Instability analysis for semi-active control systems with semi-active inerters

Nonlinear Dynamics - In this paper, the instability of semi-active control systems caused by the utilization of semi-active inerters is analyzed. The purpose of this study is to demonstrate the...     

Design and exploration of 5-nitro-3-trinitromethyl-1H-1,2,4-triazole and its derivatives as energetic materials

Molecular Diversity - According to the fact that 5-nitro-3-trinitromethyl-1H-1,2,4 triazole (NTNMT) is a successful, good explosive, energetic groups such as –CH3, –NH2, –NHNO2,...     

An effective multi-channel fault diagnosis approach for rotating machinery based on multivariate generalized refined composite multi-scale sample entropy

Nonlinear Dynamics - Fault diagnosis of critical rotating machinery components is necessary to ensure safe operation. However, the commonly used rotating machinery fault diagnosis methods are...     

How do peace dividends bring about human development and productivity?

Annals of Operations Research - The main purpose of this study was to explore the impact of peace dividends on global changes in national productivity. First, this study assessed changes in...     

Lieb–Schultz–Mattis theorem and the filling constraint

Letters in Mathematical Physics - Classical Virasoro conformal blocks are believed to be directly related to accessory parameters of Floquet type in the Heun equation and some of its confluent...     

Public key encryption with filtered equality test revisited

Designs, Codes and Cryptography - Without revealing data in the plain, public key encryption with equality test can achieve the basic cryptographic functionalities required. However, the extended...     

Design and fabrication of GeAsSeS chalcogenide waveguides with thermal annealing

We reported a chalcogenide glass-based rib waveguide fabricated using photolithography and dry etching method. A commercial software(COMSOL Multiphysics) was used to optimize the waveguide structure and the distribution of the fundamental modes in the waveguide based on the complete vector finite component. We further employed thermal annealing to optimize the surface and sidewalls of the rib waveguides. It was found that the optimal annealing temperature for Ge As Se S films is 220℃, and the roughness of the films could be significantly reduced by annealing. The zero-dispersion wavelength(ZDW) could be shifted to a short wavelength around ~2.1 μm via waveguide structural optimization, which promotes supercontinuum generation with a short wavelength pump laser source. The insertion loss of the waveguides with cross-sectional areas of 4.0 μm×3.5 μm and 6.0 μm×3.5 μm was measured using lens fiber and the cut-back method. The propagation loss of the 220℃ annealed waveguides could be as low as 1.9 d B/cm at 1550 nm.     

Uniform local well-posedness and inviscid limit for the Benjamin-Ono-Burgers equation

In this paper, we study the Cauchy problem for the Benjamin-Ono-Burgers equation \({\partial _t}u - \epsilon \partial _x^2u + {\cal H}\partial _x^2u + u{u_x} = 0\), where \({\cal H}\) denotes the Hilbert transform operator. We obtain that it is uniformly locally well-posed for small data in the refined Sobolev space \({\tilde H^\sigma }(\mathbb{R})\,\,(\sigma \geqslant 0)\), which is a subspace of L²(ℝ). It is worth noting that the low-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is scaling critical, and thus the small data is necessary. The high-frequency part of \({\tilde H^\sigma }(\mathbb{R})\) is equal to the Sobolev space H^σ (ℝ) (σ ⩾ 0) and reduces to L²(ℝ). Furthermore, we also obtain its inviscid limit behavior in \({\tilde H^\sigma }(\mathbb{R})\) (σ ⩾ 0).

     

Semi-invariants of binary forms and Sylvester’s theorem

The Ramanujan Journal - We obtain a combinatorial formula related to the shear transformation for semi-invariants of binary forms, which implies the classical characterization of semi-invariants in...