Polynomial progressions in topological fields
Forum of Mathematics, SigmaLet $P_1, \ldots , P_m \in \mathbb {K}[\mathrm {y}]$ be polynomials with distinct degrees, no constant terms and coefficients in a general local field $\mathbb {K}$ . We give a quantitative count of the number of polynomial progressions $
Ben Krause +3 more
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Local aspects of the Sidorenko property for linear equations
Forum of Mathematics, SigmaA system of linear equations in $\mathbb {F}_p^n$ is Sidorenko if any subset of $\mathbb {F}_p^n$ contains at least as many solutions to the system as a random set of the same density, asymptotically as $n\to \infty $ .
Daniel Altman
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Relative rank and regularization
Forum of Mathematics, SigmaWe introduce a new concept of rank – relative rank associated to a filtered collection of polynomials. When the filtration is trivial, our relative rank coincides with Schmidt rank (also called strength).
Amichai Lampert, Tamar Ziegler
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Simplices in large sets and directional expansion in ergodic actions
Forum of Mathematics, SigmaIn this paper, we study ergodic $\mathbb {Z}^r$ -actions and investigate expansion properties along cyclic subgroups. We show that under some spectral conditions, there are always directions which expand significantly a given measurable set with ...
Michael Björklund, Alexander Fish
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Asymmetric infinite sumsets in large sets of integers
Forum of Mathematics, SigmaWe show that for any set $A\subset {\mathbb N}$ with positive upper density and any $\ell ,m \in {\mathbb N}$ , there exist an infinite set $B\subset {\mathbb N}$ and some $t\in {\mathbb N}$ so that $\{mb_1 + \ell b_2 ...
Ioannis Kousek
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Partition regularity of Pythagorean pairs
Forum of Mathematics, PiWe address a core partition regularity problem in Ramsey theory by proving that every finite coloring of the positive integers contains monochromatic Pythagorean pairs (i.e., $x,y\in {\mathbb N}$ such that $x^2\pm y^2=z^2$ for some $z ...
Nikos Frantzikinakis +2 more
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Finding product sets in some classes of amenable groups
Forum of Mathematics, SigmaIn [15], using methods from ergodic theory, a longstanding conjecture of Erdős (see [5, Page 305]) about sumsets in large subsets of the natural numbers was resolved.
Dimitrios Charamaras, Andreas Mountakis
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A retrospective cross-sectional descriptive study to critically appraise the quality of reporting of health economic evaluations conducted in the Indian setting. [PDF]
Perspect Clin Res, 2022 Gupta SK, Tiwari RK, Goel RK.
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Structure-Guided Discovery of Potent Antifungals that Prevent Ras Signaling by Inhibiting Protein Farnesyltransferase. [PDF]
J Med Chem, 2022 Wang Y +7 more
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DNA methylation of ARHGAP30 is negatively associated with ARHGAP30 expression in lung adenocarcinoma, which reduces tumor immunity and is detrimental to patient survival. [PDF]
Aging (Albany NY), 2021 Hu S +8 more
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