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 $g(\Psi_{p_1p_2p_3})$

Advantages And Shortcomings Of Korean Chaebols

The prevalent form of business organizations in Korea is a chaebol. The chaebol is a diversified conglomerate. This paper addresses the following issues concerning Korean chaebols:  1) reasons for diversification, 2) advantages and shortcomings of chaebols, 3) issues facing Korean chaebols, and 4) chaebols’ managing the crisis and making reforms. We found that Korean chaebols managed to learn from the economic crisis and made successful reforms

Advantages And Shortcomings Of Korean Chaebols

The prevalent form of business organizations in Korea is a chaebol. The chaebol is a diversified conglomerate. This paper addresses the following issues concerning Korean chaebols:  1) reasons for diversification, 2) advantages and shortcomings of chaebols, 3) issues facing Korean chaebols, and 4) chaebols’ managing the crisis and making reforms. We found that Korean chaebols managed to learn from the economic crisis and made successful reforms

General, Strong Impurity-Strength Dependence of Quasiparticle Interference

Quasiparticle interference (QPI) patterns in momentum space are often assumed to be independent of the strength of the impurity potential when compared with other quantities, such as the joint density of states. Here, using the $T$-matrix theory, we show that this assumption breaks down completely even in the simplest case of a single-site impurity on the square lattice with an $s$ orbital per site. Then, we predict from first-principles, a very rich, impurity-strength-dependent structure in the QPI pattern of TaAs, an archetype Weyl semimetal. This study thus demonstrates that the consideration of the details of the scattering impurity including the impurity strength is essential for interpreting Fourier-transform scanning tunneling spectroscopy experiments in general.Comment: main manuscript: 8 pages, 6 figures, Supplementary Information: 3 pages, 6 figure

Jahn-Teller driven perpendicular magnetocrystalline anisotropy in metastable ruthenium

A metastable phase of body-centered-tetragonal ruthenium (bct Ru) is identified to exhibit a large perpendicular magnetocrystalline anisotropy (PMCA), whose energy E-MCA is as large as 150 mu cV/atom, which is two orders of magnitude greater than those of 3d magnetic metals. Further investigation over the range of tetragonal distortion suggests that the appearance of magnetism in the bct Ru is governed by the Jahn-Teller spit e(g) orbitals. Moreover, from band analysis, MCA is mainly determined by an interplay between two e(g) states, d(x)(-y)(2)(2)and d(z)(2) states, as a result of level reversal associated with tetragonal distortion.open1

Unusual transport characteristics of nitrogen-doped single-walled carbon nanotubes

Electrical transport characteristics of nitrogen-doped single-walled carbon nanotubes (N-SWCNTs), in which the nitrogen dopant is believed to form a pyridinelike bonding configuration, are studied with the field effect transistor operations. Contrary to the expectation that the nitrogen atoms may induce a n -type doping, the electrical transports through our N-SWCNTs are either ambipolar in vacuum or p -type in air. Through the first-principles electronic structure calculations, we show that the nitrogen dopant indeed favors the pyridinelike configuration and the Fermi level of the pyridinelike N-SWCNT is almost at the intrinsic level.open01

On Hybrid Synthesis for Hierarchical Structured Petri Nets

We propose a hybrid method for synthesis of hierarchical structured Petri nets. In a top-down manner, we decompose a system into a set of subsystems at each level of abstraction, each of these is specified as a blackbox Petri net that has multiple inputs and outputs. We stipulate that each subsystem satisfies the following I/O constraints: (1) At any instance of time, at most one of the inputs can be activated; and (2) If one input is activated, then the subsystem must consume the input and produce exactly one output within a finite length of time. We give a stepwise refinement procedure which starts from the initial high-level abstraction of the system and expands an internal place of a blackbox Petri net into a more detailed subnet at each step. By enforcing the I/O constraints of each subsystem in each intermediate abstraction, our refinement maintains the sequencing of transitions prescribed by the initial abstraction of the system. Next, for the bottom-up synthesis, we present interconnection rules for sequential, parallel, and loop structures and prove that each rule maintains the I/O constraints. Thus, by incorporating these interconnection rules into our refinement formulation, our approach can be regarded as a hybrid Petri net synthesis technique that employs both top-down and bottom-up methods. The major advantage of the method is that the modeling details can be introduced incrementally and naturally, while the important logical properties of the resulting Petri net are guaranteed