Maximum Gap in (Inverse) Cyclotomic Polynomial

Let $g(f)$ denote the maximum of the differences (gaps) between two consecutive exponents occurring in a polynomial $f$. Let $\Phi_n$ denote the $n$-th cyclotomic polynomial and let $\Psi_n$ denote the $n$-th inverse cyclotomic polynomial. In this note, we study $g(\Phi_n)$ and $g(\Psi_n)$ where $n$ is a product of odd primes, say $p_1 < p_2 < p_3$, etc. It is trivial to determine $g(\Phi_{p_1})$, $g(\Psi_{p_1})$ and $g(\Psi_{p_1p_2})$. Hence the simplest non-trivial cases are $g(\Phi_{p_1p_2})$ and $g(\Psi_{p_1p_2p_3})$. We provide an exact expression for $g(\Phi_{p_1p_2}).$ We also provide an exact expression for $g(\Psi_{p_1p_2p_3})$ under a mild condition. The condition is almost always satisfied (only finite exceptions for each $p_1$). We also provide a lower bound and an upper bound for $g(\Psi_{p_1p_2p_3})$

Meson Mass at Large Baryon Chemical Potential in Dense QCD

We reexamine the quark mass induced term in chiral Lagrangian in color-flavor locking phase in dense QCD, and show that the meson mass term is determined by three independent invariants under chiral-axial symmetry, and a meson mass is given in terms of the quark mass, gap, and the chemical potential by $m_{\pi}^2\sim m_q^2\Delta\bar{\Delta}/\mu^2\ln(\mu^2/\Delta^2)$. Thus mesons become massless as $\mu\to\infty$.Comment: 7 pages, no figures; made antiparticle gap explicit; to appear Phys. Lett.

U(1)_R mediation from the flux compactification in six dimensions

We consider a supersymmetric completion of codimension-two branes with nonzero tension in a 6D gauged supergravity. As a consequence, we obtain the football solution with 4D Minkowski space as a new supersymmetric background that preserves 4D N=1 SUSY. In the presence of brane multiplets, we derive the 4D effective supergravity action for the football background and show that the remaining modulus can be stabilized by a bulk non-perturbative correction with brane uplifting potentials at a zero vacuum energy. We find that the U(1)_R mediation can be a dominant source of SUSY breaking for a brane scalar with nonzero R charge.Comment: 3 pages, no figures, to appear in the proceedings of the 16th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY-2008), Seoul, Korea, 16-21 June, 200

Flow-based Intrinsic Curiosity Module

In this paper, we focus on a prediction-based novelty estimation strategy upon the deep reinforcement learning (DRL) framework, and present a flow-based intrinsic curiosity module (FICM) to exploit the prediction errors from optical flow estimation as exploration bonuses. We propose the concept of leveraging motion features captured between consecutive observations to evaluate the novelty of observations in an environment. FICM encourages a DRL agent to explore observations with unfamiliar motion features, and requires only two consecutive frames to obtain sufficient information when estimating the novelty. We evaluate our method and compare it with a number of existing methods on multiple benchmark environments, including Atari games, Super Mario Bros., and ViZDoom. We demonstrate that FICM is favorable to tasks or environments featuring moving objects, which allow FICM to utilize the motion features between consecutive observations. We further ablatively analyze the encoding efficiency of FICM, and discuss its applicable domains comprehensively.Comment: The SOLE copyright holder is IJCAI (International Joint Conferences on Artificial Intelligence), all rights reserved. The link is provided as follows: https://www.ijcai.org/Proceedings/2020/28

What Drives Consumers in China to Buy Clothing Online? Application of the Technology Acceptance Model

An enormous number of Internet users have made China a profitable e-commerce marketplace, and clothing is one of the most frequently purchased items. This study explores the predictors of consumers’ motivation to buy clothing online in China by extending the technology acceptance model. Data were collected via an online questionnaire, resulting in 504 returned responses. The results indicate that perceived usefulness has a significant effect on consumers’ intention to buy clothing online; however, no direct relationship between perceived ease of use and buying intention was found. Furthermore, perceived convenience, perceived money saving, and perceived time-saving can explain why consumers perceive buying clothing online as useful, and these perceptions have positive effects on buying intention. Additionally, the findings imply that fashion innovativeness and friend circles significantly influence consumers’ intention to purchase clothing online. This article discusses the results and provides recommendations for implication and future research