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 $g(\Psi_{p_1p_2p_3})$

Semiconductor integrated circuit chip, multilayer chip capacitor and semiconductor integrated circuit chip package

Disclosed are a semiconductor integrated circuit chip, a multilayer chip capacitor, and a semiconductor integrated circuit chip package. The semiconductor integrated circuit chip includes a semiconductor integrated circuit chip body, an input/output terminal disposed on the outside of the semiconductor integrated circuit chip body, and a decoupling capacitor disposed at a side face of the semiconductor integrated circuit chip body and electrically connected to the input/output terminal. The semiconductor integrated circuit chip cab be obtained, which can maintain an impedance of a power distribution network below a target impedance in a wide frequency range, particularly at a high frequency, by minimizing an inductance between a decoupling capacitor and a semiconductor integrated circuit chip

Determinants of user satisfaction and continuance intention of smartphones: Focus on interactivity perspective

The development and complexity of mobile and smart technologies continues to evolve with a greater speed, attention needs to be turned to the possibility of continuous development. It has become important to monitor users’ post-purchase behavior in order to understand their continued use of smartphones and other smart devices. This study posits interactivity as a key variable to describe customer satisfaction and continuance intention in using smartphones. We classify interactivity into five sub-dimensions: system quality, network quality, contents quality, customer support, and compatibility. The established model in this study was empirically examined through survey research. Structural equation modeling demonstrated several key findings: contents quality is the most influential factor in shaping satisfaction, followed by compatibility, system quality, and customer support. The results also showed that satisfaction has a positive effect on the continuance intention. In addition, network quality had a positive direct effect on the continuance intention. Users also exhibit significant differences in post-purchase behavior, depending on their operating systems. These results will be helpful for the practitioners to further deliver appropriate service strategies for strengthening ongoing relationship with their customers

Broad Phase Transition of Fluorite-Structured Ferroelectrics for Large Electrocaloric Effect

Field-induced ferroelectricity in (doped) hafnia and zirconia has attracted increasing interest in energy-related applications, including energy harvesting and solid-state cooling. It shows a larger isothermal entropy change in a much wider temperature range compared with those of other promising candidates. The field-induced phase transition occurs in an extremely wide temperature range, which contributes to the giant electrocaloric effect. This article examines the possible origins of a large isothermal entropy change, which can be related to the extremely broad phase transitions in fluorite-structured ferroelectrics. While the materials possess a high entropy change associated with the polar–nonpolar phase transition, which can contribute to the high energy performance, the higher breakdown field compared with perovskites practically determines the available temperature range