Existence and uniqueness of positive solutions for Kirchhoff type beam equations

This paper is concerned with the existence and uniqueness of positive solutions for the fourth order Kirchhoff type problem \begin{equation*} \begin{cases} u''''(x)-\Big(a+b\int_0^1(u'(x))^2dx\Big)u''(x)=\lambda f(u(x)),& x\in(0,1),\\ u(0)=u(1)=u''(0)=u''(1)=0, \end{cases} \end{equation*} where $a>0, b\geq 0$ are constants, $\lambda\in \mathbb{R}$ is a parameter. For the case $f(u)\equiv u$, we use an argument based on the linear eigenvalue problems of fourth order equations and their properties to show that there exists a unique positive solution for all $\lambda>\lambda_{1,a}$, here $\lambda_{1,a}$ is the first eigenvalue of the above problem with $b=0$; for the case $f$ is sublinear, we prove that there exists a unique positive solution for all $\lambda>0$ and no positive solution for $\lambda<0$ by using bifurcation method

A facile route to encapsulate ultrasmall Ni clusters within the pore channels of AlPO-5

A simple one-step method to encapsulate Ni (II) into the pore channels of AlPO-5 molecule sieve was developed by using nickel-amine complexes as templating agent for synthesis of Ni(deta)2-AlPO-5. The Ni (II) occluded in the pores can be directly reduced by reducing gases in situ generated from the decomposition of nickel-amine complexes in AlPO-5 during heat treatment. The resulted catalyst has ultra-small Ni clusters highly dispersed into the pore channels, showing a high selectivity for 1,2-propanediol in the hydrogenolysis of glycerol

Audio-aware Query-enhanced Transformer for Audio-Visual Segmentation

The goal of the audio-visual segmentation (AVS) task is to segment the sounding objects in the video frames using audio cues. However, current fusion-based methods have the performance limitations due to the small receptive field of convolution and inadequate fusion of audio-visual features. To overcome these issues, we propose a novel \textbf{Au}dio-aware query-enhanced \textbf{TR}ansformer (AuTR) to tackle the task. Unlike existing methods, our approach introduces a multimodal transformer architecture that enables deep fusion and aggregation of audio-visual features. Furthermore, we devise an audio-aware query-enhanced transformer decoder that explicitly helps the model focus on the segmentation of the pinpointed sounding objects based on audio signals, while disregarding silent yet salient objects. Experimental results show that our method outperforms previous methods and demonstrates better generalization ability in multi-sound and open-set scenarios.Comment: arXiv admin note: text overlap with arXiv:2305.1101

Dynamic analysis of offset press gear-cylinder-bearing system applying finite element method

A dynamic model of offset press gear transmission system made up of gears, cylinders and bearings is proposed in this study. The model based on finite element method (FEM) includes some nonlinearity such as time-varying meshing stiffness, backlash, static transmission error and contact nonlinearity, which lead to complex nonlinear coupling. The Darren Bell principle and Lagrangian approach are applied to derive the motion equations of system, then the Newmark method is used to solve the equations for meshing force, acceleration, shoulder iron and rubber contact force. Eigenvalue solution is used to predict the critical speed, moreover, the influence of the radial and axial stiffness on the first-order critical speed is discussed. Considering the importance of acceleration and meshing force, the RMS value of acceleration and dynamic factor are also studied in this paper. The dynamic orbits of system are observed from the phase diagram, power spectrum, Lyapunov exponent and Poincare map. The figures clearly indicate that there are various forms of periodic and chaotic motions in different conditions. The simulation results show that with the increase of rotating speed, dynamic orbits transfer from periodic motion to chaotic motion in the cylinder discrete state