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

Duchamp--Hivert--Thibon introduced the construction of a right $H_n(0)$-module, denoted as $M_P$, for any partial order $P$ on the set $[n]$. This module is defined by specifying a suitable action of $H_n(0)$ on the set of linear extensions of $P$. In this paper, we refer to this module as the poset module associated with $P$. Firstly, we show that $\bigoplus_{n \ge 0} G_0(\mathscr{P}(n))$ has a Hopf algebra structure that is isomorphic to the Hopf algebra of quasisymmetric functions, where $\mathscr{P}(n)$ is the full subcategory of $\textbf{mod-}H_n(0)$ whose objects are direct sums of finitely many isomorphic copies of poset modules and $G_0(\mathscr{P}(n))$ is the Grothendieck group of $\mathscr{P}(n)$. 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 $Y_\alpha$ of Schur functions, where $\alpha$ is a composition. We show that they can be expressed as the sum of the $P$-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

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

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

Homological properties of 0-Hecke modules for dual immaculate quasisymmetric functions

Let $n$ be a nonnegative integer. For each composition $\alpha$ of $n$, Berg $\textit{et al.}$ introduced a cyclic indecomposable $H_n(0)$-module $\mathcal{V}_\alpha$ with a dual immaculate quasisymmetric function as the image of the quasisymmetric characteristic. In this paper, we study $\mathcal{V}_\alpha$'s from the homological viewpoint. To be precise, we construct a minimal projective presentation of $\mathcal{V}_\alpha$ and a minimal injective presentation of $\mathcal{V}_\alpha$ as well. Using them, we compute ${\rm Ext}^1_{H_n(0)}(\mathcal{V}_\alpha, {\bf F}_\beta)$ and ${\rm Ext}^1_{H_n(0)}( {\bf F}_\beta, \mathcal{V}_\alpha)$, where ${\bf F}_\beta$ is the simple $H_n(0)$-module attached to a composition $\beta$ of $n$. We also compute ${\rm Ext}_{H_n(0)}^i(\mathcal{V}_\alpha,\mathcal{V}_{\beta})$ when $i=0,1$ and $\beta \le_l \alpha$, where $\le_l$ represents the lexicographic order on compositions.Comment: 44 pages, to be published in Forum of Math: Sigm

An Index to Better Estimate Tropical Cyclone Intensity Change in the Western North Pacific

A revised predictor called the net energy gain rate (NGR) is suggested by considering wind dependent drag coefficient based on the existing maximum potential intensity theory. A series of wind speed dependent NGR, known as NGR‐w, is calculated based on pre‐tropical cyclone (TC) averaged ocean temperatures from the surface down to 120 m (at 10‐m intervals) to include the TC‐induced vertical mixing for 13 years (2004–2016) in the western North Pacific. It turns out that the NGR50‐w (NGR‐w based on temperature averaged over top 50 m) has the highest correlation with 24‐h TC intensity change compared with the commonly used sea surface temperature‐based intensification potential (POT), depth‐averaged temperature‐based POT (POTDAT), and constant drag coefficient in the NGR. To demonstrate the effectiveness of the NGR50‐w, we designed and conducted experiments for training (2004–2014) and testing (2015–2016). The model with the NGR50‐w shows greater skill than the model with POTDAT or POT by reducing prediction errors by about 16%

Development of Threat Evaluation Tool for Distributed Network Environment

Current information protection systems only detect and warn against individual intrusion, and are not able to provide a collective and synthesized alert message. In this paper, we propose a new Meta-IDS system which is called ``SIA System''. The SIA system can filter redundant alert messages, analyze mixed attacks using correlation alert messages from each sensor and respond to security threats quickly, after classifying them into one of four different statuses. Then we implement the SIA system and test the efficiency of it in the managed networks. Thus we confirm that the SIA system enables security managers to deal with security threats efficiently

Rotational Resistance of Surface-Treated Mini-implants

Objective: To test the hypothesis that there is no difference in the stability and resistance to rotational moments of early loaded sandblasted and acid-etched (SLA) mini-implants and those of machined-surface implants of the same size and shape. Materials and Methods: A randomized complete block design was used in 12 skeletally mature male beagle dogs. Ninety-six orthodontic mini-implants were tested. Two types of implants were used: some had SLA surface treatment and some had machined surfaces without coating. After 3 weeks of healing, rotational moments of 150 g were applied. The success rates, maximum torque values, angular momentum, and total energy absorbed by the bone were compared. All values were subjected to mixed-model analysis to evaluate the influence of surface treatment, rotational force direction, and site of implantation. Results: The maximum insertion torque and angular momentum of SLA implants were significantly lower than those of machined implants (P = .034, P = .039). The SLA implants had a significantly higher value for total removal energy than the machined implants (P = .046). However, there were no significant differences in total insertion energy, maximum removal torque, and removal angular momentum between the 2 groups. There was no significant difference between clockwise and counterclockwise rotation in all measurements. Conclusion: SLA mini-implants showed relatively lower insertion torque value and angular momentum and higher total energy during removal than the machined implants, suggesting osseointegration of the SLA mini-implant after insertion

Properties of oriented strand board made from Betung bamboo (Dendrocalamus asper (Schultes.f) Backer ex Heyne)

Bamboo has gained increasing attention as an alternative raw material for use in the manufacture of composite boards. Three-layer OSBs were made using Betung bamboo (Dendrocalamus asper (Schultes.f) Backer ex Heyne) strands to evaluate the effects of strand length and pre-treatment techniques on the physical, mechanical, and durability properties. Three different strand lengths, namely 50, 60, and 70 mm, were prepared. Prior to the manufacture into OSB, the strands were immersed in cold water for 24 h and in 6% acetic anhydrides solution for 48 h. The OSBs were fabricated using 5% MDI resin based on the strand dry weight. The results indicated that MOR and MOE values in perpendicular to the grain direction were much influenced by strand length. The dimensional stability of OSB was slightly improved by immersing the strands in acetic anhydride solution. Immersing strands in cold water and acetic anhydride solution improved the resistance of OSB against subterranean termite (Macrotermes gylvus) attack under the adopted experimental condition. All OSB parameters manufactured in this experiment were better than the minimum requirement of CSA 0437.0 (Grade O–2) standard