text:
title: Dynamics
inshort: CRM & ERP [Salesforce]
translator: Microsoft Cognitive Services
---

Mens mange Office 365 apps og tjenester repræsenterer avancerede produkter, omfatter Dynamics 365 en række Microsoft cloud-baserede customer relationship management (CRM), menneskelige ressourcer og enterprise ressourceplanlægning (ERP) produkter, som kan arbejde alene eller sammen for at opfylde mange linjer-of-business behov.

Salg
---------

Salget er Dynamics's salesforce automation app.  Det hjælper dig med at automatisere hele salgsprocessen herunder konti, kontaktpersoner, kundeemner, muligheder og aktiviteter som aftaler, e-mails og telefonopkald.

Kundeservice
---------

Kundeservice bemyndiger kundesupport repræsentanter til at styre sager og spore løsning af problemer.  Det kan bruges til både interne eller eksterne kunder.

Field Service
---------

Field Service overkommer operationer i felten for organisationer, der udfører leverancer, installation, vedligeholdelse og inspektion.  Det spor ressourcer og mennesker gennem en afsender interface.  Mobile apps understøtter flere enheder.

Talent
---------

Talent tilbyder apps for at tiltrække talent (ansættelse og rekruttering) samt onboarding nye medarbejdere.

Finansiering og operationer
---------

Finansiering og operationer tilbyder finansielle muligheder herunder finans, kreditor, og tilgodehavender samt operations management services som supply chain automation, indkøb, asset management og logistik.

Detail
---------

Retail hjælper virksomheder med at administrere store operationer og merchandising, såsom salg, kampagner, sourcing og genopfyldning.

Projekt Service automatisering
---------

Projekt Service aids projektledelse, ressourceoptimering, forudsige projektets rentabilitet, og øge produktiviteten med en forenklet brugergrænseflade, der er nemmere at lære end mest projekt management værktøjer.  Det omfatter visuelle interfaces til Ressourceplanlægning, matchende folk til projektet roller og visning af projekternes forløb.

Marketing
---------

Det giver Marketing marketing automation og event management kapaciteter såsom automatiserede emails, give næring til marketingkampagner og begivenhed registrering. Det er ombytning nemlig Microsoft Dynamics Marketing, som ophørte i maj 2018.

Business Central
---------

Business Central omfatter økonomistyring, supply-chain management, salg, kundeservice, projektledelse, fremstilling og warehouse management kapaciteter. Det er rettet mod små og mellemstore virksomheder.

Portal
---------

Dynamics 365 inkluderer en portal interface, hvilket forenkler adgang især for lejlighedsvise brugere som debitorer, kreditorer og medarbejdere, der har brug for selvbetjening kapaciteter.  Dynamics Portal gemmer sine data og konfiguration metadata i Dynamics 365 og respekterer sikkerhedskontrol af Dynamics 365.

Konfigurationer i Dynamics 365
---------

Dynamics 365 kan udvides via løsninger, en række tilpasninger, som kan være installeret i din forekomst af Dynamics 365 til at tilføje nye objekter, felter, forespørgsler, rapporter og andre elementer.  Du kan installere flere programmer i ét tilfælde, så løsningerne, der kan bygges for dine unikke krav. Microsoft udgiver gratis løsninger, som er synlige i Dynamics 365.

Tredjeparts-apps kan du udvide Dynamics 365 med hjælpeprogrammer, præ-bygget integrationer og ekstra funktioner til implementeringer for specifikke brancher og scenarier. Microsoft [AppSource](https://appsource.microsoft.com/en-US/) er en online markedsplads for Dynamics 365 apps fra Microsoft samt tredjeparter.

Office 365 integrationer
---------

-Dynamics 365 kan du gemme dokumenter i SharePoint.

-Outlook e-mails kan spores automatisk som aktivitetsposter og tilknyttet kundeemner, kontaktpersoner, konti og salgsmuligheder.

-Data kan være output fra Dynamics 365 ved hjælp af Office skabeloner.

-Dynamics 365 kan sende rapporter og forespørgsler til statisk og dynamisk Excel-filer samt til andre formater som PDF.

-Ordet fletninger kan anvendes i Dynamics 365 til at generere tilpassede e-mail-meddelelser.

-Et Outlook app integrerer Dynamics 365 med Office 365.

Sikkerhed
---------

Indhold i Dynamics 365 er integreret med Office 365 sikkerhed, der bruges som godkendelsesprovideren.  Dynamics 365 tilbyder en rig sikkerhedsmodel, der er felt - og postniveau, og regulerer adgangen baseret på et organisationshierarki.  Det betyder, at optage adgangen kan kontrolleres af organisationsenhed (f.eks. tillader kun sælgere at se konti eller muligheder, som tilhører dem endnu så chefer til at køre rapporter for alle kunder).

Uddannelse
---------

-[Dynamics Microsoft Virtual Academy](https://mva.microsoft.com/product-training/microsoft-dynamics#! lang = 1033), Microsoft

Feedback
---------

-[Dynamics 365 ideer Forum](https://experience.dynamics.com/ideas/list/?forum=1c8854a6-5cdf-4681-bba8-4b6b806fcf7d)

Microsoft-ressourcer
---------

-[Dynamics 365 dokumentation](https://docs.microsoft.com/en-us/dynamics365/)

-[Dynamics 365 køreplanen](https://dynamics.microsoft.com/en-us/release/spring-2018-release/#release-notes)

-[Dynamics 365 på YouTube](https://www.youtube.com/channel/UCJGCg4rB3QSs8y_1FquelBQ)

-[Dynamics 365 på kvidre](https://twitter.com/MSFTDynamics365)

-[AppSource](https://appsource.microsoft.com/en-US/)

Lignende applikationer
--------------------

-SalesForce (CRM)

-SugarCRM (CRM)

-Oracle (CRM og ERP)

-SAP (CRM og ERP)

-Accumatica (ERP)

-Netsuite (ERP)

-Zendesk (Customer service)

-Arbejdsdag HCM (menneskelige ressourcer)

-HubSpot (CRM og marketing)

Forfatter
---------

-[James Townsend](https://twitter.com/jamestownsend), Dynamics 365 troede leder

Metadata
--------

-Eksterne deling understøttes

-App anvendelig nemlig desktop og ambulant

redpajama_set_name: RedPajamaGithub


Access Bank Ghana has committed to issuing a sustainability report following the world-acclaimed Global Reporting Initiative, GRI, Sustainability Reporting Standards.
When fully implemented, Access Bank will become one of the first banks in Ghana to adopt the GRI Standards for sustainability reporting. The initiative will lead to efficient and effective sustainability reporting for the Bank, as part of steps to offer superior value in reporting to the Bank's various stakeholders.
Commenting on the initiative, the Executive Director for Business Development at Access Bank Ghana, Mr. Ifeanyi Njoku indicated that the initiative was critical to the Bank's business operations and will help to ensure that opportunities and resources for future generations are not jeopardized.
He stated: "For us in Access Bank, sustainability goes beyond meeting regulatory requirements. It involves strategic planning and decision-making in creating a culture of economic, social and environmental responsibility across the Bank, its people and the entire value chain".
A one-day workshop facilitated by officials from the GRI Netherlands office was held at the Bank's Head Office in Accra to initiate the reporting process.
The workshop, which is in part of GRI's Competitive Business Programme being implemented across several countries including Ghana, was organized to train key staff from various units within the Bank.
Speaking on the occasion, the Head of Corporate Communications at Access Bank, Nana Adu Kyeremateng, expressed his appreciation to the GRI team for using the workshop to strengthen the performance and reporting capacity of participants. He was optimistic that these activities will pave way for the Bank to publish its maiden stand-alone sustainability report in 2019.
Sustainability remains the bedrock of Access Bank Group's operations which span across 8 African countries, China, India, Dubai, Lebanon and the United Kingdom. The workshop is part of a series of deliberate steps by the Bank to lead the way for sustainability across the globe.
Over the years, Access Bank has demonstrated its continued commitment to influence social, economic and environmental systems beyond making profits and continues to spearhead its sustainability drive through unrivalled investments in Education, Health, Environment, Sports and the Arts.
Currently, Access Bank is ranked as the 12th largest Bank in Ghana by assets and is operating one of the largest branch networks in the country. The Group currently boasts of a considerable number of award-winning sustainability initiatives since inception.


text:
Home Business Features Detroit: Post Bankruptcy
Detroit: Post Bankruptcy
The city's historical ward system produced mostly corruption and inefficiencies. An at-large city council wasn't much better. Now comes a city split into seven districts. Welcome to the brave new world of Detroit.
Elizabeth Bastian
Detroit has acquired many nicknames in its more than 300 years of existence — Rock City, Motor City, and Renaissance City. But there's a new name looming on the horizon: District City. In November, for the first time in almost a century, Detroiters will elect council members based on a nonpartisan, seven-district system (in addition to two at-large seats).
The new districts are intended to establish a much higher degree of accountability for residents and local business owners. The representatives will need to quickly educate themselves on the present state of affairs and offer a vision of progress in their locality. In essence, each council member overseeing a district will become the ultimate block captain, answerable to every imaginable constituent.
To get up to speed, both during and post-bankruptcy, the representatives can tap Detroit Future City, a new master plan. Within its 350-plus pages is information about new employment districts, the most promising residential neighborhoods for reinvestment, more efficient transportation modes, and innovative ideas to make use of acres of vacant land.
As the city seeks to address more than $18 billion in liabilities, align city services with the most efficient number of workers, and create more public-private partnerships to boost operations, the way forward offers hope. Trouble is, without a roadmap, the new crop of leaders may succumb to the infighting and entitlement that saw the city file for Chapter 9 bankruptcy in mid-July.
So where is Detroit going?
While the city lacked any kind of formal government until 1802, it wasn't until 1824 that the council replaced the board of trustees as the legislative body. The first council consisted of five aldermen, the mayor, and a recorder.
The system worked well, but as Detroit grew in population and the industrial age advanced, government operations became overwhelming.
By 1915, there were 42 council members representing 21 different wards. Corruption and factionalism ran rampant in a city where the population was more than 925,000. The new city charter of 1918 sought to change that by limiting the council to nine seats. The charter also switched to a nonpartisan, at-large format.
The system of at-large elections has continued — but it will end when the new city council system kicks off in January 2014. Although the early 20th century legislation may have ended the corruption of Detroit land barons, it did not permanently halt malfeasance and fraud. Over the years there have been calls for a revision to the at-large format to instill equity and responsiveness. Whether representation by district will streamline government operations, improve services, and spur development remains to be seen.
Earlier this year, the Detroit Works Project published urban planning recommendations for the city based on two years of study and community engagement. The resulting Detroit Future City Plan booklet follows in the footsteps (and, in some cases, the physical footprint) of Judge Augustus P. Woodward's street grid plan that came about following the 1805 fire that leveled what was a collection of wood-framed structures. The new plan also draws upon the city's 1951 master plan and other mapping efforts from several regional organizations such as the Southeast Michigan Council of Governments.
More recently, Dan Gilbert, founder and chairman of Quicken Loans Inc., which has located 10,000 workers downtown since 2010, released a master plan for the downtown area and the lower Woodward corridor that includes the renovation of existing buildings into office, residential, and retail uses; active streets with artists, merchants, and food carts; greater green space; and improved modes of transportation (M-1 Rail system).
Most of that activity will occur in Council District 6, which is home to most of downtown, roughly half of the Midtown area, several historic residential districts, southwest Detroit, and Corktown. Planners forecast that existing businesses and organizations in District 6 could create a combined 27,500 jobs over the next decade. The figure does not include Mike and Marian Ilitch's development of a hockey arena and urban center at the northwest corner of I-75 and Woodward.
Despite the current and anticipated influx of jobs, there are still some problems that need to be resolved in the area.
"The first thing has to be safety, because I think public safety is a real concern," says Leslie Lynn Smith, president and CEO of TechTown, a technology incubator on the campus of Wayne State University. "Transportation comes up pretty close after that, because a city this size absolutely has to be able to rely on transportation to create an independent economy for itself. The third thing is economic development, because some of the other underlying problems start to resolve themselves when you have a secure, safe neighborhood and a vibrant economy."
While District 6 may gain the most new jobs created in the next few years, District 5 won't be far behind. In addition to containing the remaining sections of downtown and Midtown, it is also home to the Dequindre/Eastern Market corridor, Indian Village, Belle Isle, Lafayette Park, and several large industrial areas including the I-94 Industrial Park and the Russell Industrial Center. It also contains the East Jefferson Avenue district, which is dominated by historic residential towers and retail centers.
The other east-side enclaves — District 3 and District 4 — consist of some established and promising businesses and operations, including Coleman A. Young International Airport, where air traffic has increased threefold since 2012; several automotive plants, including the Chrysler Jefferson North Assembly Plant; Chandler Park; and several dozen riverfront homes. Moving to the west side of Woodward, the north central area, represented by District 2, includes the University of Detroit Mercy, Marygrove College, and the Detroit Medical Center's Sinai Grace Hospital.
While some council areas, such as District 6, are teeming with infrastructure to support growth, there are some that are virtually vacant of employment, notably District 1 and District 7, both located on the far west side. The question is, are they doomed to be jobless zones of continued urban decay?
"All parts of the city are going to be in play, and all districts are going to be in play, but what we want to make sure is that where those investments are made capitalizes on those existing areas that can accommodate that growth — where the zoning is in place and is appropriate," says Dan Kinkead, director of Detroit Future City.
Because the council districts were based on population counts, things will eventually change. Already, downtown and Midtown have residential occupancy rates that are above 90 percent, and there are several housing projects in the works. The population is inevitably going to increase in these areas, as more people decide to live in close proximity to work.
Each of the districts has its own intrinsic qualities that can be built on. "Even as these districts are strong, Detroit's economy at large is anemic," Kinkead says. "One of the key points we like to make all the time is that Detroit itself is not too big; its economy is too small. We need to grow the economy in this city, and we start growing it in these districts." db
Previous articlePizza Power
Next articleHantz Woodlands to Plant 15,000 Trees on Detroit's East Side
Pure Tim
The Century Club 2019
2019 Champions of the New Economy

redpajama_set_name: RedPajamaCommonCrawl


Save 30% Discount lonelyplanet.com sale Promo Codes, which provides Travel guides, guidebooks and phrasebooks. using dayscoupon.com thousands of reliable discount voucher codes to meet your favorite commodity with more affordable price, Limited Time Offer!
Buy One Get One Free.
Escape with An eBook – Up to 70% off.


Last Christmas we received the suggestion of the this Argentinean band from the pleasant Rosario, as soon as we heard their self-titled debut, it was obvious for us that they should be in Prog Archives, but again the question was where, because they are not the typical Symphonic band with Classical or Baroque structure and a lot of solos. LAQUESIS blends different styles, genres and moods to create a fresh and eclectic sound rooted in the tradition of Argentinean Symphonic but much more aggressive.
The album is opened by Efecto Placebo (Placebo Effect) and it's sung in English, what is normally a problem in Latin American bands due to the strong accent, but this guys whisper the words in a way that reminds me of SERU GIRAM, with a heavy edge. Unlike most young bands who try to demonstrate their full potential from the first track, the Argentinean band plays with the changes creating soft and gradual transitions, with a nice vocal work. The keyboards are delightful, but the rhythm section impressed me more.
Tema X (X Theme) captures the listener from the start with a jazzy intro where the guitar and drums interplay brilliantly and are enhanced by lush organ passages and Moog reminiscent of ELP. Not the traditional Symphonic we are used to, but it's fluid and full of strength. Around the 2.50 mark, the music changes radically to enter more into Symphonic territory with a killer guitar solo.
Hamacamatic organ intro reminds clearly of KANSAS (Carry on my Wayward Son), but then it gets far more elaborate and eclectic blending itself with some form of Latin Jazz. Even when the song has nice piano and guitar solos, they keep visiting that initial organ passage making variations on the same theme. Very interesting structure.
Puestas de Sol (Sunsets) is a beautiful melodic piano based track that offers us a complete palette of styles that go from soft and romantic to frenetic and complex, surely one of the best expressions of modern Symphonic I hear in the last year. The guitar solo is powerful and addictive.
When I was expecting more powerful and heavy material LAQUESIS caught me by surprise with Lemuria, a soft melodic track with Italian Symphonic influence in the most pristine style of bands like PABLO EL ENTERRADOR or LA MAQUINA DE HACER PÁJAROS, but gets better, because after four minutes they offer us one of most impressive Mellotron and organ display, at this point the best song from the album and even better because Ariel Loza sings in Spanish, a language he's obviously comfortable with.
Laquesis ends the album with Las Moiras (Suite) a 16:05 mythological epic divided in four parts (Laquesis, Cloto, Átropos and Requiem, a song that I won't even try to describe, because words can only ruin the listening experience for an audience avid of complex material rooted in the 70's but with a modern twist. But I can say it's the perfect closure for a very good album.
Even though I enjoyed Laquesis from the first to the last note, it's obvious we are before a new band with a great debut, so won't rate it with s stars, but It's also evident for ma that this guys can offer us even better releases in a near future, so I will go with four solid stars, hoping they will give us a complete masterpiece soon.
Well, it would be a bit short-sighted to say that LAQUESIS is a new band arriving on the progressive rock scene. This quintet from Rosario/Argentina is existing for some years anyway, continuously refining and maturing their song material. In 2013 they finally felt it was about time to close this process up and to officially release their elaborations. This eponymous debut outing offers a fine blend of heavy and symphonic ingredients, with the emphasis on tricky compositions. Vocals - though Martin Puntonet is equppied with a proper singing voice - are not very present, which surprises in some way.
Efecto Placebo turns out to be a really strong opener, keyboarder Diego Actis works some Supertramp reminiscence in here. And in fact the diversified keyboard job is the band's trademark first of all, while perfectly corresponding with Guillermo Caminer's guitar appearance. The following songs, starting with Terra X, are instrumental, melodic, tricky, partially balladesque, partially groovy, comprising all the beloved ingredients which compose an excellent progressive rock production. On Lemuria vocals return again. this time in Spanish and the extended Las Moiras suite is consisting of four parts, showing some classical background.
As for my sentiment LAQUESIS have produced a really elaborated album, their patience was worth while. This is technically flawless,.featuring very melodic songs and vocals alternating in English and Spain. Though appearing a bit heaver overall, especially fans of Karmakanic or The Flower Kings will enjoy this album, I'm quite sure. Definitely a highlight and a big recommendation to prog purists, you shouldn't miss that.
Music is an endless beauty. No matter how many horrible pop or even rock bands appear in the scene, there will always be musicians whose talent, discipline and creativity keep music safe and sound from those evil moneymakers. We all know progressive rock is not a true profitable job, however, we have to thank the bands that continue making music in this scene in spite of the minimum support they receive.
But I will not support a band just because of the fact they make prog rock, no, I support them because they create good prog rock, and this is the case of Argentinean band Láquesis, whose bass player Ariel Loza has been keen on social media spreading the word, and the band caught my attention so I wanted to listen to the whole CD, which is very good.
"Tema X" is a wonderful track, I like the first minutes with first class instrumental music that has some delicious tunes of prog rock, with some funky touches that together create a sound full of cadence. Each musician puts its grain of sand, so them all are equally important to Láquesis music, and that can be actually heard while the seconds pass. This is one of my favorite songs of the album.
Every time I listen to "Hamacamatic" I cannot help but remembering Kansas "Carry on?" song, the guitar sound is alike so it is funny to have that reminiscence. I love how the band puts different figures every minute, so the music is not plain, in spite the rhythm could be he same for minutes, they always have something new to bring. This is another nice instrumental track, it is a nice mixture of A.C.T. meets Kansas.
"Puestas de sol" is literally the longest track here (though later will come a suite divided in tracks), its 12 minutes give us a nice rollercoaster of sounds and feelings. First we can listen to a soft and calm introduction, mid-tempo drums and a beautiful guitar sound, and after 2:30 minutes explosive keyboards appear like a bomb, but it lasts only some seconds before the calm returns. Later the music changes again, a new structure begins, a beautiful mellotron enters and give more beauty to the music, which is led by great guitars and supported by a solid bass and drums base. The song has different changes, but it is always interesting, so it is like a book divided in chapters that let your imagination fly. Excellent!
"Lemuria" surprised me because the lyrics return but now in Spanish, I thought they would sing all in English, but it is always great to listen the bands in their native language. The music is pastoral, calm, melodic, with a beautiful keyboard background while acoustic guitar brings that calm and mellow sound, accompanied by a good voice. The second part of the song is rockier, with some Crimsonian nuances and those keyboards that in moments remind me of Ayreon. A nice and fresh musical trip here!
Finally, "Las Moiras" bring the last 16 minutes of the album. This is a long song divided in four parts, each one with a title. The first one is "Láquesis", a heavy prog oriented instrumental track, fast tempo and cool musicianship here. "Cloto" is a cool part that brings happiness. The moment where keyboards appear make me feel great, it is like a moment for scream and run and be happy in the life. The sound reminded me of Willowglass, so that symphonic touch is always present. The bass sound is also beautiful, mostly in the last minute of the song.
"Atropos" starts with a bombastic keyboard sound in the league of Anglagard; seconds later a rocky guitar appears while drums mark the rhythm and bass accompany with its constant lines. The song simply flows, you just have to let your ears and soul fly. And the last one is "Requiem", a short piece with keyboards that produce a classical music oriented sound at least for the first minute. Later it changes, a darker sound appears, bass, drums, guitar and keyboards make together a tense moment. But guess what, the last minute changes again, so they surprise us with a great metal ending, full of power and energy. A great way to finish this album.
I am happy with Láquesis, a new band whose debut solid album make me feel completely satisfied. So if you have the chance, please listen to them and buy their music, so they can delight us with a second album soon. My final grade will be 4 solid stars.
One album and group from 2013 that well and truly slipped under the radar of many progressive rock fans was Argentinean band Láquesis and their debut self-titled work. Predominantly instrumental, the band deliver a thrilling symphonic prog masterwork performed with supreme musical taste and technical skill, perfectly bridging the sophistication of vintage sounds with some welcome heavy modern styles. The music is frequently driven by guitarist Guillermo Caminer, playing with a power not unlike that heard on the albums by Pendragon, and by the keyboards of Diego Actis, who delivers a rich and lavish sound throughout the disc, and despite plenty of epic drama, there's also a joyful and frequently uplifting quality to Láquesis' music that ensures symphonic fans will be in heaven.
Looking at the vocal pieces first, opener `Efecto Placebo' is not unlike moderns bands such as Aisles that mix strong vocal melodies with a dizzying array of prog-rock styles. It's mostly powered by heavy and brooding guitars, but despite one or two moments where the English vocals get a little awkward, Martin Puntonet's voice is actually full of confidence and true emotion. After a run of instrumental pieces, fifth track `Lemuria' starts as a gently melancholic folk ballad with acoustic guitar, weeping Mellotron flute, fragile piano and soft synth orchestration, but the Spanish vocals here, provided by bass player Ariel Loza, have a better flow and passion than the English ones on the opening track.
But it's the purely instrumental numbers that form the bulk of the album where the band and their musical talents are best displayed. The amount of instrumental sounds the band moves through starting during `Tema X', `Hamacamatic' and `Puestas de Sol' will make many other bands enviable. Late-night jazzy ruminations, slow-burn bluesy diversions, harder rock moments and classic grandiosity all seamlessly weave together, calmer serene passages with bombastic outbursts by way of a dizzying array of tempo changes expertly controlled by the powerhouse drumming of Martin Teglia. The keyboards especially are exquisite - ambient gentle synth washes, creeping gothic piano, spiralling Moog soloing and Hammond organ fire just a few examples. Ariel Loza's fluid bass slinks away in the background, always mixed loud and clear without ever intruding. Guillermo's guitars are full of epic and grand power . They'll be funky and grooving one second, heavy and blasting the next, but always atmospheric and burning with real soul, and they frequently convey a smouldering David Gilmour or Nick Barrett feel, which not many players can pull off so well. Throughout these pieces (and the whole album really), the band displays such control, that although they feature a wide variety of sounds and styles, they never come across as disjointed, instead perfectly flowing and transitioning together.
The album then delivers a four-part sixteen minute instrumental `Las Moiras' suite, bringing together all the skills displayed on the previous tracks to even great effect. A mix of vintage and modern flavours, it starts with a heavy metal driving guitar passage with suitably punchy drumming and break-neck nimble synth soloing that comes across like a mix of Neal Morse/Spock's Beard with the brooding outbursts of the Porcupine Tree albums from their final couple of years, and perhaps even a more varied take on Dream Theater's signature sound. The second movement begins as a pretty piano and acoustic guitar lament, before leaping into a jangly and adorable classic early 70's Genesis Moog whirl with a reflective fretless bass finale! In less than four minutes, the third movement darts through attacking heavy snarling guitar riffs and attacking drumming, delirious upbeat synth soloing with warm Hammond organ ripples and dreamy Pink Floyd mellow moments, and even a little space-rock mystery. The final fourth passage is a darkly dramatic orchestrated synth epilogue full of class and tasteful grandness with an uneasy tension.
2013-14 has offered several sublime symphonic and instrumental albums - Trion's `Funfair Fantasy', Willowglass' `The Dream Harbour', Phoenix Again's `Look Out' and the Mad Fellaz debut instantly come to mind, and this album can justifiably be placed alongside those examples. With so many selections of progressive related music to choose from in the modern era, the poorer and less interesting acts fall aside, but those that stand tall and proud with great music truly shine, and this is certainly the case with Láquesis and this album. Mark them down as a band to keep an eye on, and fans of progressive music in a proudly symphonic style should look into this band and their album right away, as it's one of the best modern symphonic releases of the last few years.
Post a review of LÁQUESIS "Láquesis"


text:
\section{Warm-up}

In this section, we explain the idea behind our main construction and illustrate its work in a simpler setting. We get a small improvement on one of the results of Pappacena's~\cite{Papp}, which allows us to prove the $n=5$ case of Conjecture~\ref{conjPaz}.

We say that a set $S\subset\mathrm{Mat}_n(\mathbb{F})$ is \textit{irreducible} if it generates $\mathrm{Mat}_n(\mathbb{F})$ as the $\mathbb{F}$-algebra. If a set $S$ is not irreducible, and if $\mathbb{F}$ is algebraically closed, then there exist $p\in\{1,\ldots,n-1\}$ and $Q\in\operatorname{GL}_n(\mathbb{F})$ such that, for any $A\in S$, we have
\begin{equation}\label{eq1}Q^{-1} A Q=\left(\begin{array}{c|c}
A_{11}&A_{12}\\\hline
O&A_{22}
\end{array}\right)\end{equation}
with $A_{11}$ being a $p\times p$ matrix. (This is \textit{Burnside's theorem}, see~\cite[Theorem~1.5.1]{RRBook}.)

\begin{lem}{\upshape(See Corollary~3 in~\cite{Mar}.)}\label{lemOV}
Let $\mathcal{A}$ be a matrix algebra whose elements are of the form~\eqref{eq1}, and let $\mathcal{A}_1,\mathcal{A}_2$ be the sets of all $A_{11}, A_{22}$ blocks of matrices in $\mathcal{A}$, respectively. Then $\ell(\mathcal{A})\leqslant\ell(\mathcal{A}_1)+\ell(\mathcal{A}_2)+1$.
\end{lem}

We will say that a matrix $Z\in\mathrm{Mat}_n(F)$ is \textit{square-zero} if $Z^2=0$. The main idea of the proof of Theorem~\ref{thrlen} is to control the product $\lambda\rho(\lambda)$, where $\rho(\lambda)$ is the minimal rank of non-zero square-zero matrices that arise as linear combinations of words of length at most $\lambda$. We show in Section~3 below that we can reduce $\rho$ to $1$ whilst saving the property $\lambda\rho(\lambda)\in O(n\log n)$, and then we apply Pappacena's technique to deal with low rank matrices, see~\cite[Theorem~4.1]{Papp} and Corollary~\ref{lemPap} below. More precisely, let $H\in\mathbb{F} S^{\leqslant \lambda}$ be a square-zero matrix; it can be written as
$$H=\left(\begin{array}{c|c|c}
O&O&I_\rho\\\hline
O&O&O\\\hline
O&O&O
\end{array}\right)$$
with respect to some basis. If some matrix $A$ with bottom-left block of small rank $r>0$ comes as a linear combination of words of length $l$, then the matrix $HAH$ is square-zero, has rank $r$, and comes as a linear combination of words of length at most $l+2\lambda$. As we will see in Claims~\ref{lem4} and~\ref{lem5} below, we can always find an appropriate matrix $A$ to reduce the rank of a square-zero matrix. The following lemma illustrates our approach to the proof of Claim~\ref{lem4}.

\begin{lem}\label{lemill}
Consider an irreducible set $S\subset\mathbb{F}^{n\times n}$ and a non-zero vector $v\in\mathbb{F}^{n}$. If $\mathbb{F} S^{\leqslant(n-2)}v\neq\mathbb{F}^n$, then $\mathbb{F} S$ contains a matrix with minimal polynomial of degree $n$.
\end{lem}

\begin{proof}
The sequence $$\mathbb{F} v=\mathbb{F} S^0v\subset \mathbb{F} S^{\leqslant 1}v\subset\ldots\subset \mathbb{F} S^{\leqslant k} v=\mathbb{F}^n$$ is strictly increasing~\cite[Theorem~4.1]{Papp}, so the assumption of the lemma implies $k=n-1$ and $\dim \mathbb{F} S^{\leqslant t}v-\dim \mathbb{F} S^{\leqslant (t-1)}v=1$ for all $t\in\{1,\ldots,n-1\}$. Therefore, we can set $\mathcal{B}_0=\{v\}$ and inductively complete $\mathcal{B}_{t-1}$ to a basis $\mathcal{B}_t$ of $\mathbb{F} S^{\leqslant t}$ by adding a single vector $v_{t}$. With respect to the basis $\{v,v_1,\ldots,v_{n-1}\}$, every matrix in $S$ has the form
$$A=\begin{pmatrix}
* & \ldots &\ldots&*&*\\
a_{21} & * &\ldots&*&*\\
0 & \ddots &\ddots&\vdots&\vdots\\
\vdots & \ddots &\ddots&*&*\\
0 & \ldots&0 &a_{n,n-1}&*\\
\end{pmatrix}$$
with $*$'s denoting the entries we need not specify. Since $S$ is irreducible, every of the $(i+1,i)$ entries is non-zero at some matrix in $S$, so a generic element of $\mathbb{F} S$ has all of them non-zero --- which means that its minimal polynomial has degree $n$.
\end{proof}

\begin{thr}\label{thrnond}{\upshape (Theorems~2.4 and~2.5 in~\cite{GLMS}.)}
If an irreducible set $\mathbb{F} S\subset\mathrm{Mat}_n(\mathbb{F})$ contains a matrix with minimal polynomial of degree $n-1$ or $n$, then $\ell(S)\leqslant 2n-2$.
\end{thr}

Lemma~\ref{lemill} and Theorem~\ref{thrnond} lead to a tiny improvement of the $r=1$ case of Theorem~4.1(a) in~\cite{Papp}, which is nevertherless useful to study the case of small $n$.

\begin{cor}\label{lemPap
Let $S\subset\mathrm{Mat}_n(\mathbb{F})$ be an irreducible set and $k\geqslant 2$. If $\,\mathbb{F} S^{\leqslant k}$ contains a rank-one matrix, then $\ell(S)\leqslant 2n+k-4$.
\end{cor}

\begin{proof}
If $\mathbb{F} S$ contains a matrix with minimal polynomial of degree $n$, then we are done by Theorem~\ref{thrnond}. Otherwise, we use Lemma~\ref{lemill} and get
$$\mathbb{F} S^{\leqslant(n-2)} A S^{\leqslant(n-2)} =\sum\mathrm{Mat}_n(\mathbb{F})\cdot A\cdot \mathrm{Mat}_n(\mathbb{F})=\mathrm{Mat}_n(\mathbb{F})$$
for any rank-one matrix $A$.
\end{proof}

We are almost ready to prove the $n=5$ case of Conjecture~\ref{conjPaz}.

\begin{claim}\label{cldeg2}
Assume that the minimal polynomial of every matrix in $\mathbb{F} S\subset\mathrm{Mat}_n(\mathbb{F})$ has degree at most $2$. Then $\ell(S)\leqslant2\log_2 n$.
\end{claim}

\begin{proof}
We denote by $w$ a word in $S^{\ell(S)}$ that is not spanned by shorter words. For any $A,B\in S$, the matrices $A^2$ and $AB+BA=(A+B)^2-A^2-B^2$ belong to $\mathbb{F} S^{\leqslant 1}$, which implies that the letters of $w$ are all different and their permutations do not break the property of $w$ not to be spanned by shorter words. In particular, the products corresponding to the different $2^{\ell(S)}$ subsets of letters of $w$ should be linearly independent, which implies $2^{\ell(S)}\leqslant\dim\mathrm{Mat}_n(\mathbb{F})$.
\end{proof}

\begin{thr}\label{thr5}
If $S\subset\mathrm{Mat}_5(\mathbb{F})$, then $\ell(S)\leqslant 8$.
\end{thr}

\begin{proof}
Since a set of vectors is linearly dependent over $\mathbb{F}$ if it is linearly dependent over the algebraic closure of $\mathbb{F}$, it is sufficient to prove the statement assuming that $\mathbb{F}$ is algebraically closed~\cite[page~239]{GLMS}. Moreover, Conjecture~\ref{conjPaz} is known to hold for $n\leqslant4$ (see~\cite{Paz}), so we can use Lemma~\ref{lemOV} and assume without loss of generality that $S$ is irreducible. According to Theorem~\ref{thrnond} and Claim~\ref{cldeg2}, we can restrict to the case when $\mathbb{F} S$ contains a matrix $A$ with minimal polynomial of degree $3$. A straightforward analysis of possible Jordan forms of $A$ shows that the linear span of $I, A, A^2$ must contain a rank-one matrix, so it remains to apply Corollary~\ref{lemPap}.
\end{proof}

As said above, the case of $n\leqslant 4$ in Conjecture~\ref{conjPaz} was considered in 1984 by Paz~\cite{Paz}, but the case of $n=5$ remained open until now~\cite{GLMS}. Let us mention the works~\cite{Au1, Au2}, which cover the case $n\leqslant 6$ under the additional assumption of $\dim\mathbb{F} S\leqslant 2$.

\section{The proof of Theorem~\ref{thrlen}}

Let $A$ be an $n\times n$ matrix over a field $\mathbb{F}$, which is assumed to be algebraically closed in this section. We recall that there exists
$Q\in\operatorname{GL}_n(\mathbb{F})$ such that $Q^{-1}AQ$ has \textit{rational normal form}, that is, we have $Q^{-1}AQ=\operatorname{diag}(C_{f_1},\ldots,C_{f_k})$, where
$$C_f=\begin{pmatrix}
0 & 0 &\ldots&0&-c_0\\
1 & 0 &\ldots&0&-c_1\\
0 & 1 &\ldots&0&-c_2\\
\vdots & \vdots &\ddots&\vdots&\vdots\\
0 & 0 &\ldots&1&-c_{m-1}\\
\end{pmatrix}$$
is the companion matrix of a polynomial $f=t^m+c_{m-1} t^{m-1}+\ldots+c_0$, and the \textit{invariant factors} $f_1,\ldots,f_k$ satisfy $f_1|\ldots|f_k$.

\begin{claim}\label{lem1}
Let $\delta$ be the degree of the minimal polynomial of an $n\times n$ matrix $A$ over $\mathbb{F}$. Then the $\mathbb{F}$-linear span of $I,A,\ldots,A^{\delta-1}$ contains either a non-zero projector of rank at most $n/\delta$ or a non-zero square-zero matrix of rank at most $n/\delta$.
\end{claim}

\begin{proof}
Let $\psi$ be a polynomial that has degree $\delta-1$, divides the minimal polynomial $\varphi$ of $A$, and is a multiple of any other invariant factor of $A$. Then $\psi(A)$ has equal rank-one matrices in the places of the largest blocks of the rational normal form of $A$ and zeros everywhere else.
\end{proof}

\begin{claim}\label{lem3}
For any irreducible set $S\subset\mathrm{Mat}_n(\mathbb{F})$, there exist non-zero $\lambda,\rho$ such that $\lambda\rho\leqslant 2n$ and $\mathbb{F} S^{\leqslant\lambda}$ contains a square-zero matrix of rank $\rho$.
\end{claim}

\begin{proof}
We apply Claim~\ref{lem1} to any non-scalar matrix in $S$ and find a non-zero matrix $P\in \mathbb{F} S^{\leqslant(\delta-1)}$ that has rank at most $n/\delta$ and satisfies either $P^2=P$ or $P^2=0$. We are done if $P^2=0$; otherwise $H_B=(I-P)BP$ is a square-zero matrix for all $B$. We can have $H_B=0$ only when $\operatorname{Im} P$ is invariant with respect to $B$, but since $S$ is irreducible, this obstruction cannot happen for all $B\in S$.
\end{proof}

\begin{claim}\label{lem2}
Let $A\in\mathbb{F}^{n\times n}$ and $r\in\mathbb{N}$. Assume that $\operatorname{rank}(PAQ)\leqslant r$ holds for all $P\in\mathbb{F}^{p\times n}$, $Q\in\mathbb{F}^{n\times q}$ satisfying $PQ=0$. Then $\operatorname{rank}(A-\mu I)\leqslant 2r$ for some $\mu\in\mathbb{F}$.
\end{claim}

\begin{proof}
Both the assumption and conclusion are independent of the substitution $A\to C^{-1}AC$, so we can assume that $A$ has rational normal form. We denote the number of diagonal blocks by $k$ and their sizes by $m_1,\ldots,m_k$. We have $\min_\mu\operatorname{rank}(A-\mu I)=n-k$, and we are going to conclude the proof by constructing a unit square submatrix $A'=A[I|J]$ with $I\cap J=\varnothing$ and $|I|=|J|\geqslant 0.5(n-k)$. Namely, we pick a family of $\lfloor m_t/2\rfloor$ non-consecutive sub-diagonal ones from a $t$th diagonal block of $A$, and the union of all such families will be the diagonal of $A'$.
\end{proof}

\begin{claim}\label{lem4}
Let $S\subset\mathbb{F}^{n\times n}$, $P\in\mathbb{F}^{p\times n}$, $Q\in\mathbb{F}^{n\times q}$. Let $k$ be the smallest integer such that $PS^kQ\neq0$. Then, for any $A_1,\ldots,A_k\in S$, we have $\operatorname{rank}(PA_1\ldots A_kQ)\leqslant n/k$.\end{claim}

\begin{proof}
Let $V_0=\operatorname{Im}Q$ and $V_t=\sum_{M\in S^{\leqslant t}}\operatorname{Im}MQ$. Let $\mathcal{B}_0,\ldots,\mathcal{B}_k\subset\mathbb{F}^n$ be vector families such that $\mathcal{B}_0\cup\ldots\cup\mathcal{B}_t$ is a basis of $V_t$ for $t=0,\ldots,k$. Let $\mathcal{C}\subset\mathbb{F}^n$ be such that $\mathcal{B}_0\cup\ldots\cup\mathcal{B}_k\cup\mathcal{C}$ is a basis of $\mathbb{F}^n$. Every matrix $A\in S$ has the form
$$\left(\begin{array}{c|c|c|c|c|c|c}
 & \mathcal{B}_0 &\mathcal{B}_1 &\ldots &\mathcal{B}_{k-1} &\mathcal{B}_k&\mathcal{C} \\\hline
\mathcal{B}_0 & *  &\ldots &\ldots &\ldots &*&* \\\hline
\mathcal{B}_1 & A(1,0)& *  &\ldots &\ldots  &*&* \\\hline
\mathcal{B}_2 & O & A(2,1)& *   &\ldots  &*&* \\\hline
\vdots&\vdots&O&\ddots&*&\vdots&\vdots\\\hline
\mathcal{B}_k&\vdots&\vdots&\ddots&A(k,k-1)&*&*\\\hline
\mathcal{C}&O&O&\ldots&O&*&*
\end{array}\right),$$
where the $*$'s stand for entries that we need not specify, and the left column and top row of the matrix above indicate the basis vectors the respective blocks of rows and columns correspond to. We also have $P=\left(O|\ldots|O|P'|*\right)$, $Q=(Q'|O|\ldots|O)^\top$ with some matrices $P',Q'$ at the $\mathcal{B}_k$ position of $P$ and the $\mathcal{B}_0$ position of $Q$, respectively. For $A_1,\ldots,A_k\in S$, the matrix $PA_k\ldots A_1Q$ equals $P'A_k(k,k-1)\ldots A_1(1,0)Q'$, so its rank is at most $\min_t|\mathcal{B}_t|\leqslant n/k$.
\end{proof}

\begin{claim}\label{lem5}
Let $S\subset\mathrm{Mat}_n(\mathbb{F})$ be an irreducible set, and assume that $\mathbb{F} S^{\leqslant \lambda}$ contains a square-zero matrix $H$ of rank $\rho\geqslant 2$. Then there exist $\rho_1\in\left[1,0.5{\rho}\right]$ and
$$\lambda_1\leqslant \frac{\lambda\rho}{\rho_1}+\frac{4n(\rho-\rho_1)}{\rho\rho_1}$$
such that $\mathbb{F} S^{\leqslant \lambda_1}$ contains a square-zero matrix of rank equal to $\rho_1$.
\end{claim}

\begin{proof}
Let $P\in\mathbb{F}^{p\times \rho}$, $Q\in\mathbb{F}^{\rho\times q}$ be non-zero matrices satisfying $PQ=0$. We choose a basis such that
$$H=\left(\begin{array}{c|c|c}
O&O&I_\rho\\\hline
O&O&O\\\hline
O&O&O
\end{array}\right)$$
and define $P'=(O|O|P)$ and $Q'=(Q|O|O)^\top$. Let $k$ be the smallest integer for which there exist $P',Q'$ defined as above and $A_1,\ldots,A_k\in S$ satisfying $P'A_1\ldots A_kQ'\neq0$ (such an integer exists because $S$ is irreducible). We write $A=A_1\ldots A_k$, and we denote by $A'$ the bottom left block of $A$. Since $PA'Q\neq0$, the matrix $A'$ is non-scalar, that is, its minimal polynomial has degree $\delta>1$.

\textit{Case 1.} Assume $k\leqslant 4n/\rho$. By Claim~\ref{lem1}, there is a polynomial $\psi$ of degree at most $(\delta-1)$ such that $\rho_1:=\operatorname{rank}\psi(A')\in[1, \rho/\delta]$; we see that $H_1=\psi(HA)H$ is a square-zero matrix of rank $\rho_1$. It remains to note that $H_1$ is spanned by words of length at most $(\delta-1)(\lambda+k)+\lambda \leqslant\lambda\delta+(\delta-1)k\leqslant \lambda\rho/\rho_1+4n(\rho/\rho_1-1)/\rho$.

\textit{Case 2.} Now let $k\geqslant 4n/\rho$. The matrix $HAH$ has $A'$ at the upper right block and zeros everywhere else. According to Claim~\ref{lem4}, we have $\operatorname{rank}(PA'Q)\leqslant n/k$ for any choice of $P,Q$ as above.
We set $H_1=HAH-\mu H$ with $\mu\in\mathbb{F}$, and we conclude by Claim~\ref{lem2} that $\rho_1:=\operatorname{rank}(H_1)\leqslant 2n/k$.
So we have $\rho_1\leqslant 0.5\rho$, and $H_1$ is spanned by words of length at most $2\lambda+k\leqslant \lambda\rho/\rho_1+2n/\rho_1\leqslant\lambda\rho/\rho_1+4n(1-\rho_1/\rho)/\rho_1$.
\end{proof}

\begin{proof}[Proof of Theorem~\ref{thrlen}.]
As in the proof of Theorem~\ref{thr5}, we can assume without loss of generality that $\mathbb{F}$ is algebraically closed and $S$ is irreducible. Using Claim~\ref{lem3}, we find a square-zero matrix of rank $\rho_0>0$ in $\mathbb{F} S^{\leqslant\lambda_0}$ with $\lambda_0\rho_0\leqslant 2n$; if $\rho_0=1$, then we apply Corollary~\ref{lemPap} and complete the proof. Otherwise, we repeatedly apply Claim~\ref{lem5} and obtain a sequence $(\lambda_0,\rho_0),\ldots,(\lambda_\tau,\rho_\tau)$ such that $\rho_\tau=1$ and for all $t\in\{0,\ldots,\tau-1\}$ it holds that $\rho_{t+1}\in\left[1,0.5\rho_{t}\right]$,
$$\lambda_{t+1}\leqslant \frac{\lambda_t\rho_t}{\rho_{t+1}}+\frac{4n(\rho_t-\rho_{t+1})}{\rho_t\rho_{t+1}},$$
and every $\mathbb{F} S^{\leqslant \lambda_t}$ contains a square-zero matrix of rank $\rho_t$. By induction we get
$$\lambda_t\leqslant \frac{\lambda_0\rho_0}{\rho_t}+\frac{4n}{\rho_t}\left(t-\frac{\rho_1}{\rho_0}-\ldots-\frac{\rho_{t}}{\rho_{t-1}}\right),$$
which implies (after the substitution $\alpha_t:=\rho_t/\rho_{t-1}$) that
$$\lambda_\tau\leqslant 2n+4n\left(\tau-\sum_{t=1}^\tau\alpha_t\right),$$
and since the minimum value of $\alpha_1+\ldots+\alpha_\tau$ subject to $\alpha_t>0$ and $\alpha_1\ldots\alpha_\tau=\rho_0^{-1}$ is attained when $\alpha_1=\ldots=\alpha_\tau=\rho_0^{-1/\tau}$, we get $$\lambda_\tau\leqslant 2n+4n\tau\left(1-\rho_0^{-1/\tau}\right).$$ The right-hand side of this inequality is an increasing function of $\tau$, so it attains its maximum at the largest possible value $\tau=\log_2\rho_0$. We get $\lambda_\tau\leqslant2n+2n\log_2\rho_0$, and it remains to apply Corollary~\ref{lemPap}.
\end{proof}

The author does not expect his result to be tight even asymptotically, so this paper does not show any effort on improving the $o(n\log n)$ part of the upper bound.

\medskip

The author is indebted to O.\,V.~Markova from Moscow State University for a series of talks on the topic, which he has had a privilege to attend since 2006. Mateusz Micha\l{}ek told the author in June 2018 about a very similar problem, known as the quantum version of Wielandt's inequality~\cite{WE}, and we quickly came to a conclusion that the progress on one of these problems can lead to the progress on the other. In particular, the author hopes that the techniques developed in this paper will allow one to get an asymptotically optimal $O(n^2)$ bound for the largest value of $\tau$ such that the equality $\mathbb{F} S^\tau=\mathrm{Mat}_n(\mathbb{F})$ holds for any set $S$ for which there exists a $t$ satisfying $\mathbb{F} S^t=\mathrm{Mat}_n(\mathbb{F})$ --- while the present paper gives an $O(n\log n)$ bound for the same problem but with $S^\tau$, $S^t$ replaced by $S^{\leqslant \tau}$, $S^{\leqslant t}$, respectively.

redpajama_set_name: RedPajamaArXiv


goals | | Eh! Wot?
To hell with bucket lists.
My goals for 2010 including hobbies, fitness, and self improvement goals.
What happened in 2009! I check my progress against my goals for year and get an idea of what to work on for next year.


East Africa Roofing Systems Ltd.
Haidery Building Materials (U) Ltd.
Is not only Uganda's largest online database of local businesses and services but our state-of-the-art intuitive search function allows for quicker, more accurate results.
copyrights © 2019 White pages Uganda. All rights reserved.


This is the summary of the book "Hugo Häring The Organic Versus the Geometric". The author(s) of the book is/are Peter Blundell Jones. The ISBN of the book is 9783930698912 or 3930698919. This summary is written by students who study efficient with the Study Tool of Study Smart With Chris.


From the cult director of SAVE THE GREEN PLANET comes this action-packed thriller about a 16-year-old boy raised to become the perfect assassin. Kidnapped as a child, Hwayi was raised by five dangerous, powerful criminals. Now – 14 years later – he is forced to make a hard choice when he learns the awful truth about his parents.