We construct the first examples of manifolds, the simplest one being the product of S^3, S^4, and R^5, which admit infinitely many complete nonnegatively curved metrics with pairwise nonhomeomorphic souls....
We give examples of open manifolds that carry infinitely many complete metrics of nonnegative sectional curvature such that they all have the same soul, and their isometry classes lie in different connected components of the moduli space. All previou...
In this paper, we prove the Soul Conjecture in Alexandrov geometry in dimension $4$, i.e. if $X$ is a complete non-compact $4$-dimensional Alexandrov space of non-negative curvature and positive curvature around one point, then a soul of $X$ is a poi...
For each nonnegative integer we find an open (4m+9)-dimensional simply-connected manifold admitting complete nonnegatively curved metrics whose souls are non-diffeomorphic, homeomorphic, and have codimension 2. We give a diffeomorphism classification...
Super Earths, planets between 5-10 Earth masses, are the most common type of exoplanet known, yet are completely absent from our Solar system. As a result, their detailed properties, compositions, and formation mechanisms are poorly understood. NASA'...
Corona-Australis is one of the nearest regions to the Sun with recent and ongoing star formation, but the current picture of its stellar (and substellar) content is not complete yet. We take advantage of the second data release of the Gaia space miss...
So I’ve been talking to this guy for four months, we had plans to see each other tonight and I think it’s completely over now because I lost it when he told me he drove his cheating friend to win ...
Hall and Paige conjectured in 1955 that a finite group $G$ has a complete mapping if and only if its Sylow $2$-subgroups are trivial or noncyclic. This conjecture was proved in 2009 by Wilcox, Evans, and Bray using the classification of finite simple...
(Reddit posts are limited to 20 attachments and comments at 1 attachement. You can view the full patch notes complete with images and tables on the [official website](https://tfd.nexon.com/en/news/274...
Verifying the robustness property of a general Rectified Linear Unit (ReLU) network is an NP-complete problem [Katz, Barrett, Dill, Julian and Kochenderfer CAV17]. Although finding the exact minimum adversarial distortion is hard, giving a certified...
Mirza Khazar was a Mountain Jew. He also was known as Mirza Michaeli. Mirza Khazar died on January 31, 2020, in Germany. In July 1973, Mirza Khazar completed
This page provided a complete animated walkthrough for what is sum of 2 + 5?. Every step was visualized so you can understand not just the answer, but the method behind it.
I struggle to think of another one who comes close. Rourke came out swinging in the early 1980s’ with a series of edgy, offbeat roles in acclaimed films like Body Heat, Diner, and The Pope of Green...
It seems like men are always complaining about some natural function of women's bodies, or greatly exaggerate how 'gross' they are, whilst being completely oblivious to how gross their own bodies can ...
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Dark retreat (Wylie: mun mtshams) is a spiritual retreat in a space that is completely absent of light, which is an advanced practice of Tibetan Buddhism
Let $P_n$ and $K_n$ denote the induced path and complete graph on $n$ vertices, respectively. The {\em kite} is the graph obtained from a $P_4$ by adding a vertex and making it adjacent to all vertices in the $P_4$ except one vertex with degree 1. A...
Plans for the day . Freaky Friday 2025 new , Shin Godzilla, Summer wars BD and Kill La Kill Complete series .... Morning started off Rocky but I'm just fighting through the pain with my favorite oldi...
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Hi, guys! A few months ago, although not completely, we explored one of the most beautiful region of Spain, Andalusia. We traveled with my husband during the holidays. And unfortunately we didn’t h...