Matrix recursion for positive characteristic diagrammatic Soergel bimodules for affine Weyl groups

Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular representation theory. We explicitly construct a functor from $\mathcal{D}$ to a matrix category which categorifies a recursive representation $\xi : \mathbb{Z}W \rightarrow M_{p^r}(\mathbb{Z}W)$, where $r$ is the rank of the underlying finite root system. This functor gives a method for understanding diagrammatic Soergel bimodules in terms of other diagrammatic Soergel bimodules which are "smaller" by a factor of $p$. It also explains the presence of self-similarity in the $p$-canonical basis, which has been observed in small examples. By decategorifying we obtain a new lower bound on the $p$-canonical basis, which corresponds to new lower bounds on the characters of the indecomposable tilting modules by the recent $p$-canonical tilting character formula due to Achar-Makisumi-Riche-Williamson.Comment: 62 pages, many figures, best viewed in colo

Symbols of Pseudodifferential Operators Associated to Gevrey Kernel's Type

In this article, we aim at proving the truthfulness of the inverse Theorem (1) of [5]. More precisely, we associated symbols of Gevrey type to pseudodifferential operators when the latter are given by their kernels.</p

Matrix recursion for positive characteristic diagrammatic Soergel bimodules for affine Weyl groups

Let $W$ be an affine Weyl group, and let $\Bbbk$ be a field of characteristic $p>0$. The diagrammatic Hecke category $\mathcal{D}$ for $W$ over $\Bbbk$ is a categorification of the Hecke algebra for $W$ with rich connections to modular representation theory. We explicitly construct a functor from $\mathcal{D}$ to a matrix category which categorifies a recursive representation $\xi : \mathbb{Z}W \rightarrow M_{p^r}(\mathbb{Z}W)$, where $r$ is the rank of the underlying finite root system. This functor gives a method for understanding diagrammatic Soergel bimodules in terms of other diagrammatic Soergel bimodules which are "smaller" by a factor of $p$. It also explains the presence of self-similarity in the $p$-canonical basis, which has been observed in small examples. By decategorifying we obtain a new lower bound on the $p$-canonical basis, which corresponds to new lower bounds on the characters of the indecomposable tilting modules by the recent $p$-canonical tilting character formula due to Achar-Makisumi-Riche-Williamson

Path isomorphisms between quiver Hecke and diagrammatic Bott-Samelson endomorphism algebras

We construct an explicit isomorphism between (truncations of) quiver Hecke algebras and Elias-Williamson's diagrammatic endomorphism algebras of Bott-Samelson bimodules. As a corollary, we deduce that the decomposition numbers of these algebras (including as examples the symmetric groups and generalised blob algebras) are tautologically equal to the associated $p$-Kazhdan-Lusztig polynomials, provided that the characteristic is greater than the Coxeter number. We hence give an elementary and more explicit proof of the main theorem of Riche-Williamson's recent monograph and extend their categorical equivalence to cyclotomic Hecke algebras, thus solving Libedinsky-Plaza's categorical blob conjecture

SIMULASI PERANCANGAN DAN ANALISA ANTENA MIKROSTRIP PATCH TRIANGULAR UNTUK KOMUNIKASI WLAN

Untuk mendukung sebuah sistem telekomunikasi tanpa kabel maka diperlukan sebuah antena baik sebagai pengirim maupun sebagai penerima. Pada beberapa aplikasi dibutuhkan antena yang memiliki bandwidth yang lebar. Ada berbagai jenis antena yang dapat digunakan pada WLAN diantaranya adalah antena mikrostrip. Antena mikrostrip memiliki banyak kelebihan, diantaranya memiliki bentuk yang sederhana compact, ringan, dan biayanya murah. Antena mikrostrip juga memiliki 3 komponen utama yaitu patch yang merupakan lapisan teratas, substrat yang menggunakan bahan dielektrik, dan ground plane yang merupakan bagian paling bawah dari pada antena. Pada penelitian Tugas Akhir ini akan di rancang sebuah antena mikrostrip dengan bentuk patch triangular yang diaplikasikan untuk WLAN. Proses pembuatan nya dilakukan dengan menggunakan software Advanced Design System (ADS). Nilai dimensi antena yang digunakan dalam penelitian ini yaitu a = 38,6 mm; substrat FR-4 yang digunakan yaitu h= 1,6 mm; ?_r= 4,4; dan ?= 0,02. Dari pengujian simulasi yang dilakukan, diperoleh hasil dengan nilai VSWR sebesar 1,142; gain yang didapat sebesar 8,225 dB; nilai bandwidth dari hasil simulasi didapat 104 MHz dan nilai return loss yang diperoleh sebesar RL = -23,557 dB dengan frekuensi tengah berada pada titik fc = 2,441 GHz.Kata kunci : Antena, mikrostrip, Patch Triangular, Advanced Design System (ADS), WLA

How to implement high level of team spirit in organizations?

The aim of this thesis is to explore the means by which team spirit is implemented/enhanced in an organization from the management level. The research of this thesis is important, because as the Western societies are moving more and more towards an information-based economy, the importance of team work has become timelier than ever before. Since the beginning of the 90’s, the companies have adapted team-based workshops in an increasing rate, and it has even been found that the most common attribute why managers give someone a promotion is because they are “team players”. This thesis provides a practical approach as well as a theoretical framework for the implementation and enhancement of team spirit in an organization from management perspective. It starts with a preresearch with a purpose to establish a foundation for the main research, by providing evidences for the various positive impacts team spirit has on organizations, as well as deriving the antecedents of team spirit based on the frequency of their occurrence in the various literatures used for the purpose of this thesis. The antecedents are then further researched and elaborated in the main study, and their impacts, causalities as well as the measure by which they are implemented are unwrapped. Based on the research findings a priority of order of the antecedents are established and final theoretical framework is created. The study is conceptual inductive qualitative research by its nature, and the research gap as well as the contribution of this study lies in the question HOW team spirit can be enhanced/implemented from management level in an organization. The study contributes to the subject of team spirit, not only by providing the means by which it is implemented, but also by providing a holistic approach for the research of team spirit by taking both the structural and social factors in consideration, as well as providing its own subjective perspective for what are the antecedents of team spirit