Anna Wrasse Local Live on WFHB, August 29, 2018 – 1/2 hour set.
Anna Wrasse Local Live on WFHB, Dec. 20, 2017 – featuring Phillip Hammond on violin.
Anna Wrasse Local Live on WFHB, September 7, 2016 -1/2 hour set.
Winter Farmers Market, 90-minute set, 3/2/2019.
Hype for Habitat fundraiser, half hour set, 3/1/2019, BHS South.
Asian Culture Club Lunar New Year Celebration, half hour set, 2/20/2019, BHS South.
St. Charles Hawktober fundraiser, 10/27/18, half hour set with violinist Phillip Hammond.
Performed "The Time We Have" in the 2018 BEAT Fall Show, 10/16 & 10/17, Buskirk-Chumley Theater.
Ferdinand Folk Festival, opened the festival performances on the main stage with other singer-songwriter contest winners, 9/15/18.
Midway Music Festival, 1/2 hour set at Players Pub, 9/8/18.
WFHB radio, 1/2 hour Local Live broadcast featuring interview & original songs, 8/29/18.
Ferdinand Folk Festival Singer-Songwriter Showcase – three-song set, St. Benedict's Brew Works, Ferdinand, IN, 8/19/18.
VaVaVaVaudeville – two-song set with Phillip Hammond on violin. Buskirk-Chumley Theater, 8/18/18.
People's Park, 90-minute busking concert, 8/4/18.
People's Park, Bloomington Summer Concert Series, 90-minute set, 7/31/18.
Players Pub, three hour set three hour set with Phillip Hammond on violin, 7/26/18.
Trailhead Pizzeria, three hour set, 6/26/18.
Gallery Walk at Monroe Convention Center, three hour set with Phillip Hammond on violin, 6/1/18.
Bloomington Community Farmers Market, 90-minute set, 5/26/18.
Lucky's Market, three hour set, 5/19/18.
Dance Center High School Showcase, three-song set, Buskirk-Chumley Theater, 5/13/18.
Bloomington Bicentennial Street Fair, half hour set, 4/29/18.
Julie & Ray's wedding, three-song set, Lincoln, NE, 4/27/18.
BloomingTea, 45-minute set with Phillip Hammond on violin, 4/12/18.
Players Pub, two hour set, 3/30/18.
Winter Market, 90-minute set, 3/24/18.
St. Charles Fish Fry & Auction, one hour set, 3/23/18.
"Hype for Habitat" benefit, 45-minute set, 3/3/18.
Hoosier Youth Philharmonic chili supper, two-song set, 3/2/18.
Bloomington Solo Talent Competition finals, two-song set, Players Pub, 2/17/18.
Talent Show benefitting Big Brothers/Big Sisters, two-song set, 2/2/18.
Bloomington Solo Talent Competition semi-finals, two-song set, Players Pub, 1/29/18.
WFHB radio, 1/2 hour Local Live broadcast, featuring interview & original songs, with Phillip Hammond on violin, 12/20/17.
AsaBela Wings Showcase, three-song set, 12/9/17.
Bloomington Solo Talent Competition round one, two-song set, Players Pub, 10/30/17.
Mitchell-Grissom Kiwanis Club 50th Birthday Celebration Bash, one hour set, 10/21/17.
Community Farmers Market, 90-minute set, 9/30/17.
Ferdinand Folk Festival – performed "The Exception" on the main stage, and "Scars" and "Leaving us Behind" on the market stage, 9/16/17.
Kiwanis Indiana Balloon Fest, one hour solo set and Kiwanis Idol Showcase, 9/9/17.
People's Park, 90 minute set, 9/5/17.
Ferdinand Folk Festival Singer-Songwriter Showcase – Performed "Leaving Us Behind" & "Scars"; and accompanied Dawn Keller on guitar for her songs "Everybody" and "American Made", Ferdinand, IN, 8/19/17.
VaVaVaVaudeville – performed "To You" with Phillip Hammond on violin. Buskirk-Chumley Theater, 8/19/17.
People's Park, 90 minute set, 8/5/17.
Guitar Pull, Jasper Strassenfest, 8/3/17. Anna won first place with her performance of "Games".
Tuesday Farmers' Market, 7/25/17, 90-minute set.
Fourth of July Parade, with Dawn Keller, 7/4/17.
Fairgrounds pre-fireworks show, 7/1/17, one hour set.
Players Pub, two hour set, 5/27/17.
Food Truck Friday, 45 minute set, 5/26/17.
Community Farmers Market, 90-minute set, 5/6/17.
St. Charles Fish Fry and Auction, 3/31/17, half hour solo set and half hour set with violinist Phillip Hammond.
Miss Indiana Balloon Fest Scholarship Pageant, Buskirk Chumley Theater. 3/25/17, half hour set.
Trailhead Pizzeria. 3/15/17, three hour set.
Kiwanis All about Y.O.U. Red Carpet Awards, 1/30/17.
Trailhead Pizzeria. 12/21/16, three hour set .
Winter Farmers Market. 12/10/16, two 90-minute sets.
Food Truck Friday. 11/4/16, 45 minute set.
Performed "Scars" in the 2016 BEAT Fall Show, 10/28/16, Buskirk-Chumley Theater.
Great Glass Pumpkin Patch, 10/15/16, 2 hour set.
Chocolate Moose Food Truck Friday, 10/14/16, one hour set.
Rhino's All Ages Club, 10/8/16, 1/2 hour set opening for Boyhood Bravery and Lumbercat .
"Meet the Prodigies", local chapter, National Society of Arts and Letters, twenty minute set of original songs. Also performing: Phillip Hammond (violinist) and Nicolas Narducci (pianist), 9/25/16.
Ferdinand Folk Festival, 9/17/16, one hour set -.
Kiwanis Idol Finals, Indiana Balloon Fest (placed first -17 & under division), 9/10/16.
WFHB radio, 9/6/16, 1/2 hour local live broadcast featuring interview & original songs.
Players Pub, 9/3/16, 2 hour set.
Under 18 winner. Ferdinand Folk Festival singer-songwriter contest. Astra Theatre in Jasper, Indiana, 8/13/16.
Indiana State Fair, Main Street Stage, 8/7/16, 90 minute set.
Players Pub,7/30/16, 2 hour set.
County Fair Amateur Talent Competition, 7/28/16 (first place, senior novelty).
Farmer's Market circle stage, 7/23/16, 90 minute set.
4th of July Parade, YES for MCCSC float, 7/4/16.
Chocolate Moose Food Truck Friday, 6/10/16, 50 minute set.
Trailhead Pizzeria, 6/3/16, 3 hour set.
Chocolate Moose Food Truck Friday, 5/27/16, 1 hour set.
Players Pub, 5/14/16, 2 hour set.
Chocolate Moose Food Truck Friday, 5/6/16, opening for James Dupre.
Women in Music Festival to benefit Middle Way House. Rhino's All Ages Club, 4/30/16.
Chocolate Moose Food Truck Friday, 4/1/16.
Rhino's All Ages Club, 1/2 hour singer-songwriter sets, 4/8/16, 3/12/16.
Solo, Contest of Champions show choir competition, 2/5/16.
Music in the Air Musical Recital and Aerial Showcase, 11/13/15.
Performed "This Story" in the 2015 BEAT Fall Show, 10/18/15, Tri-North Middle School.
Farmers Market circle stage, 9/19/15.
Kiwanis Idol Finals, Indiana Balloon Fest, 9/12/15, 2nd place 17 & under.
Indiana State Fair Youth Talent Contest (junior vocal solo). 8/7/15.
Food Truck Friday at Chocolate Moose. 7/31/15, 8/21/15, 9/4/15, 10/2/15.
County Fair Amateur Talent Competition (first place, junior vocal solo). 7/27/15.
Original song set at Hayden's Post Songwriters Alley, Jackson, Wyoming, 6/24/15.
Players Pub, 2 hour sets: 6/18/15, 9/5/15, 12/10/15.
Trailhead Pizzeria, 3 hour sets: 7/9/15, 5/23/15, 9/19/15.
Guitarist in rock band for StagesCamp Rock the Musical. Five performances, 5/7/15-5/10/15.
Rhino's All Ages Club -3/1/15, 3/14/15, 4/11/15 & 6/20/15, 5/29/15 10/2/15.
2nd place 17 & under.
Valses Poeticos by Granados. Performed December 22, 2108.
The Little Shepherd/Serenade for the Doll by Debussy. Young Hoosier State Piano Competition, second place mid-teen classical solo, Indiana State Fair, 8/12/18.
Three Preludes by Gershwin. Duet performed with D at Indiana State Fair piano audition, 6/21/18. Honorable mention in Young Hoosier State Piano Competition, mid-teen ensemble, 2018 Indiana State Fair.
Serenade for the Doll by Debussy. Performed at Rocky Ridge Music Center, 6/16/18.
Two Rondos Op. 40 by Kabalevsky. Performed 12/17/17.
Romanian Dances #2-6 by Bartok. Performed at Rocky Ridge Music Center, 6/16/17.
Tarentelle Op. 96 by Moritz Moszkowski, duet with D, 5/28/17.


text:
Whiskey Row - Downtown Prescott
The city of Prescott (pronounced "Preskitt") was named after famed historian and author William H. Prescott, which started in 1864 and was incorporated in 1883. Prescott was named the capital of the Arizona Territory as President Lincoln wanted the capital far away from Confederate leaning cities in the south. Prescott remained the capital until 1867 when the honor was bestowed upon Tucson. 10 years later Prescott again became the capital, only to have the capital moved to Phoenix in 1889.
Today, the city of Prescott remains the County Seat of Yavapai County which includes the cities of Prescott Valley and Chino Valley among others. With its Victorian style homes it is considered to be one of the most Midwestern appearing cities in the Southwest and there are over 800 buildings in the city of Prescott on the National Register of Historic Places.
"Everybody's Hometown," downtown Prescott has a small town flavor with the center square holding the granite courthouse in a beautiful setting of green grass and large beautiful trees. Surrounding streets have a great variety of shops from restaurants and boutique shops to specialty shops for hiking gear. With nearly 450 miles of hiking trails in the 1.25 million acres of the Prescott National Forest, you may just wear out a pair of boots trying to hike them all.
At an elevation of over 5,000 feet, the city of Prescott has a wonderfully mild four season climate with bountiful sunshine 300 days a year. Mild winters with an average daytime high of 55 degrees result in the occasional light snow melting quickly, often before Noon the next day. Winter low temperatures average 30 degrees, though in recent years the days below freezing have been minimal. Spring comes early to the area yielding to a summer with an average high in the mid to upper 80's. Because of the desert climate, even summer nights tend to cool down with an average low during the summer of 55 degrees.
In 2012 the U.S. Census estimated the population of the city of Prescott at over 40,000 residents.
Prescott Arizona Business Directory
Solid 5 stars throughout the process. Todd negotiated a complex sale easily and delivered a solution that satisfied both buyer and seller. Hats off to Todd and his very competent and professional back office coordinator, Lisa Pellin.
...it was important for me to select a broker who intimately knew the Prescott real estate market and had a proven track record there.
Tracy S.

redpajama_set_name: RedPajamaCommonCrawl


text:
Home News The stop-and-search myth that maligns our police
The stop-and-search myth that maligns our police
By David Fraser
THE Guardian reported in October on research authored by a group of legal, academic and community activists campaigning for, among other things, 'fairness' for drug users, and the end of what they call the disproportionate use of stop-and-search powers by the police.
The report, called The Colour of Injustice, documents stop-and-search figures in England and Wales in 2016-17 and claims that racial bias in police stops is getting worse, with black people nine times more likely to be stopped than white. David Lammy, MP for Tottenham in north London, called the figures a 'profound injustice'.
His protest is unnecessary because the report's conclusions are based on a false premise.
The authors compared the number of stops of different racial groups with the ethnic population estimates from the 2011 Census, which remains the most recent well-validated source of information about the ethnic composition of England and Wales. Because they found a disproportionate number (by comparison with the overall demographic) of black stops they assumed the reason to be discrimination.
But it has been known for many years that this is not a valid or correct way to investigate possible police discrimination in their use of stop-and-search.
As long ago as 2000, research by the Home Office showed that it was necessary to compare stop-and-search figures, not with the racial composition and demographics of the national population (or even the resident population), but with the racial composition of those available for stop-and-search, i.e. those who hang around in public places, often at night, and who are therefore potential targets for police stops.
This research concluded that based on data from five different areas of London, including Greenwich, the borough where Stephen Lawrence was murdered, white people tended to be stopped or searched at a higher rate to the available population, while Asian people tended to be 'under-represented' and black people had a more mixed experience.
In 2004, additional research findings based on Slough and Reading found once again that, compared with the 'available population', (i.e. those out and about) those stopped and searched were not disproportionately drawn from minority groups, and again it demonstrated it was the whites who were over-represented in stops by the police. These authors state: 'The primary research error in the analysis of police stop-and-search decisions has been to compare the racial proportion of those stopped to their racial proportion in the general population rather than their proportion in the "available population".'
Thus, The Colour of Injustice repeats the false propaganda presented in the 1999 Macpherson Report, written in the aftermath of the killing of Stephen Lawrence on 22 April 1993. Paragraph 6.45 of Macpherson said: 'The over-representation of racial minorities in the national stop-and-search figures led to the clear core conclusion of racist stereotyping.' But, as illustrated, this was a seriously flawed argument. Macpherson criticised the police for the way the murder inquiry had been handled and furthermore said they were institutionally racist. This was despite the fact that he later contradicted himself by saying that 'we have not heard evidence of overt racism or discrimination'.
Macpherson's misuse of the stop figures was highly damaging. In 1999, the year his report was published, the police stopped and searched over a million individuals. The following year this number had fallen by 20 per cent to 857,000, and by 2004 it had been scaled down even further to 734,000, equating to thousands of fewer arrests and a reduced level of public protection from street violence and other crimes.
Between 2010 and 2017, the use of stop-and-search overall fell by 75 per cent. The possibility that this is one of the causes of the significant escalation in street violence over this period, especially knife crimes, resulting in so many deaths, cannot be discounted.
Why, once the flaws in Macpherson's accusation of racially biased stop-and-search practices had been identified, did no one come to the rescue of the police? Why did no one publicly explain that the investigators had not found evidence that their stop-and-search activity was discriminatory against ethnic minorities? No MP, minister or official has stepped forward to defend the police against accusations of discrimination, and free them from the burden of this false and damaging accusation.
Few events have proved so destructive to the morale of the British police than the broadcasting of this misleading propaganda. Our police have deserved better than false accusations, and they deserve better now than to have them re-worked in such documents as The Colour of Injustice, a pseudo-academic report, whose Left-wing ideology could not be more obvious, and whose scholarship could not be more threadbare.
Previous articleMay's dangerous deal and a warning the media has ignored
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David Fraser
David Fraser is the author of Licence to Kill, Britain's Surrender to Violence. He is a former senior probation officer and criminal intelligence analyst with the National Criminal Intelligence Service (now the National Crime Agency).


British Triathlon has unveiled Swim Smooth as a new consultant to the British Triathlon GE Coaching Programme. Swim Smooth will be working with the British Triathlon Coach Education team to create world class video footage for a new e-resource to be launched later this year.
The relationship highlights British Triathlon's commitment to continuous professional development for coaches, with Swim Smooth delivering an additional package of swim resources, enabling British Triathlon coaches to continue to deliver excellence in the sport of triathlon.
Swim Smooth specialises in triathlon and open water focused swimming technique and has worked with a number of athletes including British triathlete, Jodie Swallow.
Paul Moss, British Triathlon Workforce Development Manager is delighted to be working alongside the Australian company and said that "Swim Smooth has built an impressive international reputation and it is exciting that we can now utilise their experience and skills to develop this new e-resource as part of the British Triathlon GE Coaching Programme.


text:
Q: How to open monitor case? (LG Flatron L196WTQ) My monitor (LG Flatron L196WTQ) has broken recently and I know the problem is with the inverter.  From what I have read online, replacing the capacitors on the inverter board might fix it.  The problem is that I can't open the monitor.  I took off all the screws but still cannot get at the insides.  Does anyone have any ideas how I might go about doing it?

A: I actually found the post below which was quite helpful.  I just had to give it some more force with a flathead screwdriver.  I will be repairing the caps tomorrow.
http://www.ccl-la.com/blog/index.php/lg-l196wtq-bf-lcd-monitor-repair/

A: I found a service manual, which describes how to disassemble the monitor: http://www.fixdevice.com/smanuals/file/39118.html
And yes you are probably right about the caps, they are most likely dead if they are electrolytic capacitors.

redpajama_set_name: RedPajamaStackExchange


text:
Arthur Henry Fox Jr. (26 March 1924 – 15 June 1953) was an Australian rules footballer who played with South Melbourne in the Victorian Football League (VFL).

The son of Richmond Football Club player Arthur Fox, Sr., Fox arrived in Melbourne from Red Cliffs. His best season came in 1949 when he played 18 of a possible 19 games for South Melbourne. A wingman, he was selected to represent the VFL interstate team that year in Adelaide.

Once his time at South Melbourne ended he returned to Red Cliffs as coach for two seasons, in 1951 and 1952. He joined Wimmera Football League club Rupanyup in 1953 but his time with them was short. On 16 June 1953, Fox was driving from Rupanyup on the Calder Highway when he crashed his motor cycle, near Ouyen. He was rushed to a hospital in Mildura but never regained consciousness and died aged 29.

References
 Hillier, K. (2004) Like Father Like Son, Pennon Publishing, Melbourne. .

Sources

1924 births
1953 deaths
Sydney Swans players
Rupanyup Football Club players
Australian rules footballers from Victoria (Australia)
Road incident deaths in Victoria (Australia)
Motorcycle road incident deaths
Royal Australian Air Force personnel of World War II
Royal Australian Air Force airmen

redpajama_set_name: RedPajamaWikipedia


The largest sporting goods retailer in the West offers a good variety of namebrand lax gear. They have pads, helmets, training aids, heads, shafts and more. Their online site is now merged with Sports Authority.


text:
\section{Introduction}
\label{sec::1}
Einstein's crowning achievement was the geometrisation of gravity. In the general theory of relativity, space-time is not just a stage on which physical processes take place, but it has become an active actor of the whole drama. Gravity has been integrated into the geometrical structure of space-time. The modern approach to geometry exploits the duality between space and the algebra of functions on it. Building geometry in terms of function algebras turns out to be more flexible and more amenable to generalisations than direct exploration of space by traditional methods. It was Vinogradov who defined what it means for an algebra to be geometric and studied this concept in depth \cite{Nestruev,Zoo}. In order to benefit from his work, we have to use an algebraic approach to general relativity. This had already been prepared by Geroch \cite{Geroch72} and two of the authors of this paper, who proposed and developed the notion of Einstein algebras \cite{Heller92,HS95a}. However, in order to derive new information from these already well-known theoretical facts, one should place Einstein algebras in a categorical context, i.e., to regard them as objects of the category \textbf{Einst} of Einstein algebras (which is a subcategory of the category $C^\infty  $ of smooth algebras\footnote{For more generality we will also put our analyses in the context of $\mathbb{R} $-algebras.}). According to the basic idea of category theory, any Einstein algebra can be considered from the point of view of any object of the category ${C^\infty }$, which is then called a stage. Our leading example is when the stage is a Weil algebra, which can be interpreted as an ``Einstein algebra with infinitesimals''.

A given Einstein algebra, considered as an object of the category \textbf{Einst} or $C^\infty  $, describes macroscopic gravity (understood as the geometry of the spectrum of this algebra), whereas if we contemplate this Einstein algebra from the point of view of the stage, which we choose to be the ``algebra with infinitesimals'' (Weil algebra), then we can suppose it penetrates the microscopic (or submicroscopic) level, on which quantum gravity functions. It turns out that if we apply Vinogradov's notion of geometricity (adapted to this situation), this level (i.e. quantum gravity level) is geometric, but then it is unobservable from the macro-level. Technically, both algebras, the algebra responsible for the macro-level and the algebra responsible for the micro-level, are isomorphic, so the micro-level does not add anything new to the macro-level. One way of breaking this isomorphism is by dropping the geometricity condition at the micro-level. This can be done, for instance, by relaxing the assumption that the considered algebra must be commutative.

An analogous situation occurs when as stages, instead of Weil algebras, we take many other algebras, for example those that describe spaces in which with ordinary points there are associated ``generalized points'', for example closed curves (loops).

Putting general relativity, formulated in terms of Einstein algebras, in the context of category theory reveals those aspects of general relativity that remain invisible for standard tools. This works especially clearly when a given Einstein algebra, understood as an object of the relevant category, is considered from the point of view of other objects of this category. Then morphisms between these objects become dominant over objects themselves and disclose new relational properties of the system.

The plot of our work unfolds as follows. In Section \ref{sec::2}, we present some technical aspects of the algebraic approach to geometry, with particular emphasis on the notion of geometricity. We also take a step, in Section \ref{sec::3}, towards extending this notion to noncommutative algebras. From the outset we place our considerations in the context of category theory. In Section \ref{sec::4}, we define the category of Lorentz modules, and in Section \ref{sec::5} we discuss the category of Einstein algebras. In Subsection \ref{sec::5_1}, we define this category, and in Subsection \ref{sec::5_2}, we discuss its functorial aspects and show that the category of Einstein algebras is geometric\footnote{Strictly speaking, there are more than one categories of Einstein algebras, but they all have similar functorial and geometric properties.}. In the last two sections, we summarise the conclusions that emerge from our analyses. The first conclusion, commented upon in Section \ref{sec::6}, concerns the future theory of quantum gravity: if it is to be sought within the formalism analysed in this paper, and if it is to lead to effects measurable at the macro-level, it cannot be geometric (all ``background free'' theories are not geometric).  The second type of conclusions, considered in Section \ref{sec::7}, concerns rather philosophical aspects of general relativity: its placement in the milieu of category theory reveals new aspects of its relational character.

This paper can be regarded as a follow-up to \cite{Reports20}.

\section{Geometric algebras}
\label{sec::2}
Let $C$ be a commutative unital $\mathbb{R} $-algebra. Such algebras as objects, together with $\mathbb{R} $-linear algebra homomorphisms as morphisms, form a category of commutative $\mathbb{R} $-algebras, denoted $\R \textnormal{-} \mathbf{ComAlg} $. In this section, we will stay in the area of this category.

Let us define the real spectrum of an $\mathbb{R} $-algebra $C$ as
\begin{align*}
|C|_{\mathbb{R} } := [C, \mathbb{R}]_{\R \textnormal{-} \mathbf{ComAlg}}.
\end{align*}
Its point $\chi \in |C|_{\mathbb{R} }$ is a morphism $\chi: C \to \mathbb{R} $
such that
\begin{align*}
& \chi (kf+g) = k\chi(f) + \chi (g),
\\
& \chi(fg) = \chi(f) \chi(g),
\\
& \chi ({\bf 1}_C) = 1
\end{align*}
for $k \in \mathbb{R} ,\, f, g \in C$.

Now, for every $f \in C$, we define the function $\bar{f}^{\mathbb{R} }: |C|_{\mathbb{R} } \to \mathbb{R}$ by
\begin{align*}
\bar{f}^{\mathbb{R} } (\chi ) = \chi (f).
\end{align*}
If we define $\bar{C}^{\mathbb{R} } = \{\bar{f}^{\mathbb{R} } \, | \, f \in C \}$, we obtain the ringed space
$(|C|_{\mathbb{R} }, \bar{C}^{\mathbb{R} })$.

Let us consider the $\mathbb{R} $-algebra homomorphism $\Theta : C \to \bar{C}^{\mathbb{R} }$ given by $\Theta(f) = \bar{f}^{\mathbb{R} }$. It is obviously a surjection but not necessarily an injection. Let us define $J(C) = \bigcap_{\chi \in |C|_{\mathbb{R} }} \mathrm{ker}\, \chi $.

\begin{Lemma}
\label{lem1}
\begin{align*}
\mathrm{ker} \, \Theta = J(C).
\end{align*}
\end{Lemma}

\noindent \textbf{Proof.} We have the following chain of equivalences:
\begin{align*}
f \in \mathrm{ker}\, \Theta & \ \ \Leftrightarrow \ \ \Theta (f) = 0 \ \ \Leftrightarrow \ \ \bar{f}^{\mathbb{R} }(\chi ) = \chi (f) = 0, \forall \chi \in |C|_{\mathbb{R} }
\\
& \ \ \Leftrightarrow \ \ f \in \mathrm{ker} \, \chi, \forall \chi \in |C|_{\mathbb{R} } \ \ \Leftrightarrow \ \ f \in \bigcap _{\chi \in |C|_{\mathbb{R} }} \mathrm{ker} \, \chi.
\end{align*}
\hfill $\Box$

Following Vinogradov \cite{Nestruev,Zoo} we adopt the following definition
\begin{Definition}
An $\mathbb{R} $-algebra $C$ is said to be geometric if the following two equivalent conditions are satisfied
\begin{align*}
(i) & \quad J(C) = 0,
\\
(ii) & \quad \Theta \; \mathrm{is \; an \; isomorphism}.
\end{align*}
\end{Definition}

Vinogradov \cite{Zoo} observes that the elements of $\ker \Theta $ are in a sense invisible and calls them ``ghosts'', i.e., an algebra is geometric if it has no ghosts. The name ``geometric'' is justified in so far as an algebra with this property can be interpreted as a function algebra on its spectrum.

Our next move is to generalise the above construction by looking at a commutative $\mathbb{R}$-algebra $C$ from the perspective of different stages (different $\mathbb{R} $\textnormal{-}algebras) what is a typical procedure in category theory. Let us then consider the functor:
\begin{align*}
[C,-]_{\R \textnormal{-} \mathbf{ComAlg} }: \R \textnormal{-} \mathbf{ComAlg} \to \mathbf{Set}.
\end{align*}

If $A$ is an object of the category $\R \textnormal{-} \mathbf{ComAlg} $, we call $|C|_A = [C,A]_{\R \textnormal{-} \mathbf{Alg} }$ the $A$-spectrum of $C$, and the arrows $\rho : C \to A$ the points of $|C|_A$. We then proceed in close analogy to the above case when $\mathbb{R} $ was a stage.

For any $f \in C$ we thus define $\bar{f}^A: |C|_A \to A$ by
\begin{align*}
\bar{f}^A (\rho ) = \rho (f), \quad \rho: C \to A
\end{align*}
and denote $\bar{C}^A =\{\bar{f}^A \, | \, f \in C\}$. We thus have a (generalised) ringed space $(|C|_A, \bar{C}^A)$. Let us consider the homomorphism $\Theta^A : C \to \bar{C}^A$ given by
\begin{align*}
\Theta^A(f) = \bar{f}^A.
\end{align*}
It is obviously a surjection. Just as above, there is the ideal
\begin{align*}
J^A(C) = \bigcap_{\rho \in |C|_A} \mathrm{ker}\, \rho,
\end{align*}
and we also have the following analogue of Lemma \ref{lem1}.
\begin{Lemma}
\label{lem2}
\begin{align*}
\ker \Theta^A = J^A(C).
\end{align*}
\end{Lemma}

This enables us to formulate the following definition.
\begin{Definition}
An $\mathbb{R} $-algebra $C$ is said to be $A$-geometric if the following two equivalent conditions are satisfied
\begin{align*}
(i) & \quad \ker \Theta^A = \bigcap_{\rho \in |C|_A} \mathrm{ker}\, \rho = 0,
\\
(ii) & \quad  \Theta^A \; \mathrm{is \; an \; isomorphism}.
\end{align*}
\end{Definition}

If it is necessary to distinguish the case when the stage is $\mathbb{R} $ or $A$, we will refer to a given algebra as $\mathbb{R}$-geometric or $A$-geometric, respectively.

\begin{Lemma}
\label{lem3}
If $\mathbb{R} $-algebra $C$ is $\mathbb{R} $-geometric then $C$ is $A$-geometric, for every $A \in \R \textnormal{-} \mathbf{ComAlg} $.
\end{Lemma}

\noindent \textit{Proof.} Let $f \in C$. We have:
\begin{align*}
\bar{f}^A = 0 \ \ \Leftrightarrow \ \ \rho (f) = 0 \ \mathrm{ for \; every} \; \rho \in |C|_A.
\end{align*}
In particular, for $\rho = \chi \cdot \mathbf{1}_A, \, \chi \in |C|_{\mathbb{R} }$,
\begin{align*}
\bar{f}^A(\chi \cdot \mathbf{1}_A) = 0 \ \ \Leftrightarrow \ \ \chi (f) \cdot \mathbf{1}_A =0 \ \ \Rightarrow \ \ \chi (f), \; \forall \chi \in |C|_{\mathbb{R} }.
\end{align*}
Hence, since $C$ is ${\mathbb{R} }$-geometric, $f = 0$. \hfill $\Box $

The lemma is obviously also true ``in the opposite direction''. It states that it is sufficient to check $\mathbb{R} $-geometricity to conclude geometricity at any stage.

The ``quality'' of the considered spaces can be significantly improved if we restrict our analyses from the category of $\mathbb{R} $-algebras to its subcategory of smooth algebras (and their smooth homomorphisms as morphisms), denoted by $C^\infty  $. Of course, all our results will be preserved, but in many respects they could be significantly "smoothed out".

Let then now $C \in C^\infty  $, and let us consider its spectrum $|C|_A := [C, A]_{C^\infty  }$ with $A \in C^\infty  $ (using the same symbol for the spectrum as in the case of the broader category $\R \textnormal{-} \mathbf{ComAlg} $ should not lead to confusion). By definition, any $\rho \in |C|_A$ satisfies
\begin{align*}
\rho (\omega (f_1, \ldots , f_n)) = \omega(\rho(f_1), \dots , \rho (f_n))
\end{align*}
for every $\omega \in C^\infty  (\mathbb{R}^n)$ (cf. \cite{Reports20}). By repeating the constructions from the first part of this section, we obtain the ringed space $(|C|_A, \bar{C}^A)$, where $\bar{C}^A$ is itself a $C^\infty $-algebra with $\Theta^A : C \to \bar{C}^A$ being a $C^\infty $-algebra isomoprhism. In particular, we have that
\begin{align*}
\omega(\bar{f}^A_1, \ldots , \bar{f}^A_n) = \overline {\omega (f_1, \dots , f_n)}^A.
\end{align*}

Let us recall that a ringed space $(N,D)$, where $D$ is a set of real-valued functions on $N$ satisfying the following conditions
\begin{enumerate}
\item[(a)]
$\textrm{sc} \, D=D$, where $\textrm{sc} \, D := \{\omega(f_1,...,f_n) \, | \, f_1,...,f_n\in D, \omega \in C^\infty({\mathbb{R}}^n)\}$,
\item[(b)]
$D_N=D$, where $D_N$ is the set of all local $D$-functions in the topology $\tau_D$ induced on $N$ by $D$, i.e. the weakest topology on $N$ in which all functions from $D$ are continuous,
\end{enumerate}
is called a \emph{Sikorski differential space}, and $D$ is called its \emph{structural algebra} \cite{Sikorski1967,Sikorski1971}.

Observe that the ringed space $(|C|_\mathbb{R}, \bar{C}^\mathbb{R})$ constructed above automatically satisfies Sikorski's condition (a). If one endows $|C|_\mathbb{R}$ with the induced topology $\tau_{\bar{C}^\mathbb{R}}$, one can convert this ringed space into an actual Sikorski differential space by performing the ``localisation closure'' on $\bar{C}^\mathbb{R}$ \cite{Sikorski1967,Sikorski1971}. Note, however, that the localisation closure $(\bar{C}^\mathbb{R})_{|C|_\mathbb{R}}$ is often larger than $\bar{C}^\mathbb{R}$ and so it is no longer isomorphic with $C$. All in all, we have the following fact.

\begin{Proposition}
Any geometric $\mathbb{R}$-algebra $C$ can be canonically embedded in a structural algebra of a Sikorski differential space.
\end{Proposition}
\noindent \textbf{Proof.} $\Theta : C \to \bar{C}^{\mathbb{R} }$ is an isomorphism and $\bar{C}^{\mathbb{R} }$ is canonically embedded in $(\textnormal{sc} \,\bar{C}^{\mathbb{R} })_{|C|_\mathbb{R}}$, a structural algebra of the Sikorski space $(|C|_\mathbb{R}, (\textnormal{sc} \,\bar{C}^{\mathbb{R} })_{|C|_\mathbb{R}})$. \hfill $\Box $

\vspace{0.5cm}
\noindent \textbf{Example: Weil algebras.} To close this section, let us consider the Weil algebra $W = \mathbb{R} \oplus \mathbb{R} \epsilon , \, \epsilon^2 = 0$ and ask if it is geometric. Any element of its spectrum $\pi \in |W|_{\mathbb{R} }  = [W, \mathbb{R} ]_{C^\infty  }$ is given by $\pi (x + y\epsilon ) = x$.

Indeed, we have $\pi (1) \cdot \pi (1) = \pi (1 \cdot 1) = 1$, which means that either $\pi (1) = 1$ or $\pi (1) = - 1$, but the latter is excluded. Similarly, $\pi (\epsilon ) \cdot \pi (\epsilon ) = \pi (\epsilon^2) = 0$, and hence $ \pi (\epsilon ) =  0$. By linearity, we obtain that
\begin{align*}
\pi (x + y \epsilon ) = x \pi (1) + y \pi (\epsilon ) = x.
\end{align*}

Hence, $|W|_{\mathbb{R} } = \{\pi \}$. The differential structure on a one-point spectrum is $\mathbb{R} $, i.e. $\bar{W}^{\mathbb{R} } = \mathbb{R} $ which is given by
\begin{align*}
\overline{x +y \epsilon} (\pi ) = \pi (x + y \epsilon ) = x \in \mathbb{R} ,
\end{align*}
and so $\bar{W}^{\mathbb{R} }$ is not isomorphic with $W$ (we have the injection $W \hookrightarrow \bar{W}^{\mathbb{R} }$ but it is not surjective). Therefore $W = \mathbb{R} \oplus \mathbb{R} \epsilon $ is not geometric. The same can be easily shown for $W^k = \mathbb{R} [\epsilon]$ with $\epsilon^{k+1} = 0$, for any fixed $k > 0$.

\section{Geometric algebras in a generalized sense}
\label{sec::3}
Vinogradov's concept of geometric algebra is limited to commutative algebras. This narrows the scope of the concept's application to physics, especially on the quantum and subquantum scales, where noncommutativity is the rule rather than the exception. In this section, we are taking a step towards extending the concept of geometricity to include at least some noncommutative situations.

Let $A$ be a noncommutative $\mathbb{R}$-algebra, and let $\mathcal{Z}(A)$ be its center.  The idea is to call the algebra $A$ geometric in a generalized sense if it is $\mathcal{Z}(A)$-geometric. To show that the concept is far from being obvious, let us consider the example of Grassmann algebras in which noncommutativity is only ``partial'' (these algebras have only antisymmetric ``part'').

Let us first recall the definition. Associative unitary algebra is said to be a Grassmann algebra if it has a system of linearly independent generators $(\xi_1, \ldots , \xi_q)$ such that
\begin{align*}
\xi_i \xi_j + \xi_j \xi_i = 0,
\end{align*}
in particular $\xi_i^2 = 0$. Grassmann algebras will be denoted by $\Lambda $ or $\Lambda (\xi ) = \Lambda (\xi_i, \ldots , \xi_q )$ if generators, called canonial generators, are to be displayed \cite{Berezin,DeWitt,Rogers}.

Any element $a \in \Lambda (\xi )$ can be written as
\begin{align*}
a = a(\xi ) = \sum_{k \geq 0} \sum_{i_1, \ldots , i_k} a_{i_1, \ldots , i_k} \xi_{i_1} \ldots  \xi_{i_k}.
\end{align*}

In order for this formula to be unequivocal, we must assume that the factors $a_{i_1, \ldots , i_k}$ are antisymmetric with respect to their indices or that the indices are ordered in the form $i_1 < i_2 < \ldots < i_k$. The element corresponding to $k = 0$ is proportional to the unit.

Grassmann algebras are $\mathbb{Z}_2$-graded, i.e. two subspaces of $\Lambda $, $\Lambda_0$ and $\Lambda_1$, can be chosen in such a way that
$\Lambda = \Lambda_0 \oplus \Lambda_1$ and $\Lambda_i \Lambda_j \subseteq \Lambda_{i+j}$, where addition of indices is understood modulo 2.
Elements of $\Lambda_0$ are called even, and elements of $\Lambda_1$ are called odd. Elements that are either even or odd are called homogeneous. $\Lambda_0$ is a subalgebra, but $\Lambda_1$ is only a vector subspace of $\Lambda $. Homogeneous elements $a, b \in \Lambda (\xi )$ satisfy the following ``supercommutativity'' relation
\begin{align*}
ab = (-1)^{\alpha(a) \alpha(b)}ba
\end{align*}
where $\alpha (a)$ is the so-called parity function defined to be equal 0 if $a$ is even, and 1 if $a$ is odd.

Let $C^\infty(M, \Lambda)$ be the algebra of all smooth functions on a differential manifold $M$ with values in $\Lambda $. If $(\xi_1, \ldots , \xi_q)$ is a system of canonical generators then any  $f(x, \xi) \in C^\infty(M, \Lambda )$, $x \in M$, can be written as
\begin{align*}
f(x, \xi ) = \sum_{k \geq 0} \sum_{i_1, \ldots , i_k} f_{i_1, \ldots , i_k}(x) \xi_{i_1} \ldots  \xi_{i_k}
\end{align*}
where $f_{i_1, \ldots , i_k} \in {\Cinf}(M) $.

The concepts of even and odd elements are naturally transferred to $C^\infty(M, \Lambda )$. The set of all even elements in $C^\infty(M, \Lambda)$ coincides with $C^\infty(M, \Lambda_0)$, and the set of all odd elements of $C^\infty(M, \Lambda)$ coincides with $C^\infty(M, \Lambda_1)$. To denote them, we will keep the same symbols as above.

Let us notice that $\Lambda_0$ is the center of $\Lambda $. We thus can define the algebra $C^\infty(M, \Lambda )$ geometric in a generalized sense (in this case it could be called supergeometric) if it is $\Lambda_0$-geometric. However, the sets of morphisms with codomain in $\Lambda_0$ and of those with codomain in $\Lambda$ are not equal. The former set naturally embeds in the latter, but $|C^\infty(M,\Lambda)|_{\Lambda}$ is much richer than $|C^\infty(M,\Lambda)|_{\Lambda_0}$. An illustrative example is provided by the morphism $\chi_{v,a} \in [C^\infty(M,\Lambda),\Lambda]_{C^\infty}$ given by
\begin{align*}
\chi_{v,a}(f) := f(x,0) + v(f(\cdot,0))a
\end{align*}
for any fixed vector $v$ tangent to $M$ at $x$ and any \emph{nilpotent} $a \in \Lambda$ (for example, $a$ may be taken as one of the generators $\xi$).

The situation certainly deserves more attention and will be addressed in a forthcoming work.

\section{Category of Lorentz modules}
\label{sec::4}
Let us first define the category \textbf{Mod} of modules. Its objects are pairs $(V, R)$, where $R$ is a ring (not necessarily commutative or unital) and $V$ is a (left) $R$-module (the pair $(V, R)$ will also be called an $R$-module). Its morphisms $\Phi: (V, R) \to (V', R')$ are pairs of mappings $\Phi = (F, \phi)$, where $\phi : R \to R'$ is a morphism of rings, and $F: V \to V'$
satisfies the condition
\begin{align*}
F(r_1v_1 + \ldots + r_kv_k) = \phi (r_1)F(v_1) + \ldots + \phi (r_k)F(v_k),
\end{align*}
for $r_1, \ldots , r_k \in R$, $v_1, \ldots , v_k \in V$, or, in a compact form,
\begin{align*}
& F(v_1 + v_2) = F(v_1)+ F(v_2),
\\
& F(rv) = \phi(r)F(v).
\end{align*}
In this way, we have the category of $R$-modules with $(V, R)$ as objects and $\Phi = (F, \phi )$ as morphisms.

Let us now assume that $V$ is a free $R$-module of rank $n+1$, i.e. that every basis of $V$ has $n+1$ elements. Let $g: V \times V \to R$ be a 2-linear, nondegenerate, symmetric mapping, which we shall call a scalar product on $V$. Such a scalar product is said to have the Lorentz signature if on $V$ there exists an orthonormal basis $W_0, W_1, \dots , W_n$ in which
\begin{align*}
g(W_i, W_j) =
\left\{
\begin{array}{rl}
{\bf 0}_R & \mbox{if $i\neq j$} \\
-{\bf 1}_R & \mbox{if $i=j=1, \dots, n$} \\
{\bf 1}_R & \mbox{if $i=j=0$}
\end{array}
\right.
\end{align*}
If $g$ has a Lorentz signature, it is said to be a \emph{Lorentz metric}.

The triple $(V, R, g)$, where $g$ is a Lorentz metric, will be called a Lorentz module (we shall also write $(V, g)$ if the ring $R$ is obvious). Let us consider two such $R$-modules $(V, R, g)$ and $(V', R', g')$, and a morphism of $R$-modules $\Phi = (F, \phi): (V, R) \to (V', R')$ such that
\begin{align*}
g'(F(X), F(Y)) = g(X, Y)
\end{align*}
for $X, Y \in V$.\footnote{Let us notice that $g'(F(X), F(Y)) = (F^*g')(X, Y)$.} Then $\Phi $ is said to be a morphism of Lorentz modules $(V, R, g) \to (V', R', g')$.

Lorentz modules, as objects, with mappings $\Phi = (F, \phi)$ as morphisms naturally form the category of Lorentz modules, denoted by \textbf{Lor}. It is a subcategory of the category of $R$-modules.

The archetypical example of a Lorentz module is $(\textrm{Der}(C^\infty(M)),C^\infty(M), g)$, where $(M,g)$ is a Lorentz manifold and $\textrm{Der}(C^\infty(M))$ is the $C^\infty(M)$-module of derivations\footnote{Recall that a derivation of an $\mathbb{R}$-algebra $C$ is an $\mathbb{R} $-linear map $X: C \to C $ satisfying the Leibniz condition $X(fg) = X(f)g + fX(g)$, $f,g \in C$.} of the algebra $C^\infty(M)$. This can be generalised by replacing $C^\infty(M)$ with a $C^\infty$-algebra $\bar{C}$ understood either as $\bar{C}^{\mathbb{R} }$ or as $\bar{C}^A, \, A \in C^\infty  $, along with replacing the metric $g$ with a 2-linear, nondegenerate, symmetric mapping $\bar{g}: \mathrm{Der}(\bar{C}) \times \mathrm{Der}(\bar{C}) \to \bar{C}$ with the Lorentz signature. In what follows, we shall sometimes denote such a Lorentz module by $(\bar{C}, \bar{g})$.

\section{Category of Einstein Algebras}
\label{sec::5}
\subsection{Einstein Algebras}
\label{sec::5_1}
In this subsection, we briefly summarise standard geometric constructions leading to Einstein's equations resp. Einstein algebras (for full account see, e. g., \cite{Heller92,Neill,Sachs}).

Let $C$ be a geometric $C^\infty  $-algebra and the module of its derivations $V = \mbox{${\mathrm{Der}(C)}$} $. We assume that it is a free module of rank $n$. Let further  $(V, C, g)$ be a Lorentz  module. We thus have a symmetric and nondegenerate 2-form $g: V \times V \to C$.

From its nondegeneracy it follows that, for $X \in V$, we have $\iota_X g \in V^*$ with
\begin{align*}
(\iota_X g)(Y) = g(X,Y).
\end{align*}
This leads to the isomorphism $\Psi_g: V \to V^*$ given by
\begin{align*}
\Psi_g(X) = \iota_X g \in V^*.
\end{align*}

With the help of the Lorentz metric $g$ we define the Levi-Civita connection $\nabla $, i.e., a unique connection $\nabla : V \times V \to V$ such that
\begin{align*}
(i) & \quad [X,Y] = \nabla_XY - \nabla_YX,
\\
(ii) & \quad Xg(Y,Z) = g(\nabla_XY,Z) + g(Y, \nabla_XZ),
\end{align*}
for all $X, Y, Z \in V$. This connection allows us to determine all basic curvature structures necessary to define Einstein's equations. First of all, the curvature tensor $R: V \times V \times V \to V$
\begin{align*}
R(X, Y)Z = \nabla_X \nabla_Y Z - \nabla_Y \nabla_X Z - \nabla_{[X, Y]}Z,
\end{align*}
and the endomorphism $R_{XY}: V \to V$ given by
\begin{align*}
R_{XY}(U) = R(X,U)Y.
\end{align*}
Now, we define the Ricci tensor
\begin{align*}
\mathrm{Ric} (X, Y) = \tr\, R_{XY}.
\end{align*}

We also define the endomorphism $\mathcal{R}: V \to V$ by
\begin{align*}
\mathcal{R}(X) = \Psi_g^{-1}(\iota_X \mathrm{Ric}).
\end{align*}
It satisfies
\begin{align*}
g(\mathcal{R}(X), Y) = \mathrm{Ric}(X, Y).
\end{align*}
Finally, we define the scalar curvature
\begin{align*}
r = \tr \, \mathcal{R}.
\end{align*}

Now, we have  all structures needed to define the Einstein algebra \cite{Geroch72,Heller92,HS95a}.

\begin{Definition}
The Lorentz module $(V, C, g)$ is called an Einstein algebra, if Einstein's equations are satisfied, i.e. if on the Lorentz module $(V, C, g)$ the following conditions hold
\begin{align*}
(i) & \quad \mathrm{Ric} - \tfrac{1}{2}rg  + \Lambda g = 8 \pi T,
\\
\textrm{or} \quad (ii) & \quad \mathrm{Ric} = \Lambda g,
\end{align*}
where $\Lambda $ is the cosmological constant and $T$ a suitable energy--momentum tensor.
\end{Definition}

If the energy--momentum tensor is zero $(T = 0)$, equations (i) reduce to equations (ii), called the \emph{vacuum} Einstein's equations\footnote{With $\Lambda$ suitably rescaled.}. In some applications (for example, to calculate effects in a weak gravitational field), one assumes $\Lambda = 0$ (for a more detailed discussion of the above definition see \cite{Heller92}).

Let us notice that the category of Einstein algebras, denoted \textbf{Einst} or $\mathbf{Einst}_0$, depending on whether (i) or (ii) is satisfied, is a subcategory of the category of Lorentz modules.

Rosenstock, Barrett and Weatherall \cite{Rosen} have demonstrated that the categories of general relativity and Einstein algebras are dual with respect to each other, which implies that they are ``theoretically equivalent'' (equivalent as theories), however these authors limited themselves to the case when, using our terminology, the starting point for constructing Einstein algebras is a differential manifold. In our approach, it is, in general, a ringed space $(|C|_A, \bar{C}^A)$ (of which differential manifold is a special instant with $A = \mathbb{R}$ and $C = C^\infty (M)$). In such a case, Einstein algebras are genuine generalisations of general relativity. For example, a relativistic world model with quasiregular space-time singularities, which evidently violates the smooth manifold structure, can be organized into an Einstein algebra \cite{Heller92}.

\subsection{Functorial Einstein Algebras}
\label{sec::5_2}
In constructing Einstein's algebra at a stage $A$, one could explicitly use the isomorphism $\Theta^A: C \to \bar{C}^A$, but for the sake of illustration we will sketch briefly the main steps of this construction.
Let $C$ be, as above, a geometric $C^\infty  $-algebra. In this section, we consider the algebra $\bar{C}^A$ with $A \in C^\infty  $. Its elements are of the form $\bar{f}^A: |C|_A \to A$ given by $\bar{f}^A(\rho ) = \rho(f), \, \rho \in |C|_A := [C, A]_{C^\infty  }$, $f \in C$. By Lemma \ref{lem2}, $\bar{C}^A$ is a geometric algebra.

From the isomorphism of the algebras $C$ and $\bar{C}^A$ it follows that  all tensors, corresponding to these algebras, are also respectively isomorphic (see \cite{Reports20}). Thus we may proceed in close analogy with what has been done in the previous subsection. We construct the module of derivations $\bar{V}^A = \mathrm{Der}(\bar{C}^A)$. If $X \in \mbox{${\mathrm{Der}(C)}$}$ then $\bar{X}^A (\bar{f}^A) = \overline{X f}^A$, and the Lorentz metric $\bar{g}^A$ on it satisfies
\begin{align*}
\bar{g}^A(\bar{X}^A,\bar{Y}^A) = \overline{g(X,Y)}^A.
\end{align*}
We thus have a Lorentz module $(\bar{V}^A, \bar{C}^A, \bar{g}^A)$, and if we proceed just as in the preceding subsection, we arrive at the following definition
\begin{Definition}
The Lorentz module $(\bar{V}^A, \bar{C}^A, \bar{g}^A)$ at a stage $A$ is called an Einstein algebra at the stage $A$ if Einstein's equations, analogous to (i) or (ii), are satisfied.
\end{Definition}

The above constructions can be summarised in the form of the following statement.
\begin{Statement}
If the triple $(V, C, g)$ is an Einstein algebra then $(\bar{V}^A, \bar{C}^A, \bar{g}^A)$ is an Einstein algebra at the stage $A$.
\end{Statement}

Let now $\bar{C}$ be a functorial $C^\infty  $-algebra, i.e. an algebra the elements of which are
\begin{align*}
\bar{f} = \{\bar{f}^A \, | \, f \in C\}_{A \in C^\infty  }.
\end{align*}

Consequently, we consider the functorial module of derivations $\bar{V} = \{\bar{V}^A\}_{A \in C^\infty  }$, and by proceeding as above, we arrive at the following definition
\begin{Definition}
The functorial Lorentz module $(\bar{V}, \bar{C}, \bar{g})$ is called a functorial Einstein algebra if Einstein's equations, analogous to (i) or (ii), are satisfied.
\end{Definition}

And again, we summarise the above construction in the following way.
\begin{Statement}
If the triple $(V, C, g)$ is an Einstein algebra, then $(\bar{V}, \bar{C}, \bar{g})$ is a functorial Einstein algebra.
\end{Statement}
In fact, we have a functor from the category of Einstein algebras to the category of functorial Einstein algebras.

We can summarise our analyses by formulating the following theorem.
\begin{Theorem}
All three Einstein algebras $(V, C, g)$, $(\bar{V}^A, \bar{C}^A, \bar{g}^A)$ and $(\bar{V}, \bar{C}, \bar{g})$, for any $A \in C^\infty  $, where $C$ is a geometric $C^\infty  $-algebra, are isomorphic with each other.
\end{Theorem}

\noindent \textbf{Proof.} We shall show this for the first two algebras; extension to the third algebra is obvious.

We have the isomorphism: $(\Theta^A)^{-1}: \bar{C}^A \to C$ which induces the isomorphism of modules of derivations $V = \mbox{${\mathrm{Der}(C)}$} $ and $\bar{V}^A = \mathrm{Der}(\bar{C}^A)$. The equality $\bar{g}^A (\bar{X}^A, \bar{Y}^A) = \overline{g(X, Y)}^A$, $X, Y \in V$, guarantees that the Lorentz modules $(V, C, g)$ and $(\bar{V}^A, \bar{C}^A, \bar{g}^A)$ are isomorphic. \hfill $\Box $

\section{Infinitesimals and parametrised points}
\label{sec::6}
One of the important tools, used in this work, was the strict definition of geometric algebra proposed by Vingradov. As expected, the general theory of relativity (in terms of Einstein's algebras) turned out to be geometric in this strict sense. An algebra is geometric if it is isomorphic to the algebra of real-valued functions defined over its spectrum. Then, in terms of these functions, geometry may be developed. Therefore, no geometric algebra leads to the ``background free'' theory. Meanwhile, it is quite commonly believed that the final theory of quantum gravity should be ``background free''. If so, the corresponding algebra should not be geometric. Let us consider the following ``toy model''.

We associate with a given Einstein algebra a Weil algebra representing infinitesimal quantities, and make the working assumption that the quantum theory of gravity (at the Planck level) uses infinitesimal quantities. Below, we will replace the infinitesimal quantities by other structures, but this will not change the situation significantly.

Let us consider a Weil algebra of the form $W = \mathbb{R} \oplus \mathbb{R} \epsilon , \, \epsilon^2 = 0$, like in Example at the end of Section \ref{sec::2}, and an Einstein algebra $(V, C, g)$. It immediately follows from Lemma \ref{lem3} that the algebra $C$ is $W$-geometric. However, to see this more clearly, let us trace the reasoning more closely.

The ``real spectrum'' of $C$ is $|C|_{\mathbb{R} } := [C, \mathbb{R} ]_{C^\infty  }$. Its ``points'' are the arrows: $\chi : C \to \mathbb{R}$. We define, as usual, $\bar{f}^{\mathbb{R} }: |C|_{\mathbb{R} } \to \mathbb{R}$ by
\begin{align*}
\bar{f}^{\mathbb{R} }(\chi ) = \chi (f), \ f \in C
\end{align*}
and
\begin{align*}
\bar{C}^{\mathbb{R} } = \{\bar{f}^{\mathbb{R} } \, | \, f \in C\}.
\end{align*}
Now, we include infinitesimals by looking at the Einstein algebra from the stage $W$. The ``infinitesimal spectrum'' is $|C|_{W} = [C, W]_{C^\infty  }$, and its ``points'' are arrows $\rho : C \to W$
given by
\begin{align*}
\rho (f) = \chi (f) + v(f)\epsilon
\end{align*}
where $f \in C$, $\chi \in |C|_{\mathbb{R} }$ and $v \in \mathrm{Der}_{\chi }C$; $v$ can be regarded as a vector tangent to $|C|_\mathbb{R}$ at the ``point'' $\chi $ \cite{Reports20}.

And finally, we have the isomorphism $\Theta^W: C \to \bar{C}^W$, which is equivalent to saying that $C$ is $W$-geometric.
Since it is an isomorphism, the effects from the infinitesimal level (gravitational micro-level), do not contribute anything new to the level described by Einstein algebras (gravitational macro-level), that is, the micro-level is not visible from the macro-level. If this diagnosis is accurate and if we want to have quantum gravity effects measurable at the macro-level, then a quantum theory of gravity should be sought by constructing non-geometric models. In such models, the spectrum might be ``too small'', i.e. the algebra of real-valued functions on this spectrum is isomorphic only to a proper subalgebra of the original algebra. In the extreme case, the spectrum could be even empty. However, by allowing noncommutative algebras, the situation can change (see Section \ref{sec::3}).

We have used the Weil algebra example mainly for illustrative reasons: we can imagine that infinitesimals are associated with the lowest (Planck) level of physics, but as a stage we can choose, in principle, any object of the $C^\infty $-algebra category (or even the $\mathbb{R}$-algebra category, depending on the needs). This gives us a freedom in choosing the objects we want to consider on the micro-level. This is particularly clear on the example of the so-called parametric points.

We could start with abstract $\mathbb{R} $-algebras, as we have done in the previous sections, and progressively move to differential spaces, but for the sake of simplicity let us start right away by considering two differential spaces $(M, C^\infty (M))$, representing space-time manifold, and $(P, C^\infty (P))$ a differential space representing a typical ``parametrized point''.

We define
\begin{align*}
M^P = \{\phi: P \to M \, | \, \phi^*(C^\infty (M)) \subset C^\infty (P)\}.
\end{align*}

If $f \in C^\infty (M)$ then its extension to $M^P$ is defined to be $\hat{f}: M^P \to C^\infty  (P)$ with
\begin{align*}
\hat{f}(\phi) := \phi^\ast(f) = f \circ \phi
\end{align*}
for any $\phi \in M^P$, which leads to
\begin{align*}
C^\infty (M^P) := \{\hat{f} \, | \, f \in C^\infty (M) \}.
\end{align*}

Arrows $\phi: P \to M$ are called parametrised points of $M$. Elements of $M^P$ may be, for example, ``loops'' (if $P=S^1$), tori (if $P=S^1 \times S^1$), ``strings'' (if $P=\mathbb{R}$ or $P=S^1$) or ``branes'' (if $P=\mathbb{R}^n$ etc.) We assume that dim $M$ $>$ dim $P$.

We thus obtain the differential space $(M^P, C^\infty (M^P))$.

Let us define
\begin{align*}
M_0^P := \{\phi_m \, | \, m \in M\} \quad \textnormal{with} \quad \phi_m(p) = m, \ \ \forall p \in P.
\end{align*}
Clearly, we have the bijection $M \cong M_0^P$ given by $m \leftrightarrow \phi_m$, and the differential structure on $M_0^P$ is $C^\infty (M^P)|M_0^P$.
Indeed, we have
\begin{align*}
\hat{f}(\phi_m)(p) = (f \circ \phi_m)(p) = f(\phi_m(p)) = f(m).
\end{align*}

We can also easily see that the two differential structures $C^\infty  (M)$ and $C^\infty  (M^P)$ are isomorphic, the isomorphism being given by $f \mapsto \hat{f}$. The situation is summarised in the following commutative diagram

\begin{center}
\begin{tikzcd}
{(M, C^{\infty }(M))} \arrow[rrr, "{(\Phi, \, \Phi^*)}"] \arrow[rrrd, "{(\Phi, \, \Phi_0^*)}"', shift right] &  &  & {(M^P, C^{\infty}(M^P))}                                             \\
                                                                                &  &  & {(M^P_0, C^{\infty }(M^P_0))} \arrow[u, "{(\iota, \, \iota^*)}"', hook]
\end{tikzcd}
\end{center}
Here we have defined:
\begin{align*}
& \Phi: M \to M^P \quad \textnormal{by} \quad \Phi(m) = \phi_m,
\\
& \iota : M^P_0 \to M^P \quad \textnormal{by} \quad \iota (\phi_m) = \phi_m,
\\
& \Phi_0: M \to M^P_0 \quad \textnormal{by} \quad \Phi_0(m) = \phi_m,
\end{align*}
\noindent
for any $m \in M$, and their pullbacks, correspondingly.

The mapping $\Phi_0$ is a bijection, whereas $\iota$ and $\Phi$ are injections. The geometry on $M^P$ is the same as that on $M^P_0$ since the respective algebras of functions are isomorphic.

As we can see, adding parametric points to space-time does not significantly change the differential structure of space-time; consequently, it does not change its geometry (geometry is encoded in the differential structure of space-time, not in the collection of its points). Moreover, the whole procedure does not change the differential dimension of space-time.

\section{Comments and interpretation}
\label{sec::7}

Let us now turn to drawing some conclusions from the algebraic formulation of general relativity (as Einstein algebras) and from placing it in a categorical context. Geroch's motivation, when he introduced the notion of Einstein algebras, was to reduce the role of sharply defined events as points in a space-time manifold. In quantum physics, for instance, ``the influence of the measuring apparatus on the system being observed cannot, even in principle,  be made arbitrarily small'' \cite{Geroch72}. In his opinion, Einstein algebras, in which the underlying manifold plays practically no role, may offer a convenient starting point to ``smearing out of events'' in the future quantum gravity theory. A fairly natural motivation for considering Einstein algebras is provided by the idea that smooth functions on a manifold can be interpreted as scalar fields on space-time \cite{Demaretetal}; Chen and Fritz \cite{ChenFritz} have even attempted to show that other physical fields too can be interpreted algebraically.

It is significant that Einstein algebras have interested philosophers of science more than physicists. For instance, John Earman claimed that the Einstein algebra approach could make precise Leibniz relational philosophy of space-time. That is why he called them Leibniz algebras \cite[p. 193]{Earman1989}. As a reaction, Rynasiewicz \cite{Rynasiewicz} argued that in the algebraic approach points can be recovered, and philosophically one gains nothing by dealing with $C^\infty  (M)$ rather than with $M$. The discussion, in a sense, was closed by Weatherall \cite{Weath}, who defined the category \textbf{GR} of standard general relativity theory and the category \textbf{AE} of Einstein algebras and, citing \cite{Rosen}, showed that there is a functor $F: \mathbf{GR} \to \mathbf{AE}$ which ``forgets nothing'', i.e. points in \textbf{AE} exist just as they do in \textbf{GR}.\footnote{We should only remember that our treatment of Einstein algebras is more general than the treatment considered by the cited authors, who limit themselves to the category of smooth manifolds.} We can add from ourselves that this is so precisely because Einstein algebras are geometric: one can always reconstruct their spectra, and hence all the points.

Putting Einstein algebras into the context of category theory brings yet another benefit: it shows the aspect of relational character of general relativity, which the cited authors did not pay attention to. To see this in its full light, we must turn to tools often used in category theory.

Yoneda Lemma, in its covariant version, states that for  every object $X$ in a (locally small) category $E$, and every functor $F: E \to \mathbf{Set} $, the set of natural transformations from $[X, - ]_E$ to $F$ is isomorphic with $FX$ \cite[Section 0.2.3]{TopCat}, i.e.,
\begin{align*}
\mathrm{Nat}([X, - ]_E, F) \cong FX.
\end{align*}
Let us apply this result to the category $C^\infty  $ and put $F = [A, -]_{C^\infty  }$, $A \in C^\infty  $. We thus obtain
\begin{align*}
\mathrm{Nat}([X, - ]_{C^\infty  }, [A, - ]_{C^\infty  }) \cong [A, X]_{C^\infty  }.
\end{align*}
Now, the direct corollary from the Yoneda Lemma is
\begin{align*}
X \cong A \; \; \; \mathrm{iff} \; \; \; [X, - ]_{C^\infty  } \cong [A, - ]_{C^\infty  }.
\end{align*}
One direction in proving this corollary is the consequence of the fact that the Yoneda embedding is a functor, and the other direction of the fact that this functor is faithful \cite{TopCat}.

The corollary tells us that any object $A$ can be viewed as a functor $[A,-]_{C^\infty  }$ (or as a functor $[-,A]_{C^\infty  }$ if we repeat the whole argument for the contravariant version of the Yoneda lemma). This means that any object is entirely determined by all outgoing or incoming arrows. In other words, any algebra of smooth functions (any object of $C^\infty  $) is completely determined by its relationship with other objects.

When we identify a given object with all arrows going to or coming from it, new elements appear in this object that were not originally there. This is typical for category theory. Treating these new elements on equal footing with ``original objects'' often makes the theory more transparent and  logically compact.

In the view of the above, any (functorial) Einstein algebra is completely determined by its relationship to other (functorial) Einstein algebras. Intuitively speaking, this is another expression of a strongly relational character of general relativity (and its possible generalisations). Let us notice that this does not only apply to Einstein algebras. By virtue of the generality of the Yoneda lemma, the same may be said of any theory which can be expressed in the language of category theory. This shows the universality of the ``principle of relationality''.

If a solution to Einstein equations is regarded as a pair $(M, g)$ where, for simplicity, we assume that $M$ is a manifold, and $g$ is a Lorentz metric on $M$ (or the equivalence class of physically equivalent Lorentz metrics on $M$), satisfying Einstein equations, then it can be represented as an Einstein algebra, an object of of the category \textbf{Einst} or $\mathbf{Einst}_0$. Consequently, every solution of Einstein equations is entirely determined by all arrows emanating from this solution to all other solutions or coming from all other solutions to this solution. It is well known that solutions of any differential equation (and Einstein equations are far from being an exception), are not independent entities but constitute elements of highly structured ``solution space'' (see, for instance, \cite{Fischer}); it seems, however, that the ``categorical holism'' goes further in combining all Einstein algebras into a single category.

redpajama_set_name: RedPajamaArXiv


text:
package org.openid4java.infocard;

import org.openid4java.message.Message;
import org.openid4java.message.ParameterList;
import org.openid4java.OpenIDException;
import org.apache.commons.logging.Log;
import org.apache.commons.logging.LogFactory;
import org.w3c.dom.Document;
import org.xml.sax.SAXException;

import javax.xml.parsers.DocumentBuilderFactory;
import javax.xml.parsers.DocumentBuilder;
import javax.xml.parsers.ParserConfigurationException;
import java.io.ByteArrayInputStream;
import java.io.IOException;

/**
 * Models the OpenID Infocard token used to transport OpenID messages.
 * An OpenID token encapsulates an OpenID message in key-value form into
 * an <openid:OpenIDToken> element.
 * <p>
 * Provides functionality for OPs / Servers to create OpenID tokens from
 * OpenID messages, and for RPs / Consumers to parse received tokens into
 * OpenID messages.
 */
public class OpenIDToken
{
    private static Log _log = LogFactory.getLog(OpenIDToken.class);
    private static final boolean DEBUG = _log.isDebugEnabled();

    /**
     * Token type data structure.
     */
    private OpenIDTokenType _tokenType;

    /**
     * The encapsulated OpenID Message.
     */
    private Message _openidMessage;

    /**
     * Constructs an OpenID token encapsulating the provided OpenID Message.
     * Should be used on the OP/STS side to generate a RSTR.
     *
     * @param openidMessage     The OpenID message obtained from
     *                          ServerManager.authResponse().
     */
    public OpenIDToken(Message openidMessage)
    {
        setOpenIDMessage(openidMessage);

        if (DEBUG)
            _log.debug("Created " + _tokenType +" token");
    }

    /**
     * Parses the data posted by the selector into an OpenID token.
     * Should be used on the RP side.
     *
     * @param       xmlToken The "xmlToken" parameter posted by the selector.
     * @return      An OpenIDToken encapsulating the OpenID AuthResponse.
     */
    public static OpenIDToken createFromXmlToken(String xmlToken)
        throws InfocardException
    {
        if (xmlToken == null)
            throw new InfocardException("Error processing xmlToken: null value");

        if (DEBUG)
            _log.debug("Processing xmlToken: " + xmlToken);

        try
        {
            DocumentBuilderFactory documentBuilderFactory =
                    DocumentBuilderFactory.newInstance();
            documentBuilderFactory.setNamespaceAware(true);

            DocumentBuilder documentBuilder =
                    documentBuilderFactory.newDocumentBuilder();

            Document document = documentBuilder.parse(
                    new ByteArrayInputStream(xmlToken.getBytes("utf-8")));

            String keyValueForm;
            try
            {
                keyValueForm = document.getElementsByTagNameNS(
                    Message.OPENID2_NS, "OpenIDToken")
                    .item(0).getFirstChild().getNodeValue();
            }
            catch (Exception e)
            {
                throw new InfocardException(
                    "Error extracting OpenID message from the xmlToken", e);
            }

            Message message = Message.createMessage(
                ParameterList.createFromKeyValueForm(keyValueForm));

            return new OpenIDToken(message);

        // DOM exceptions :
        }
        catch (ParserConfigurationException e)
        {
            throw new InfocardException("Parser configuration error", e);
        }
        catch (SAXException e)
        {
            throw new InfocardException("Error parsing XML token document", e);
        }
        catch (IOException e)
        {
            throw new InfocardException("Error reading xmlToken document", e);
        }
        catch (OpenIDException e)
        {
            throw new InfocardException("Error building OpenID message from xmlToken", e);
        }
    }

    /**
     * Gets the OpenID message contained in the OpenID token.
     */
    public Message getOpenIDMessage()
    {
        return _openidMessage;
    }

    /**
     * Gets the OpenID message as a ParameterList.
     * @return
     */
    public ParameterList getOpenIDParams()
    {
        return new ParameterList(_openidMessage.getParameterMap());
    }

    /**
     * Sets the OpenID Message to encapsulate into the token.
     */
    public void setOpenIDMessage(Message openidMessage)
    {
        this._openidMessage = openidMessage;

        if (OpenIDTokenType.OPENID20_TOKEN.toString().equals(
                    openidMessage.getParameterValue("openid.ns")))
            _tokenType = OpenIDTokenType.OPENID20_TOKEN;

        else
            _tokenType = OpenIDTokenType.OPENID11_TOKEN;
    }

    /**
     * Gets the OpenID token type.
     *
     * @see org.openid4java.infocard.OpenIDTokenType
     */
    public OpenIDTokenType getTokenType()
    {
        return _tokenType;
    }

    /**
     * Generates the XML string representation of the OpenID token.
     */
    public String getToken()
    {
        StringBuffer token = new StringBuffer();

        token.append("<openid:OpenIDToken xmlns:openid=\"" +
                        Message.OPENID2_NS + "\">");

        token.append(_openidMessage.keyValueFormEncoding());

        token.append("</openid:OpenIDToken>");

        return token.toString();
    }
}

redpajama_set_name: RedPajamaGithub


Tx steak in Madrid: in pursuit of the best high loin steak in the kingdom. Casa Julián de Tolosa.
The travel magazine suggests a visit to Madrid through the steaks served in the capital. One of the restaurants chosen is Julían de Tolosa and its legendary steak.


Brewer, Rebecca and Cook, Richard and Bird, Geoffrey (2016) Alexithymia: a general deficit of interoception. Royal Society Open Science , ISSN 2054-5703.
Alexithymia is a sub-clinical construct, traditionally characterized by difficulties identifying and describing one's own emotions. Despite the clear need for interoception (interpreting physical signals from the body) when identifying one's own emotions, little research has focused on the selectivity of this impairment. While it was originally assumed that the interoceptive deficit in alexithymia is specific to emotion, recent evidence suggests that alexithymia may also be associated with difficulties perceiving some non-affective interoceptive signals, such as one's heart rate. It is therefore possible that the impairment experienced by those with alexithymia is common to all aspects of interoception, such as interpreting signals of hunger, arousal, proprioception, tiredness and temperature. In order to determine whether alexithymia is associated with selectively impaired affective interoception, or general interoceptive impairment, we investigated the association between alexithymia and self-reported non-affective interoceptive ability, and the extent to which individuals perceive similarity between affective and non-affective states (both measured using questionnaires developed for the purpose of the current study), in both typical individuals (n = 105 (89 female), mean age = 27.5 years) and individuals reporting a diagnosis of a psychiatric condition (n = 103 (83 female), mean age = 31.3 years). Findings indicated that alexithymia was associated with poor non-affective interoception and increased perceived similarity between affective and non-affective states, in both the typical and clinical populations. We therefore suggest that rather than being specifically associated with affective impairment, alexithymia is better characterized by a general failure of interoception.


We're revolutionizing the conventional mapping paradigm with our Dynamic 3DHD mapping technology.
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Crowdsourced and vision-based data provide more timely and reliable information than legacy mapping sources.


text:
Materials Science (General)
General Materials Science
Advances in Quantum Chemistry
DV-Xa for Atomic Spectroscopy and Materials Science
View on ScienceDirect
DV-Xa for Atomic Spectroscopy and Materials Science, Volume 37
Serial Editors: John Sabin
Serial Volume Editors: Michael Zerner Erkki Brandas Masayuki Uda Rika Sekine Hirohiko Adachi
Editor-in-Chiefs: Per-Olov Lowdin
Hardcover ISBN: 9780120348374
Published Date: 17th October 2000
View all volumes in this series: Advances in Quantum Chemistry
Print - Hardcover
× In Stock
For regional delivery times, please check When will I receive my book? in our Support Hub.
× Print on demand
This title is printed on demand. For regional delivery times, please check When will I receive my book? in our Support Hub.
Advances in Quantum Chemistry publishes articles and invited reviews by leading international researchers in quantum chemistry. Quantum chemistry deals particularly with the electronic structure of atoms, molecules, and crystalline matter and describes it in terms of electron wave patterns. It uses physical and chemical insight, sophisticated mathematics, and high-speed computers to solve the wave equations and achieve its results. Advances highlights these important, interdisciplinary developments.
Volume 37 includes proceedings of the 1998 Korea-Japan DV-Xa Joint Symposium. Emphasis is placed on atomic spectroscopy and material science, including the computation of electronic states of materials.
Researchers in quantum chemistry, applied mathematics, biology and physics; universities and industrial research and development groups working on biological molecules and new materials, such as semiconductor chips, polymers, and alloys.
Hardcover ISBN:
@qu:"Quantum chemistry has emerged as a subject in it own right. The appearance of a review publication which surveys recent achievements in the field is therefore very appropriate and, when it has the quality of this volume, is most welcome." @source:--PROCEEDINGS OF THE PHYSICAL SOCIETY @qu:"The juxtaposition of the oldest of quantum chemical studies, atomic structure, and one of the newest, quantum biology, highlights the importance of quantum theory in modern chemistry. Thus, having first opened the book in search of a particular article, the reader is stimulated to delve into fields of which he has but a superficial knowledge. In this way the book can be instrumental in broadening the interests and background of those who turn to it." @source:--THE ROYAL INSTITUTE OF CHEMISTRY
About the Serial Editors
John Sabin Serial Editor
John R. Sabin is Professor of Physics and Chemistry Emeritus at the University of Florida, and Adjungeret Professor at the University of Southern Denmark. He received the AB degree from Williams College in 1962 and the PhD from the University of New Hampshire in 1966. Thereafter he was a postdoctoral student at Uppsala University and at Northwestern University. He was Assistant Professor at the University of Missouri for three years (1968-1971) and then came to the University of Florida where he has been since.
Sabin's research interest is in the theoretical description of the interaction of fast charged baryon projectiles with atomic and molecular targets, both as neutrals and ions. In this work, he uses molecular quantum mechanics to describe such interactions. In particular, he is interested in the mechanism of absorption of the projectile's mechanical energy by the target, where it is mostly converted to electronic energy, which is measured by the target's mean excitation energy. He has written some 250 articles in this and related fields.
Sabin is editor of Advances in Quantum Chemistry and has been editor of the International Journal of Quantum Chemistry. He has edited some 90 volumes and proceedings.
University of Florida, Gainesville, USA
About the Serial Volume Editors
Michael Zerner Serial Volume Editor
Quantum Theory Project, University of Florida, Gainesville, U.S.A.
Erkki Brandas Serial Volume Editor
Erkki Brändas was born in Tampere, Finland in July1940 and was, as a Finnish war child, transported to Sweden in February 1942, finally adopted by his Swedish parents and given Swedish citizenship in 1947. He received his FL (PhD) in 1969 and Doctor of Philosophy (habilitation) in 1972, both at Uppsala University. Except for guest professorships in USA, Germany, Israel, he spent his professional career in Uppsala employed as Assistant- Associate- and Full Professor from 1975 until retirement in 2007. In addition to serving as chairman of the department of Quantum Chemistry, he was appointed Executive Director of the Uppsala Graduate School Advanced Instrumentation and Measurement supervising the doctoral education of 35 PhD's from 1997-2007. He has served on various international scientific and editorial boards, e.g. Wiley, Elsevier and Springer including the service as Editor-in-Chief for the International Journal of Quantum Chemistry, Series Editor of the Advances in Quantum Chemistry. He is the current President of the International Society for Theoretical Chemical Physics, since 15 years, chairing a variety of international congresses and other numerous meetings, schools and workshops. He has published over 260 articles and edited more than 50 books on fundamental theoretical chemical physics from research on atoms, molecules and solid-state physics to complex enough systems in biology – from the microscopic realm to the cosmological rank.
Masayuki Uda Serial Volume Editor
Waseda University, Tokyo, Japan
Rika Sekine Serial Volume Editor
Shizuoka University, Shizuoka, Japan
Hirohiko Adachi Serial Volume Editor
About the Editor-in-Chiefs
Per-Olov Lowdin Editor-in-Chief
Quantum Chemistry Group, Uppsala University, Sweden, and Quantum Theory Project, University of Florida, Gainesville, U.S.A.


Legislative Assembly for the ACT: 1997 Week 9 Hansard (3 September) . . Page.. 2842..
Mr Humphries: Mr Speaker, I rise on a point of order. Speaking over the Speaker or another member of the chamber while taking a point of order is not very polite, but that is probably as much as can be said about it.
Mr Humphries: Again, he is breaching standing orders by using standing order 46 to make an attack on another member. It is strictly outside standing orders.
MR BERRY: No; I was just explaining myself. My position stands up well against those other members'.
Mr Humphries: It is an attack on Mrs Carnell.
MR BERRY: No, it is not; it is just that I compare better.
MR SPEAKER: You went too far, Mr Berry.
MR BERRY: It is a pretty tight interpretation.
MR SPEAKER: Yes, it is a very tight interpretation, and it will remain so.
MR SPEAKER: I present, for the information of members, a report of a study trip undertaken by Bill Wood, MLA, to Darwin from 10 to 11 July and to Alice Springs from 13 to 14 July.
MR SPEAKER: I present, for the information of members and pursuant to the Auditor-General Act 1996, Auditor-General's Report No. 8 of 1997, entitled "Salaried Specialists' Use of Private Practice Privileges".
That the Assembly authorises the publication of the Auditor-General's Report No. 8 of 1997.


Popular wood grate US Stove Ashley models EC95 & BEC95. (2) required.
Mendota Blower Impeller & Housing Energy King 550 Shaker Grate Warm Morning 4225 Slide Grate Condar Catalytic Combustor CC550 3.7" x 9.1" x 2" Catalytic Combustor.


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text:
What is CDT for Eclipse?
Eclipse CDT (C/C++ Development Tooling) The CDT Project provides a fully functional C and C++ Integrated Development Environment based on the Eclipse platform.
How do I start Eclipse CDT?
2. Writing your First C/C++ Program in Eclipse
Step 0: Launch Eclipse. Start Eclipse by running " eclipse.exe " in the Eclipse installed directory.
Step 1: Create a new C++ Project.
Step 2: Write a Hello-world C++ Program.
Step 3: Compile/Build.
Step 4: Run.
What is CDT build console?
The C/C++ Development Toolkit (CDT) is a set of Eclipse plug-ins that provide C and C++ extensions to the Eclipse workbench. The CDT provides a C/C++ IDE that simplifies many of the same tools that you can use from the command line.
What is Eclipse Linux?
Eclipse is a free integrated development environment IDE that is used by programmers around to write software mostly in Java but also in other major programming languages via Eclipse plugins. Instead, you can install Eclipse IDE in Ubuntu or Debian based Linux distributions via the compressed installer file.
Is Eclipse C++ good?
In summary, Eclipse is a good IDE for C/C++, but if you require qt or Cmake support, I would advise using Netbeans, Qt Creator or Clion (if you are a student or willing to pay the subscription) instead of Eclipse.
What version of Eclipse should I download for Java?
Current releases of Eclipse require Java 11 JRE/JDK or newer. A Java Development Kit (JDK) includes many useful extras for Java developers including the source code for the standard Java libraries. Regardless of your operating system, you will need to install some Java virtual machine (JVM).
Can idle run C++?
Idle can be used for almost any C++ application type e.g. servers, GUIs, or graphic engines. Therefore, Idle can automatically reload headers, compilation units, embedded resources and also takes changes of dependencies and build-system files into account.
How do I know if Eclipse CDT is installed?
In the About Eclipse dialogue, click the Installation Details button. The Eclipse Installation Details dialogue appears. In the list of installed software, you should see "C/C++ Development Tools". The version displayed in the version column is the version of CDT.
Which version of Eclipse is best?
Generally Java 8 works the best for most/all versions of Eclipse, including older ones. But if you want to use newer language/library features for Java development and need a newer version of Java for that purpose then newer versions should work with 2019-03 as well.


Polar bear tracks near the village of Barrow, Alaska. More frequent polar bear visits in communities across the North Slope are a cause for concern for residents.
At a recent meeting with biologists and social science researchers, Joe Kaleak, an Iñupiaq from Alaska's North Slope, explained that hungry polar bears often try to break into his house, attracted by his seal oil supply—a fairly recent problem. With changes in the sea ice, Kaleak and community patrols in his village now must deal with polar bears on a regular basis.
Other Native experts from across the region told similar stories. They explained that, in addition to wider ecological changes, the impacts of the changing polar bear presence in their communities—and the different behaviors of those bears—are of great local concern.
Polar bears have long been a "cultural keystone" species for Iñupiaq subsistence communities. In totality, the Alaska Native experts who attended the March 18th meeting at the USGS office in Anchorage, Alaska, contributed hundreds of years of cumulative knowledge about polar bear behavior, as well as more recent insights into unusual polar bear occurrences.
Together, they're helping to shape the future of a new local knowledge project about polar bears in the northernmost part of the state.
Polar Bears International is partnering in this effort, called "Contemporary Iñupiaq Knowledge of Polar Bears in the Southern Beaufort Sea," with funding by the North Pacific Research Board and the National Fish and Wildlife Foundation. As an anthropologist from Alaska, I'm organizing and managing the project in collaboration with the North Slope Borough Department of Wildlife Management.
Alaskan Native experts shared insights on polar bears at a recent meeting in Anchorage. Photo copyright Robert Sarren.
As the Arctic rapidly loses its summer sea ice, polar bears are losing critical habitat in Alaska, but gaps in scientific knowledge about how this change is affecting polar bears remain. Alaska has two subpopulations of polar bears: the Chukchi Sea and southern Beaufort Sea bears. Of these, the latter is the best-studied scientifically, but local perspectives on polar bear ecology in the region have not been documented since the early 1990s, long before climate change came to be recognized as an existential threat.
Alaska Native subsistence communities that overlap with southern Beaufort Sea polar bear habitat have observed the bears over time, and can attest collectively to changes in their feeding habits, physical condition, seasonal movements, and local abundance, as well as to the nature of human-bear interactions.
At the meeting, I joined biologists and social scientists in listening to Alaska Native experts explain the best ways to approach Elders and other polar bear experts in their communities for interviews in order to document this knowledge accurately and respectfully. Alaska Native experts in attendance included Nora Jane Burns, Fred Tagarook Sr., and Joe Kaleak (Kaktovik), Moses Nayakik (Wainwright), and Bobby Sarren (Barrow). Taqulik Hepa, Billy Adams, and Andy Von Duyke generously contributed to the planning process, with Billy also serving as an Inupiaq translator for Elders in attendance.
Based on their extensive experience living and working the region, both Taqulik Hepa and Susi Miller (USFWS) recommended conducting Traditional Knowledge interviews as life histories centering on polar bear encounters, stories, and memories. In keeping with this advice, our interviews, which we will carry out in conjunction with community subsistence and social calendars within the next eight months, will center on maps of each village and their surrounding hunting territory, populated with local place names. Everyone at the meeting agreed that within an open-ended, map-based interview approach, certain topics, such as sea ice (and its affects on bears), seasonal movements, human-bear interactions, ice seals, and polar bear condition would be the most important to cover.
This map, created by Dr. Karyn Rode of the USGS, shows the locations of the villages taking part in the study as well as the boundaries of the polar bear populations in and near Alaska.
Larry Carpenter, chair of the Canadian Northwest Territories Wildlife Management Advisory Council, made a special trip to this research planning meeting to share his community's recent mirrored experience with documenting the ecology of southern Beaufort Sea polar bears across the Canadian border. Larry explained how the Inuvialuit Game Council's research included youth in all interviews with Elders to ensure that knowledge would be passed down in the course of the ethnographic work, an approach that will be followed on the Alaskan side as well.
Additional important project advisors in attendance included Dr. Karyn Rode, who helped guide the meeting, and Dr. George Durner, both with the U.S. Geological Survey. Dr. Henry Huntington, of Huntington Consulting, offered critical insights on social science design. Geoff York, senior director of conservation for Polar Bears International, a key organizer of this project, attended the March 18th meeting via teleconference.


Energy efficiency is a fast moving area of building which is regularly being updated within the building codes.
Most new buildings will need to comply with the energy efficiency requirements of the Building Code of Australia (BCA) and the Queensland Development Code (QDC) MP4.1 and MP4.2. Energy consultants can compute the appropriate star-rating of your building or a deemed to satisfy method can be used.
These buildings must comply with the requirements of the Queensland Development Code.