We prove a category-theoretic independence theorem for four fundamental notions: meaning, object, name, and existence. Working in a Lawvere-style categorical semantics and in particular in toposes, we show that these notions occupy distinct structura...
Michael Handel proved in Handel (1999) the existence of a fixed point for an orientation preserving homeomorphism of the open unit disk that can be extended to the closed disk, provided that it has points whose orbits form an oriented cycle of links...
Events have always been one of the most popular ways for organizations to fundraise. Events are great opportunities to use peer-to-peer fundraising, sponsorships, ticket sales, or any combination of these …
Recent advancements in Neural Machine Translation (NMT) models have proved to produce a state of the art results on machine translation for low resource Indian languages. This paper describes the neural machine translation systems for the English-Hin...
This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples $n$ and their dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with $0<y<1$. We prove that when t...
In unpublished notes Pila proposed a Modular Zilber-Pink with Derivatives (MZPD) conjecture, which is a Zilber-Pink type statement for the modular $j$-function and its derivatives. In this article we define D-special varieties, then state and prove t...
In this paper we prove that the family of colored Jones polynomials of a knot in $S^3$ determines the family of ADO polynomials of this knot. More precisely, we construct a two variables knot invariant unifying both the ADO and the colored Jones poly...
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We prove that random low-degree polynomials (over $\mathbb{F}_2$) are unbiased, in an extremely general sense. That is, we show that random low-degree polynomials are good randomness extractors for a wide class of distributions. Prior to our work, su...
We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)]...
An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the torus, with elementary branch points and prescribed ramification type over infinity. This proves a conjecture of Goulden, Jackson...
We prove that any $3$-uniform hypergraph whose minimum vertex degree is at least $\left(\frac{5}{9} + o(1) \right)\binom{n}{2}$ admits an almost-spanning tight cycle, that is, a tight cycle leaving $o(n)$ vertices uncovered. The bound on the vertex d...
We strengthen Han's Fourier entropy-influence inequality $$ H[\widehat{f}] \leq C_{1}I(f) + C_{2}\sum_{i\in [n]}I_{i}(f)\ln\frac{1}{I_{i}(f)} $$ originally proved for $\{-1,1\}$-valued Boolean functions with $C_{1}=3+2\ln 2$ and $C_{2}=1$. We show, b...
May 13, 2024 · Vegan pancakes are as tasty as non-vegan ones, and we're here to prove it! Made with a blend of basic ingredients like flour, baking powder, and vanilla, these pancakes cook up fluffy and …
Gamble writes that the injunction was forgotten and that she "proved a very step-mother." The Icelandic fairy tale The Horse Gullfaxi and the Sword Gunnfoder
You can't argue with facts: a fact is something proven to be true. It's important to distinguish between fact and fiction.
Kim and Drake used generating functions to prove that the number of 2-distant noncrossing matchings, which are in bijection with little Schroeder paths, is the same as the weight of Dyck paths in which downsteps from even height have weight 2. This w...
In this paper, we prove a conjecture proposed by George Beck, which involves gap-free partitions and partitions with distinct parts....
In his paper, "On a Partition Function of Richard Stanley," George Andrews proves a certain partition identity analytically and asks for a combinatorial proof. This paper provides the requested combinatorial proof....
Signed networks and balance theory provide a natural setting for real-world scenarios that show polarization dynamics, positive/negative relationships, and political partisanship. For example, they have been proven effective in studying the increasin...
In this note, we prove that Kim-dividing over models is always witnessed by a coheir Morley sequence in NATP theories. Following the strategy of Chernikov and Kaplan [8], we obtain some corollaries which hold in NATP theories. Namely, (i) if a form...
We prove that the space of smooth Riemannian metrics on the three-ball with non-negative Ricci curvature and strictly convex boundary is path connected; and, moreover, that the associated moduli space (i.e., modulo orientation-preserving diffeomorphi...
Life on the farm proves to be challenging for a plucky pig in this endearing family comedy.
We prove that the Real Johnson-Wilson theories ER(n) are homotopy associative and commutative ring spectra up to phantom maps. We further show that ER(n) represents an associatively and commutatively multiplicative cohomology theory on the category o...
We prove that every Polish group with more than two elements admits a non-trivial topological group automorphism. As a consequence, a hypothetical uniquely homogeneous Polish space with more than two points cannot be a semitopological group....
Showboats prediction, odds, spread, time: 2025 UFL picks, Week 1 bets from proven football expert". CBS Sports. Retrieved April 7, 2025. "NFL Cuts To UFL
When news of the Wang Fuk Court blaze first broke, my mind went somewhere very specific, not to bamboo, or green mesh, or “Chinese standards,” but to four US fires that every safety professional s...
This is weird so I need to know if I'm crazy for going as far as I did. I have a condition of chronic pain. The way I explain it to people without chronic pain is that if pain were on levels from 1 t...
It may seem a funny notion to write about theorems as old and rehashed as Descartes's rule of signs, De Gua's rule or Budan's. Admittedly, these theorems were proved numerous times over the centuries. However, despite the popularity of these results,...
The width of a convex curve in the plane is the minimal distance between a pair of parallel supporting lines of the curve. In this paper we study the width of nodal lines of eigenfunctions of the Laplacian on the standard flat torus. We prove a varie...
We prove a lower bound on the rank of tensors constructed from families of linear maps that `expand' the dimension of every subspace. Such families, called {\em dimension expanders} have been studied for many years with several known explicit constru...
Let $M$ be a $\mathbb{Q}$-homology solid torus. In this paper, we give a cohomological criterion for the existence of an interval of left-orderable Dehn surgeries on $M$. We apply this criterion to prove that the two-bridge knot that corresponds to t...
While India has been one of the hotspots of COVID-19, data about the pandemic from the country has proved to be largely inaccessible at scale. Much of the data exists in unstructured form on the web, and limited aspects of such data are available thr...
We prove unconditionally that for each $\ell \geq 1$, the difference $φ(p-\ell) - φ(p+\ell)$ is positive for $50\%$ of odd primes $p$ and negative for $50\%$....
We show that Vojta's conjecture for some rational surfaces is related to the $abc$ conjecture. More specifically, we prove that Vojta's conjecture on these surfaces implies a special case of the $abc$ conjecture, while the $abc$ conjecture implies Vo...
This paper is an excerpt from the author's 1968 PhD dissertation [Yale University, 1968] in which the (now) well-known result, commonly known as the Folkman-Rado-Sanders theorem, is proved. The proof uses (finite) alternating sums of integers and an...
Amazon Vine is an invitation-only program in which proven insightful reviewers have the opportunity to review new products, free of charge, in exchange for honest and unbiased product reviews. Amazon …
In [15] Robert Osserman proved that the image of the Gauss map of a complete, non flat minimal surface in R^3 with finite total curvature miss at most 3 points. In this paper we prove that the Gauss map of such a minimal immersions omit at most 2 poi...
We prove that a Hausdorff limit of Griffith almost-minimizers remains a Griffith almost-minimizer. For this purpose, we introduce a new approach to the uniform concentration property of Dal Maso, Morel and Solimini which does not rely on the coarea f...
A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given goal. Noneth...