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@arXiv_mathDS_bot@mastoxiv.page
2025-07-31 08:11:31

Computing Periodic Billiard Orbits in $L^p$ Balls via Newton's Method and Smale's $\alpha$-Criterion
Igor Rivin
https://arxiv.org/abs/2507.22251 https://

Computing Periodic Billiard Orbits in $L^p$ Balls via Newton's Method and Smale's $α$-Criterion
We present a computational method for finding and verifying periodic billiard orbits in $L^{p}$ balls ($p>2$) using Newton's method applied to a variational formulation. The orbits are verified with Smale's alpha-criterion, which provides a rigorous certificate of existence. We implement efficient batched computations in JAX and present systematic results for various $p$ and bounce counts $N$. Our experiments reveal striking patterns in the critical-point structure, including a predominance of …

@leftsidestory@mstdn.social
2025-10-13 00:30:01

Moody Urbanity - Oracles III 🈳
情绪化城市 - 谕 III 🈳
📷 Nikon FE
🎞️ Ilford HP5 Plus 400, expired 1993
#filmphotography #Photography #blackandwhite

Ilford HP5 Plus 400 (FF)

English Alt Text:
A narrow alleyway between two aged buildings is viewed through vertical black bars in the foreground. The concrete path is cracked and stained. The walls are peeling, with exposed pipes and wires overhead. A barred window sits on the left wall. The alley leads into a darker area, evoking mystery. Sunlight casts sharp shadows, and the black-and-white palette emphasizes texture and decay.

中文替代文字：
透过前景中的黑色栏杆，可见两栋老旧建筑之间的狭窄小巷。混凝土地面布满裂痕与污渍，墙面斑驳脱落，上方管线交错。左侧…

Ilford HP5 Plus 400 (FF)

English Alt Text:
Two blurred figures on bicycles or scooters speed past in the foreground, capturing motion. Behind them, a quiet urban wall features a handicapped-accessible sign, a bench with a small paper, and a covered object—possibly a scooter. Tree shadows fall across the wall. The contrast between movement and stillness is heightened by the monochrome tones.

中文替代文字：
前景中两位骑行者模糊掠过，展现速度与动感。背景是一面城市墙壁，设有残障通道标志、长椅和一张小纸条，旁边覆盖着一件物品，可能是电动车。树影洒落墙面，黑白色调强化了动与静的对比。

Ilford HP5 Plus 400 (FF)

English Alt Text:
A group of identical bicycles with front baskets are parked neatly on a sidewalk beneath dense tree cover. The scene is shaded, creating a quiet, contemplative mood. These bikes appear to be part of a public bike-sharing system. In the background, a person walks through a tree-lined opening, suggesting a path or park entrance. The black-and-white tone adds a nostalgic, documentary feel to this urban moment.

中文替代文字：
一群带有前篮的共享单车整齐地停放在人行道上，头顶是茂密的树冠，营造出安…

Ilford HP5 Plus 400 (FF)

English Alt Text:
Railway tracks cross a paved area in the foreground. Two people sit near a tree—one on a chair, the other beside a small stand with a signboard. A bench behind them holds large bags, possibly recyclables. A building with windows and an open garage is in the background. Bollards line the area, and tree shade softens the scene. The monochrome effect adds depth and quietness.

中文替代文字：
前景中铁轨穿过铺设区域。两人坐在树旁，一人坐椅上，另一人靠近带招牌的小摊。后方长椅上堆放着大袋子，可能是可回收物。背景是有窗户和敞开车库的建…

@Stomata@social.linux.pizza
2025-09-26 16:39:23

Have to say Sharkey is beautiful :pika:
Here is my profile on Sharkey @…
#fediverse #Sharkey

@leftsidestory@mstdn.social
2025-09-14 00:30:01

On The Road - To Xi’An/Before & After 🌬️
在路上 - 去西安/之前之后🌬️
📷 Pentax MX
🎞️Lucky SHD 400
#filmphotography #Photography #blackandwhite

Lucky Lucky SHD 400 (FF)

English Alt Text:
A black-and-white urban photo captures a modern high-rise apartment building with balconies and clean lines. Behind it stands a more industrial-looking structure with a grid-like facade and exposed upper section. In the foreground, a pedestrian bridge or overpass with metal railings crosses the scene. The architectural contrast and geometric shapes give the image a stark, modern aesthetic.

中文替代文本：
这是一张黑白城市照片，画面中是一栋现代高层公寓楼，带有阳台和简洁的线条。其后是一座工业风格的建筑，外墙呈网…

Lucky Lucky SHD 400 (FF)

English Alt Text:
A nighttime cityscape in black and white features several buildings. On the left, tall residential or office towers with lit windows rise into the dark sky. In the foreground, a low building with utility lines adds depth. On the right, a darker structure displays two glowing circular clock faces, suggesting a clock tower. The contrast between light and shadow creates a quiet, contemplative mood.

中文替代文本：
这是一张黑白城市夜景照片。左侧是几栋高层住宅或办公楼，窗户中透出灯光，直指夜空。前景中有一座低…

Lucky Lucky SHD 400 (FF)

English Alt Text:
A black-and-white photograph shows a wire basket filled with handheld fans. The fans are arranged with their handles pointing downward and their circular heads fanning outward like petals. Each fan has a mesh or slatted surface, and they vary slightly in shape and size. The basket rests on a smooth indoor floor, possibly in a communal or recreational space. The background is softly blurred, with indistinct furniture and objects. The monochrome tones a…

@schachjugend@schach.social
2025-09-17 13:10:02

5 Jahre DSJ e. V.
Jubiläum in Lüneburg: Der DSJ-Vorstand feierte 5 Jahre DSJ e. V. – mit Kuchen, intensiven Sitzungen und Billard. Diskutiert wurden u. a. Qualitätssiegel, die DEM 2026 und Projektideen für nächstes Jahr.
Mehr lesen: https://www.deutsche-schachjugend.de/news/

Titel: 5 Jahre DSJ Vorstand tagt in Lüneburg. Menschengruppe lächelt in die Kamera. Chessy ( Maskottchen) in der Mitte.

Titel: "Zu jedem Geburtstag gibt es natürlich Kuchen." Kuchen in Schiffsoptik mit kleinen Chessys ( Maskottchen) und einer Kerze in Form einer Fünf.

@gscherer2@social.linux.pizza
2025-09-18 21:55:05

Allen’s Hummingbird stretching its wing. LA Arboretum, Arcadia, California, USA. #laarboretum #hummingbird #allenshummingbird

Allen's hummingbird, with white chest feathers, tan wings and iridescent reddish throat feathers, sitting on a tiny isolated branch, facing the camera. The bird has extended its right wing, which is blurred by motion.

@mgorny@social.treehouse.systems
2025-09-20 18:53:26

So I've started going through photos from 2015/2016 to add location tags to them. Conclusions so far:
1. Damn, these photos have low resolution. I mean, 2560 x 1440? That's smaller than my screen right now!
2. So many of them are really bad, like blurred, or really non-level, or with fingers.
3. I seemed to enjoy panoramas. Very low resolution panoramas, I should add.
4. I hate apps for defaulting not to store location data. Before I noticed it, I made so many photos I can't figure out.
5. That said, I still can recognize a lot of places by seemingly random scenery elements.
6. In many cases, "what? *that* was 10 years ago?!"

@arXiv_mathDS_bot@mastoxiv.page
2025-08-27 08:00:03

What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems
Weiqi Chu, Matthew Dobson
https://arxiv.org/abs/2508.18519 https://arxiv…

What Do Bouncing Balls Tell Us About the Universe? A Journey into Billiard Systems
Have you ever played or watched a game of pool? If so, you have already seen a billiard system in action. In mathematics and physics, a billiard system describes a ball that moves in straight lines and bounces off walls. Despite these simple rules, billiard systems can produce remarkably rich behaviors: some table shapes generate regular, periodic patterns, while others give rise to complete chaos. Scientists also study what happens when we shrink the ball down to the size of an electron to a w…

@midtsveen@social.linux.pizza
2025-09-26 23:17:45

01:17—Good night #Fediverse! 😴💤
#BuddhaQuotes #Buddhism #Buddha

A monk sits peacefully in meditation against a green, blurred natural backdrop. The text reads, “Conquer the angry one by not getting angry; conquer the wicked by goodness; conquer the stingy by generosity, and the liar by speaking the truth." – Buddha.

@arXiv_mathDS_bot@mastoxiv.page
2025-09-23 08:29:50

Chaotic Boltzmann's Billiard Systems at positive energy
Irene De Blasi, Airi Takeuchi, Susanna Terracini
https://arxiv.org/abs/2509.17132 https://arxiv…

Chaotic Boltzmann's Billiard Systems at positive energy
This paper deals with the so-called Boltzmann billiard, that is, a billiard subjected to a central force of the type $V(r)=-α/r-β/r^2$, $α$ and $β$ being positive constants, and with a straight reflection table. In the particular case of $α$ and $β$ positive, we prove the presence of a symbolic dynamics, and hence of positive topological entropy, at positive energy and for $β$ sufficiently small.

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