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Given $p,N>1,$ we prove the sharp $L^p$-log-Sobolev inequality on noncompact metric measure spaces satisfying the ${\sf CD}(0,N)$ condition, where the optimal constant involves the asymptotic volume r...

We present a three-stage model for a long GRB inner engine to explain the prompt gamma ray emission, and interpret recent Swift satellite observations of early X-ray afterglow plateaus followed by a s...

Dorset. In 2008, Sharp went to North America and worked as a carpenter and handyman, and in call centres often, in Canada. At times, he travelled to Latin

We are concerned with the stability of thin liquid films overflowing single microstructures with sharp corners. The microstructures were of rectangular and triangular shape. Their heights and widths w...

Police in Lapeer, Michigan, are investigating after more than 40 sharp spikes, described by officials as fence spikes, were found in two city parks.

Police in Lapeer, Michigan, are investigating after more than 40 sharp spikes, described by officials as fence spikes, were found in two city parks.

As a corollary to our main result we deduce sharp A_p$ inequalities for T being either the Hilbert transform in dimension d=1, the Beurling transform in dimension d=2, or a Riesz transform in any dime...

Get Started with AARP Rewards AARP's loyalty program just got even more exciting. You can earn points for completing activities on Staying Sharp, including videos, recipes, meditations, and …

Exploiting the mass transportation method, we prove a dual principle which implies directly the sharp Gagliardo-Nirenberg trace inequalities which was recently proved by Bolley et al. [BCFGG17]. Moreo...

minor include Handel's Keyboard Suite HWV 431, Carl Philipp Emanuel Bach's Fantasia H. 300, Carel Anton Fodor's Sonata Op. 2/2, Muzio Clementi's Piano

We revisit the celebrated family of BDG-inequalities introduced by Burkholder, Gundy \cite{BuGu70} and Davis \cite{Da70} for continuous martingales. For the inequalities $\mathbb{E}[τ^{\frac{p}{2}}] ...

We present a foundation model for zero-shot metric monocular depth estimation. Our model, Depth Pro, synthesizes high-resolution depth maps with unparalleled sharpness and high-frequency details. The ...

In this short note we employ the Briot-Bouquet differential subordination to determine the best possible inclusion relation within a certain family of analytic functions defined by the Salagean deriva...

We measure the absolute magnitude, $H$, distribution, $dN(H) \propto 10^{αH}$ of the scattering Trans-Neptunian Objects (TNOs) as a proxy for their size-frequency distribution. We show that the H-dis...

In this paper, we investigate single and double layer potentials mapping boundary data to interior functions of a domain at high frequency $λ^2\to\infty$. For single layer potentials, we find that th...

Winter sudoku is played on a chilly nine by nine board complete with cozy mittens to keep you warm while playing this free online game! The sudoku board is divided into 3x3 squares.

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If you’ve never watched Bob Munden on YouTube you need to check it out. Not only was the he the gunslinger with the quickest draw he also held about 18 world records for sharpshooting. His videos ar...

implementations of data structures such as ArrayList, Stack, Queue, HashTable and SortedList. All four of the concrete data structure implementations enable one to