how we are called to be a living example, and point to Jesus in our conversation.
Simon continues the series - challenging us to share our faith with our friends, after all what's the worst that could happen?
This week Andrew introduced our new 3 part series, Just Ask, focusing on creating a culture of invitation within our lives.


Cryptocurrency is the most popular example that is intrinsically tied to blockchain technology. It is also the most controversial one. Nonetheless, blockchain technology itself is not contentious, has worked flawlessly over the years and is being successfully applied to both financial and non-financial applications within Uganda.
Several crypto to fiat currency exchanges have been launched in Uganda, like BitPesa, Coin Pesa and Binance Uganda. Binance is the the biggest fiat to crypto currency exchange by trade volume in the world. And some businesses like restaurants , hotels, shops accept payment in crypto currencies in Uganda.
The government of Uganda is also considering the use of blockchain in various ministries like the Ministry of Lands; where all properties in Uganda will be registered on the blockchain. This project is being fore fronted by Bitland Uganda, in partnership with Bitland Global, a land registry application on the blockchain that maintains tamper proof, immutable land records. We believe this process will spark a lot of growth in the real estate industry, as it will get rid of the major ills that the industry has grappled with for a long time, like fraud. Land title registration on the blockchain will mean transparent, tamper-proof, fast and inexpensive transactions.
With the range of blockchain applications being implemented in Uganda, from enabling micropayment systems, to digital identity management to smart contracts, there is no doubt that blockchain-based solutions can leapfrog traditional or non-existent technology infrastructures in the country and the continent at large. Such revolutionary developments are the drivers of a new era of more inclusive growth in which "no one is left behind".
Agriculture, we have experienced a mushroom growth of Agri Tech businesses based on blockchain.
The biggest challenge is the absence of a regulatory regime . Regulators and lawyers are still trying to figure out how to navigate the new technology. The market situations require the co-existence of both traditional and digital players side by side, for some time, in order to build bridges from the old to the new regulatory environment.
It helps that Uganda is one of the few countries on the African continent whose government has shown willingness to embrace the technology. Most of the blockchain technologies and cryptocurrencies are not facing much resistance from regulators in Uganda, unlike in most countries across the continent, majorly because most governments feel threatened or don't understand the benefits of these new technologies.
The Ugandan Government is in the process of introducing tax mechanisms and incentives that encourage the private sector to invest in blockchain. This would open up new opportunities for public-private partnership.
The Government is also availing education and training opportunities to build the necessary manpower, and more investment in startups to support their growth and in return boost the economy.


text:
O T-34-85 foi um carro de combate médio utilizado durante a Segunda Guerra Mundial pela União Soviética. Desenvolvido como o sucessor do revolucionário T-34, o tanque médio símbolo da resistência soviética durante a ofensiva alemã.

Sua nova torre, com 3 tripulantes, cúpula para o comandante e um novo canhão mais poderoso foi uma resposta ao Panther e Tiger das forças do eixo, que possuíam blindagem demasiadamente espessa para serem derrotadas a uma distância segura pelo T-34.

Descrição

Desenvolvido entre 1943 e 1944, a partir do padrão T-34 armados com canhões do período, passando dos 76,2 mm do T-34/76, o T-34/85 foi construído com o mesmo casco dos modelos anteriores do T-34, mas difere do seu antecessor, devido à torre muito maior, que, ao contrário das versões anteriores tinham uma blindagem muito espessa e poderia acomodar três tripulantes no interior (comandante, artilheiro e municiador) o seu  armamento principal, constituído por uma arma de cano longo de 85 mm.

Pretendeu-se alcançar a igualdade de armas contra o Panther alemão e tanques Tiger, armados com armas, respectivamente de calibres entre 75 e 88 mm, o que até então tinha-se mostrado superior ao armamento do T-34/76.

Inicialmente, foi também avaliado o canhão de 57 mm de alta velocidade, que deram resultados superiores do que arma anti-tanque de 85 milímetros, mas não teve um bom desempenho anti-infantaria, isso numa doutrina militar soviética foi uma falha grave, porque os tanques estavam a ser verdadeiramente uma maquina multi-função, com bom contraste, não apenas em tanques inimigos, mas também para a infantaria, bunkers e artilharia.

Esta filosofia foi diametralmente oposta à da Alemanha, que incide sobre a especialização dos tanques, cada um deles foi capaz de realizar adequadamente uma ou duas funções, no máximo.

O T-34/85 foi bem sucedido em batalha, principalmente na de Kursk e em pouco tempo os T-34/76 foram retirados de serviço de primeira linha, como eles ficaram disponíveis foram transferidos para novas unidades blindadas dentro da união soviética ou foram transferidos para unidades blindadas da Polônia e Iugoslávia.

No final da guerra os tanques T-34/85 haviam se tornado o principal tanque em serviço no exército soviético e nos países da Europa Oriental que receberam as primeiras entregas do carro em 1946 e permaneceu por muitos anos como principal plataforma blindada do país durante a Guerra Fria, até que foi substituído por uma versão mais moderna derivada de seu irmão T-40 os T-54/T-55.

No entanto, com o fim da Segunda Guerra Mundial ele ainda foi utilizado durante a Guerra da Coréia, pelo Exército norte-coreano e durante a Revolução Húngara, onde foi empregado por ambos os lados durante o conflito. E durante a Guerra árabe-israelense utilizado principalmente pelo Egito e Síria, e finalmente, na fase final da Guerra do Vietnã.

Em resumo, era um carro bem gerido, bem armado e protegido, mas, inevitavelmente, tornou-se obsoleto com o surgimento da primeira geração de tanques pós-guerra, mas manteve uma mobilidade invejável, rusticidade e boa alimentação tudo considerado baixo quando comparado potência do motor. No entanto, ele permanece na reserva do exército cubano e vietnamita.

As versões de produção do T-34/85 divide-se em 1943, 1944 e 1945, diferentes uns dos outros apenas em pequenos detalhes da configuração de sistemas ópticos e ventilação da torre.

Problema com o sistema de suspensão

Embora famoso pela inovação que representou a sua blindagem inclinada, o que é normalmente esquecido pelos analistas, é que o T-34 nunca foi considerado completamente satisfatório pelos militares soviéticos, sendo-lhe apontados vários defeitos.

O principal problema que nunca foi resolvido, foi o do sistema de suspensão Christie, inventado nos Estados Unidos nos anos 20, que foi utilizado no T-34.

Esse sistema utilizava molas extremamente volumosas, que ocupavam grande quantidade de espaço dentro do veículo. Foram feitas várias tentativas para resolver o problema, mas ainda durante a guerra, o aparecimento dos carros de combate alemães Panther levaram a que todos os esforços de desenvolvimento do T-34 se centrassem num novo armamento mais poderoso sendo escolhido o de calibre 85mm.

A questão do sistema de suspensão nunca chegou por isso a ser resolvida, e só mais tarde quando um novo carro de combate foi desenhado (o T-547), essa questão foi considerada.

Principal Utilizador

 Designação Local: T-34/85
 Quantidade Máxima: 19.430
 Quantidade em serviço: 0
 Situação operacional: Em reserva secundária na Rússia

Outros Utilizadores

Variantes
 T-34/76A - Modelo produzido de 1940.
 T-34/76B - Modelo produzido de 1941.
 T-34/76C - Modelo produzido de 1942 com maior armadura.
 T-34/76D - Modelo produzido de 1943.
 T-34/76E - Modelo produzido de 1943.
 T-34/76F - Modelo produzido de 1943.
 T-34/85 - Modelo produzido de 1943 com uma arma de 85mm.
 Panzerkampfwagen T-34(r) - T-34 capturado pela Alemanha.

Ver também
 Lista de veículos blindados de combate por país

Ligações externas

Tanques da União Soviética
Tanques médios
Tanques da Segunda Guerra Mundial
Tanques da guerra da Coreia
Equipamentos militares da União Soviética
Tanques soviéticos da Segunda Guerra Mundial
Veículos militares de 1940-1944

redpajama_set_name: RedPajamaWikipedia


text:
Devitt Loyal Orange Lodge No. 43
Devitt's Corners, Ontario, Canada
Devitt Loyal Orange Lodge No. 43 received its warrant in 1847 in the town of Devitt's Corner's, Ontario. The first Worshipful Master was Matthew Devitt who was born March 13th, 1815 in Fermanagh County, Ireland.
Matthew was a Wesleyan Methodist that came to Canada in 1827 and settled first in West Gwilliambury in 1827 and then Cartwright between 1839-1840. The Bowmanville Canadian Statesman mentions that Matthew served the Crown during the 1837 Rebellion. He married Rachel Girvin (daughter of Charles Girvin and Rachel Carlton) in about 1840. They would go on to have ten children; Elizabeth, Ann May, twins John and Charles, Rachel, Matthew, Ellen Jane "Nellie", George Wright, Caroline and Samuel.
In June 1840, Matthew purchased 200 acres (all of lot 19, Concession 3) in Cartwright Township from Charles J. Dunlop and later gave land on his farm to the Wesleyan Methodist Church. While the church has been gone for many years, Devitt's Cemetery still remains. The Orange Hall was located across from the Cemetery on the southeast side of Devitt's Corners.
Matthew passed away on November 8th, 1860 in Cartwright Township in Ontario as a result of falling from a wagon with a run away team of horses.
Location of the former Orange Hall located on the southeast side of Devitt's Corners in what is now considered part of Nestleton Station, Scugog Township, Ontario (Source: Google Maps, 2020).
Where is Devitt's Corners?
Orange Archives is looking for further information on Devitt Loyal Orange Lodge No. 43 and the Devitt family. If you have any information that you would like to share please contact us.


text:
Sony Boasts About Move Shipments, Games Press Falls For It
Sony has sent out a press release crowing about their strong shipments of their Move controller, stating that they have sold 4.1m units, and sending a statement to Industry Gamers boasting about the "incredible demand" for the device while pointing out the momentum that the company has heading into Christmas.
"Heading into the home stretch of this holiday season, and early 2011 with two huge Move compatible titles LittleBigPlanet and Killzone 3 right around the corner, PlayStation Move is the leading choice of consumers for both their hard core and their family gaming experiences."
There's only one problem. They haven't actually sold that many units to consumers. SFX-360's Jose Betancourt made the point via Twitter that these were just consoles shipped, meaning sold to retailers, and not sold-through to consumers. Don Reisinger of CNET confirmed with Sony that the numbers reflected shipped numbers, whereas Microsoft's boast of 2.5m Kinect units sold – the announcement of which Sony was following up – has been confirmed by CNET as being sell-throughs. Sony has said they are not releasing the number of sold-through Move units, but told CNET that it doesn't matter because they keep getting orders.
"While we don't disclose our exact sell-through number, the key is that our retailers continue to ask for more Move units and are taking every unit we can supply them with based on their sales."
I'm going to take a moment to call bullshit on that. Retailers aren't necessarily placing those orders because the units are flying off the shelves, they could be placing those orders because today's date is November 30th, and they're getting ready for the potential to sell Move units. There's no way to really verify how many units are being sold – Sony's not telling, and the NDP Group has neutered itself into irrelevance at the behest of the publishers – but it's important to note that Sony is being deceitful about Move's sales, and possibly its demand, which is in line with what was reported yesterday.
So, who fell for it, and reported this number as "sales" instead of "shipments"? A depressing number of outlets.
* Steve Watts of 1UP reported, then updated their post upon confirmation to their credit. G4 falls in the same boat.
* USA Today's Game Hunters blog reported it as sales, exceptionally disappointing considering it's USA Today. I'll bet if this was a political article, it would have been put through a more stringent editorial process.
* Ben Strauss of Industry Gamers reported them as sales, while noting Michael Pachter's analysis of inflated demand.
* Worst of all, Tom Ivan of UK-based CVG not only reported it as sales, but stated as fact that Sony was "currently winning the PS3-360 motion war" and at the end of the article, stated that it was "your move, MS". That was a journalistic catastrophe.
So, to review: Sony is pulling the wool over peoples' eyes regarding demand and sales of their devices with the intention of spurring more sales and more demand, and are able to do so based on the knowledge that very few people are actually going to double check.
Bad games industry. Bad.
Christopher Bowen
kinect, move
2 responses to "Sony Boasts About Move Shipments, Games Press Falls For It"
Diehard GameFAN | Microsoft: Kinect Shortages Not Managed
[…] response to Wedbush Morgan's Michael Pachter accusing both Microsoft and Sony of "managing" (read: lying about) shortages of Kinect and Move, Microsoft's Neil […]
Diehard GameFAN | Unbranding the Sheep: The Perils Of What We Call "Journalism"
[…] press releases that so many disdain – with editorial analysis. One example of this would be my work regarding Sony's boasting of Move sales around the holidays, where I reported what was being […]


text:
\section{Introduction}
Following the successful isolation of single-layer graphene in 2004 \cite{Novoselov},  the study of quasi two-dimensional materials -- either single atomic layers or stacks of a few layers -- has become one of the most important areas of research in materials science.   It is expected that the unprecedented flexibility of these  materials, which can be assembled in many different combinations, including insulating, metallic, and superconducting layers, will lead in time to major technological advances.  Basic physics concepts such as massless Dirac Fermions and coupled valley-spin dynamics can also be studied in these systems.  From the point of view of computational electronic structure theory the challenge is to reliably predict the properties of a quasi-2D structure with minimal input from experiment.   Ideally we would like to be able to decide, based  on computation, which structures are stable, which are metals and which are insulators, what their excitation spectra look like.   Most of the methods  that are presently in use in solid state physics to address these questions --  Kohn-Sham density functional theory, GW approximations, Bethe-Salpeter (BS) equations, dynamical mean field theory --  have been developed for 3D systems and are now being applied to quasi-2D systems (important exceptions are Octopus\cite{Octopus} and GPAW \cite{gpaw}, which allow the user to specify a reduced number of periodic directions).

However, the transition from 3D to quasi-2D is not free of pitfalls.  Bulk 3D crystals exhibit periodicity in all three directions and are treated with the help of periodic boundary conditions.   This means, in practice, that computational methods are implemented on a basis of wave functions that exhibit three-dimensional periodicity, such as plane waves~\cite{Gonze20092582,QE-2009,gpaw,PhysRevB.54.11169}, augmented plane waves (APW) \cite{Exciting!,elk-code,PhysRevB.81.125102}, LMTO \cite{LMsuite} or periodic sums of atomic orbitals \cite{Fhi-Aims,Siesta,gpaw, Octopus}.  Quasi 2D materials on the other hand,  have crystalline periodicity in two dimensions only.  In the third direction (which we will call the $z$-direction)  the wave function is that of a polyatomic molecule, possibly a very large one, but in any case decaying exponentially at sufficiently large distance from the atomic layers. Therefore, strictly speaking, periodic boundary conditions cannot be used in the third direction.  Another key difference is that, due to the quasi-two dimensional character of the electronic charge distribution,  electric field fluctuations are not screened at sufficiently large distance in the plane of the layers \cite{PhysRevB.84.085406,PhysRevB.92.245123}: therefore electron-electron interaction effects are much stronger than in conventional 3D materials.

It turns out that these difficulties are connected.  In order to keep using 3D computer codes with periodic basis sets it is customary to resort to an artifice known as the  ``supercell method", whereby the quasi-2D material is periodically repeated in the $z$ direction.  The distance between the artificial replicas, $d$,  is chosen to be large in the hope that interaction effects between the replicas can be ignored.  If everything goes well, the results should  become independent of  $d$ in the limit $d \to \infty$.  Unfortunately, because of the failure of screening, the Coulomb interaction between artificial replicas decreases very slowly with increasing $d$, and may cause spurious results.  In addition the exchange-correlation potentials of density functional theory, when treated exactly, are known to be highly nonlocal functionals of the density, which decay very slowly, with the inverse of the distance from the plane of the material \cite{Lang_Kohn,vBarth,Silkin}.  The problem is particularly acute in the calculation of dynamical response properties, where the replicas create an artificial dynamical environment.

To counter these difficulties two main techniques have been developed so far.  The first ~\cite{Rozzi_cutoff,Castro_cutoff} relies on truncating the Coulomb interaction beyond a certain cutoff distance {in the $z$ direction}. Thus one hopes  eliminate  the unphysical interaction between the replicas while preserving the long-range interaction within the physical layer, or set of layers.   Another solution~\cite{Nazarov_2d} is to calculate the mean field created by the replicas and subtract it from the field that acts on the electrons in the physical layer: for the dynamical dielectric function and related properties this can be done in a relatively inexpensive way.

Ultimately,  the best and most elegant solution would be to do the calculations with  a code that recognizes at the outset the quasi-2D character of the system and takes advantage of its structure by using a basis set of wave functions that are periodic (plane-wave like) in the $(x,y)$ plane and atomic-like in the $z$-direction.  We refer to such a code as a ``native" quasi-2D code.  A similar approach has been proposed, very recently,  in Ref.~[\onlinecite{PhysRevB.92.115132}], where the full-potential linearized augmented plane-wave method is modified to account for the exponential decay of the basis function in the $z$-direction.

In this paper we take a first step towards the construction of a native quasi-2D code by introducing a set of  basis functions with the properties outlined above,  and by showing  how some of the basic tools of ab initio electronic structure theory -- density functional theory, GW approximation and Bethe-Salpeter equation -- are implemented in this basis.  Our approach is inspired by the FHI-AIMS basis set, in which periodic functions in 3D are constructed from Bloch sums of numerically generated  {Natural Atom-centred Orbitals (NAO) - see Appendix \ref{app_c}.  We insert these orbitals into two-dimensional Bloch sums to arrive at the desired basis functions.  While the FHI-AIMS code is already able to perform ``native" Kohn-Sham DFT on a quasi-2D basis,   our implementation of GW and BS equations on this basis set is new and will prove to be a powerful and versatile tool for the calculation of electronic properties of quasi-2D materials.

It might be objected that the use of NAO orbitals for the $z$-dependence of the wave function will become unpractical (i.e., require many terms for good convergence)  when the wave function is very extended in that direction, as is the case for high-energy unoccupied states.  This is partially true, but we counter that (i) these extended states would become anyway unreliable when treated in the conventional supercell method, due to spurious cross-talk between replicas, (ii) extended basis sets have recently been developed and optimized to treat the excited states in FHI-AIMS\cite{Extended_aims1,Extended_aims2}, and  (iii) a new technology exists, based on the Sternheimer equation \cite{PhysRevB.81.115105,PhysRevB.88.075117} to avoid the use of excited states in the implementation of the GW method.
Finally, we expect that the two-dimensional implementation of these tasks will speed up the calculations and make them more reliable, once the required computer codes are fully developed.

This paper is organized as follows: in section \ref{section_repre_vectors} we introduce the quasi-2D basis functions and review their formal properties.
In particular, because these functions are not mutually orthogonal, we find it convenient to introduce covariant and contravariant components of vectors in the Hilbert space -- the two types of components being connected by a ``metric tensor", which is the matrix of the overlaps. In section \ref{section_repre_two_points}, the two space point functions are described in this new formalism. Therefore, we represent the Dyson equation for the GW self-energy (section \ref{section_gw}), the polarization function (section \ref{section_pol_function}) and screened potential W (section \ref{section_screen_inter}) on the quasi-2D basis.  Finally, in section \ref{section_bse}, the BS equation for the two-particle propagator on the quasi-2D basis is made explicit and we introduce the effective two-band exciton equation (sub section \ref{subsection_bse}).  The last section \ref{summary} contains our summary and outlook for the development of the ideas presented in this paper. In appendix \ref{app_a} a  single pole approximation is revisited. In appendix \ref{app_b}, the contour integration technique for the GWA is derived in our formalism. Finally,  a brief overview of the FHI-AIMS NAO orbitals is provided in appendix \ref{app_c}.

\section{Hybrid basis set and representation of vectors}
\label{section_repre_vectors}
For a system that is periodic in the $(x,y)$ plane, but not in the $z$ direction --  an array of molecules arranged in a 2D lattice -- we introduce basis functions of the Bloch type, characterized by a Bloch wave vector ${\bf k}$ in the $(x,y)$ plane.  The general form of these basis functions is~\cite{PhysRevB.48.17791,PhysRevLett.75.3489,PhysRevB.62.4927}
\begin{equation}\label{CovariantBasis}
\chi_{\alpha{\bf k}}(\mbox{\boldmath $\xi$})\equiv\frac{1}{\sqrt{N}}\sum_{{\bf R}} e^{i {\bf k} \cdot{\bf R}}\phi_{nlm}(\mbox{\boldmath $\xi$} -{\bf R}-{\bf d}_a)
\end{equation}
where  $\mbox{\boldmath $\xi$} = ({\bf x},z)$ is a three dimensional position vector; ${\bf R}$ is a lattice vector in the $(x,y)$  plane, ${\bf d}_a$ is a three-dimensional vector specifying the position of the $a$-th atom in the two-dimensional unit cell labelled by ${\bf R}$, and $\phi_{nlm}(\mbox{\boldmath $\xi$} -{\bf R}-{\bf d}_a)$ are orthonormal atomic orbitals labeled by atomic quantum numbers $(n,l,m)$ and centered at ${\bf R}+{\bf d}_a$.   $N$ is the number of cells in the two-dimensional lattice, and $\alpha = n,l,m,a$ is a composite index including the atomic quantum numbers and the position of the atom in the unit cell. The form of the $\phi$ orbitals will be left unspecified for the time being: explicit numerical expressions that are used in the FHI-AIMS code will be discussed later (see  Appendix \ref{app_b})}.   Note that
\begin{equation}
\chi_{\alpha{\bf k}}(\mbox{\boldmath $\xi$}+{\bf R})=e^{i {\bf k} \cdot{\bf R}} \chi_{\alpha{\bf k}}(\mbox{\boldmath $\xi$})\,,
\end{equation}
as required for a Bloch wave of wave vector ${\bf k}$.

The basis functions satisfy the ``orthonormality" relation
\begin{equation}
 \int d\mbox{\boldmath $\xi$}  \chi^{*}_{\alpha{\bf k}}(\mbox{\boldmath $\xi$})\chi_{\beta {\bf p}}(\mbox{\boldmath $\xi$})  \equiv S_{\alpha\beta}({\bf k})\delta_{{\bf k},{\bf p}}\,,
 \end{equation}
where $S_{\alpha\beta}({\bf k})=S^*_{\beta\alpha}({\bf k})$ is a hermitian matrix.
In addition to the covariant basis functions of Eq.~(\ref{CovariantBasis}) it is convenient to introduce the contravariant basis set
\begin{equation}
\chi^{\alpha}_{{\bf k}}(\mbox{\boldmath $\xi$})  \equiv  \sum _{\beta} S^{\alpha \beta}({\bf k}) \chi_{\beta{\bf k}}(\mbox{\boldmath $\xi$})
\end{equation}
where $S^{\alpha\beta}({\bf k})\equiv[S^{-1}({\bf k})]_{\beta\alpha}$ is the transposed inverse of the ``metric tensor" $S({\bf k})$. In Quantum Chemistry, $S^{\alpha\beta}$ is referred as overlap matrix. In terms of covariant and contravariant basis elements the ``orthonormality" relations take the simpler form
\begin{equation}\label{Orthonormality2}
\int d\mbox{\boldmath $\xi$}  \chi^{\alpha*}_{{\bf k}}(\mbox{\boldmath $\xi$})\chi_{\beta {\bf p}}(\mbox{\boldmath $\xi$})  =\delta_{\alpha\beta}({\bf k})\delta_{{\bf k},{\bf p}}\,.
 \end{equation}
 We can also write the completeness relation in the form
 \begin{equation}\label{Completeness}
 \sum_{\alpha{\bf k}}\chi_{\alpha {\bf k}}(\mbox{\boldmath $\xi$})\chi^{\alpha*}_{{\bf k}}(\mbox{\boldmath $\xi$}') = \delta(\mbox{\boldmath $\xi$}-\mbox{\boldmath $\xi$}')\,,
 \end{equation}
 where the sum over ${\bf k}$ runs over the vectors of the first Brillouin zone of the reciprocal 2D lattice.  This is evident from the fact that for an arbitrary function  $f(\bm{\xi})=\sum_{\beta {\bf p}} f^\beta_{{\bf p}}\chi_{\beta{\bf p}}(\bm{\xi})$ we have,  by virtue of Eq.~(\ref{Orthonormality2}),
 \begin{equation}
 \int d\bm{\xi}' \sum_{\alpha{\bf k}}\chi_{\alpha {\bf k}}(\mbox{\boldmath $\xi$})\chi^{\alpha*}_{{\bf k}}(\mbox{\boldmath $\xi$}') f(\bm{\xi}') = \sum_{\alpha{\bf k}} f^\alpha_{{\bf k}}\chi_{\alpha{\bf k}}(\bm{\xi})  = f(\bm{\xi})\,.
 \end{equation}

A Bloch wave function $\psi_{{\bf k}}(\mbox{\boldmath $\xi$})$ in the Hilbert space can be expressed as a contravariant vector as follows:
\begin{equation}
\psi_{\bf k}(\mbox{\boldmath $\xi$}) = \sum_{\alpha}\psi_{{\bf k}}^\alpha \chi_{\alpha{\bf k}}(\mbox{\boldmath $\xi$})\,,~~~{\rm where}~~~ \psi_{{\bf k}}^\alpha =\int d\mbox{\boldmath $\xi$} \chi^{\alpha*}_{{\bf k}}(\mbox{\boldmath $\xi$}) \psi_{{\bf k}}(\mbox{\boldmath $\xi$})\,.
\end{equation}
The scalar product of two Bloch wave functions $\psi_{{\bf k}}(\mbox{\boldmath $\xi$})$ and $\varphi_{{\bf k}}(\mbox{\boldmath $\xi$})$ is then given by
\begin{equation}
(\psi_{{\bf k}},\varphi_{{\bf k}}) = \int d\mbox{\boldmath $\xi$}\psi^*_{{\bf k}}(\mbox{\boldmath $\xi$})\varphi_{{\bf k}}(\mbox{\boldmath $\xi$}) = \sum_\alpha \psi^*_{{\bf k}\alpha} \varphi_{{\bf k}}^{\alpha} = \sum_\alpha \psi^{*\alpha}_{{\bf k}} \varphi_{{\bf k}\alpha} \,.
\label{Bloch_wf}
\end{equation}

Covariant and contravariant components of the same vector are  connected by the metric tensor:
\begin{equation}
\psi_{{\bf k}\alpha} = \sum_{\beta}\psi_{{\bf k}}^{\beta}S_{\beta\alpha}({\bf k}) \,.
\end{equation}

In the following, the solutions of, say, the Kohn-Sham equations for a given layered structure will be represented as covariant or contravariant vectors in the hybrid atomic-plane wave basis.

 \section{Representation of two-point functions}
 \label{section_repre_two_points}
 We now consider the representation of a periodic two-point function $f(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')$, i.e., a function such that
 \begin{equation}
 f(\mbox{\boldmath $\xi$}+{\bf R},\mbox{\boldmath $\xi$}'+{\bf R})=f(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')\,,
 \end{equation}
 where ${\bf R}$ is a two-dimensional lattice vector.  Making use of the completeness relation~(\ref{Completeness}) we easily see that
 \begin{equation}\label{Eq12}
 f(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')=\sum_{\alpha\beta{\bf k}} \chi_{\alpha{\bf k}}(\mbox{\boldmath $\xi$}) f^{\alpha\beta}({\bf k}) \chi_{\beta{\bf k}}^*(\mbox{\boldmath $\xi$}')\,,~~~~{\rm where}~~~f^{\alpha\beta}({\bf k})=\int d\mbox{\boldmath $\xi$} d\mbox{\boldmath $\xi$}'  \chi^{*\alpha}_{{\bf k}}(\mbox{\boldmath $\xi$})f(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')
 \chi^{\beta}_{{\bf k}}(\mbox{\boldmath $\xi$}')
 \end{equation}

 or, alternatively
 \begin{equation}\label{Eq13}
 f(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')=\sum_{\alpha\beta{\bf k}} \chi^{\alpha}_{{\bf k}}(\mbox{\boldmath $\xi$}) f_{\alpha\beta}({\bf k}) \chi^{*\beta}_{{\bf k}}(\mbox{\boldmath $\xi$}')\,,~~~~{\rm where}~~~f_{\alpha\beta}({\bf k})=\int d\mbox{\boldmath $\xi$} d\mbox{\boldmath $\xi$}'  \chi^{*}_{\alpha{\bf k}}(\mbox{\boldmath $\xi$})f(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')
 \chi_{\beta{\bf k}}(\mbox{\boldmath $\xi$}')
 \end{equation}

 We notice in passing that the first of Eqs.~(\ref{Eq12}) and the second of Eqs.~(\ref{Eq13}) correspond, respectively, to Eqs. (6) and (7) of Ref.~\onlinecite{PhysRevB.48.17791}, i.e., $f^{\alpha\beta}$ and $f_{\alpha\beta}$ correspond, respectively, to the ``angular bracket" and ``square bracket" matrix elements of Ref.~\onlinecite{PhysRevB.48.17791}.

 These representations apply, in particular to the Green's function $G(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)$ and the screened electron-electron interaction $W(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)$.  We now show how the two representations are combined in the GW approximation.

As an example, consider the noninteracting Green's function (advanced and retarded Green's function):
\begin{equation}\label{GF1}
  G_0(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)= \sum_{n{\bf k}}\frac{\psi_{n{\bf k}}(\mbox{\boldmath $\xi$})\psi_{n{\bf k}}^{*}(\mbox{\boldmath $\xi$}')} {\omega- E_{n{\bf k}}\pm i0^+ }\,.
\end{equation}

 Then, expanding in Bloch  functions:
 \begin{equation}\label{GF2}
 G_0^{\alpha\beta}({\bf k},\omega)= \sum_{n}\frac{\psi^{\alpha}_{n{{\bf k}}}\psi^{\beta*}_{n{\bf k}}} {\omega-E_{n{\bf k}}\pm i0^+}
 \end{equation}
 where $\psi_{n{\bf k}}(\bm{\xi})\equiv\sum_{\alpha}\psi^{\alpha}_{n{{\bf k}}}\chi_{\alpha{\bf k}}(\mbox{\boldmath $\xi$})$ are non-interacting one- electron wave functions and $E_{n{\bf k}}$ the one-electron energies.

\section{GW Self-Energy}\label{section_gw}
In the GW approximation the self-energy is a parallel convolution product of G and W, usually approximated by their lowest-order forms $G_0$ and $W_0$:
\begin{equation}
\Sigma(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)=\frac{i}{2\pi}G_0(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)*W_0(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)e^{-i\eta\omega}\,.
\end{equation}
Here the $*$ represent the convolution product: $f(\omega)*g(\omega)\equiv \int d\omega' f(\omega-\omega')g(\omega')$ and .
The corresponding diagram is shown in Fig.~(\ref{GW}).

\begin{figure}
\includegraphics[width=4.0 in]{GW}
\caption{Diagrammatic representation of the $G_0W_0$ self-energy and the three-point vertices.}
\label{GW}
\end{figure}

We expand the product as
\begin{equation}
\Sigma(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)= \sum_{{\bf p}'{\bf q}}G_{0}^{\alpha\beta}({\bf p}',\omega)\chi_{\alpha{\bf p}'}(\mbox{\boldmath $\xi$})\chi^*_{\beta{\bf p}'}(\mbox{\boldmath $\xi$}')*W_{0,\gamma\delta}({\bf q},\omega)\chi^{\gamma}_{{\bf q}}(\mbox{\boldmath $\xi$})\chi^{*\delta}_{{\bf q}}(\mbox{\boldmath $\xi$}')
\end{equation}
where the sum over repeated indices is understood.
Then the matrix element of the self-energy is
\begin{equation}
\Sigma_{\mu\nu}({\bf p},\omega) =\frac{i}{2\pi} \sum_{{\bf p}'{\bf q}} \left[\int d\mbox{\boldmath $\xi$} \chi^*_{\mu{\bf p}}(\mbox{\boldmath $\xi$})\chi_{\alpha{\bf p}'}(\mbox{\boldmath $\xi$}) \chi^{\gamma}_{{\bf q}}(\mbox{\boldmath $\xi$})\right]G_{0}^{\alpha\beta}({\bf p}',\omega) \left[\int d\mbox{\boldmath $\xi$}' \chi^*_{\beta{\bf p}'}(\mbox{\boldmath $\xi$}') \chi^{*\delta} _{{\bf q}}(\mbox{\boldmath $\xi$}')  \chi_{\nu{\bf p}}(\mbox{\boldmath $\xi$}') \right]*W_{0,\gamma\delta}({\bf q},\omega)
\end{equation}
The quantities in the square brackets vanish unless ${\bf p}'={\bf p}-{\bf q}$.  We define
\begin{equation} \label{Gamma1}
\int d\mbox{\boldmath $\xi$} \chi^*_{\mu{\bf p}}(\mbox{\boldmath $\xi$})\chi_{\alpha{\bf p}'}(\mbox{\boldmath $\xi$}) \chi^{\gamma}_{{\bf q}}(\mbox{\boldmath $\xi$}) \equiv \Gamma^{\gamma}_{\mu\alpha}({\bf p},{\bf p}-{\bf q})
\end{equation}
and
\begin{equation} \label{Gamma2}
\int d\mbox{\boldmath $\xi$}' \chi^*_{\beta{\bf p}'}(\mbox{\boldmath $\xi$}') \chi^{*\delta} _{{\bf q}}(\mbox{\boldmath $\xi$}')  \chi_{\nu{\bf p}}(\mbox{\boldmath $\xi$}') \equiv \Gamma^{\delta}_{\beta\nu}({\bf p}-{\bf q},{\bf p})\,.
\end{equation}
These matrix elements are illustrated in Fig.~(\ref{GW} (b)).  Note that $\Gamma^{\delta}_{\beta\nu}({\bf p}-{\bf q},{\bf p}) = [\Gamma^{\delta}_{\nu\beta}({\bf p},{\bf p}-{\bf q})]^*$.
Then complete result for the self-energy is
\begin{equation}
\Sigma_{\mu\nu}({\bf p},\omega) =\frac{i}{2\pi}\sum_{{\bf q}}\Gamma^{\gamma}_{\mu\alpha}({\bf p},{\bf p}-{\bf q})G_{0}^{\alpha\beta}({\bf p}-{\bf q},\omega)\Gamma^{\delta}_{\beta\nu}({\bf p}-{\bf q},{\bf p}) *W_{0,\gamma\delta}({\bf q},\omega)
\end{equation}

\section{Polarization function}\label{section_pol_function}
Another crucial two-point function is the polarization function.  The noninteracting polarization function is an antiparallel convolution of two Green's functions
\begin{equation}
P_0(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)=G_{0}(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)*G_{0}(\mbox{\boldmath $\xi$}',\mbox{\boldmath $\xi$},-\omega)\,,
\end{equation}
where $*$ represents the convolution product. A graphical representation of this formula is shown in Fig.~\ref{P0}.
\begin{figure}
\includegraphics[width=4.0 in]{P0}
\caption{Diagrammatic representation of the polarization propagator.}
\label{P0}
\end{figure}

We expand the product as
\begin{equation}
P_0(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}',\omega)= \sum_{{\bf p}\pv'}G_{0}^{\alpha\beta}({\bf p},\omega)\chi_{\alpha{\bf p}}(\mbox{\boldmath $\xi$})\chi^*_{\beta{\bf p}}(\mbox{\boldmath $\xi$}')*G_{0}^{\gamma\delta}({\bf p}',-\omega)\chi_{\gamma{\bf p}'}(\mbox{\boldmath $\xi$}')\chi^*_{\delta{\bf p}'}(\mbox{\boldmath $\xi$})
\end{equation}
Then the matrix element of the polarization propagator is
\begin{equation}
P_0^{\mu\nu}({\bf q},\omega) =\sum_{{\bf p}\pv'}\left[\int d\mbox{\boldmath $\xi$} \chi^{*\mu}_{\bf q} (\mbox{\boldmath $\xi$}) \chi_{\alpha{\bf p}}(\mbox{\boldmath $\xi$})  \chi^*_{\delta{\bf p}'}(\mbox{\boldmath $\xi$}) \right] G_{0}^{\alpha\beta}({\bf p},\omega)\left[\int d\mbox{\boldmath $\xi$}'\chi^*_{\beta{\bf p}}(\mbox{\boldmath $\xi$}') \chi^{\nu}_{{\bf q}}(\mbox{\boldmath $\xi$}')  \chi_{\gamma{\bf p}'}(\mbox{\boldmath $\xi$}')\right]*G_{0}^{\gamma\delta}({\bf p}',-\omega)
\label{Polarization_af}
\end{equation}
Again,  the quantities in the square brackets vanish unless ${\bf p}'={\bf p}-{\bf q}$.  With the three-point vertices $\Gamma$ defined in Eqs.~(\ref{Gamma1}) and ~(\ref{Gamma2}) we easily get the following representation of the polarization propagator:
\begin{equation}
P_0^{\mu\nu}({\bf q},\omega) =\sum_{{\bf p}}\Gamma^\mu_{\delta\alpha}({\bf p}-{\bf q},{\bf p})
 G_{0}^{\alpha\beta}({\bf p},\omega)\Gamma^\nu_{\beta\gamma}({\bf p},{\bf p}-{\bf q})*G_{0}^{\gamma\delta}({\bf p}-{\bf q},-\omega)
\end{equation}

\section{The screened interaction}\label{section_screen_inter}
The covariant  components of the RPA screened interaction can be obtained from the formula
\begin{equation}
W_{0,\alpha\beta}({\bf q},\omega) = [v^{1/2}({\bf q})]_{\alpha\gamma}[\tilde \epsilon^{-1}({\bf q},\omega)]^{\gamma\delta}   [v^{1/2}({\bf q})]_{\delta\beta}\,.
\end{equation}
Here
\begin{equation}
[v^{1/2}({\bf q})]_{\alpha\gamma} = \int d\mbox{\boldmath $\xi$} d\mbox{\boldmath $\xi$}'  \chi^*_{\alpha{\bf q}}(\mbox{\boldmath $\xi$})v^{1/2}(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}')\chi_{\gamma{\bf q}}(\mbox{\boldmath $\xi$}')
\end{equation}
where
\begin{equation}
v^{1/2}(\mbox{\boldmath $\xi$},\mbox{\boldmath $\xi$}') = \frac{e}{\pi^{3/2}|\mbox{\boldmath $\xi$}-\mbox{\boldmath $\xi$}'|^2}\,,
\end{equation}
is the ```square root" of the Coulomb interaction.  Further we have
\begin{equation}
\tilde \epsilon_{\alpha\beta}({\bf q},\omega) = S_{\alpha\beta}({\bf q}) - [v^{1/2}({\bf q})]_{\alpha\gamma}  P_0^{\gamma\delta}({\bf q},\omega)[v^{1/2}({\bf q})]_{\delta\beta}
\end{equation}

A simple single-pole approximation for $\tilde \epsilon({\bf q},\omega)$ is described in the Appendix.

 \section{The Bethe-Salpeter Equation}\label{section_bse}

Besides one-particle properties,  which are usually described in terms of the Kohn-Sham wave functions and the self-energy, two-particle properties also play a prominent role in computational materials science.  For example, the information about the optical spectrum and the refractive index of materials is contained in the macroscopic dielectric function $\epsilon_M(\omega)$, which, in ordinary three-dimensional periodic systems, is defined as the ratio between the  macroscopic external electric field and the macroscopic total electric field, where ``macroscopic" means averaged over a region much larger than the size of the unit cell.  For 2D materials care must be exerted to construct the appropriate response function for the experimental situation under study\cite{Nazarov_2d}.  In the case of optical properties, the macroscopic dielectric function reduces to $1$ and we focus instead on the longitudinal in-plane polarizability per unit cell, which we define as
\begin{equation}\label{P00}
\chi_P(\omega)= \frac{1}{N_c}\lim_{{\bf q} \to 0}\frac{e^2}{q^2 }\int d\bm{\xi} \int d\bm{\xi}' e^{-i{\bf q}\cdot({\bf r}-{\bf r}')} \bar L(\bm{\xi},\bm{\xi},\bm{\xi}',\bm{\xi}';\omega)\,,
\end{equation}
where $\bar L(\bm{\xi}_1,\bm{\xi}_2,\bm{\xi}_3,\bm{\xi}_4;\omega)$ is the proper four-point electron-hole propagator, integrated over the frequencies of the external legs and $N_c$ is the number of unit cells.  We remind the reader that the most general form of the electron-hole propagator is $\bar L_{full}(\bm{\xi}_1,\bm{\xi}_2,\bm{\xi}_3,\bm{\xi}_4; \epsilon_1,\epsilon_2,\epsilon_3,\epsilon_4)$, where $\epsilon_2 = \epsilon_1-\omega$ and $\epsilon_4=\epsilon_3-\omega$ are the frequencies of the external legs.  The simpler propagator $L$ (still referred to as electron-hole propagator for brevity)  is obtained from $L_{full}$ by integrating over $\epsilon_1$ and $\epsilon_3$ at fixed $\omega$.  The bar over $L$ is a reminder that we are calculating $L$  {\it with exclusion of the long-range Coulomb interaction}~\cite{rmp_onida} in the so-called exchange electron-hole channel.
To explain this point more clearly we recall that the interacting electron-hole propagator is given by the solution of the Bethe-Salpeter Equation (BSE) (Fig. \ref{BSE} (a))
\begin{equation}\label{BSEL}
\begin{split}
L(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4;\omega) &= L_{0}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4;\omega)\\
 &+\int d\mbox{\boldmath $\xi$}'_1d\mbox{\boldmath $\xi$}'_2d\mbox{\boldmath $\xi$}'_3d\mbox{\boldmath $\xi$}'_4 L_{0}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_1',\mbox{\boldmath $\xi$}_2';\omega)I(\mbox{\boldmath $\xi$}'_1,\mbox{\boldmath $\xi$}_2',\mbox{\boldmath $\xi$}_3',\mbox{\boldmath $\xi$}_4')L(\mbox{\boldmath $\xi$}_3',\mbox{\boldmath $\xi$}_4',\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4;\omega)
\end{split}
\end{equation}
where $L_{0}$ is the non interacting electron-hole propagator (also integrated over the frequencies of the external legs)  and $I$ is the {\it irreducible} 4-point interaction function, which includes only diagrams that cannot be separated into two parts by cutting a single  noninteracting electron-hole propagator $L_{0}$ (see Fig.~\ref{BSE} (b)).   Notice that in writing the above equation we have assumed that the irreducible 4-point interaction is instantaneous in time, i.e., it does not depend on the frequencies of the external legs.  This is, of course, an uncontrolled approximation, and we know that it misses some important physics\cite{Romaniello,Strinati}   -- yet it is this assumption that enables us to write a closed equation for the frequency-integrated electron-hole propagators.
\begin{figure}
\includegraphics[width=5.0 in]{BSE}
\caption{Diagrammatic representation of the Bethe-Salpeter equation in real space (a) and in the localized basis (b).}
\label{BSE}
\end{figure}

\begin{figure}
\includegraphics[width=5.0 in]{kernel}
\caption{Diagrammatic representation of the Bethe-Salpeter Kernel $I$ for the electron-hole Green's function in real space (a) and in the gaussian-plane wave basis (b).}
\label{KernelBSE}
\end{figure}
The instantaneous irreducible interaction $I$ contains, among many terms, an exchange-type electron-hole interaction of the form
\begin{equation}
I^{x}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4)=-i\delta(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_2)\delta(\mbox{\boldmath $\xi$}_3-\mbox{\boldmath $\xi$}_4)v(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_3)\,
\label{kernel_hartree}
\end{equation}
(see Fig.~(\ref{KernelBSE}(a))).
The  Coulomb interaction can be separated into a long-range part
\begin{equation}
v_{lr}(\bm{\xi}-\bm{\xi}') = \int_{BZ2} \frac{d^2 {\bf q}}{(2\pi)^2}\frac{2\pi e^2}{q} e^{-q|z-z'|}e^{i{\bf q}\cdot({\bf r}-{\bf r}')}
\end{equation}
 where the integral runs over all values of $q_z$ and over ${\bf q}$ in the first Brillouin zone of the two-dimensional periodic lattice (BZ2), and a short-range part
 \begin{equation}
\bar v(\bm{\xi}-\bm{\xi}') = \sum_{{\bf G} \neq 0}\int_{BZ2} \frac{d^2 {\bf q}}{(2\pi)^2}\frac{2\pi e^2}{|{\bf q}+{\bf G}|} e^{-|{\bf q}+{\bf G}||z-z'|}e^{i({\bf q}+{\bf G})\cdot({\bf r}-{\bf r}')}\,.
\end{equation}
where  the sum runs over all the two-dimensional reciprocal lattice vectors different from {\bf 0}.
The  electron hole propagator $\bar L$, which enters Eq.~(\ref{P00}), satisfies the same equation as $L$ (Eq.~(\ref{BSEL})), the only difference being that the long-range part of the interaction  is excluded: only  the short-range part, $\bar v$, is retained in $I^x$.

The BSE for $\bar L$ has the form
\begin{equation}
\begin{split}
L(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4;\omega) &= L_{0}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4;\omega)\\
 &+\int d\mbox{\boldmath $\xi$}'_1d\mbox{\boldmath $\xi$}'_2d\mbox{\boldmath $\xi$}'_3d\mbox{\boldmath $\xi$}'_4 L_{0}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_1',\mbox{\boldmath $\xi$}_2';\omega)\bar{I}(\mbox{\boldmath $\xi$}'_1,\mbox{\boldmath $\xi$}_2',\mbox{\boldmath $\xi$}_3',\mbox{\boldmath $\xi$}_4')\bar{L}(\mbox{\boldmath $\xi$}_3',\mbox{\boldmath $\xi$}_4',\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4;\omega)
\end{split}
\end{equation}
where $\bar I$ is $I$ minus the long-range interaction term $I^{x}_{lr}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4)=-i\delta(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_2)\delta(\mbox{\boldmath $\xi$}_3-\mbox{\boldmath $\xi$}_4)v_{lr}(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_3)$.

A further approximation that is commonly made at this point is to approximate the irreducible interaction as the sum of short-range exchange and direct terms (Fig.~\ref{KernelBSE}(a)):
\begin{equation}
\bar I(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4)= \bar I^{x}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4)+\bar I^{d}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4)\,,
\end{equation}
where
\begin{equation}
\bar I^{x}(\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4)  = -i\delta(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_2)\delta(\mbox{\boldmath $\xi$}_3-\mbox{\boldmath $\xi$}_4)\bar v(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_3)
\end{equation}
and
 \begin{equation}
    \bar I^{d} (\mbox{\boldmath $\xi$}_1,\mbox{\boldmath $\xi$}_2,\mbox{\boldmath $\xi$}_3,\mbox{\boldmath $\xi$}_4) = \delta(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_3)\delta(\mbox{\boldmath $\xi$}_2-\mbox{\boldmath $\xi$}_4)W_{0}(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_2, \omega=0)
    \label{kernel_corr}
    \end{equation}
where $W_{0}(\mbox{\boldmath $\xi$}_1-\mbox{\boldmath $\xi$}_2, \omega=0)$ represents the statically screened Coulomb interaction.

The four-point functions are straightforwardly represented in our basis set.  Taking as a prototype  $L(\bm{\xi}_1,\bm{\xi}_2,\bm{\xi}_3,\bm{\xi}_4;\omega)$  we see that this is replaced by the matrix $L_{\alpha\beta,\gamma\delta}({\bf k},{\bf k}',{\bf q};\omega)$ according to the scheme illustrated in the figure and analytically described by the equation
\begin{equation}
L(\bm{\xi}_1,\bm{\xi}_2,\bm{\xi}_3,\bm{\xi}_4;\omega) = \sum_{{\bf k},{\bf p},{\bf q}}\sum_{\alpha\beta\gamma\delta}\chi^\alpha_{{\bf k}}(\bm{\xi}_1)[\chi^\beta_{{\bf k}-{\bf q}}(\bm{\xi}_2)]^*L_{\alpha\beta,\gamma\delta}({\bf k},{\bf p},{\bf q};\omega)[\chi^\gamma_{{\bf p}}(\bm{\xi}_3)]^*\chi^\delta_{{\bf p}-{\bf q}}(\bm{\xi}_4)
\label{L_real_space}
\end{equation}
where
\begin{equation}
L_{\alpha\beta,\gamma\delta}({\bf k},{\bf p},{\bf q};\omega)=\int d\bm{\xi}_1\bm{\xi}_2\bm{\xi}_3\bm{\xi}_4 [\chi_{\alpha,{\bf k}}(\bm{\xi}_1)]^*\chi_{\beta,{\bf k}-{\bf q}}(\bm{\xi}_2)
L(\bm{\xi}_1,\bm{\xi}_2,\bm{\xi}_3,\bm{\xi}_4;\omega)
\chi_{\gamma,{\bf p}}(\bm{\xi}_3)[\chi_{\delta,{\bf p}-{\bf q}}(\bm{\xi}_4)]^*
\end{equation}
In this basis, the BSE takes the form
\begin{eqnarray}
L_{\alpha\beta,\gamma\delta}({\bf k},{\bf p},{\bf q};\omega)&=&L_{0 (\alpha\beta,\gamma\delta)}({\bf k},{\bf p},{\bf q};\omega)\nonumber\\&+& \sum_{{\bf k}'{\bf p}'}\sum_{\alpha'\beta'\gamma'\delta'}L_{0,(\alpha\beta,\alpha'\beta')}({\bf k},{\bf k}',{\bf q};\omega) I _{\alpha'\beta',\gamma'\delta'}({\bf k}',{\bf p}',{\bf q})L_{\gamma'\delta',\gamma\delta}({\bf p}',{\bf p},{\bf q};\omega)\,.\nonumber\\
\end{eqnarray}
The noninteracting electron-hole propagator is given by
\begin{equation}\label{non_inter_L0}
L_{0(\alpha\beta,\gamma\delta)}({\bf k},{\bf p},{\bf q};\omega) = ~G_{0,\alpha\gamma}({\bf k},\omega)* G_{0,\delta\beta}({\bf k}-{\bf q},-\omega) \delta_{{\bf k},{\bf p}}\,.\
\end{equation}
The frequency integral implied by the convolution product in this equation can be done analytically, with the help of the Kohn-Sham Green's functions given in Eq.~(\ref{GF2}), the result being
\begin{equation}\label{L0abcd}
L_{0(\alpha\beta,\gamma\delta)}({\bf k},{\bf p},{\bf q};\omega) =- i\delta_{{\bf k},{\bf p}}\sum_{n,m}\psi_{\alpha,n{\bf k}}\psi^*_{\gamma,n{\bf k}}\frac{f(E_{n{\bf k}})-f(E_{m{\bf k}-{\bf q}})}{\omega-E_{n{\bf k}}+E_{m{\bf k}-{\bf q}}\pm i0^+}\psi_{\beta,m{\bf k}}\psi^*_{\delta,m{\bf k}}\,,
\end{equation}
where $E_{n{\bf k}}$ and $\psi^\alpha_{n{\bf k}}$ are, respectively, the Kohn-Sham energy and the Kohn-Sham wave function of the Bloch state $n{\bf k}$ in our representation,  and $f(E_{n{\bf k}})$ is the Fermi-Dirac occupation factor of the same state.
The  two components of the irreducible four-point interaction function are (Fig.~\ref{KernelBSE}(b))
\begin{equation}
I^{x}_{\alpha\beta\gamma\delta}({\bf k},{\bf p},{\bf q})=-i\sum_{\mu\nu}\Gamma^\mu_{\alpha\beta}({\bf k},{\bf k}-{\bf q})v_{\mu\nu}({\bf q})\Gamma^\nu_{\delta\gamma}({\bf p}-{\bf q},{\bf p})
\end{equation}
and
\begin{equation}
I^{d}_{\alpha\beta\gamma\delta}({\bf k},{\bf p},{\bf q})=\sum_{\mu\nu}\Gamma^\mu_{\alpha\gamma}({\bf k},{\bf p})w_{\mu\nu}({\bf k}-{\bf p})\Gamma^\nu_{\delta\beta}({\bf k}-{\bf q},{\bf p}-{\bf q})\,,
\end{equation}
where the three-point vertices are defined by Eqs.~(\ref{Gamma1}) and ~(\ref{Gamma2}). Here $v_{\mu\nu}({\bf q})$ denotes the matrix elements of the Coulomb interaction in our basis set, i.e.,
\begin{equation}
v_{\mu\nu}({\bf q})= \int d\bm{\xi} \int d\bm{\xi}'  \chi^*_{\mu{\bf q}}(\bm{\xi}) v(\bm{\xi}-\bm{\xi}')\chi_{\nu{\bf q}}(\bm{\xi}')
\end{equation}
and similarly for $w_{\mu\nu}({\bf q})$, where $w\equiv W_{0}(\omega=0)$ is the statically screened interaction in the same basis.  A similar expression holds for the regularized 4-point interaction $\bar I$ in terms of the regularized interaction $\bar v$, as previously discussed.

\subsection{Bethe-Salpeter equation in the single pole approximation }\label{subsection_bse}

The Bethe-Salpeter equation (BSE) for the electron-hole propagator is very complex, even after having made the simplifying assumption that the 4-point electron-hole interaction is instantaneous in time (i.e., the kernel $I$ has been taken to be frequency-independent).  A major simplification can be achieved if we restrict our attention to a single pair of bands, which we call $c$ for conduction and $v$ for valence and stipulate that the electron is in conduction band and the hole is in the valence band. Thus, in Eq.~(\ref{L0abcd}) we consider only the resonant term at the frequency $\omega = E_{c{\bf k}}-E_{v,{\bf k}-{\bf q}}$, i.e., out of the entire sum over bands, we keep only the term with $n=c$, $m=v$, $f(E_{n{\bf k}}=0)$,  $f(E_{v{\bf k}-{\bf q}}=1)$.  This is called the ``Tamm-Dancoff approximation" and it is usually  good when the system under investigation has a band gap.  Thus, the approximate form of $L_0$ for the two chosen bands is
\begin{equation}\label{PPEH}
L_{0,(\alpha\beta,\gamma\delta)}({\bf k},{\bf p},{\bf q};\omega) = i\delta_{{\bf k}{\bf p}}{\psi^{\alpha*}_{c{\bf k}}\psi^{\gamma}_{c{\bf k}}\frac{1}{\omega-E_{c{\bf k}}+E_{v{\bf k}-{\bf q}}\pm i0^+}\psi^{\delta*}_{v{\bf k}-{\bf q}}\psi^{\beta}_{v{\bf k}-{\bf q}}} \,,
\end{equation}
or, switching to the Bloch band representation
\begin{equation}
L_{0,(cv,cv)}({\bf k},{\bf p},{\bf q};\omega) \equiv i \frac{\delta_{{\bf k},{\bf p}}}{\omega-E_{c{\bf k}}+E_{v{\bf k}-{\bf q}}\pm i0^+}\,.
\end{equation}

 The interacting electron-hole Green's function, restricted to the chosen pair of bands is then given by
 \begin{equation}
   [L_{cv,cv}]^{-1}({\bf k},{\bf p},{\bf q};\omega)= [L_{0,(cv,cv)}]^{-1}({\bf k},{\bf p},{\bf q};\omega)-I_{cv,cv}({\bf k},{\bf p},{\bf q})\,.
   \label{exc_ham}
 \end{equation}
  where $I_{cv,cv}=I^x_{cv,cv}+I^d_{cv,cv}$ and
  \begin{equation}
I^{x}_{cv,cv}({\bf k},{\bf p},{\bf q})=-i\sum_{\mu\nu}\sum_{\alpha\beta\gamma\delta}\psi^{\alpha*}_{c{\bf k}}\psi^{\beta}_{v{\bf k}-{\bf q}}\Gamma^\mu_{\alpha\beta}({\bf k},{\bf k}-{\bf q})v_{\mu\nu}({\bf q})\Gamma^\nu_{\delta\gamma}({\bf p}-{\bf q},{\bf p}) \psi^{\delta^*}_{v{\bf p}-{\bf q}}\psi^{\gamma}_{c{\bf p}}
\end{equation}
and
\begin{equation}
I^{d}_{cv,cv}({\bf k},{\bf p},{\bf q})=\sum_{\mu\nu}\sum_{\alpha\beta\gamma\delta}\psi^{\alpha*}_{c{\bf k}} \psi^{\gamma}_{c{\bf k}}\Gamma^\mu_{\alpha\gamma}({\bf k},{\bf p})w_{\mu\nu}({\bf k}-{\bf p})\Gamma^\nu_{\delta\beta}({\bf k}-{\bf q},{\bf p}-{\bf q})\psi^{\delta*}_{v{\bf p}-{\bf q}}\psi^{\beta}_{v{\bf p}-{\bf q}}\,.
\end{equation}
Finally, the matrix $ [L_{cv,cv}]^{-1}({\bf k},{\bf p},{\bf q};\omega)$ for given momentum ${\bf q}$ of the center of mass of the electron-hole system is identified as $\omega \delta_{{\bf k},{\bf p}} - H^{2p,res}_{cv,cv}({\bf k},{\bf p},{\bf q})$ where
\begin{equation}
H^{2p,res}_{cv,cv}({\bf k},{\bf p},{\bf q}) =  [E_{c{\bf k}} - E_{v{\bf k}-{\bf q}}]\delta_{{\bf k},{\bf p}}+ I_{cv,cv}({\bf k},{\bf p},{\bf q})
\label{exc_kernel}
\end{equation}
is the effective Hamiltonian matrix, with indices ${\bf k}$ and ${\bf p}$. Diagonalizing this Hamiltonian is equivalent to solving the Schr\"odinger equation for the relative motion of the electron and the hole, and gives the energy of the exciton.   The excitonic eigenvalues $\Omega^S_{cv}$ and eigenfunctions $A^{S}_{vc}({\bf k})$ are obtained from the solution of the eigenvalue problem
  \begin{equation}
\sum_{\bf p} H^{2p,res}_{vc,vc}({\bf k},{\bf p},{\bf q}) A^{S}_{vc,{\bf q}}({\bf p})=\Omega^S_{cv,{\bf q}}A^{S}_{vc,{\bf q}}({\bf k})\,,
    \label{secular_eq.}
   \end{equation}
where ${\bf q}$ is the momentum of the center of mass of the exciton.

The imaginary part of the macroscopic dielectric function  is derived, taking into account the  eqs. (\ref{L_real_space}):
\begin{equation}
L(\bm{\xi}_1,\bm{\xi}_2,\bm{\xi}_3,\bm{\xi}_4;\omega) = \sum_{{\bf k},{\bf p},{\bf q}}\psi_{c{\bf k}}(\bm{\xi}_1)[\psi_{v({\bf k}-{\bf q})}(\bm{\xi}_2)]^*L_{cv,cv}({\bf k},{\bf p},{\bf q};\omega)[\psi_{c{\bf p}}(\bm{\xi}_3)]^*\psi_{v,{\bf p}-{\bf q}}(\bm{\xi}_4)
\label{L_real_Space}
\end{equation}
In the macroscopic limit, we have  ${\bf p}={\bf k}$. Expanding Eq.~(\ref{P00}) with the help of Eqs.~(\ref{exc_kernel}), (\ref{L_real_Space}), and writing  $L_{cv,cv}=\sum_S A^{*S}_{vc,{\bf q}}({\bf k})\left(\omega-\Omega^S_{cv,{\bf q}}\right)^{-1}A^{S}_{vc,{\bf q}}({\bf k}) $ in the eigenvector basis set, we find

\begin{equation}
     - \Im m~\chi_P(\omega)= \frac{1}{N_c}\lim_{{\bf q} \to 0}\frac{e^2}{q^2}\sum_S\sum_{{\bf k} vc}\left| \int d \bm{\xi}  \psi_{c,{\bf k}}(\bm{\xi}) e^{i{\bf q}\cdot{\bf r}} \psi^{*}_{v,{\bf k}}(\bm{\xi})\right |^2 \left|A^{S}_{cv,{\bf q}}({\bf k}) \right|^2   \pi\delta(\omega -\Omega^S_{cv{\bf q}})\,,
      \label{eps_bse}
 \end{equation}
which is the generalization of the equation in ref. (\onlinecite{PhysRevB.62.4927}) to the quasi-2D case.

The above formulas take into account only the resonant part of the electron-hole propagator between the two selected bands.  When the antiresonant part is also considered, the e-h effective Hamiltonian $H^{2p,exc}$ becomes a $2\times 2$ matrix:

\begin{equation}
 \left( \begin{array}{cc}
 H^{2p,res}_{vc,vc}&  I_{vc,cv}  \\
-(I_{vc,cv})^{*} &-(H^{2p,res}_{vc,vc})^* \\
 \end{array} \right)\,,
\end{equation}
where all the entries are matrices with indices ${\bf k}$ and ${\bf p}$.  The  excitonic eigenvalues and eigenvectors are obtained by diagonalizing this more general Hamiltonian, resulting in  Casida-like equations \cite{casida_Eq}.

\section{Summary and outlook}\label{summary}
In this paper we have proposed that calculations of the electronic structure of quasi-two dimensional materials be performed on a native two-dimensional basis, consisting of two-dimensional Bloch sums of numerically generated atomic orbitals, such as the ones used in the AIMS-FHI approach.  This approach removes the unphysical assumption of periodicity in the third dimension, which may be a cause of spurious results.    The formal structure that we have developed in this paper lays the foundation  for a direct two-dimensional numerical implementation of Kohn-Sham, GW, and Bethe-Salpeter equations in quasi 2D systems. We expect that the two-dimensional implementation of these tasks will speed up the calculations and make them more reliable, once the required computer codes are fully developed.  While it may take a considerable initial effort  to write the computer codes that will accomplish these tasks, we are confident that the payoff will be very high in the long run, resulting in a powerful computational tool occupying an intermediate position between those of molecular quantum chemistry and those of conventional solid state physics.

\section{Acknowledgements}
  The authors thank A. H. Castro-Neto for his suggestions and support.
  PET gratefully acknowledges support from NRF under Grant No. R-723-000-001-281.
  GV gratefully acknowledges the hospitality of the Center for Advanced 2D Materials at NUS and support from DOE Grant No. DE-FG02-05ER46203.

redpajama_set_name: RedPajamaArXiv


I was in the gym this morning, with what looked like a tough set to achieve. The set included Jerks (heavy), Bumps (heavy), Swings (heavy) and Farmer's Hold, heavy, max time. I was going to struggle to get in 12 reps per minute with the Jerks, and the Farmer's Hold, coming at the end when I was tired, was going to be testing.
This entry was posted in going for reps, Jerks, kettlebells, pentathlon, pre-fatigue, strength training, swing sets, Uncategorized, warm up and tagged indian clubs, Jerk, kettlebells, Pentathlon training, strength training, warm up by admin. Bookmark the permalink.


Made with the finest quality care and materials, the L7 Rehabilitation Treadmill provides the best and safest support for all your rehabilitative programs. The L7 offers a large 20" x 58" running surface and a 400-pound user weight capacity. With a zero starting speed, 300 micro-amp isolation leakage kit and extended parallel medical handrails, this treadmill is ideal for any physical therapy center. A number of unique options are also available such as a reversing treadbelt for downhill walking.
The Landice Control Center comes standard on the L7 Rehabilitation Treadmill. Included is an integrated reading/accessory rack; a personal cooling fan; and a convenient water bottle holder. Check out our additional items that will enhance your workout in the console image.
The hand-held remote stop-start switch allows therapists to manipulate the patient's legs while remaining in control of the treadmill operation. (Hand Held stop-start can also be purchased independently of reverse for $225); moreover, the reversing belt option is ideal for practitioners who prescribe downhill and retro-walking therapies.


text:
Home Top News Tsunami warning issued for West Coast, Chile and Japan
Tsunami warning issued for West Coast, Chile and Japan
Cory Weinberg Jan 16, 2022 0 Comments
In the United States, a tsunami alert was issued for the western coast of Hawaii, which has already been hit by "minor flooding." The National Weather Service recommends "leaving beaches, harbors and marinas" in the affected areas, noting that the U.S. Hawaiian Islands did not cause damage and that "only minor ones" were affected by the flood.
The states of California, Oregon and Washington may be affected, with Alaska and the Canadian province of British Columbia referring to the NWS.
The Met Office warned that "the main expected damage is strong currents and flooding of beaches and low-lying areas."
In Tonga, people were evacuated from the tsunami following a volcanic eruption
Who can save the Tongan Islands from people fleeing high on Saturday to escape the tsunami caused by the spectacular eruption of the Hunga Tonga-Hunga Ha'bai volcano that alerted the US, Chile and Japan to the tsunami alert.
Shot footage taken from space showed the moment of the eruption, where the volcano released smoke and ash clouds, as well as the wave immediately kicking into the sea.
Hunga Tonga-Hunga Ha'apai volcano is one of the uninhabited islands of Tonga, 65 km from the country's capital Nuku'alofa, where the eruption caused a 1.20m tsunami on Friday, the Australian Meteorological Office said.
The previous tsunami did not exceed 30 cm. The warning was also removed as the volcano erupted again.
"It's a big explosion," Mere Taufa, a resident of the house at the time, told the Stuff news site.
"The ground shook, the whole house shook. It was coming in waves. My brother thought bombs would explode near our house," he said.
See also Eurostar speeds up between London, Paris and Brussels
A few minutes later, water invaded their house and she saw the wall of a nearby house collapse.
The expelled king
"We knew immediately that it was a tsunami and this water flowed into the house. You could hear the screams all over and everyone started running to the high ground," he added.
King Tubo VI of Tonga was evicted from the royal palace of Nuku'aloba and taken to a villa not far from the coast.
The eruption lasted eight minutes, and Fiji officials said they heard "distant thunder-like noises" off the Fiji Islands 800 km away.
They warned residents to shut off the water supply to protect them from acid rain or ash.
Victorina Kyova of the Tonga Public Utilities Commission called on the people to "stay away from all threatened areas, beaches, reefs and all flat beaches."
Authorities have advised the entire population to stay indoors as much as possible and wear masks if they have to go outside and to protect all water supplies there.
Tsunami warnings have been issued for Fiji and Samoa, New Zealand and Australia.
Australian authorities have warned people around Sydney and New South Wales to "get out of the water and stay away from the water's edge".
In Chile, the National Emergency Office warned of a possible "small tsunami" of Easter Island and other Chilean archipelagos.
As a precautionary measure, the Juan Fernண்டndez archipelago has been asked to evacuate coastal areas prone to small tsunami after a volcanic eruption on the islands of San Felix, Easter Island and Chile. , "Said Onmi.
See also Presented by Halot in Australia - Construction Koyola


text:
|}

Die Bahnstrecke Portland–Island Pond ist eine Eisenbahnhauptstrecke in Maine, New Hampshire und Vermont (Vereinigte Staaten). Sie ist Teil der Eisenbahnverbindung von Portland (Maine) nach Montreal. Der Personenverkehr wurde 1967 eingestellt, Güterverkehr besteht noch zwischen New Gloucester und Island Pond und wird durch die St. Lawrence and Atlantic Railroad durchgeführt. Ein kurzer Abschnitt im Stadtgebiet von Portland bis East Deering ist stillgelegt und dient teilweise heute dem Maine Narrow Gauge Railroad Museum als Trasse für ihre Museumsbahn. Der Streckenabschnitt von East Deering bis hinter New Gloucester ist außer Betrieb, aber noch nicht offiziell stillgelegt.

Geschichte

1845 gründete John Alfred Poor in Portland die Atlantic and St. Lawrence Railroad mit dem Ziel, eine Bahnstrecke von Portland in Richtung Montreal zu bauen. In Kanada gründete ein befreundeter Geschäftsmann die St. Lawrence and Atlantic Railway, die die Strecke von Montreal aus bauen sollte. In Island Falls (Vermont) sollten die beiden Strecken aufeinander treffen. Da weite Teile des damals bestehenden Bahnnetzes in Kanada die Kolonialspur, also 5½ Fuß (1676 mm), hatten, einigte man sich auch auf diese Spur. Gleichzeitig wollte man damit erschweren, dass kanadische Kunden ihre Transportgüter nach Boston fahren ließen, von wo aus ebenfalls eine Strecke in Richtung Montreal in Planung war, allerdings in Normalspur (1435 mm). Am 20. August 1846 begann der Bau von Portland aus. Die Strecke wurde abschnittsweise wie folgt eröffnet:

Im Oktober 1846 hatte auch die kanadische Gesellschaft von Longueuil am Sankt-Lorenz-Strom gegenüber von Montreal aus mit dem Bahnbau begonnen. Die Verbindung bei Island Pond ging am 11. Juli 1853 in Betrieb. Bereits am 1. Juli jenes Jahres erwarb die Grand Trunk Railway die kanadische Gesellschaft, die ab dem 5. August auch die Atlantic&St. Lawrence pachtete.

Nachdem schon bald viele kanadische Strecken auf Normalspur umgebaut worden waren, erwies sich auch auf der Strecke Portland–Montreal die Kolonialspur als nicht mehr zeitgemäß. Ab 1871 hatte die Strecke keine Verbindung mehr zu anderen Bahnen. Innerhalb von nur 12 Stunden in der Nacht vom 25. zum 26. September 1874 nagelte man daher die gesamte Strecke von Portland bis Montreal auf 1435 Millimeter Spurweite um. Daraufhin wurden im Raum Portland auch Verbindungsstrecken zu den anderen Bahngesellschaften gebaut. Da die Strecke sich regen Verkehrs erfreute, wurde der alte Endbahnhof in Portland bald zu klein. Dennoch dauerte es bis zum 4. November 1903, bis ein neues größeres Empfangsgebäude eröffnet werden konnte. Entworfen vom Architekturbüro Spier&Rohns besaß der Bau einen hohen Uhrenturm sowie eine mit rotem Granit verzierte Fassade. Zwei kleinere runde Türme flankierten den Haupteingang.

Nach 1916 ging das Transportaufkommen zunehmend zurück, da einerseits die Wirtschaft durch den Krieg geschwächt war und andererseits mit Flugzeugen und Straßenfahrzeugen andere Transportmittel zur Verfügung standen. 1923 ging die Grand Trunk Railway in den Canadian National Railways auf. Die neue Bahnverwaltung entschied, ihre zu verschiffenden Güter mehr zu kanadischen Häfen in Halifax und St. John zu transportieren, als zu US-amerikanischen, um Exportkosten zu sparen. Auch das brachte einen deutlichen Rückgang der Transportzahlen.

Nach dem Zweiten Weltkrieg nahmen die Fahrgastzahlen weiter drastisch ab. Nachdem 1948 schon der Turm des Bahnhofsgebäudes in Portland abgerissen worden war, fiel im März 1966 auch der Rest des Gebäudes der Abrissbirne zum Opfer. Nachdem schon ab 1960 nur noch einmal pro Woche in der Sommersaison ein Expresszug zwischen Portland und Montreal verkehrte, endete der Personenverkehr auf der Strecke am 12. August 1967 ganz.

Im Januar 1984 brannte die Back-Cove-Brücke in Portland ab, und wurde auch danach nicht wieder aufgebaut. Die Strecke vom nördlichen Brückenkopf bei East Deering und Portland India Street sowie das Verbindungsgleis zum Güterbahnhof an der Commercial Street wurden stillgelegt. Auf der Trasse zwischen India Street und dem südlichen Brückenkopf der Back-Cove-Brücke errichtete das 1993 eröffnete Maine Narrow Gauge Railroad Museum eine Museumsbahn in der in Maine früher üblichen Schmalspurweite von 610 Millimetern. Am 22. Mai 1989 verkaufte die Canadian National die gesamte Strecke an die Emons Transportation Group für 12 Millionen US-Dollar. Diese gründete die St. Lawrence and Atlantic Railroad mit Sitz in Island Pond und betreibt seitdem den Güterverkehr auf der Strecke.

Von Dezember 1993 bis Anfang 1997 verkehrte in der Wintersaison der Sunday River Silver Bullet Ski Express zwischen East Deering und dem Wintersportort Bethel, teilweise sogar täglich. Der Betrieb rentierte sich jedoch nicht und wurde im Herbst 1997 nicht wieder aufgenommen. Am 27. November 2013 stellte die St. Lawrence&Atlantic den Güterverkehr zwischen East Deering und dem Streckenpunkt New Glouster (km 41,79) ein und beantragte die Stilllegung dieses Abschnitts.

Streckenbeschreibung

Der Ausgangsbahnhof der Strecke befand sich in Portland direkt am Strand östlich der Kreuzung India Street/Commercial Street. Hier befindet sich heute das Schmalspurbahnmuseum. Die Strecke verlief zunächst entlang der Strandpromenade bis zur Back-Cove-Brücke. Auf diesem Abschnitt liegt heute das Gleis des Museums in einer Spurweite von 610 Millimetern. Die Drehbrücke steht zwar noch, ist jedoch seit dem Brand 1984 nicht mehr befahrbar. Die Gleise beginnen unmittelbar am nördlichen Brückenkopf. Das Stück von hier bis zum Güterbahnhof East Deering wurde zuletzt noch als Rangiergleis benutzt. Seit 2013 ist der Abschnitt von hier bis kurz vor Danville Junction jedoch außer Betrieb und steht vor der Stilllegung. Kurz nach dem Bahnhof East Deering überquert die Bahn den Presumpscot River und verlässt dabei das Stadtgebiet von Portland. Parallel zur Küste verläuft die Strecke nordöstlich weiter bis Yarmouth, wo sie nach Norden abbiegt und die südliche Hauptstrecke der Pan Am Railways niveaugleich kreuzt. Entlang dem Royal River bewegt sich die Trasse weiter bis Danville, wo die nördliche Pan-Am-Hauptstrecke ebenfalls niveaugleich gekreuzt wird. An beiden Kreuzungen bestehen Verbindungsgleise.

Nach Danville biegt die Bahn nach Nordwesten ab und erreicht nach wenigen Kilometern Lewiston Junction, wo über ein Gleisdreieck die Stichstrecke nach Lewiston abzweigt. Bei Mechanic Falls quert die Strecke den Little Androscoggin River. Hier kreuzte früher die Strecke der Portland and Rumford Falls Railway. Die Trasse verläuft parallel zum Fluss weiter und kreuzt ihn erneut in South Paris, wo auch die kurze Stichstrecke nach Norway abzweigt. In West Paris, unmittelbar vor dem ehemaligen Bahnhof, befindet sich eine weitere Flussbrücke. Hier verlässt die Strecke den Fluss und führt weiter nordwärts entlang mehrerer Seen bis Locke Mills. Östlich der Stadt überquert die Bahn den Round Pond auf einem Damm und verläuft ab hier westwärts. In Bethel trifft die Strecke auf den Androscoggin River, den sie bis Berlin an dessen Südufer begleitet.

In Berlin befinden sich verschiedene Industrieanschlüsse, die früher der Berlin Mills Railway gehörten, inzwischen aber in den Besitz der St. Lawrence&Atlantic übergegangen sind. Die Strecke verlässt nun das Flusstal und verläuft bis Groveton über einen Höhenzug. In Groveton biegt die Trasse in das Tal des Connecticut River ab, den sie bei North Stratford quert. Danach verläuft die Strecke erneut über einen Höhenzug und erreicht schließlich Island Pond am gleichnamigen See. Die Bahn geht hier in die Strecke nach Montreal über.

Personenverkehr

Im Mai 1869 fuhren ein Expresszug Portland–Montreal, ein Expresszug zwischen Portland und South Paris sowie ein Personenzug von Portland nach Island Pond. Diese Züge hielten zwar an allen Stationen, dennoch benötigte der Express für die Strecke bis Island Pond acht Stunden und 50 Minuten, der Personenzug 15 Stunden und 20 Minuten.

Der Fahrplan vom 28. September 1913 sah an Werktagen zwei Expresszüge Portland–Montreal sowie einen Personenzug Portland–Island Pond vor. An Sonntagen fuhr nur ein Expresszug Portland–Montreal. Die Fahrzeit zwischen Portland und Island Pond betrug für die Expresszüge fünf Stunden und 35 Minuten, für den Personenzug sechs Stunden.

Nach dem Fahrplan vom 7. Januar 1934 gab es damals nur noch einen täglich verkehrenden Expresszug Portland–Montreal, der für die Strecke bis Island Pond fünf Stunden und zehn Minuten, in Richtung Portland sogar nur vier Stunden und 45 Minuten benötigte.

Literatur
 Ronald D. Karr: Lost Railroads of New England. Branch Line Press, Pepperell MA 1996, ISBN 0-942147-04-9.
 Robert M. Lindsell: The Rail Lines of Northern New England. Branch Line Press, Pepperell, MA 2000, ISBN 0-942147-06-5.

Einzelnachweise

Bahnstrecke in Vermont
Bahnstrecke in New Hampshire
Bahnstrecke in Maine
Spurweite 1676 mm
Spurweite 610 mm
Grand Trunk Railway
Canadian National Railway


Image gallery nutmeg cabinets is just one of the many collections of pictures or photos that are on this website. Image gallery nutmeg cabinets is posted on the category Shea Homes Design Studio in the dwigallery.com website. This post of "image gallery nutmeg cabinets" was published on 27-05-2018 by dave and has been viewed 825,473 times.
We hope you can find what you need here. We always effort to show a picture with HD resolution or at least with perfect images. Image gallery nutmeg cabinets can be beneficial inspiration for those who seek an image according specific categories, you can find it in this site. Finally all pictures we have been displayed in this site will inspire you all. Thank you for visiting.
Image gallery nice homes is posted in the category Nice House Image and published on 20-05-2018 by martin. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery nice homes is posted in the category Nice House Image and published on 22-08-2018 by martin. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery nice homes is posted in the category Nice House Image and published on 04-07-2018 by jonshon. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery nice homes is posted in the category Nice House Image and published on 16-01-2018 by jonshon. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery modern homes is posted in the category House Images Gallery and published on 22-05-2018 by paul. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery nice mansions is posted in the category Nice House Image and published on 05-07-2018 by martin. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery nutmeg cabinets is posted in the category Shea Homes Design Studio and published on 27-05-2018 by dave. Image source: keywordsuggest.org. Click on the title to see more..
Image gallery home design front 28 images home design ultra modern home designs bungalow is posted in the category House Design Image Gallery and published on 24-01-2018 by martin. Image source: bedlamagora.com. Click on the title to see more..


text:
How Formula 1 Kills its Heroes
Formula 1 F1 Insider - 11. June 2019
The penalty against Sebastian Vettel splits Formula 1, as well as his behavior afterward. But it's exactly these emotions this sport lives of. A commentary by Bianca Garloff editor in chief at German motorsport magazine Auto Bild...
F1 Teammate Comparison So Far
Formula 1 F1 Insider - 21. April 2019
The teammate is the most important performance benchmark in Formula 1. ABMS and F1 Insider look back on the team-internal data for 2019 so far. You always want to beat your own teammate...
Valtteri Bottas – No More Mr. Nice Guy!
Formula 1 F1 Insider - 21. February 2019
The Mercedes driver doesn't want to be number two anymore. We had a special appointment with Mercedes driver Valtteri Bottas (29) at the tracks in Barcelona, sitting in a conference room on the first...
Vettel vs. Leclerc – Does Ferrari Mismanage the Rivalry?
Formula 1 F1 Insider - 15. May 2019
The Italian press is merciless. After five Ferrari defeats in a row, the hunt is on for the Scuderia. "Ferrari crashes into a real crisis," wrote Gazetta dello Sport. Corriere dello Sport wasn't any...
Schumi Documentation Comes to the Theaters
Formula 1 F1 Insider - 8. July 2019
The Schumi News Ticker: The Latest On Michael Schumacher +++ May 12: Michael Schumacher's life comes on the big screen! The documentary "Schumacher" about the record champion of Formula 1 will run in the...


The Poulan Pro PP5020AV 20-inch 50cc 2 stroke gas powered chain saw is a surprisingly powerful machine, considering the market it targets and the price point. In other words, the Poulan Pro PP5020AV is a novice-targeted chainsaw that can take many professional lumberjacks by surprise.
What Makes the Poulan Pro The best Chainsaw?
Weighing in at 10 pounds, the Poulan Pro PP5020AV offers the best and latest features at a competitive price. Aimed at users who do not use chainsaw for professional use, the Poulan Pro PP5020AV is equipped with a pull start procedure and decreased apparatus handle that ensures lessened operator fatigue. Some of the other salient features of this chainsaw are the spring and purge assist, 50cc DuraLife engine, SuperClean air filtering system, ability to access the spark plug and air filter sans tools, automatic chain oiler, etc.
Of all the consumer chainsaws on the market, the Poulan Pro PP5020AV packs in the maximum power (50cc). And the power comes in at a competitive price. Most other similar chainsaws don't pack in so much engine displacement and cost at least 100 dollars more.
The Poulan Pro PP5020AV is ideal for beginners who are not too sure about spending a lot on chainsaws, but at the same time do not want a major dip in performance.
The chainsaw consumes bar oil optimally, ensuring the bar and chain do not overheat when it's at full throttle.
Upon arrival, the saw comes completely assembled, along with the mixing oil. If you're a newbie who hasn't used a chainsaw before or if reading the instruction manual doesn't seem encouraging to you, the ability to use the chainsaw right out of the box should be quite inviting.
The Poulan Pro PP5020AV certainly won't be your go-to tool if you make money cutting and trimming trees. You'll have to look for the "pro" models that cost significantly higher.
The saw isn't right for larger trees or diameter stumps. Though you may certainly get through the wood, it may not be extremely smooth and convenient.
The chain that comes with the saw isn't the best, but it still does the job. If you can, get the chain replaced and you'll see a marked difference in functionality.
Do not use the saw as soon as you power it on. Idle the saw for some time and let it warm up a bit. This warming up is essential if you want to push the saw to its limit and derive maximum power. Not doing so could harm the bar and chain.
As aforementioned, the Poulan Pro PP5020AV is a fairly potent chainsaw that's both reliable and versatile. You can certainly expect this chainsaw to carry out a range of cutting and trimming tasks. However, don't expect it to perform heavy-duty tasks, especially frequently. If you do not use this chainsaw too hard, the Poulan Pro PP5020AV would come along fine for quite a few years. Though not the best or the most powerful chainsaw ever made, the Poulan Pro PP5020AV is certainly the best chainsaw for the money.


text:
Reading: Nigeria's inflation falls to 21.34 per cent first time in 11 months
Nigeria's inflation falls to 21.34 per cent first time in 11 months
Nigeria's inflation rate eased for the first time in 11 months to 21.34 per cent.
Last updated: January 16, 2023 at 5:15 PM
By SU9 staff 2 weeks ago Add a Comment
The country's inflation rate had risen for 10 consecutive months, up to November 2022, when it reached 21.47 per cent.
The National Bureau of Statistics in its latest report said the country's inflation rate showed a decline of 0.13% between November and December.
The report read, "In December 2022, the headline inflation rate eased to 21.34% compared to November 2022 headline inflation rate which was 21.47%.
"Looking at the trend, December 2022 inflation rate showed a decline of 0.13% when compared to November 2022 inflation rate.
"However, on a year-on-year basis, the headline inflation rate was 5.72% points higher compared to the rate recorded in December 2021, which was (15.63%). This shows that the headline inflation rate increased in the month of December 2022 when compared to the same month in the preceding year (i.e., December 2021).
"On a month-on-month basis, the percentage change in the All Items Index in December 2022 was 1.71%, which was 0.32% higher than the rate recorded in November 2022 (1.39%). This means that in the month of December 2022, the general price level was 0.32% higher relative to November 2022.
"The percentage change in the average Consumer Price Index for the 12 months ending December 2022 over the average of the CPI for the previous 12 months period was 18.85%, showing 1.89% increase compared to the 16.95% recorded in December 2021."
TAGGED: inflation
SU9 staff January 16, 2023
Previous Article Policeman shot dead as Gunmen Attack INEC office in Enugu
Next Article Enugu police repel attack on INEC office, one killed


Process of extracting chromium from a chromium ore or concentrate by oxidation, which comprises suspending the chromium ore or concentrate in a bath of molten salts and introducing an oxygen-containing gas into the suspension in a sufficient amount and for a sufficient amount of time to oxidize chromium therein.
Two kinds of chromite with various Fe(II) contents were employed to verify the proposed speculation on the role of Fe(II) in the leaching process of chromite. Moreover, the subsequent extraction of chromium from the leachate was studied, and a new process for chromium oxide production from chromite is put forward in this paper. 2.
Extraction Chromite, FeCr 2 O 4, is the most commercially useful ore, and is extensively used for extraction of chromium. Chromium is produced in two forms: (Chemistry of the Elements, Greeenwood and Earnshaw, Chapter 23). (a) Ferrochrome by the reduction of chromite with coke in an electric arc furnace.
The use of chromite as a refractory is next in importance to the metallurgical applications of chromium. A typical analysis of a chromite suitable for refractory purposes is 38 to 48 percent Cr 2 O 3, 12 to 24 percent Al 2 O 3, 14 to 24 percent Fe 2 O 3, 14 to 18 percent MgO, and less than 10 percent SiO 2.
may be used for extraction instead of the costly rectified spirit. ¾ The detailed procedure is as follows: ¾After the imbibition stage the material is packed in a percolator.


We currently have automatic recording and I have programmed 2 buttons on users snom 715 phones to pause and resume the recording (using the starcode F key http://wiki.snom.com/Settings/fkey/starcode) is there any way we could get this to notify the user? eg the BLF button lights up when paused and extinguishes when resumed?
That would be a pretty cool feature to have. We might have to put it in our bucket list if possible.
either that or an email notification perhaps?
Wouldn't that completely flood your inbox? or an Admin's inbox in case of an agent, in an agent group doing that?
IMHO the best way would be to control the BLF for the recording mode. It might not work with every phone, but that would IMHO the most intuitive way to signal the user.
im sure this could be implemented the same way as the login agent button on a snom phone?
maybe we could get this put in for the next release?
Actually at least snom, Grandstream and Yealink have a recording function on their buttons. Right now we have it for ad-hoc. They way this works is a INFO message with a special header; we need to try if the PBX can actually send it to tell the phone that recording is on.
yes I have seen the button http://wiki.snom.com/Settings/recording_mechanism i did try and set this up with DTMF tone but snom requires the same sequence to pause and resume.
the agent group button has this BLF interaction so i suppose it may not be that difficult to provide interaction.
is there any update on implementing this feature?
when the key is pressed I am seeing the below in logs.
but this has the undesired effect of sending the DTMF tones when the button is pressed.