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Characterization of ????-concavity preserved by the Dirichlet heat flow

Kazuhiro Ishige, Paolo Salani and Asuka Takatsu
Trans. Amer. Math. Soc. 377 (), 5705-5748.
Abstract, references and article information




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Calafate

seveni.1999 posted a photo:




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Calafate

seveni.1999 posted a photo:




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LEGO Classic Space: the robot final rebellion on the capital planet ousts the federation rule and replace with a techno republic and dictatorship (the final episode (for a while)) (AFOL toy hobby photography with droids, police and minifigures city MOC

dannyhennesy posted a photo:

On the Capital planet the rebellious droids had followed maily the Bat-Bot, but as time progressed his circuits had gone all mushy at 780 years or so without maintenance…

Several splinter groups all with their local bot leaders emerged such as the Che-bot, the traffic-light-robot and the Butt-bot, but none of these collected enough sentient circuits to call themselves a popular (or Animata) mass movement!

That was until a cyborg came along, one known as Jones, a long time prisoner and terrorist, his easy solutions to every problem rang well in the masses' auditory circuits!!!

His slogans and simple rhetoric were simple enough for the simple traffic-light to comprehend and cheer!

His language was full of hate towards the organics and especially the humans who were the most common races among the ruling class of the federation!!!

Despite being a “Fleshie” himself his message collected the angry enslaved
bot community by only weeks all rebellious robots except for a few fringe loonies had forgotten the old leaders…

One morning at Jones gave the signal…

All over the capital planet hordes and swarms of any form of mechanical sentient beings attacked first the police stations, then the Company boards running the planet and the federation as well as their starfleet…

Many died, especially the low level police and army! Many mechanicals died too, but their ranks were soon filled by Mutant fleshie allies of the lower levels who hated the Federation feudal society and upper classes as much as their technological allies…

The Federation state apparatus and ruling class, most of their fleet army fled when they knew the game was up, they activated the emergency escape plan and whole city blocks with important factories, administrational units, valuable assets and so on separated from the capital by hidden rocket engines and homed in their course to Mars…

On Mars the federation regrouped and formed their new society…

On the Capital planet, the robots proclaimed the first Techno-republic of the advanced inorganic civilization, the low level fleshies left behind, became slaves and their mutant allies got to rule their own minute chiefdoms as protectorates under the Techno-republic…

Jones was now the undisputed ruler of the capital planet, but the victory was a pyrros one since, all important buildings, all of value was now one Mars!

But as Jones put it:

Our proud race the Techno-species didn’t need the Fleshies administration, their infrastructure, their spaceships…

We shall start from scratch, with a new administration, a new order, every droid shall work at 4x speed than they did during human oppression since now we are free and the fleshies shall work twice as hard than the Techno-Race, until we have breed enough new fleshies so they can do all work!

Our future is bright and shiny like glistering shiny metal!

The snapshot seen here is from the first police station attacked in sector 45-34v-ss-g the first one to fall according to official techno-history!

———————————————/
Designers note:

I am sad to say that this is the last episode in this years-spanning space series… At least for a while, I will still post LEGO hobby stuff here but without a storyline, perhaps small designs and builds… and occasionally a story when I feel like it!!!

I would like to thank all who had been in this journey of our heros, but it has taken far to much time and effort and since the state of the world is as it is, I am spiraling down in another depression, I must stop it before I reach the abyss, so I have remove some stress out of my equation… I ended it in a cliffhanger so I can easily restart it when my mental health improves… I hope that won’t be forever???

I would love if someone used my characters or ideas, please send me a link if you do, I would love to read it or look at it!!!

But there will be more Lego, just in different format without long stories, I need to focus more on my art and to be honest that is the only time the mental pain eases, when I create!!!


Peace and Noise!

MushroomBrain a FOL




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Corgi Toys - Corgi Whizzwheels - Porsche 917 - Miniature Diecast Metal 1/43 Scale Model Motor Vehicle

firehouse.ie posted a photo:




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Corgi Toys - Corgi Whizzwheels - Porsche 917 - Miniature Diecast Metal 1/43 Scale Model Motor Vehicle

firehouse.ie posted a photo:




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Corgi Toys - Corgi Whizzwheels - Porsche 917 - Miniature Diecast Metal 1/43 Scale Model Motor Vehicle

firehouse.ie posted a photo:




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Tekno - The Irish Collection - Ref. 258 - Scania Articulated Truck - Glynns, Galway - Miniature Diecast Metal Scale Model Heavy Goods Vehicle

firehouse.ie posted a photo:




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Tekno - The Irish Collection - Ref. 258 - Scania Articulated Truck - Glynns, Galway - Miniature Diecast Metal Scale Model Heavy Goods Vehicle

firehouse.ie posted a photo:




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The history of model railroading the the Walthers 1970 O Scale Catalog

Tangled Bank posted a photo:




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The history of model railroading the the Walthers 1970 O Scale Catalog

Tangled Bank posted a photo:




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The history of model railroading the the Walthers 1970 O Scale Catalog

Tangled Bank posted a photo:




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Mum's 'ome-made froot cake, perfick fer pusslin'!

WendyHarris1955 posted a photo:

unbranded
plywood (basswood)
175 pieces
280 x 350 mm

TED: "I fink this lickle cat an' tiger pussle's cute. It's got pussycat wimsys an' it's shaped, so it's gonna be a keeper. The wobbly edj wuz a bit fiddly an' I 'ad to check the pikchur to make shure I 'ad it rite, but uvverwise it's a good'un.
That peece of cake I'm abowt to eat is Mum's 'ome-made froot cake spredd wiv butter - s'nice cuz she puts whisky in it. That's the cake, not the butter!"




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Strong laws of large numbers for weighted sums of ????-dimensional arrays of random variables and applications to marked point processes

Ta Cong Son, Tran Manh Cuong, Le Quang Dung and Le Van Dung
Theor. Probability and Math. Statist. 111 (), 153-165.
Abstract, references and article information




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????²-spectrum, growth indicator function and critical exponent on locally symmetric spaces

Lasse L. Wolf and Hong-Wei Zhang
Proc. Amer. Math. Soc. 152 (), 5445-5453.
Abstract, references and article information







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Can a chemotaxis-consumption system recover from a measure-type aggregation state in arbitrary dimension?

Frederic Heihoff
Proc. Amer. Math. Soc. 152 (), 5229-5247.
Abstract, references and article information







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On the analyticity of the maximal extension of a number field with prescribed ramification and splitting

Donghyeok Lim and Christian Maire
Proc. Amer. Math. Soc. 152 (), 5013-5024.
Abstract, references and article information







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Caraiani to Receive 2025 AMS Satter Prize

Ana Caraiani, Royal Society University Research Fellow and professor of pure mathematics, Imperial College London, has been awarded the 2025 Ruth Lyttle Satter Prize in Mathematics by the American Mathematical Society (AMS). She has been honored for contributions to arithmetic geometry and number theory: in particular, the Langlands program.

Ana Caraiani
Louise Rose Photography

From the citation

Ana Caraiani’s work is characterized by a combination of novel ideas and a fearlessness in the face of technical obstacles that would daunt almost any other researcher. This has enabled her to prove several fundamental theorems in the Langlands program.

In the joint paper with Scholze, titled “On the generic part of the cohomology of non-compact unitary Shimura varieties” (Annals of Math., 2024), Caraiani proved very general results about the torsion cohomology classes in non-compact Shimura varieties, strengthening the early results in their 2017 paper in the compact case. The proof is a tour de force, combining perfectoid spaces, a mastery of the trace formula, and a new theory of perverse sheaves in p-adic geometry. These results are of intrinsic interest (for example, they give the first indications of a characteristic p version of Arthur’s conjectures), but they also have many applications throughout the Langlands program. One spectacular application of these results is in her joint paper, “Potential automorphy over CM fields” (with Allen, Calegari, Gee, Helm, Le Hung, Newton, Scholze, Taylor, and Thorne, Annals of Math., 2023), which among other results proves the Ramanujan conjecture for Bianchi modular forms, a problem that had been thought of as being completely out of reach.

The Ramanujan conjecture is of analytic nature, asserting a bound on the eigenvalue of a certain differential operator, but the only way in which cases of it have been proved is via algebraic geometry. In particular, the original Ramanujan conjecture for modular forms was proved by Deligne in the 1970s, as a consequence of his proof of the Weil conjectures. However, in the case of Bianchi modular forms there is no direct relationship with algebraic geometry, and it seems to be impossible to make any direct deductions from the Weil conjectures. Langlands (also in the 1970s) suggested a strategy for proving the Ramanujan conjecture as a consequence of his functoriality conjecture. Caraiani and her coauthors’ proof of the Ramanujan conjecture for Bianchi modular forms proceeds via a variant of Langlands’ strategy, and in particular does not use the Weil conjectures.

Most recently with James Newton, in the paper “On the modularity of elliptic curves over imaginary quadratic fields” (arXiv: 2301.10509), Caraiani has improved upon these results and applied them to the modularity of elliptic curves over imaginary quadratic fields. They come close to completely solving it, with only a small number of exceptions (which constitute 0% of cases).

Response of Ana Caraiani

First, I would like to thank Joan Birman and the AMS for establishing an award that recognizes research contributions by women mathematicians. This is particularly meaningful to me because I looked to many of the previous recipients of the Satter Prize for inspiration at challenging moments in my career. It is a great honour to be selected as a recipient!

I am indebted to my many collaborators, mentors and colleagues who have generously shared their mathematical ideas with me over the years and supported me in different but crucial ways. Special thanks go to Peter Scholze for the wonderful opportunity to collaborate with him on understanding a part of the geometry and cohomology of Shimura varieties, to Richard Taylor for initiating the "ten author" collaboration, which was much more successful than we had originally expected, and to James Newton for our joyful exploration of elliptic curves over imaginary quadratic fields. I also particularly want to acknowledge Jessica Fintzen and Toby Gee for their longstanding friendship and moral support.

Finally, I want to thank my family, especially my husband, Steven, my mother, Zoe, and my daughter, Nadia.

Biographical sketch of Ana Caraiani

Ana Caraiani was born in Bucharest, Romania, in 1984. She received a bachelor's degree in mathematics from Princeton University in 2007 and completed her PhD at Harvard University in 2012. After temporary positions at the University of Chicago, Princeton and the Institute for Advanced Study (IAS), and the University of Bonn, she moved to Imperial College London in 2017, where she is currently a Royal Society University Research Fellow and Professor of Pure Mathematics. She is a Fellow of the AMS, a recipient of an EMS Prize and a New Horizons Prize in Mathematics and was an invited speaker at the 2022 ICM. 

About the prize

Awarded every two years, the Ruth Lyttle Satter Prize in Mathematics recognizes an outstanding contribution to mathematics research by a woman in the previous six years. The prize was established by Joan Birman in honor of her sister, Ruth. The 2025 prize will be recognized during the 2025 Joint Mathematics Meetings in January in Seattle.

Read more and see the list of past recipients.

Contact: AMS Communications

* * * * *

The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through our publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.

 




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McCann to Receive 2025 AMS-SIAM Wiener Prize

Robert McCann, University of Toronto, will receive the 2025 American Mathematical Society (AMS) - Society for Industrial and Applied Mathematics (SIAM) Norbert Wiener Prize in Applied Mathematics “in recognition of his groundbreaking contributions to optimal transport theory, and for pioneering deep applications to economics and physics,” according to the citation. McCann holds a Canada Research Chair in Mathematics, Economics, and Physics.

Robert McCann
Credit: Carolyn McCann

From the citation

Robert McCann has made fundamental contributions to optimal transport theory, reflecting remarkable technical abilities and amazing conceptual creativity. His discovery of displacement convexity and his solution to Monge’s (1746-1818) problem for different transportation costs were early, foundational advances that preceded by nearly 30 years the current enormous attention bestowed on optimal transport theory and its applications. Beyond these, McCann produced many important, unexpected results, linking optimal transport to new areas of application within and outside mathematics: different notions of curvature, new and hidden convexities in the economics of information, and a non-smooth theory of gravity based on the interaction of entropy with the Einstein field equation.

Response of Robert McCann

I am honored and humbled to have my work on optimal transportation and its applications to economics and physics recognized by the AMS-SIAM 2025 Norbert Wiener Prize (endowed by MIT). I think the whole optimal transport community can join me in taking pride in this acknowledgement of the impact and success of our efforts and can view this award as an incentive to further achievements. After singling out my PhD advisor, Elliott Lieb, who first taught me about the mines and the factories, I'd like to thank the many other mentors, collaborators, colleagues, and students – too numerous to name – who shared in my mathematical, physical, and economic adventures (and those who wrote letters to document!). Our interactions inspire and sustain me on my scientific journey; I could not have achieved these results without you, and my life is enriched by your presence. I try to pass it forward by giving as good as I got, and I encourage you to do the same. I also thank my family for their love and support, and their willingness to share me by putting up with my long hours of distraction and frequent travels. I hope this recognition helps to reassure them that their sacrifices are not for nought.

Biographical sketch of Robert McCann

Robert McCann studied engineering and physics before graduating with a degree in mathematics from Queen's University at Kingston, Ontario, and a doctorate from Princeton University. Following a Tamarkin appointment at Brown University and a postdoctoral fellowship at Institut des Hautes Études Scientifiques (IHES), he became a professor of mathematics at the University of Toronto, where he now holds a Canada Research Chair in Mathematics, Economics, and Physics. He is an authority on optimal transportation and has played a pioneering role in its rapid development since the 1990s. In particular, the notion of displacement convexity introduced in his 1994 PhD thesis lies behind many of the area's myriad applications. He serves on the editorial board of various journals, and as editor-in-chief of the Canadian Journal of Mathematics since 2007 (with a hiatus from 2017-21). His research has been recognized by awards such as an invitation to lecture at the 2014 International Congress of Mathematicians in Seoul; election to the Royal Society of Canada in 2014; the 2017 Jeffery-Williams Prize of the Canadian Mathematical Society; and the 2023 W.T. and Idalia Reid Prize of the Society for Industrial and Applied Mathematics (SIAM).

About the prize

The AMS-SIAM Norbert Wiener Prize in Applied Mathematics is awarded every three years for an outstanding contribution to applied mathematics in the highest and broadest sense.The American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM) award the prize jointly. Recipients must be a member of one of these societies. 

This prize was established in 1967 in honor of Professor Norbert Wiener and was endowed by a fund from the Department of Mathematics of the Massachusetts Institute of Technology. The endowment was supplemented further by a generous donor. The current award is $5,000.

The 2025 prize will be presented at the 2025 Joint Mathematics Meetings in Seattle.

Learn more about the prize and previous recipients.

Contact: AMS Communications

*****

The American Mathematical Society is dedicated to advancing research and connecting the diverse global mathematical community through our publications, meetings and conferences, MathSciNet, professional services, advocacy, and awareness programs.




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When will we see below-freezing temperatures in Milwaukee? First frost, snow forecasts




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If You Think Blocking People Over Political Views Is Petty, Just Wait Until You See The Other Reasons People Shared




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US Navy destroyers unscathed after fighting off a complex attack of cruise and ballistic missiles and exploding drones




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Woman, 23, had a 'burning sensation' in her stomach. It was the first sign of a rare cancer




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Warren Buffett Told Young Investors To Buy Homes Instead Of Stocks, Calling 30-Year Mortgages 'A Terrific Deal'




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Community scrambles after top insurance company refuses to pay out homeowners following destructive hurricane: 'Denied or closed with no payment'




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2025 Medicare Part B premium increase outpaces both Social Security COLA and inflation




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The Nightly Habit Cardiologists Are Begging You to Never, Ever Do




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Here are 5 signs you’re financially healthy in America even if you don't feel like it — how many do you show?




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Man heard using racial slur resigns from a Penn State commonwealth campus’ board




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Doctor’s ‘pizza topping’ trick to tell the difference between hemorrhoids and a sign of colon cancer




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Too many wild deer are roaming England's forests. Can promoting venison to consumers help?




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China reveals reusable cargo shuttle design for Tiangong space station (video)




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Toyota, A Company With Almost No EVs, Says California's EV Mandates Are 'Impossible' To Meet




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Driver rams his car into crowd in China, killing 35. Police say he was upset about his divorce




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Northern California man goes missing after Uber ride from Bay Area to Placer County




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Scammers posing as Nigy Boy’s team trick promoter

Nigy Boy's management team was forced to put out a scam alert on Thursday as news surfaced that a promoter in the Turks and Caicos Islands, inadvertently wired thousands of US dollars to who he believed was the artiste's booking team as a deposit...




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Cali P enjoys buzz with ‘Secret Hater’

Switzerland-based reggae and dancehall recording artiste Cali P has expressed gratitude to the public for supporting his music, following the release of his latest single ' Secret Hater'. The song, which was produced jointly by himself and Suku...




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Shocking Murray looks to Africa

Reggae artiste and TikToker Shocking Murray says he is both eager and excited about the prospect of touring Africa early next year to promote his recently released EP, Unchained. "I'll never forget the first time I toured Africa; it was in 2022...




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Recall was electric

Mas Camp on Arthur Wint Drive in St Andrew was transformed into a retro paradise last weekend as Recall, a retro party, took fans on a journey back to the golden days of dancehall. The 'Print Pink' theme was in full effect, and the ladies were...




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Making the dead look better - Jamaican morticians get advanced skills in embalming and cosmetics

For many Jamaicans, the deceased are more than just loved ones who have passed on; they are cherished family members who deserve to look as presentable as they did in life. In a culture where the appearance of the deceased is paramount, morticians...




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Police make arrest relating to bags of cash that allegedly fell from Beryllium vehicle

The police have arrested an individual in the probe surrounding two bags of cash that allegedly fell from a Beryllium security vehicle en route to the Norman Manley International Airport in Kingston last week.