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Catskill Chill Artist Spotlight: SOLARiS
Post on: September 18, 2015
It's Christmas Eve, readers. Catskill Chill is tomorrow, and we can't wait. We've had an incredible experience interviewing some of the fantastic groups on Chill's festival bill this year, and we're excited to stuff your festival stockings with another great interview from another great band. With this post, we bring to you SOLARiS: a 3 piece all-instrumental electronic trance/fusion jamband from Binghamton, New York. Dan, Jared and Vincenzo are a talented trio with an uncanny sense of humor. These guys are Chillfam vets, and are performing for a fourth straight year this Sunday at 3:30. So, enjoy this interview, and make sure to call sick tomorrow and stuff your trunk with a tent, sleeping bag, and festival survival kit. Tickets are still available here.
Hey guys, thanks so much for taking some time to answer some questions for our readers, your fans, and the Chillfam. Much appreciated. So let's get into it! How did you guys meet and ultimately end up forming a band together?
SOLARiS met in the sprawling vista of Binghamton NY, home of the triple-bacon nacho cheese dog and our favorite sports team, the Binghamton Beavers. We started our band when we realized the one thing Binghamton needed most was a 3 piece jamtronica powerhouse to come slaughter all local talent and music in the city. We did so, and in the process, became the best of friends.
It seems like most of your shows this summer are around the Upstate NY or Mid-Atlantic regions, do you hope to use your music to do some more traveling and touring in the future?
Yes. We will use our music to travel and tour. Traveling and touring would actually be extremely awkward without our music. I'm not sure what our excuse would be for showing up to these venues without instruments. We've considered getting on stage and just eating breakfast before. We once had a DJ eat a plate of french fries and a burger while he performed as our opener in Wilkes Barre, PA. We wanna maybe try that, but without the performing part; just the food. We all love eating. All 3 members of the band are cooks, but we are also all classically trained at eating, too.
Where is your favorite venue to perform?
Wherever can provide us with fried food, a couple hundred bones, some encouraging words, and a slightly negotiable but wishy-washy bar tab. Sometimes they write down the drinks, but sometimes they write down every other one and give us a shot or two on top of it, which is great. Usually if there's a cute, short bartender, she's the one that writes the drinks down. The guy in the hockey jersey with the pen behind his ear usually is the one that gives us rounds on the house. Which is weird, because he's the one who actually has a pen on him. Oh, and Brooklyn Bowl. Love that place.
The Brooklyn Bowl (our favorite venue as well)
Your shows usually contain a lot of improvisation, what process do you use to prepare sets for concerts?
Every show has a setlist. Improvisation comes from the heart. Whichever one of us is the least grumpy usually leads the jam. In SOLARiS, somebody's gotta go through the ringer every night. Whoever manages to be the most aloof, the least concerned, and the best dressed, typically leads the jam. I've seen Jared (keys) do things on stage when wearing a bowling shirt that have completely blown my mind. The dude has redefined cool.
Your music consistently covers a broad range of genres, but would you say there is specific sound or style that serves as the foundation for your music? If so, what is it?
Whatever can make you dance. But more specifically, four-on-the-floor jamtronica. But we like the kind of records people were bulldozing during "Disco Sucks" in that big stadium. One or more members of our band are actually spiritually black, like Rachel Dolezal, so we feel a lot of funk and blues in there underneath it all. I'd like to think there's some punk influence in there, too. The music we play is loud, raw, in your face, and allows me to wear black every night.
Your drummer, Dan Lyons, is also a member of Horizon Wireless. Are there ever conflicts when trying to split the time up between the two groups?
We hate Horizon Wireless, and Horizon Wireless hates us. Not since the split-up of Sylvester Stallone and Brigitte Nielson has their been a more hotly conflicted and painfully awkward dichotomy between two artists. We let Dan do his thing, and god bless him he's trying, but we all know where the true power is. Dan in SOLARiS makes Dan in Horizon Wireless look like Paul McCartney in Wings. Everyone's just looking at him like, "Dude, when the hell are you just gonna forget about Wings and just make a NEW, FULL album with Michael Jackson?" I'm just saying, "The Girl is Mine" is better than anything the friggin Beatles put out after the White Album and surely more timeless than anything Wings put out. I mean, was there even another member of Wings? Did McCartney play every single instrument? Was Pete Best ever given residual checks? These are the things that keep me up at night, and the reason why we don't like to talk too much about the whole Horizon Wireless fiasco.
Do you have any big plans for 2016?
Continue struggling to be alive, be happy, play music together, and figure out more comfortable ways to sleep in the back of my van at festivals because so far it just gets so hot back there and honestly I don't know how to make it any better, and now I have a girlfriend so like I want to snuggle but it's so hot and she's there like breathing the same stale air and it's like even hotter because now there's two people in there and it makes me feel like a sardine, but at least those little fish aren't uncomfortable because by the time they're in the tin they're already dead.
What's in store for your upcoming performance at Catskill Chill?
We have like an hour to play, just come and you'll see it's obviously going to be amazing, haven't you seen us nail it there twice in a row? 3 times a charm, bud. Except for Ninja Turtles 3. Horrific. Their mouths literally are like, not even moving when they talk.
What have your past 4 experiences there been like?
It's our favorite festival. It's been a home to us. Literally, like if you added up all the days I've slept at Camp Minglewood, I could technically have my mail sent there.
There's a pretty stacked line-up at Catskill Chill this year, which acts are you most excited to see?
Horizon Wireless.
Any closing remarks?
Don't even get me started! We'll see you at Catskill Chill!
Tags: SOLARiS
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PATCH: Same NHC changes, another file to patch; see downloads for the patch.
PATCH: The NHC made a slight change to their products, and the filter needs two files to be replaced. See downloads for the new files.
The WX-ATLAN e-mail list, the source of data for all you Unix users out there, has CHANGED. You will have to re-subscribe and set your sub-topics on the new site. The information on doing so is here. Assuming you've used the procmail rules I show below, you should not need to adjust them at all.
JStrack is a freeware hurricane tracking program. It's currently tested under Unix and Windows (i.e., what I have access to).
Here is a sample of JStrack's main display from 18 August 2007 at 2100Z showing not only the track of Hurricane Dean, but also one of the new features in JStrack—the ability to overlay GOES-East imagery directly onto the tracking chart. NOTE: If you use IE, and have it configured to reduce images to fit the browser window, I strongly advise you to turn that off and use the scrollbars...if I remember correctly (I don't use IE) it's under the "Advanced" tab. Otherwise, IE's scaling of the image will make it look terrible!
It's written in Tcl/Tk, and is the result of my not being able to find a freely available hurricane tracking system for Unix. Note that while it was originally designed for running under Unix, as of version 2.0.0, it is now MUCH more friendly towards people running it under Windows (Windows 9x/NT/2k/ME/XP)!
As before, it should run on any other system for which Tcl/Tk is available (Mac users—I don't have a Mac, or access to one, so any feedback and/or help you can offer would be appreciated).
I've created an e-mail discussion list for JStrack users (and myself) at jstrack@googlegroups.com. To subscribe or unsubscribe, see JStrack e-mail list instructions.
11 October 2010 Update: JStrack 3.3.2 is out.
Version 3.3.2 is a bug-fix release from 3.3.1a.
19 September 2010 Update: JStrack 3.3.1 is out.
Version 3.3.1 changes the FTP updates from the NHC's old, legacy FTP server, which is a much lower priority when down, over to the http server, which is on a newer, better system and has a much higher priority. It also adds some new EXEs for the windows EXE users.
13 September 2010 Update: JStrack 3.3.0 is out.
Version 3.3.0, among other things, includes a new map: a close-up view of the Caribbean. See the JStrack downloads section for more details. Also remember to check back from time to time in the downloads page for patches and updates that may fix problems detected by me or reported to me by users.
28 August 2010 Update: JStrack 3.2.1 is out...includes Windows EXE!
Yes, I finally figured out how to make Windows EXE files for JStrack work, and thanks to help from comp.lang.tcl, it should no longer care where you install it (3.2.0 very definitely cared).
Basically, the Windows EXE version is just extract and run.... Data is up-to-date as of Saturday, 28Aug2010 at 17:55 CDT. The ftp timestamp files and initial_timestamps.tcl are updated to match the storm data (I've been forgetting to do this!).
This new release took a great deal of effort and some minor re-design. I've tested just about everything I can think of, and fixed a few self-inflicted errors in that re-design along the way. Please contact me at the e-mail address shown below if you have any problems, questions, comments, etc..
Watches and warnings are now "plotted" as text written into a text window. The previous releases should have been 3.1.x, but were not, so this one makes that step up.
This release includes and improves the plotting of watch/warning zones, and changes the console (for testing, etc.) to TkCon for all systems.
This release is mostly aesthetic changes, e.g., toplevel menus (such as the plot-point menu), etc., that could go off-screen and thus require the user to move them back on-screen now fix themselves, text widgets now use black/white instead of Tk's usual black/grey, etc.).
It also moves old storm data (except for 2007) out to another file. The old storm data was no doubt getting annoying for users with slower connection speeds who had to download it over and over again.... So it's moved out (still available, but by itself).
So, what's the number-one thing JStrack has really been missing? Yeah, documentation. Well, I'm hoping everyone will like the docs I've put together since releasing 3.0.0 (and 3.0.1, which fixed a few things I found while working on the documentation).
So here it is: JStrack Documentation (PDF) (NEW!). This covers everything from installing Tcl/Tk (required to run JStrack) to installing, configuring, and using JStrack. It also covers how to join the WX-ATLAN e-mail list for getting updates via e-mail.
This is basically a quick patch based on some minor glitches I found while doing the first cut (w/o any typesetting, still unfinished, etc.) at the new documentation. Includes the new documentation as of today.
Yes, folks, I finally decided to call it version 3. The big thing stopping me was the plotting of city/location names, and this morning, I saw the whole solution (or at least, one that would work) in a flash...and then proceeded to implement what I'd seen in that brief instant. After that, I decided it was time to officially make version 3.0.0 a reality.
See hrdean_GoesE_18-2100z.jpg for a sample of what I'm working on now...specifically, getting satellite imagery loaded on the tracking plot (optional, requires netpbm, or at least, a portion of it).
I have now officially beaten the hell out of the cancer that attacked me. On my diagnosis day, I told my oncologist that, very much contrary to the 50/50 odds he'd just given me for simply getting out of the hospital alive, I WAS going to beat the cancer. That was the only acceptable outcome at that time, and still is. I am still unable to work, still living on a disability check, and still dealing with the long-term (15–20 years in some cases, a lifetime in others) recovery issues. Some of these may slow me down at times when updates need to be made to JStrack, so please be patient. Fortunately, JStrack is pretty stable at this point...until, that is, someone (perhaps you) sees somthing missing and lets me know (or, of course, I see it).
Yes, JStrack is freeware. I have no intention of charging money for it now or in the future. After all, one of the reasons for writing it in the first place was to address the lack of a freely-available hurricane tracking program for Unix! It just wouldn't make sense to turn around and charge for it.... I do, however, have an important request.
If you use JStrack, I really need your feedback. If there's anything that could make JStrack more useful for you, letting me know is the first step toward making that happen. See below for the e-mail address.
If you REALLY love JStrack and want to send money, I ask that you send it to the Red Cross/Red Crescent, Salvation Army, etc., and specifically, not to send it to me. Of course, you're not required to donate to anyone.
Folks who are looking for a tracking program for an area other than the tropical Atlantic, please note: at this time, JStrack does not currently support your region of the world. HOWEVER, there is NO reason why it can't. Note that I am no longer able to help with this, but if you're familiar with Tcl and Tk, you should be able to tweak the existing code to work for you. I'm not saying it'll be easy, though (a lot of the code you'd need to work with is from my early days working with Tcl/Tk, and while it's correct code, it certainly could have been written better, making it easier to work with). Good luck. If you get a version working for other oceans, please send a copy to me so I can get it posted here.
Basically, you need a tracking chart for your region in a GIF, JPEG, or other image format that you can convert to a bitmap. The coordinates on the chart need to be something that you can read, but that's about it. Once you have that, the rest is simple! the location where I can ftp it or fetch it from a web site, and I'll The filter program for the NHC advisories may not work for you, but you might be able to fix that, too.
JStrack is named after my two cats (at that time), Jack and Shadow. I wasn't satisfied with any name I'd come up with, and was trying to think of a name...and there was Shadow, just sitting there staring at me like he had something to say on the subject.... The rest is history.
If you have any comments, suggestions, bugs, etc., regarding JStrack, please let me know. Send e-mail to me at spooky130u AT gmail.com.
I've only glanced at it, but it looks like a great resource for patients and survivors alike.


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(VIDEO) The 24 Hour War
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redpajama_set_name: RedPajamaCommonCrawl


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City of Charlotte > Citywide Newsroom > News releases > Body-Worn Camera Footage Release of Officer-Involved Shooting
Body-Worn Camera Footage Release of Officer-Involved Shooting
Today, the Charlotte-Mecklenburg Police Department (CMPD) released body-worn camera (BWC) video of an officer-involved shooting that occurred on Aug. 19, 2022.
Today, the Charlotte-Mecklenburg Police Department (CMPD) released body-worn camera (BWC) video of an officer-involved shooting that occurred on Aug. 19, 2022. Based on the wording of the request, only the body-worn camera footage of South Division Officer Brandon Graham is being released after a media member petitioned the courts.
The subject who died, Ms. Brenda Donahue, was being served an involuntary commitment order by Officers Brandon Graham, Lauren Ehlke, and Kristian Kurtzke, when she fired several shots at officers, striking Officer Ehlke in the chest. The bullet lodged in Ehlke's body-worn camera, and she was not injured in the shooting. South Division Officer Brandon Graham returned fire striking Ms. Donahue. Officers performed life-saving measures including CPR until paramedics arrived. Ms. Donahue was later pronounced deceased at the hospital.
The North Carolina State Bureau of Investigations (NCSBI) is handling the officer-involved shooting investigation.
For further information on this case please refer to the incident report: 20220819-1626-00.
You can view a critical incident briefing video breaking down BWC footage & explaining the incident in greater detail here
You can view the full body-worn camera video here
Case Update: Officer Involved Shooting in the South Division
Charlotte, N.C. – (Monday, August 29, 2022) – The suspect who fired shots at officers before being struck by return gunfire has been identified as Brenda Donahue (DOB 10/10/1961). Donahue died as a result of her injuries on August 25, 2022. Her next of kin has been notified of her death.
The officer involved in this shooting is Officer Brandon Graham of the South Division. Officer Graham has been placed on paid administrative leave, which is standard policy in any officer-involved shooting.
The investigation into this case is active and ongoing. Any additional questions should be directed to the North Carolina State Bureau of Investigations (SBI). CMPD is not releasing any further information regarding this case at this time. The incident report number is 20220819-1626-00.
Officer Involved Shooting in the South Division
Charlotte, N.C. – (Friday, August 19, 2022) – Detectives with the Charlotte-Mecklenburg Police Department and the North Carolina State Bureau of Investigation are investigating an officer-involved shooting investigation in the 8900 block of St. Croix Lane in the South Division.
On Friday, August 19, shortly after 5:30 p.m., officers were attempting to serve an involuntary commitment order. Upon arrival, a male at the residence opened the door and greeted the officers. Officers called out to the female who was inside the residence. The female responded with gunfire toward three CMPD officers and one officer was shot in the chest. The officer's protective equipment stopped the bullet.
One officer returned gunfire and struck the female. CMPD officers immediately began rendering aid. The female was transported to the hospital with life-threatening injuries. The three responding officers were transported to a nearby hospital for observation. A firearm was recovered from the scene.
Homicide Unit detectives and the State Bureau of Investigation responded to the scene to conduct an investigation, and Crime Scene Search responded to process the scene and collect physical evidence. CMPD's Operations Command, Community Policing Crisis Response Team, Victim Services, Mecklenburg County District Attorney's Homicide Prosecution Team, Medic, and CFD also responded to assist.
As is standard procedure with any officer-involved shooting, the Internal Affairs Bureau will conduct a separate but parallel investigation.
The investigation into this case is active and ongoing. As additional information develops, it will be released by the CMPD's Public Affairs Office. Anyone with information about this incident is asked to call 704-432-TIPS to relay information. The public can also leave information anonymously with Crime Stoppers at 704-334-1600 or http://charlottecrimestoppers.com/. For additional information about this case, please refer to the report: 20220819-1626-00.


Find this post at it's original home on the Buenos Aires Delivery Blog!
There is something magical about the simple humita empanada. The exact definition of humita can change drastically depending on the country, but in Buenos Aires, humita usually refers to a type of creamed corn, made with fresh ingredients. It makes the perfect empanada! Should one ever care to attempt making these at home – the recipe is fun and easy!
This recipe makes 12 empanadas. These empanadas could make a great meal by themselves, be served with a salad or as an appetizer at your next dinner party!
12 empanada 'tapas', or pre-made empanada dough. These are easy to find in any grocery store.
1 egg, beaten with a tablespoon of water to coat empanadas before baking.
If using fresh corn (recommended!), place in a large pot of water and bring to a boil. Let boil until the corn turns bright yellow. Let the cobs cool and then slice to remove the kernels from the cob. If using frozen corn, defrost in the microwave and drain excess water. Then get chopping! Finely chop the onion and red pepper and dice the tomato.
In a large bowl, combine your chopped veggies with the two egg yolks and the casan creme. Mix well. Season with salt and pepper to taste.
Now the challenging part – filling the empanadas. Place the 'tapa' in your hand and spoon two tablespoons of the humita mixture into the middle. Seal around the outside, making sure that the edges are firmly pressed together. This is important, otherwise they can come apart while baking. Experiment with different sealing techniques such as crimping the edges with a fork or twisting to seal.
Then brush the empanadas with the beaten egg. This makes them look pretty!
Bake in the oven at 350º F or 175 Celsius for about 40 minutes, until they look golden brown. Enjoy!


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Anna Mary Hotchkis (Renfrewshire, 30 de mayo de 1885, Kirkcudbright; 14 de octubre de 1984) fue una artista, escritora y conferenciante de arte escocesa. Expuso en Londres, Beijing, Hong Kong y en exposiciones en Escocia. Fue miembro y expuso en la Real Academia Escocesa (RSA) 1915-1968.

Biografía
Hotchkis nació en Crookston House, Renfrewshire, Escocia (cerca de Glasgow). Tenía tres hermanas, Margaret, Catherine e Isobel (1879-1947, también pintora), y seis hermanos, de los cuales se sabe que solo uno, Richard, sobrevivió hasta la edad adulta.

Hotchkis heredó el amor por la pintura de su madre y quería ser artista desde los 14 años. Comenzó su formación en la Escuela de arte de Glasgow a los 21 años, a pesar de las objeciones de sus padres, preocupados por su delicada salud. Su familia se mudó a Edimburgo en 1907 y ella se matriculó en el Edinburgh College of Art estudiando con Robert Burns durante tres años. Completó sus estudios pero se fue sin obtener un diploma. Por esta época, tres de las hermanas Anna, Margaret e Isobel, fueron a Múnich para estudiar arte con Hans Lasker.

A sugerencia de su maestra de Edimburgo, Hotchkis montó un estudio en la pequeña ciudad de Kirkcudbright, inicialmente alquilado y luego comprado a Jessie M. King, una conocida de su maestra. Conservó el estudio desde 1915 hasta su muerte en 1984.

Primer encuentro con China
En 1922 Hotchkis viajó a China a través de Estados Unidos, Japón y Corea para visitar a su hermana Catherine en Mukden (ahora Shenyang), donde se había establecido desde 1915 y trabajaba en una escuela para niñas de la Asociación Cristiana de Mujeres Jóvened (YWCA, por sus siglas en inglés). Después de Mukden, pasó tres meses en Shanghái, donde realizó una exposición de su trabajo. Mientras pintaba a niños trabajadores en una fábrica de algodón allí, contrajo una infección grave, lo que la obligó a regresar a Mukden y luego trasladarse a Pekín para recibir tratamiento. Decidió quedarse en Pekín aceptando una oferta para ocupar el puesto de profesora de arte en la Universidad de Yenching.

Hotchkis enseñó en Yenching durante un año y luego regresó a Escocia en 1924, viajando en el Transiberiano hasta Moscú, donde se quedó con la misión cuáquera, y luego a su casa en Londres a través de Berlín. Trajo consigo más de 70 cuadros que expuso en la Brook Street Gallery de Londres. Regresó a China en 1926, alojándose con una familia china en Pekín, donde permaneció hasta la invasión japonesa de China en 1937.

Viajes a través de China
En julio de 1924, mientras estaba convaleciente en la casa de vacaciones de su hermana en la localidad costera de Beidaihe, conoció a la pintora estadounidense Mary Augusta Mullikin que, al enterarse de que había una compañera artista en la ciudad, se acercó en un burro para presentarse. A pesar de que Hotchkis vivía en Pekín y Mullikin en Tianjin, las dos se hicieron buenas amigas y después del regreso de Hotchkis a China viajaron mucho juntas, escribiendo varios libros y artículos sobre sus viajes allí.

Su primer viaje juntas fue a Japón y Corea en 1927. En 1929 Hotchkis visitó a sus hermanas en el Reino Unido, viajando a través de Japón y Los Ángeles. Regresó a China al año siguiente y, en septiembre de 1931, ella y Mullikin hicieron su primer viaje a las grutas de Yungang, cerca de la ciudad de Datong, en la provincia norteña de Shanxi. Regresaron allí en junio siguiente, habiendo concebido la idea de publicar un libro sobre las esculturas rupestres de Yungang, para ilustrarlo con sus propias pinturas y dibujos. Regresaron de Yungang por el camino más largo, a través de Hangzhou y la isla sagrada de Putuoshan, una de las Cuatro Grandes Montañas del Budismo en China.

En un intento por encontrar un editor inglés para el libro que pretendían, Hotchkis volvió a visitar el Reino Unido a finales de 1932, pero regresó con las manos vacías. Mientras estuvo en Londres, realizó otra exposición en las Brook Street Galleries, esta vez con pinturas de las grutas de Yungang de Mary Mullikin y la suya propia. Una noticia de The Times tenía comentarios favorables: "Tanto por su iniciativa y coraje como por su juicio y talento son estas damas dignas de elogio. Haciendo caso omiso de los intereses habituales del trotamundos, se han concentrado en los valores artísticos y arqueológicos propios de los lugares visitados, que pocos tienen la oportunidad de ver". Finalmente encontraron un editor para el libro en Pekín, Henri Vetch, cuya Librairie Francaise se especializaba en libros en inglés y francés sobre temas chinos. Habiendo aceptado publicar su primer libro, Vetch sugirió entonces que viajaran por China a las montañas budistas y taoístas más sagradas para otro libro. Mientras tanto, un viaje planeado a Kaifeng y Luoyang en 1934 tuvo que cancelarse debido a los combates entre los señores de la guerra en el área, pero en octubre de 1934 las dos artistas lograron pasar una semana pintando en el monte Tai en la provincia de Shandong, el pico sagrado más importante para los taoístas y una de las montañas que había sugerido Vetch. Aparentemente, este fue el primer viaje de Hotchkis allí, aunque Mullikin ya había estado varias veces.

En 1935 Hotchkis se mudó a una casa en Xie He Hutong, en el distrito este de Pekín. La casa había sido alquilada desde 1931 por Laurence Sickman, un estadounidense que más tarde se convertiría en el Director del Museo de Arte Nelson-Atkins en Kansas City, y su madre. Cuando Sickman regresó a los Estados Unidos en 1935, su madre deseaba quedarse en Pekín e invitó a Hotchkis a compartir la tradicional casa con patio bellamente amueblada. En la primavera de 1935, Mullikin llegó a Pekín para quedarse con Hotchkis y celebrar la publicación de Vetch de su libro sobre las cuevas de Yungang. El 27 de agosto partieron de Pekín en el viaje sugerido inicialmente por Vetch, un autodenominado "peregrinaje" a las montañas sagradas. Esto lo completaron en dos viajes formidables, durante dos meses, en el otoño de 1935 (al norte de Heng Shan, Wutai Shan y Hua Shan ) y cuatro meses en la primavera y verano de 1936 (a Song Shan, Emei Shan, al sur de Heng Shan y Jiu Hua Shan). En las empinadas laderas de Hua Shan en la provincia de Shanxi, Hotchkis, de 50 años, sufrió una tensión cardíaca, pero después de descansar en Pekín durante el invierno de 1935-36 estaba en condición es de continuar.

Regreso a Escocia
En julio de 1937, el ejército japonés, que había ocupado la provincia de Manchuria, en el norte de China, desde 1932, invadió el resto de China y tomó Pekín en agosto. Hotchkis decidió a regañadientes abandonar China y regresar en barco a través de Japón, luego Hong Kong, Sri Lanka, India e Irak a Grecia. Otro barco la llevó vía Constantinopla a Venecia, donde tomó un tren nocturno a París, y luego de regreso a Londres, donde llegó en abril de 1938, unos cinco meses después de salir de Pekín.

Hotchkis se instaló en su estudio en Kirkcudbright en Escocia. En 1940 visitó a unos amigos en París, donde tomó uno de los últimos barcos de Francia a Inglaterra durante la invasión alemana. De regreso a Escocia, durante la guerra trabajó como supervisora en una fábrica de cordita en Dalbeattie durante 10 meses, antes de verse obligada a retirarse del esfuerzo bélico debido a problemas de salud y regresar a Kirkcudbright para pintar. Después de la guerra, viajó mucho por Europa y América del Norte e hizo dos viajes a Hong Kong, donde Henri Vetch había restablecido su negocio editorial. El segundo libro de Mullikin y suyo, Las nueve montañas sagradas de China, se publicó finalmente allí en diciembre de 1973, 37 años después de la peregrinación que documenta.

Activa y exhibiendo casi hasta el final de su vida, Hotchkis murió pacíficamente en Kirkcudbright en 1985, en su centésimo año. Nunca se casó ni tuvo hijos.

Publicaciones
(con Mary Mullikin):

 Buddhist Sculptures of the Yun Kang Caves (Henri Vetch, Pekín, 1935)
 The Nine Sacred Mountains of China (Vetch & Lee, Hong Kong, 1973).

Otras lecturas
Se puede encontrar una biografía breve y en algunos aspectos inexacta en Peter McEwan, Dictionary of Scottish Art and Architecture (1995).

Referencias

Enlaces externos

Pintoras de Escocia
Pintores de Escocia del siglo XX
Centenarios de Escocia
Escocesas del siglo XIX
Escocesas del siglo XX
Alumnado de Glasgow School of Art

redpajama_set_name: RedPajamaWikipedia


Amazing; they just don't rust here and my 605 fronts were a doddle to remove.
addo wrote: Amazing; they just don't rust here and my 605 fronts were a doddle to remove.
Chris you left a bottle of bubbley stuff here! only noticed at about 10pm as i crawled to bed after i lifted the car onto some new brick plinths!
I got the engine and gearbox out of the boot this morning, the car is much happier now it's not got all that weight behind the rear axle!
Any thoughts on replacement parts? I see they are available for £12 on e-bay, but are they any good....???
RichardW wrote: Any thoughts on replacement parts? I see they are available for £12 on e-bay, but are they any good....???
I get the Abs light staying on the Zx when it's not been used for a while too , I've found a good bit of use and a good wash of the wheels believe it or not sorts it . Thankfully I've got a front and a rear sensor I got of Malcolm Lockwood at the National at Wicksteed a few weeks ago so if all else fails I can get it sorted . I'm hoping she behaves this week as its MoT day Friday .
Mark, all good luck for the MOT on Friday. I'm sure she'll pass with all the care you lavish on her.
Her owner is busy checking her spheres. The car is utterly immaculate in al, respects and currently has all her original spheres, all bright green still and each one has come off with no effort whatsoever. This car does not know what rust or corrosion is.
Some of the spheres are a bit weak and will need replacement before long. Not bad for 14 years old though.
I'll pop up some pictures later to show the stunning condition of this car.
Will you bee keeping it?


text:
Newcastle United 0 – 1 Chelsea
on Thursday, 21 December 2006 at 11:50am
Daily Telegraph, Tim Rich: "Newcastle's search for a trophy has come to grief at Chelsea's hands with what by the Tyne must seem depressingly regular intervals. This was the eighth time in 10 years they had barred Newcastle's way in cup competitions and only once, when they lost an FA Cup tie in the January snows last year, had the outcome been anything other than defeat."
The Guardian, Michael Walker: "As Glenn Roeder surveyed his visitors' teamsheet he quipped that the Chelsea substitutes constituted "the best five-a-side team in the world". Sadly for Newcastle, their manager was to be proved near the mark with that analysis as Frank Lampard, Michael Ballack and finally Didier Drogba made their way from the sidelines and into the action. Drogba required a mere five minutes to strut forward and score his 17th goal of a rousing season."
The Times, George Caulkin: "The first recorded expression of regret from José Mourinho did not pre-empt an apologetic performance by his Chelsea team last night. The sorrow was all Newcastle United's; that a meaningful trophy remains elusive, that Glenn Roeder did not buy Didier Drogba for West Ham United many moons ago and that where Chelsea have a Russian owner, Tyneside could not conjure a Russian linesman."
The Independent, Simon Rushworth: "[T]he incident which ultimately decided a predictably hard-fought game between two familiar cup foes was a clear case of foul play as the Newcastle midfielder Nicky Butt crudely halted Arjen Robben's run on goal. The Dutchman already had just cause to go down a second earlier when United's emergency right-back, Nolberto Solano, clipped his heels but, to his credit, the midfielder stayed on his feet."
Black & White & Read All Over, Paul: "For the second time in eight days, Drogba proved to be the difference, as he again came off the bench to score with about quarter of an hour left to play. This time his goal coming from a well struck free-kick, won after first Solano and then Nicky Butt had done their best to flatten Arjen Robben (unsurprisingly Butt proving the more effective). However, that foul took place a good four yards from where the free kick was taken, with Chelsea surreptitiously relocating the ball to give Drogba a better angle to strike the set piece, and in doing so enabling him to curl the ball beyond Shay Given."
We're through to the semi-finals of the League Cup. Jose Mourinho's only loss in the competition to date was last season's penalty shoot-out defeat to Charlton at Stamford Bridge.
The performance may not have set the world on fire, but we never really looked like losing. Obafemi Martins' shot which struck the underside of Hilario's crossbar and landed plum on the goal line was the nearest the Magpies came to scoring.
Though clearly not the finished article, Salomon Kalou does impress me at times. It's just a shame he couldn't produce it over the whole 90 minutes.
Of the players on the pitch from the start, Michael Essien and Ricardo Carvalho stood out. Carvalho is playing with an ankle injury too. An unsung hero. Frank Lampard made a difference after coming off the bench.
Didier Drogba. Within five minutes of coming on, the Ivorian scored his 17th goal of the season. Our reliance on Drogba is worrisome.
The 4-3-3 formation made very little difference. Many of us had called for Andriy Shevchenko to be played in a 4-3-3 with two wingers, but in this game the wide players offered him no support whatsoever. He's sure to come in for more undeserved criticism.
Bar Shevchenko's only shot on goal which struck Shay Given's right-hand post on the stroke of half time, we created very little in the Magpies' penalty box. All our efforts on goal were limited to long range shots, as they were against Everton on Sunday.
Arjen Robben has the same problem as Andy Johnson, in that his reputation for "diving" precedes him. The free kick from which Drogba scored the winner was perfectly legitimate: Robben did his best to ride a rash tackle from Nolberto Solano before being flattened by Nicky Butt. Try telling 35,000 myopic Geordies that.
I've lost count of the number of times we've hit the woodwork in recent games.
When are we going to turn up for both halves?
Didier Drogba, despite only playing around 15 minutes of the second half?
We are not playing well, but we're through to the semi-finals of the League Cup, the last sixteen of the Champions League, and two points off top spot in the Premiership. It can't be all bad.
Reaction: Clarke – The importance of Didi
Roeder denies Mourinho argument
Andriy ShevchenkoArjen RobbenDidier DrogbaFrank LampardGlenn RoederHenrique HilarioJose MourinhoLeague CupMichael EssienNewcastle UnitedRicardo CarvalhoSalomon Kalou
League Cup preview: Newcastle United v. Chelsea
Letter from America: José Mourinho is our prat, God bless him


Knights Templar is today an international spiritual, Christian, and military Order of Chivalry that is open, independent and apolitical. Knights Templar counts originated from the Knights Templar which was established in Jerusalem in 1118 and which for two centuries served as protection for the Christian pilgrims who wished to visit the Holy Land. The Knights would be an example through his actions, words and deeds. The Knights were through their vows, stand for high morals that would permeate the business.
The modern Knights Templar want to take advantage of the virtues that the Templars during the Crusades sat high and put them into words, and actions in today's society. Order's Grand Master Count Fernando Pinto de Sousa Fontes based in Portugal.
The Scandinavian Grand Priory of Knights Templar is an autonomous storpriorat and has been in Scandinavia in its present form for over 25 years. Today is National priory in Denmark, Finland, Norway and Sweden. Our weapons todays example and good deeds. Knights Templar caters primarily to men and women who are operating within or adjacent to our countries militaries. The words are many professions such as professional officers, reserve officers, priests, lawyers, teachers and business leaders.
With the development of the armed forces in the Nordic countries experience more and more officers and vederlikar to work and serve in areas of conflict far from home countries. Very often they are faced with strange circumstances and situations that require quick and immediate action. It may be the case of situations where one's morals and ethics put to the test. Then they own the promises given before the Knights Templar help and support.
Humanitarian activities pursued by the Knights of the Order Humanitarian Fund. Funds raised go entirely to remediation in our geographical neighborhood. Over the years the Knights Templar including supported an orphanage in Tallinn and a child sanatorium in Kaunas with concrete measures to improve conditions for the children. All administrative costs associated with the relief effort funded by the Order's membership fees.


Discussion of roadblock permits garnered the most lengthy discussion on a light agenda for the Town of Woodbury Board of Mayor and Aldermen during its July meeting Tuesday (July 3).
Mayor Harold Patrick appointed a three-person committee to consider various parameters for road blocks that serve as fund-raisers for area civic organizations, sports teams and school clubs. Jo Anne Davis, Dottie Duggin and Charlie Harrell will serve on the committee and report back with suggestions at the August meeting.
"I would like an orderly situation to occur," Patrick said. "I would like to see them spread out and not have them several weekends in a row, if possible."
It is not the Board's desire to cease roadblocks for any organization, according to Patrick.
"Contrary to what we have seen on some of the postings on the (Cannon Courier), it is not the intent that we are going to the Lions Club and tell them they can't have a road block in October to raise money for White Cane," Patrick said. "It is not the intent of this (Board) to put all the names in the hat and have a blind draw and to suggest so is silly and ludicrous."
Davis said the Board is supportive of road blocks for fundraisers for worthwhile causes.
"I think it is wonderful," Davis said. "I don't care what you do someone is always going to complain, but I support these road blocks."
Alderman Faye Knox told the Board she would like to see young people educated about how to conduct themselves at road blocks. She also said protective vests should be worn at all times.
Alderman Adam Melton told the newly-formed committee the Board needs guidelines and parameters that "we can live within."
In other business, the Board unanimously approved adoption of Ordinance No. 444 on second and final reading. Harrell made the motion and Alderman Lois Larimer seconded. The ordinance amends the zoning ordinance of the Town of Woodbury to delete references to residential rear yard setbacks in the C-3 commercial zoning district within the zoning ordinance.
The Board also adopted Ordinance No. 445 on second and final reading. Melton made the motion, seconded by Knox. It passed unanimously. The ordinance amends the original budget ordinance for the fiscal eyar 2011-12.
The Board also adopted an ordinance to amend the 2006 Edition of the International Building Code, as recommended by the State of Tennessee. It must pass second reading in August.
"It is a minor thing the State of Tennessee has recommended," Patrick said. "We adopted the same building codes as the City of Murfreesboro and they have to make the same amendment. I think it is proper we do that."
Discussion on a proposal from Unison Site Management was tabled indefinitely as attorneys from both sides meet.
Woodbury Police Chief Kevin Mooneyham reported the department is back to 100 percent staffed with the recent hiring of Tracy Stoetzel.
The new truck purchased for the Woodbury Fire Department by the Town of Woodbury was expected to be delivered Friday (July 6).


text:
Billy Long & Sheila Jackson Lee
Compare the voting records of Billy Long and Sheila Jackson Lee in 2017-18.
Represented Missouri's 7th Congressional District. This is his 4th term in the House.
Billy Long and Sheila Jackson Lee are from different parties and disagreed on 70 percent of votes in the 115th Congress (2017-18).
Dec. 21, 2018 — Nuclear Energy Innovation and Modernization Act
Dec. 19, 2018 — Museum and Library Services Act
Dec. 19, 2018 — Modernizing Recreational Fisheries Management Act
Dec. 19, 2018 — National Quantum Initiative Act
Dec. 19, 2018 — Traumatic Brain Injury Program Reauthorization Act
July 13, 2017 — Garamendi of California Amendment No. 1
Feb. 28, 2017 — Krishnamoorthi of Illinois Amendment No. 6


text:
Luis de Zulueta y Escolano (Barcelona, 8 de abril de 1878-Nueva York, 2 de agosto de 1964) fue un escritor, profesor y político español, miembro del Partido Reformista y diputado en tres ocasiones de las Cortes de la Restauración.

Tras proclamarse la República, se presentó a las elecciones de 1931 como independiente, saliendo elegido diputado de las Cortes republicanas en representación de la provincia de Badajoz. Fue ministro de Estado en uno de los gabinetes de Gobierno presidido por Azaña y embajador de España en Berlín y ante la Santa Sede, puesto en el que permaneció al estallar la guerra civil española y que desempeñó hasta el momento en que la Santa Sede reconoció el Gobierno del general Franco. Terminada la contienda se exilió a Colombia, donde trabajó como profesor en la Escuela Superior Normal de Bogotá, y, luego, a Estados Unidos, donde falleció.

Biografía

Infancia y Juventud
Luis de Zulueta y Escolano nació en Barcelona en el año 1878, del matrimonio formado por Juan Antonio de Zulueta, criollo nacido en Cuba, y María Dolores Escolano y de la Peña, catalana de origen. El padre, abogado, estaba relacionado con el nivel más alto de la banca barcelonesa. Luis era uno de los seis hermanos, de los cuales cabe destacar la figura de Antonio de Zulueta, biólogo y pionero de la investigación genética en España. Cursó estudios en el Colegio del Sagrado Corazón, donde coincidió con Eduardo Marquina; poco a poco, nació entre ellos una profunda y entrañable amistad que se mantendrá durante toda la vida. Marquina y Zulueta colaboraron con escritos propios y traducciones en Luz, publicación de corte modernista, y, desaparecida ésta, en Barcelona Cómica. Zulueta y Marquina van adentrándose en círculos literarios y, a principios de siglo, escribían ambos en La Publicidad, diario republicano que había dirigido Lerroux. En 1903, el día 26 de julio, apareció en La Publicidad un artículo firmado por Luis de Zulueta. El artículo llevaba como título «La prudencia de León XIII». Hacía pocos días que el papa había muerto y Luis de Zulueta rememoraba la figura del papa, si bien en términos no muy elogiosos. Este artículo llamó la atención de Miguel de Unamuno, rector de la Universidad de Salamanca, y será el inicio de una larga y profunda amistad, como puede apreciarse a través de una dilatada correspondencia entre Unamuno y Zulueta.

Cursó estudios en París, Ginebra, Bruselas y Alemania. Le llamaron la atención temas como la Reforma protestante o las enseñanzas filosóficas de Rousseau. Tras su regreso a España, se decidió a estudiar Filosofía y Letras, y, contando con el apoyo de Unamuno —su mentor—, optó por proseguir estudios en la Universidad de Salamanca; matriculado como alumno libre, terminó la carrera en un solo curso. En todas las asignaturas obtuvo brillantes calificaciones, excepto en griego. En este mismo curso, en septiembre, realizó los exámenes de licenciatura obteniendo la calificación de sobresaliente (septiembre de 1906).

Trayectoria
En el verano de 1906 se incorporó a las colonias de San Vicente de la Barquera y comenzó a dar clases en la Institución. Ya como licenciado, firmó oposiciones a cátedras de diferentes institutos de provincias (Soria, Baeza, Teruel, Figueras, Cuenca, Zamora y Huesca), pero no llegó a presentarse a ninguna, como tampoco opositó a una auxiliaría en la Sección de Filosofía de la Facultad de Filosofía y Letras de la Universidad Central, a pesar de haber firmado la solicitud. Del mismo modo, no llegó a opositar a otra auxiliaría de la Facultad de Filosofía y Letras de Sevilla. El 11 de diciembre de 1908 contrajo matrimonio con Amparo Cebrián, con quien tuvo cinco hijos: Concepción, Luis, Inés, Carmen y Julián.

En 1910, Zulueta empieza a tomar parte activa en la vida política, primero a nivel regional y más tarde a nivel nacional. Es nombrado diputado por Barcelona y se doctora ese mismo año en la Universidad Central, obteniendo premio extraordinario con una tesis sobre la pedagogía de Rousseau. Fue nombrado profesor por Real Orden de 17 de agosto de 1910, a propuesta de la Facultad de Filosofía y Letras de la Universidad Central. La actividad docente realizada por Zulueta en la Escuela de Estudios Superiores del Magisterio se prolongó hasta su desaparición, pasando junto con otros profesores de la Escuela a formar parte del claustro de la recién creada Sección de Pedagogía de la Facultad de Filosofía y Letras de la Universidad Central.

Político
En las elecciones generales de España de 1910 fue proclamado diputado, representando a la fracción política republicana en uno de los distritos de la ciudad de Barcelona por la Junta Provincial de Barcelona. Obtuvo 23 623 votos de los 135 924 emitidos. Elegido nuevamente diputado por la circunscripciones de Madrid en 1919, Pontevedra en 1923 y Badajoz en 1931, fue ministro de Estado en el Gobierno de la Segunda República que, entre el 16 de diciembre de 1931 y el 12 de junio de 1933, presidió Manuel Azaña.

Embajador en Berlín entre 1933 y 1934, pasará en 1936 a representar al Gobierno republicano ante la Santa Sede. No obstante, el inicio de la Guerra Civil y el reconocimiento por parte de la Sede Apostólica del gobierno del general Franco impulsarán al político y diplomático a exiliarse en Colombia, para después pasar a los Estados Unidos, donde permanecería hasta su muerte en 1964.

Obras
Colaborador en los periódicos de más alto nivel intelectual del país como El Liberal, El Sol y La Libertad. También en revistas relacionadas con temas educativos, como el Boletín de la Institución Libre de Enseñanza, la Revista de Pedagogía, la Revista de Occidente y la revista España

Sus obras más destacadas son:

 El alma de la escuela (1910);
 El maestro (1914);
 La edad heroica (1916);
 El ideal de la educación (1922);
 La democracia educadora (1930);
 La nueva edad heroica (1942);
 El rapto de América (1952).

Véase también
 Antonio de Zulueta, hermano.
Julián de Zulueta y Cebrián, hijo.

Referencias

Bibliografía

Embajadores de España en Alemania
Embajadores de España ante la Santa Sede
Políticos de España de ámbito estatal
Políticos de España del siglo XX
Políticos de la Restauración borbónica
Diputados de la XV legislatura de España de la Restauración
Diputados de la XIX legislatura de España de la Restauración
Diputados de la XXI legislatura de España de la Restauración
Ministros de España del siglo XX
Ministros de la Segunda República Española
Ministros de Asuntos Exteriores de España
Diputados de la I legislatura de la Segunda República Española
Escritores de España del siglo XX
Escritores en español del siglo XX
Exiliados del franquismo en Colombia
Alumnos de Filosofía y Letras de la Universidad Complutense de Madrid
Políticos de Barcelona
Exiliados del franquismo en Estados Unidos
Ministros del Gobierno de España nacidos en Cataluña
Ministros del Gobierno de España de Acción Republicana
Segundo Gobierno Azaña (1931-1933)
Diputados por Barcelona de las Cortes de la Restauración
Diputados por Madrid de las Cortes de la Restauración
Diputados por Redondela de las Cortes de la Restauración
Diputados por la circunscripción electoral de Badajoz durante la Segunda República
Junta para Ampliación de Estudios e Investigaciones Científicas
Residentes
Krausistas
Nacidos en Barcelona
Fallecidos en Nueva York


Home > News and Events > Speakers for Schools is hiring!
Speakers for Schools is a small team with national reach and profile. We are looking for a volunteer to support our programme lead in contacting schools and basic administration to ensure they are able to take a part of our free programme.
This role is based in our London office supporting our 8 person team.
S4S requires an Admin volunteer to process and drive forward engagement with our speaker and school networks. The volunteer will be working closely with the Programme Manager on a specific set of tasks, contacting schools about free opportunities for speakers to help secure a date for the event and documenting communications and information on our databases.


Ryan Fields goes up for two of his 29 points.
LYNCHBURG, Va.- It took an extra session but in the end, Randolph men's basketball came out on top as they knocked off Eastern Mennonite 79-71 on Saturday afternoon at the RAD Center. The victory, the WildCats' second in the last three games, lifts Randolph to 6-17 overall and 3-11 in the ODAC. The Royals drop to 9-13 and 4-10 in the conference.
Ryan Fields (Edgewood, Md./Loyola Blakefield) and Sammy Hooper (Richmond, Va./Midlothian) accounted for 63% of the WildCats' offensive output with 29 and 21 points, respectively. For Fields, it was a season-best as it topped his 28-point output against Emory and Henry on January 24.
Randolph led 5-2 early on in the first half until the Royals took over the lead, 6-5, at 14:39. A Nick Goble (Charlotte, N.C./Myers Park) layup 24 seconds later restored the advantage back the WildCats. EMU stole the lead back and went ahead 18-15 at 10:39 but back-to-back jumpers from Fields and Elijah Ford (Chantilly, Va./Chantilly) gave the lead back to the 'Cats. EMU pulled ahead thanks to a 14-4 run for its biggest lead of the game, 32-25, with 3:09 left in the half. Randolph drew even with an 11-4 run, ending with a Hooper three-point basket, with 42 ticks left and the teams went into the locker room tied at 36-all.
Eastern Mennonite started the second half strong with a 7-0 run to go up 43-36. Randolph cut their deficit to three points, 43-40, but EMU added to their lead with a 13-0 run and break away to a 55-40 lead with just over 11 minutes remaining in regulation.
Randolph's deficit stood at 13 points at 62-49 with 7:07 left on the game clock. A pair of free throws from Fields and Hooper cut it to nine. The Royals edged ahead 64-53 after two foul shots from DJ Hill at 5:31. A quick 7-0 WildCat run put Randolph to within four points of tying. Two more free throws by EMU staked the visitors to a 66-60 advantage with three minutes left. Fields cut it in half with a trey with two minutes left and hit another with a little under a minute to go to knot the contest at 66-66. The score would stay that way as EMU could not get a final shot off before the horn sounded as the game headed to overtime.
It was all WildCats in the extra period as they outscored the Royals 13-5. Eastern Mennonite took a one-point lead on the first throw by Isaiah Harris-Winn at 4:42. The 'Cats scored six straight points to take a lead it would not relinquish.
Also contributing for Randolph on the afternoon was Brian Smith (Dumfries, Va./C.D. Hylton) who scored nine points and dished out a season-high eight assists while coming down with four rebounds and two steals. Goble added six points and grabbed a team and season-best 10 rebounds. Colton Lee (Raleigh, N.C./North Raleigh Christian Academy) also chipped in six points.
"I'm proud of our guys because when we were down 15, we had a lot of reasons to stop and we didn't," said head coach Pete Hamilton after the game. "In the first half of the season, this game would have gone a different way. I think we found a good rhythm with Ryan and Sammy.
Randolph edged out EMU in shooting with a 44.6-42.1% advantage. Rebounds did favor EMU 39-37. The WildCats committed a season-low eight turnovers on the afternoon. It did take advantage of 15 EMU turnovers with 15 points scored off them.
"The low turnovers is a testament to our focus and our ability to learn and move forward," remarked Hamilton. "We are showing a much better focus on that. It makes a huge difference especially when you are down 15, you can't afford to turn the ball over. Our guys are doing more focused job at ball security."
The WildCats go on the road Wednesday to face Roanoke. It will be a rematch of the game on December 6 that the Maroons claimed 72-43 at the RAD. Game time is set for 7:00 p.m.
January 31 and into February we had a mindset of 'Lets have a new season and forget about the bad situations we put ourselves in or the bad situations we have been in an just move forward," stated Hamilton. "We haven't won every game but we have played our best basketball during this stretch. Looking foward, we are still excited abnd positive about where we could go."


text:
Q: Let a,b,c real numbers. Show that the system of linear equations has only one solution $$x_1 + x_2 + x_3 = a$$
$$2x_1 - x_2 + 3x_3 = b$$
$$4x_1 + x_2 + 9x_3 = c$$
Now, looking at the solution of this, the author does the following:

The matrix of the coefficients is invertible because $det(E) \ne 0$ (where E is the matrix). Therefore the linear system has only one solution.

Can someone elaborate of the above solution? I do not understand this deduction.

A: See the invertible matrix theorem. http://mathworld.wolfram.com/InvertibleMatrixTheorem.html

A: When the matrix is not singular, i.e. $\det(A)\neq 0$, the columns of $A$ are linearly independent and thus, since $A\vec x$ represents a combination of column vectors which are a basis and span $R^3$, we have that $$A\vec x=b$$
has always one and only one solution.

A: If you write the system as a matrix equation
\begin{align*} \left(
\begin{matrix}
1 &1 &1\\
2 &-1 &3\\
4 &1 &9
\end{matrix} \right) \left( \begin{matrix}
x_1\\
x_2\\
x_3
\end{matrix}\right) = \left( \begin{matrix}
a\\
b\\
c
\end{matrix}\right),
\end{align*}
then the determinant of your coefficient matrix is non-zero, so there is a unique solution, which is the right hand side of your equation times the inverse of the coefficient matrix:.

A: Multiplying the first equation by $-2$ and adding to the second:
$$-3x_2+x_3=b-2a$$
Multiplying the first by $-4$ and adding to the third we get
$$-3x_2+5x_3=c-4a$$
From this equations we get
$$4x_3=-2a-b+c$$

A: Theorem: If $A$ is an invertible $n\times n$  matrix, then $\forall b\in\Bbb R^n$, the system $Ax=b$ has a unique solution.
You must know this theorem by heart!
Proof: Indeed, if $x_0$ is a solution, then $$Ax_0 = b\Rightarrow A^{-1}(Ax_0) = A^{-1}b \Rightarrow (A^{-1}A)x_0 = Ix_0 = x_0 =A^{-1}b$$
so this proves that the only possible solution is $A^{-1}b$.
Now, $A^{-1}b$ is really a solution since $A(A^{-1}b) = (AA^{-1})b = Ib = b$.
Hence $Ax=b$ has one and only one solution if $A$ is invertible.$\;\;\blacksquare$
Remark: Of course, this is only a possible proof, and other answers above are also good.

redpajama_set_name: RedPajamaStackExchange


text:
ENGIE and Equitix secure deal with the University of Birmingham
By ENGIE
A consortium comprising leading energy and services specialist ENGIE, and prominent UK infrastructure investor and developer, Equitix, has secured a contract with the University of Birmingham to transform Pritchatts Park student accommodation village into a state-of-the-art low carbon campus.
The project involves the creation of 496 new highly energy efficient student homes and an accompanying 482-space modular construction multi-storey car park. In addition, 734 existing rooms will benefit from an extensive refurbishment, bringing them up to modern standards.
ENGIE will also undertake 50-year facilities management and lifecycle works contracts, providing ongoing repairs, security and cleaning services to support the day-to-day lives of the student residents.
The new accommodation will be constructed in the form of townhouses to complement existing buildings in the surrounding area. A key element in the design of the new facilities is energy efficiency. The overall scheme will be powered and heated entirely through electricity – with the refurbished building heated by air source heat pumps – which the consortium has pledged will be from 100% renewable sources. The new multi-storey car park will also feature 24 EV charge points, with infrastructure in place for a further 72 in the future.
The project sees ENGIE continue its partnership with Equitix, who will be the lead equity partner in the project, following the success of similar developments for the University of Leicester and Kingston University. ENGIE and the University of Birmingham will also take equity stakes in Pritchatts Park.
Jake Fellows, Divisional Development Director for ENGIE UK & Ireland, said: "This is an exciting project for ENGIE, as it gives us the opportunity to showcase our wide-ranging placemaking capabilities across energy, services and regeneration, as well as demonstrating our long-term commitment through the investment model. It's also great that we can continue our strong partnership with Equitix, which is already having such a positive impact in Leicester and Kingston.
"The University of Birmingham is one of the UK's most highly-ranked institutions, so we're delighted to have been chosen to create market-leading accommodation that is highly sustainable and equipped to meet the university's ever-growing demand for places, as well as providing the best experience possible for the students who decide to call it home."
Ben Leech, Director for Equitix, said "We are delighted to be working with our long-standing partner ENGIE and the University of Birmingham to deliver this exciting project which will enhance the university experience for students in Birmingham.
"Equitix is committed to the sustainability and stewardship of its assets in the student accommodation sector. We look forward to developing this fantastic scheme, constructing a sustainable development that connects with and respects the city environment, and which has a positive impact on the community."
Simon Bray, Director of Campus Services at the University of Birmingham said: "The University's overriding objective is to enhance its attractiveness to students, and positively impact recruitment and retention, through providing high-quality housing that meets their needs and expectations, now and in the future. The plans to expand Pritchatts Park will play a key role in providing the infrastructure to help deliver this vision. We are delighted to be working with ENGIE and Equitix."
Building work is set to begin in the summer, with completion expected in August 2023.
Posted in Buildings, Education, ENGIE news
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text:
The Octavian Report: March 2017
Vol 3, No 2 / The Octavian Report: March 2017
An Interview with Barry Eichengreen
Asian Awards. British PM Theresa May is riding a wave of uncertainty, much like Donald Trump.
Octavian Report: Barry Eichengreen, how do you see economic policy and financial policy unfolding under Donald Trump?
Barry Eichengreen: You're definitely starting with a broad question. I think the key decisions will concern corporate taxation, individual income taxation, infrastructure spending, and trade policy. Trade policy is the one thing that the President has considerable authority to do unilaterally without agreement and cooperation from Congress. The most likely scenario is one where the President grows impatient and feels the need to do something visible. The one thing he can visibly do unilaterally — by invoking the Trading with the Enemy Act or the escape clause in NAFTA — is to do something on the trade policy front.
I think there's a high likelihood of this happening. In addition, there is agreement, apparently, between the President and the Congress on the desirability of corporate income tax reform — although we're receiving mixed signals about whether or not they agree on the details.
On the individual income tax front, there's the danger of doing something that will blow a hole in the budget. We will find out in due course whether there still are deficit hawks on the Republican side of the aisle in Congress who will resist going down that path, or whether they can agree on significant spending cuts that will make those individual income tax cuts deficit-compliant.
On the infrastructure front, I'm skeptical that we will see much of anything because tax-credit-based infrastructure spending is going to be very hard to ramp up and because Congressional Republicans are skeptical about the ability of government to select and implement these kind of spending programs.
OR: Do you think that any forthcoming protectionist policies will offset any benefit that might come from tax reform?
Eichengreen: Let me step back and ask: benefit for whom? Lightening up on business regulation, environmental regulation, safety regulation, and fuel economy standards might be good for business profitability. But that doesn't necessarily imply that it's good for the economy overall or that it will have a positive impact on economic growth. We haven't even gotten to the trade policy issues yet. All this leads to the question of whether markets have overreacted. In my view, that's what markets do. They overreact. So it's conceivable that second thoughts will develop over whether some of the regulatory changes will be a positive or negative for the economy.
On the trade policy front, there is no upside, it seems. My very first scholarly article in economics — published in 1981; it's almost embarrassing to recall — was about the effects of tariffs when you have a flexible exchange rate. I wrote down that model because I was writing my dissertation on the Great Depression. The United Kingdom imposed a tariff in 1932 after it had gone off the gold standard and had a flexible exchange rate. What the model showed was that you can boost output in the short run because you're shifting spending toward domestically produced goods, but the effects on the economy are negative in the longer run because you're disrupting business, creating uncertainty, and disrupting global supply chains. And the situation in 1932 was one with a lot of excess capacity, where shifting spending toward locally produced goods had a positive effect in the short run.
If you believe the U.S. is close to full employment with a 4.7 percent unemployment rate and that there isn't a lot of spare capacity at the moment, then you're not going to get those positive short-run effects. Markets are going to look forward toward the negative, longer-term consequences.
OR: What scenarios worry you at the moment as those most likely to create a real economic crisis?
Eichengreen: Well, I am reminded of the 1930's. Some people would say I'm always reminded of the 1930's. I am reminded of the 1930's not only because of the economic risks, but because of the geopolitical risks as well. If Trump were to slap a tariff on imports from China, China would not take it lying down. They would respond tit for tat, and that sounds a lot like the 1930's, where we had the Smoot-Hawley Tariff and then retaliation by other countries. That pretty much spelled the end of the multilateral trading system.
And the economic risks would be greater now because companies in the United States and abroad are more invested in multi-national production. They source more of their components from abroad. Merchandise while in production often crosses national borders multiple times. Little, if any, of that had developed by the 1930's. It follows that the risk of serious economic disruption is greater now. The other lesson of the 1930's is that trade warfare can spill over into other forms of warfare and specifically diplomatic and geopolitical conflict. Countries that are at loggerheads over trade are not going to be able to partner as allies on other issues.
Imagine if the United States and China engaged in what we could call politely a trade dispute or label more alarmingly as a trade war. Imagine them then cooperating to deal with North Korea. It's hard to see.
OR: How do you see the future of the dollar playing out against that backdrop?
Eichengreen: There are a number of different avenues from which one could approach that question. Number one, U.S. policies will clearly make for an even stronger dollar. There's going to be a move toward looser fiscal and tighter monetary policies. That's the Reagan policy mix of the first half of the 1980's. That looser fiscal policy will weaken the current account of the balance of payments, while the tighter monetary policy — by attracting capital inflows — will strengthen the capital account. That made for a dramatically stronger dollar in the 1980's.
And that mechanism will operate more powerfully now: in the 1980's, there was spare capacity in the U.S. economy. You could stimulate domestic spending because you could elicit more supply. Now that we're at full employment, you've got to do something to shift that additional spending back toward foreign sources of supply — and that happens through a still stronger dollar.
Then there's the proposal for a destination-based corporate tax, which would tax goods according to where they're consumed and not where they're produced. It would tax imports. That would shift Americans' spending toward domestically produced goods. If you think we're close to full employment, that requires something else to shift that spending back to foreign sources. That's a second, entirely separate, independent, reinforcing factor making for a still stronger dollar.
Then you've got tariffs. If Trump imposes tariffs on imports from Mexico or China (or both), that will shift spending toward domestic goods. If you think we're close to full employment, more domestic supply will not be forthcoming. Something else has to happen to shift spending back toward foreign sources of supply. Tariffs are thus a third, separate, independent, reinforcing factor making for a stronger dollar.
How much stronger are we talking about? To make a 20 percent destination-based corporate tax rate trade-neutral, you need 25 percent appreciation of the dollar. And that's only one of the three effects that I've been describing.
Policy will make for a significantly stronger dollar, something that the President would not like, since it will make life harder for U.S. exporters and make imports cheaper. That's a recipe for a trade war, if there is a continued failure to recognize the tension between the policy proposals of the new administration and Congress and the implications for the dollar.
A second avenue from which one could approach your question is whether the dollar will remain the world's safe-haven currency. Whenever there has been a period of uncertainty and volatility, the dollar has benefited because the dollar is the only true safe haven when things go wrong. Even when the United States causes the bad thing, as on September 15th, 2008, people rush into dollars because the dollar is liquid, because it has a long history of stability, and because the full faith and credit of the U.S. government stands behind it.
Now we have a president who, while a candidate, mooted the possibility of "renegotiating" the federal debt. If those kinds of ideas were to resurface, investors would have reason to rethink whether or not the dollar is a safe haven currency. This is not something that we should take for granted.
OR: If the dollar disappeared as a reserve currency, what do you see as replacing it?
Eichengreen: There isn't a good substitute out there. There is a limited amount of gold above ground. If everyone looking for a safe haven all shifted into gold, that would imply an immensely higher price of gold. Other commodities, too: commodity prices tend to move together. The only other economies with the scale to supply a safe haven currency are the euro area and China. And we know that, for the moment, neither of them is up to the task. Europe is troubled; there are existential questions about the future of the euro with elections coming up in France and Germany and anti-Europe, anti-euro parties making gains at the polls.
China, for its part, is regressing rather than progressing on internationalizing the renminbi: in response to the weakness of the currency and the desire of people to there to diversify their currency holdings, Chinese policy makers have been tightening capital controls.
OR: Do you see gold going up?
Eichengreen: I have a long history of reminding people of Keynes's phrase about how gold is a barbarous relic, and how in a modern financial system there are better ways of hedging inflation risks. I've been predicting lower gold prices for many years — and I'll keep predicting them until I'm right!
OR: Do you think central banks have painted themselves into a corner?
Eichengreen: I'd draw a strong contrast between the Fed and other advanced countries' central banks. The Fed was on its way toward normalizing the level of interest rates before the election. To the extent that we'll now see more expansionary fiscal policies and more inflation pressure, it will be likely to move more quickly than otherwise. That's in contrast to the situation in Europe, where the ECB is undershooting its inflation target. It's in contrast to the situation in Japan, where defeating inflation requires not only negative short-term interest rates but also taking the 10-year bond yield to low levels.
The thing that has been driving the dollar up until now has been policy divergence between central banks: the difference in interest rate policy, actual and expected, between the central bank here and central banks there. Now we will have those three additional, powerful tailwinds for the dollar reinforcing that divergence.
The problem for central banks has been created by the fact that they were the only game in town, and that they were forced to shoulder a disproportionate share of the burden of supporting the economy when the economy needed support. People now recognize that it would've been better to rely a bit more on fiscal policy and not to rely all but exclusively on monetary policy for economic support in the U.S. and Europe starting in 2010. Our political leaders, in their wisdom, opted for what they in Europe call austerity and what here we call fiscal consolidation. Its common implication was that somebody had to fend off deflation — something which remains a risk in Europe and was a risk in the United States until recently. And that somebody was the central bank.
Central banks had to take interest rates down to historically unprecedented levels and expand their balance sheets to unprecedented extents. Reversing that out now is difficult. Getting interest rates up to normal levels when you start from zero is harder than getting them up to normal levels when you start from two percent, or wherever interest rates are in the typical downturn. So central banks are between a rock and a hard place, yes, but it's the politicians and fiscal policymakers who put them there.
OR: Even though our debt has almost doubled over the last eight to 10 years?
Eichengreen: Debt goes up when you have a financial crisis. That doesn't mean that the economy has all the support that it needs. The visible indication that it lacked the necessary policy support was that inflation was significantly below target, and we've remained dangerously close to outright deflation for a period of years. Deflation is a condition that, once you get into it, is difficult to get out of. Ask our Japanese friends.
That the debt went up is unfortunate. But it was an unavoidable consequence of the financial crisis. It was the fault of the inadequate supervision and regulation of financial institutions in the period before 2007-2008. The debt went up because we passed the TARP to prevent the banking and financial system from collapsing as it did in 1933. The debt went up because unemployment was rising toward 10 percent and would've risen very much higher without Obama's stimulus.
Does that imply that the economy had the support it needed? Absolutely not.
OR: Do you think that we're going into an era of more inflationary pressures?
Eichengreen: We in the United States are exiting from a period of dangerously low inflation, where the risk of collapsing into outright deflation was significant. Do I expect this to be followed by a surge of inflation like in the 1970's? No, I think the Fed is committed to keeping inflation close to its two-percent target. If it retains its independence, and if the intellectual composition of the Federal Reserve Board is not significantly different in the future, then I would expect the Fed to succeed in keeping inflation close to two percent, regardless of what happens with other policies.
But if you imagine that very different people are appointed to the Federal Reserve Board, people who think that much lower interest rates are needed to enable the President to hit his four-percent growth target, then all bets are off.
OR: You're suggesting somebody even more dovish would come in under political pressure?
Eichengreen: I don't think "doves" versus "hawks" would any longer be the right labels. When we think about President Trump, is he conservative or liberal? Answer: He's a different kind of politician. It's possible that we would have different kinds of monetary policy makers on the Federal Reserve Board. But anything we say along those lines is in the realm of speculation at this point.
One could speculate that Mister Trump is a businessman, that he has a preference for low interest rates, and that he would be able to draw a link between low interest rates and more corporate borrowing, more corporate investment, and faster growth. One could speculate that he will appoint people to the board who prioritize low interest rates and want the two percent inflation target. Would I call such a person a dove or a hawk? I'm not sure. It simply is not the appropriate set of labels.
OR: Speaking of uncertainty, what is your view of Brexit? Do you see any way that the euro survives?
Eichengreen: Many people have been surprised that the British economy hasn't suffered more from the fallout from the referendum, that there hasn't been an outright recession yet, and that spending has held up relatively well. To which I would continue to respond: "Be patient." What we've seen so far has been largely British households front-loading their spending. They see a significantly weaker pound. They know import prices are going up. They have been told that Brexit is raising the price of marmite and want to get their marmite (and their big-screen televisions) before prices go up more.
There's been quite a consumer spending spree in the U.K., but business investment in the most recent quarter was down and disappointed expectations. Uncertainty around Brexit is rising rather than falling due to unresolved legal issues and the incompatibility of Prime Minister May's various proposals to retain single market membership but restrain immigration. That will be an impressive needle to thread. As this uncertainty rises, investment will fall farther and the British economy will suffer.
That will be something of a deterrent to other countries contemplating going down the same road. In addition, I think that getting out of the European Union when you're not a member of the euro is easier than extracting yourself when you're in the euro. Way back in 2007, I was commissioned to write an article for a conference. The volume was called Europe and the Euro. My commission was to write a chapter titled "The Breakup Of The Eurozone."
My conclusion was that holding the euro together would be immensely difficult and costly, but breaking it up would be even more difficult and costly. As soon as there was serious talk about a country withdrawing from the euro, that country would experience a bank run and a bond-market collapse — the mother of all financial crises — as everyone shifted their money to Frankfurt on the first day.
I have grey hair because I'm on record with that forecast. But so far, 10 years later, I've been right. That's not a guarantee that I will still be right a year from now, of course. But talking about getting out of the euro is easy. Actually getting out without suffering immensely large economic and financial costs is hard. It's appealing to pundits and intellectuals to think about separate Northern European and Southern European euros, but I regard that as equivalent to standing on one rim of the Grand Canyon and imagining that the view is better on the other rim: take a step forward to get from here to there, and where do you end up?
OR: Given Europe's climate of political insurgency, do you see a scenario where a country in the euro decides to leave it despite the risks?
Eichengreen: Absolutely. The story I just told you was one where not only experts but also politicians weighed the economic costs and benefits of alternative courses of action. That's what Tsipras did when he took office in Greece. He realized that what he had said about the euro while he was campaigning was not economically rational to implement once he was in power.
But we know that politicians, in the heat of the moment, can take decisions based on pride, self-image, and other considerations that trump — if you allow me to use that word — purely economic calculus. Yes, it can happen and you don't have to go very far back in history to see it happen. But a majority of voters in the euro area still support the single currency. It's not simply an elite project. In countries where people do not entirely trust their own government, whether because of corruption or for other reasons, they're more inclined to support European government which, in this context, means the euro. I think even the young people who have suffered from 30, 40, or 50 percent levels of youth unemployment, depending on country, are often committed Europeans.
In my view, the single most powerful force making for European integration has been Ryanair: these young people flying for low-cost weekends between secondary airports in one country and another. They have grown up together with their friends in other European countries in a way that their parents never could.
OR: What do you see as the biggest risk to the monetary system? What do you see as the most likely potential cause of a problem?
Eichengreen: If we get a further, strong rise in the dollar, that will cause serious financial problems for emerging markets with dollar-funding needs — for emerging markets that borrow from international banks and international financial markets. These countries fund themselves with dollars, which will become more expensive. I don't think it's a coincidence that Turkey is now in the sights of international investors as a country with a very large external funding need — a country whose troubles are going to be compounded by the rise of the dollar.
The other thing we know is that there are big financial institutions out there — we don't know who they are; I certainly don't know who they are — that could be wrong-footed by a further, sudden rise in the dollar. Institutions that are short dollars and long something else. That's what worries me first and foremost: the dollar strengthening due to U.S. policies and the certain negative impact on emerging markets and the possible negative impact on global financial stability.
OR: Do you think that would ironically give a boost to the economy in Europe, or do you think with tariffs that scenario is going to be more problematic?
Eichengreen: Europe needs a weaker euro because inflation is still well below two percent. Economic growth is subdued. The same is true of Japan, but President Trump will see a weaker euro and weaker yen as evidence of currency manipulation, as frustrating his efforts to bring manufacturing jobs back to the United States. What the U.S. gives with one hand — i.e., more competitive euro and yen exchange rates — it takes away with the other — i.e., trade restrictions. There's no way you get one without the other.
OR: How do you see China fitting into all this?
Eichengreen: China has been doing its best to be a positive moderating influence at Davos and elsewhere. But China is also a proud country and would not take U.S. sanctions or trade restrictions lying down. It would respond tit for tat and try to occupy whatever space the U.S. vacated in Asia and elsewhere with preferential trade deals with its neighbors and with foreign investment through the Asia Infrastructure Investment Bank.
Another implication of the new administration in the United States will be less support for the IMF and World Bank. That will open up space for the Asia Infrastructure Investment Bank and the Chiang Mai Initiative — technically the Chiang Mai Initiative Multi-lateralization — in which China is a leading player. It's not incidental that an additional couple of dozen countries have just applied for membership in the Asia Infrastructure Investment Bank.
OR: Do you think that this is the end of the liberal postwar order, of the IMF and the World Bank serving as anchor institutions and the U.S. leading the world? Do you think that the ramifications will lead to a snapback?
Eichengreen: I think this President and this Congress are on the same page in that they do not see the advantages for the United States of — number one — international entanglements and — number two — a rules-based international system where they see the rules or their application as biased against the United States. They see these institutions and organizations as limiting U.S. autonomy and room for maneuver.
Normally, a President can think what he wants, but there are checks and balances coming from the Congress, public opinion, and the corporate sector. Here, however, there is an apparent alignment of views hostile toward what we call the post-war international economic order between Congress and the administration. And we will see if public opinion is still an effective countervailing force.
Again, to invoke what happened in Greece after Syriza took power, it typically requires a major crisis for people with these strongly held views to pause and rethink. Obviously that would be a high price to pay in order to save the global order.
OR: What would you do if you had unlimited powers and scope to fix the system?
Eichengreen: We got into this mess partly because we experienced a major financial crisis, one of the two gravest financial crises of the last century. So I would be sure that the United States and other countries had measures in place to limit the likelihood of another. I'm deeply worried, therefore, that the mania for deregulation that we now see in the United States will include financial deregulation and that will set the stage for more financial instability.
I also worry that some of the international institutions that have been positive forces in recent years — the Basel Committee on Banking Supervision, the Bank for International Settlements and the Financial Stability Forum — are at risk because U.S. participation in those fora and willingness to conform to their standards for financial regulation, capital adequacy, and liquidity will no longer exist.
The danger is that we will not subject ourselves to those same high standards. So I would start there. Beyond that, the global trading system is worth preserving. If there are things about the World Trade Organization that the President or the Congress doesn't like, they should be negotiated rather than throwing the baby out with the bathwater.
At the same time, I would avoid trying to replicate the other things that were achieved at Bretton Woods, like a system of pegged exchange rates, because the world has moved on. The world in the 21st century is very different from the world in 1944. I don't think that's something that can be replicated.
OR: Going back to where you started on infrastructure: are you skeptical Trump will be able to do it at scale?
Eichengreen: It's clear that the United States has significant infrastructure needs, and you can make a plausible case that repairing roads and bridges will reduce wear and tear on cars and trucks and increase the efficiency of commerce and production. It's not always the case that infrastructure investment translates into faster growth, but I don't think it would be hard to identify some key infrastructure projects that would be good for growth.
I would add two caveats. Number one, I don't think this can be efficiently done by providing tax credits for private investment alone because those private investors are don't have an incentive to start with the infrastructure projects that matter most for growth. Number two, the construction companies that build infrastructure projects don't have cash flow for several years, so they have to sell the tax credits to someone else. That market, which is called the tax equity market, is small. It exists for solar farms and solar panels but doesn't appear to work very efficiently, and it's not clear how quickly it can be scaled up. I think doing something significant on infrastructure requires the Congress to acknowledge that the government is the agency that has to do it — an acknowledgment that sits uneasily with contemporary Republican ideology.
A second point I would make is that we should be talking here not only about investing in physical capital but also in human capital. President Trump wants to increase the growth rate from two to four percent. In the long run, the only way that can be achieved is through faster productivity growth, which means a more productive labor force, which in turn means more investment in early childhood education and vocational training. That doesn't appear to be part of the discussion at the moment.
Barry Eichengreen is the George C. Pardee and Helen N. Pardee Professor of Economics and Political Science at Berkeley and the author, most recently, of Hall of Mirrors: The Great Depression, The Great Recession, and the Uses — and Misuses — of History.
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Calculate the dot product of two given vectors.
Determine whether two given vectors are perpendicular.
Find the direction cosines of a given vector.
Explain what is meant by the vector projection of one vector onto another vector, and describe how to compute it.
Calculate the work done by a given force.
If we apply a force to an object so that the object moves, we say that work is done by the force. In Introduction to Applications of Integration on integration applications, we looked at a constant force and we assumed the force was applied in the direction of motion of the object. Under those conditions, work can be expressed as the product of the force acting on an object and the distance the object moves. In this chapter, however, we have seen that both force and the motion of an object can be represented by vectors.
In this section, we develop an operation called the dot product , which allows us to calculate work in the case when the force vector and the motion vector have different directions. The dot product essentially tells us how much of the force vector is applied in the direction of the motion vector. The dot product can also help us measure the angle formed by a pair of vectors and the position of a vector relative to the coordinate axes. It even provides a simple test to determine whether two vectors meet at a right angle.
u · v = u 1 v 1 + u 2 v 2 + u 3 v 3 .
u · v = u 1 v 1 + u 2 v 2 .
When two vectors are combined under addition or subtraction, the result is a vector. When two vectors are combined using the dot product, the result is a scalar. For this reason, the dot product is often called the scalar product . It may also be called the inner product .
Find the dot product of u = 〈 3 , 5 , 2 〉 and v = 〈 −1 , 3 , 0 〉 .
Find the scalar product of p = 10 i − 4 j + 7 k and q = −2 i + j + 6 k .
u · v = u 1 v 1 + u 2 v 2 + u 3 v 3 = 3 ( −1 ) + 5 ( 3 ) + 2 ( 0 ) = −3 + 15 + 0 = 12.
p · q = u 1 v 1 + u 2 v 2 + u 3 v 3 = 10 ( −2 ) + ( −4 ) ( 1 ) + ( 7 ) ( 6 ) = −20 − 4 + 42 = 18.
Find u · v , where u = 〈 2 , 9 , −1 〉 and v = 〈 −3 , 1 , −4 〉 .
Like vector addition and subtraction, the dot product has several algebraic properties. We prove three of these properties and leave the rest as exercises.
Let u , v , and w be vectors, and let c be a scalar.


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The Moorcroft Boys Golf Team traveled to Douglas, WY for a tournament on Friday. Moorcroft was one of two 2A teams that competed in this tournament; the remainder of the field was made up of 3A and 4A schools.
Lane Wood led us in scoring with a 92, Caden Connally shot a 98 and Payton Timberman a 102. Overall, I was happy with how the boys competed. Because of weather, we haven't had a lot of opportunities to get on an actual course.