A solitary number is a positive integer that shares its abundancy index only with itself. $10$ is the smallest positive integer suspected to be solitary, but no proof has been established so far. In this paper, we prove that not all half of the expon...
We consider the discrete shrinking target problem for Teichmüller geodesic flow on the moduli space of abelian or quadratic differentials and prove that the discrete geodesic trajectory of almost every differential will hit a shrinking family of tar...
Meta-data from photo-sharing websites such as Flickr can be used to obtain rich bag-of-words descriptions of geographic locations, which have proven valuable, among others, for modelling and predicting ecological features. One important insight from...
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We prove interlacing inequalities between spectral minimal energies of metric graphs built on Dirichlet and standard Laplacian eigenvalues, as recently introduced in [Kennedy et al, arXiv:2005.01126]. These inequalities, which involve the first Betti...
In this paper, we prove the local well-posedness for the Navier-Stokes equations describing the motion of isotropic barotoropic compressible viscous fluid flow with non-slip boundary conditions, where the fluid domain is the $N$ dimensional half-sapc...
[Here's the full thread](https://reddit.com/r/interestingasfuck/comments/kp6g55/_/ghwkhph/?context=2), but I've included some choice exchanges below. Things here started when somebody explains the rot...
In this experimental work we study billiard trajectories in triangular pyramids and try to establish conditions that guarantee the existence (or absence) of 4-cycles (there can be not more, than three of them). We formulate conjectures and prove some...
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Let $n\ge 1$ be an integer and $\mathbb{F}_q$ be a finite field of characteristic $p$ with $q$ elements. In this paper, it is proved that the Wenger graph $W_n(q)$ and linearized Wenger graph $L_m(q)$ are edge-girth-regular $(v,k,g,λ)$-graphs, and t...
Fessler and Gutierrez \cite{Fe,Gu} proved that if a non-singular planar map has Jacobian matrix without eigenvalues in $(0,+\infty)$, then it is injective. We prove that the same holds replacing $(0,+\infty)$ with any unbounded curve disconnecting th...
We prove weighted estimates for singular integral operators which operate on function spaces on a half-line. The class of admissible weights includes Muckenhoupt weights and weights satisfying Sawyer's one-sided conditions. The kernels of the operato...
Connect with millions of developers and technologists on Stack Overflow. Drive brand awareness, engagement, and demand with our proven advertising solutions.
Connect with millions of developers and technologists on Stack Overflow. Drive brand awareness, engagement, and demand with our proven advertising solutions.
Connect with millions of developers and technologists on Stack Overflow. Drive brand awareness, engagement, and demand with our proven advertising solutions.
Connect with millions of developers and technologists on Stack Overflow. Drive brand awareness, engagement, and demand with our proven advertising solutions.
Connect with millions of developers and technologists on Stack Overflow. Drive brand awareness, engagement, and demand with our proven advertising solutions.
We prove several results for the Dirichlet, Neumann and Regularity problems for the Laplace equation in graph Lipschitz domains in the plane, considering $A_{\infty}$-measures on the boundary. More specifically, we study the $L^{p,1}$-solvability for...
Given a bilinear (or sub-bilinear) operator $B$, we prove restricted weighted weak type inequalities of the form $$ ||B(f_1, f_2)||_{L^{p, \infty}(w_1^{p/p_1}w_2^{p/p_2})}\lesssim ||f_1||_{L^{p_1, 1}(w_1)}||f_2||_{L^{p_2, 1}(w_2)}, $$ whenever $B(f_1...
We prove that splendid Morita equivalences between principal blocks of finite groups with dihedral Sylow $2$-subgroups realised by Scott modules can be lifted to splendid Morita equivalences between principal blocks of finite groups with generalised...
Descubre Francia: París y la Torre Eiffel, la región de la Provenza, castillos del Loira, los Alpes, playas en la Riviera y una gastronomía inigualable. Guía completa para tu viaje a Francia.
Si se trata de pueblos medievales idílicos, Francia cuenta con muchos para elegir. Saint-Cirq-Lapopie es uno de ellos, entregado al arte, como lo es Gordes, en el corazón de la Provenza, y también â¦
Desde París hasta la Provenza, acompaña a los héroes de tus series y películas favoritas en un viaje por Francia recorriendo los escenarios más emblemáticos del país.
We prove and demonstrate here for the example of the large scale pixel detector of ATLAS that Serial Powering of pixel modules is a viable alternative and that has been devised and implemented for ATLAS pixel modules using dedicated on-chip voltage...
In this paper, we propose a conjectural multiplicity formula for general spherical varieties. For all the cases where a multiplicity formula has been proved, including Whittaker model, Gan-Gross-Prasad model, Ginzburg-Rallis model, Galois model and S...
The all-new E-Z-GO® Liberty is a first-of-its-kind, short wheel base vehicle with four-forward facing seats. It is exclusively an ELiTE⢠lithium vehicle, powered by a proven, maintenance-free Samsung â¦
Here we present the University of California San Francisco Preoperative Diffuse Glioma MRI (UCSF-PDGM) dataset. The UCSF-PDGM dataset includes 500 subjects with histopathologically-proven diffuse gliomas who were imaged with a standardized 3 Tesla pr...
We prove a new four parameter q-hypergeometric series identity from which the three parameter key identity for the Goellnitz theorem due to Alladi, Andrews, and Gordon, follows as a special case by setting one of the parameters equal to 0. The new...
In the realm of mobile security, where OS-based protections have proven insufficient against robust attackers, Trusted Execution Environments (TEEs) have emerged as a hardware-based security technology. Despite the industry's persistence in advancing...
Dec 13, 2025 · Get help in Windows 11 using 10 proven methods. From the Get Help app and troubleshooters to Copilot and Microsoft support—fix any Windows problem fast.
The BMV conjecture states that for $n\times n$ Hermitian matrices $A$ and $B$ the function $f_{A,B}(t)=trace{\, } e^{tA+B}$ is exponentially convex. Recently the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is based on ingen...
An elementary mathematical example proves, thanks to the Routh-Hurwitz criterion, a result that is intriguing with respect to today's practical understanding of model-free control, i.e., an "intelligent" proportional controller (iP) may turn to be mo...
Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $\mathscr{C}_0, \mathscr{C}_1$ and $\mathscr{C}_2$. They also showed that any vertex-multiplication of a tree with diameter at least 3 does not belong to...
Koh and Tay proved a fundamental classification of $G$ vertex-multiplications into three classes $\mathscr{C}_0, \mathscr{C}_1$ and $\mathscr{C}_2$. In this paper, we prove that vertex-multiplications of cartesian products of graphs $G\times H$ lie i...