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pro vyhledávání: '"Thomas, Y."'
Recently, Andrews and Newman studied the minimal excludant of a partition, which is defined as the smallest positive integer that is not a part of a partition. In this article, we consider the minimal excludant size of an overpartition, which is an o
Externí odkaz:
http://arxiv.org/abs/2410.19669
Kolmogorov-Arnold Networks (KAN) \cite{liu2024kan} were very recently proposed as a potential alternative to the prevalent architectural backbone of many deep learning models, the multi-layer perceptron (MLP). KANs have seen success in various tasks
Externí odkaz:
http://arxiv.org/abs/2410.01803
Building upon the idea in \cite{HNWarXiv24}, we establish stability of the type-I blowup with log correction for the complex Ginzburg-Landau equation. In the amplitude-phase representation, a generalized dynamic rescaling formulation is introduced, w
Externí odkaz:
http://arxiv.org/abs/2407.15812
In this article, we first investigate the partitions whose parts are congruent to $a$ or $b$ modulo $k$ with the aid of separable integer partition classes with modulus $k$ introduced by Andrews. Then, we introduce the $(k,r)$-overpartitions in which
Externí odkaz:
http://arxiv.org/abs/2406.19823
Photon detectors featuring single-photon sensitivity play a crucial role in various scientific domains, including high-energy physics, astronomy, and quantum optics. Fast response time, high quantum efficiency, and minimal dark counts are the charact
Externí odkaz:
http://arxiv.org/abs/2406.17839
Autor:
Chen, Y. H., He, Thomas Y.
Bressoud introduced the partition function $B(\alpha_1,\ldots,\alpha_\lambda;\eta,k,r;n)$, which counts the number of partitions with certain difference conditions. Bressoud posed a conjecture on the generating function for the partition function $B(
Externí odkaz:
http://arxiv.org/abs/2405.19918
Autor:
Hou, Thomas Y.
We perform numerical investigation of nearly self-similar blowup of generalized axisymmetric Navier-Stokes equations and Boussinesq system with a time-dependent fractional dimension. The dynamic change of the space dimension is proportional to the ra
Externí odkaz:
http://arxiv.org/abs/2405.10916
Autor:
Liu, Ziming, Wang, Yixuan, Vaidya, Sachin, Ruehle, Fabian, Halverson, James, Soljačić, Marin, Hou, Thomas Y., Tegmark, Max
Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable a
Externí odkaz:
http://arxiv.org/abs/2404.19756
We propose an alternative proof of the classical result of type-I blowup with log correction for the semilinear equation. Compared with previous proofs, we use a novel idea of enforcing stable normalizations for perturbation around the approximate pr
Externí odkaz:
http://arxiv.org/abs/2404.09410
In 1980, Bressoud conjectured a combinatorial identity $A_j=B_j$ for $j=0$ or $1$. In this paper, we introduce a new partition function $\overline{B}_0$ which can be viewed as an overpartition analogue of the partition function $B_0$. An overpartitio
Externí odkaz:
http://arxiv.org/abs/2312.00466