skip to main content


Title: Sedimentary n-alkanes and n-alkanoic acids in a temperate bog are biased toward woody plants
Award ID(s):
1636740
NSF-PAR ID:
10125119
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Organic Geochemistry
Volume:
128
Issue:
C
ISSN:
0146-6380
Page Range / eLocation ID:
94 to 107
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. null (Ed.)
    Abstract We show that for some even $k\leqslant 3570$ and all  $k$ with $442720643463713815200|k$, the equation $\phi (n)=\phi (n+k)$ has infinitely many solutions $n$, where $\phi $ is Euler’s totient function. We also show that for a positive proportion of all $k$, the equation $\sigma (n)=\sigma (n+k)$ has infinitely many solutions $n$. The proofs rely on recent progress on the prime $k$-tuples conjecture by Zhang, Maynard, Tao, and PolyMath. 
    more » « less
  2. Abstract

    We describe convenient preparations ofN,N′‐dialkyl‐1,3‐propanedialdiminium chlorides,N,N′‐dialkyl‐1,3‐propanedialdimines, and lithiumN,N′‐dialkyl‐1,3‐propanedialdiminates in which the alkyl groups are methyl, ethyl, isopropyl, ortert‐butyl. For the dialdiminium salts, the N2C3backbone is always in thetrans‐s‐transconfiguration. Three isomers are present in solution except for thetert‐butyl compound, for which only two isomers are present; increasing the steric bulk of theN‐alkyl substituents shifts the equilibrium away from the (Z,Z) isomer in favor of the (E,Z), and (E,E) isomers. For the neutral dialdimines, crystal structures show that the methyl and isopropyl compounds adopt the (E,Z) form, whereas thetert‐butyl compound is in the (E,E) form. In aprotic solvents all four dialdimines (as well as the lithium dialdiminate salts) adoptcis‐s‐cisconformations in which there presumably is either an intramolecular hydrogen bond (or a lithium cation) between the two nitrogen atoms.

     
    more » « less
  3. Flow-based generative models have recently become one of the most efficient approaches to model data generation. Indeed, they are constructed with a sequence of invertible and tractable transformations. Glow first introduced a simple type of generative flow using an invertible 1×1 convolution. However, the 1×1 convolution suffers from limited flexibility compared to the standard convolutions. In this paper, we propose a novel invertible n×n convolution approach that overcomes the limitations of the invertible 1×1 convolution. In addition, our proposed network is not only tractable and invertible but also uses fewer parameters than standard convolutions. The experiments on CIFAR-10, ImageNet and Celeb-HQ datasets, have shown that our invertible n×n convolution helps to improve the performance of generative models significantly. 
    more » « less
  4. Megow, Nicole ; Smith, Adam (Ed.)
    A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) n-input Subset Sum problem that runs in time 2^{(1/2 - c)n} for some constant c > 0. In this paper we give a Subset Sum algorithm with worst-case running time O(2^{n/2} ⋅ n^{-γ}) for a constant γ > 0.5023 in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical "meet-in-the-middle" algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time O(2^{n/2}) in these memory models [Horowitz and Sahni, 1974]. Our algorithm combines a number of different techniques, including the "representation method" introduced by Howgrave-Graham and Joux [Howgrave-Graham and Joux, 2010] and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof [Austrin et al., 2016], and Nederlof and Węgrzycki [Jesper Nederlof and Karol Wegrzycki, 2021], and "bit-packing" techniques used in the work of Baran, Demaine, and Pǎtraşcu [Baran et al., 2005] on subquadratic algorithms for 3SUM. 
    more » « less
  5. null (Ed.)
    Abstract We show that, as n goes to infinity, the free group on n generators, modulo {n+u} random relations, converges to a random group that we give explicitly. This random group is a non-abelian version of the random abelian groups that feature in the Cohen–Lenstra heuristics. For each n , these random groups belong to the few relator model in the Gromov model of random groups. 
    more » « less