2,133 research outputs found

    Tracking Control for Reliable Outdoor Navigation Using Curb Detection

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    Poset modules of the 00-Hecke algebras and related quasisymmetric power sum expansions

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    Duchamp--Hivert--Thibon introduced the construction of a right Hn(0)H_n(0)-module, denoted as MPM_P, for any partial order PP on the set [n][n]. This module is defined by specifying a suitable action of Hn(0)H_n(0) on the set of linear extensions of PP. In this paper, we refer to this module as the poset module associated with PP. Firstly, we show that n0G0(P(n))\bigoplus_{n \ge 0} G_0(\mathscr{P}(n)) has a Hopf algebra structure that is isomorphic to the Hopf algebra of quasisymmetric functions, where P(n)\mathscr{P}(n) is the full subcategory of mod-Hn(0)\textbf{mod-}H_n(0) whose objects are direct sums of finitely many isomorphic copies of poset modules and G0(P(n))G_0(\mathscr{P}(n)) is the Grothendieck group of P(n)\mathscr{P}(n). We also demonstrate how (anti-)automorphism twists interact with these modules, the induction product and restrictions. Secondly, we investigate the (type 1) quasisymmetric power sum expansion of some quasi-analogues YαY_\alpha of Schur functions, where α\alpha is a composition. We show that they can be expressed as the sum of the PP-partition generating functions of specific posets, which allows us to utilize the result established by Liu--Weselcouch. Additionally, we provide a new algorithm for obtaining these posets. Using these findings, for the dual immaculate function and the extended Schur function, we express the coefficients appearing in the quasisymmetric power sum expansions in terms of border strip tableaux.Comment: 42 page

    Low-temperature synthesis of CuO-interlaced nanodiscs for lithium ion battery electrodes

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    In this study, we report the high-yield synthesis of 2-dimensional cupric oxide (CuO) nanodiscs through dehydrogenation of 1-dimensional Cu(OH)2 nanowires at 60°C. Most of the nanodiscs had a diameter of approximately 500 nm and a thickness of approximately 50 nm. After further prolonged reaction times, secondary irregular nanodiscs gradually grew vertically into regular nanodiscs. These CuO nanostructures were characterized using X-ray diffraction, transmission electron microscopy, and Brunauer-Emmett-Teller measurements. The possible growth mechanism of the interlaced disc CuO nanostructures is systematically discussed. The electrochemical performances of the CuO nanodisc electrodes were evaluated in detail using cyclic voltammetry and galvanostatic cycling. Furthermore, we demonstrate that the incorporation of multiwalled carbon nanotubes enables the enhanced reversible capacities and capacity retention of CuO nanodisc electrodes on cycling by offering more efficient electron transport paths

    Video-Based Stylized Rendering using Frame Difference

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    In this paper, we suggest video based stylized rendering using frame difference. Stylized rendering using video frame has a temporal problem that occurs a difference between the previous and current frame. To reduce the temporal problem, we generate reference maps using temporal frame difference in correction and rendering steps. A correction method using reference maps can be reduced flickering effect caused by frame difference between the previous and current frame. We use a background map, an average map, and a quadtree-based summed area table as reference maps. Among these reference maps, the method using quadtree based summed area table can completely remove a flickering and popping effect. Also, a post-blurring method using bilateral filtering can be represented smooth, stylized rendering by removing unnecessary noise. Suggested stylized rendering system can be used in various fields such as visual art, advertisement, game and movie for stylized image contents generation

    The projective cover of tableau-cyclic indecomposable Hn(0)H_n(0)-modules

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    Let α\alpha be a composition of nn and σ\sigma a permutation in S(α)\mathfrak{S}_{\ell(\alpha)}. This paper concerns the projective covers of Hn(0)H_n(0)-modules Vα\mathcal{V}_\alpha, XαX_\alpha and Sασ\mathbf{S}^\sigma_{\alpha}, which categorify the dual immaculate quasisymmetric function, the extended Schur function, and the quasisymmetric Schur function when σ\sigma is the identity, respectively. First, we show that the projective cover of Vα\mathcal{V}_\alpha is the projective indecomposable module Pα\mathbf{P}_\alpha due to Norton, and XαX_\alpha and the ϕ\phi-twist of the canonical submodule Sβ,Cσ\mathbf{S}^{\sigma}_{\beta,C} of Sβσ\mathbf{S}^\sigma_{\beta} for (β,σ)(\beta,\sigma)'s satisfying suitable conditions appear as Hn(0)H_n(0)-homomorphic images of Vα\mathcal{V}_\alpha. Second, we introduce a combinatorial model for the ϕ\phi-twist of Sασ\mathbf{S}^\sigma_{\alpha} and derive a series of surjections starting from Pα\mathbf{P}_\alpha to the ϕ\phi-twist of Sα,Cid\mathbf{S}^{\mathrm{id}}_{\alpha,C}. Finally, we construct the projective cover of every indecomposable direct summand Sα,Eσ\mathbf{S}^\sigma_{\alpha, E} of Sασ\mathbf{S}^\sigma_{\alpha}. As a byproduct, we give a characterization of triples (σ,α,E)(\sigma, \alpha, E) such that the projective cover of Sα,Eσ\mathbf{S}^\sigma_{\alpha, E} is indecomposable.Comment: 41 page
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