Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions

In this paper, we consider a four-point coupled boundary value problem for systems of the nonlinear semipositone fractional differential equation \begin{gather*}\left\{ \begin{array}{ll} \mathbf{D}_{0+}^\alpha u+\lambda f(t,u,v)=0,\quad 0<t<1, \lambda >0,\\ \mathbf{D}_{0+}^\alpha v+\lambda g(t,u,v)=0,\\ u^{(i)}(0)=v^{(i)}(0)=0, 0\leq i\leq n-2,\\ u(1)=av(\xi), v(1)=bu(\eta), \xi,\eta\in(0,1) \end{array}\right.\end{gather*} where $\lambda$ is a parameter, $a, b, \xi,\eta$ satisfy $\xi,\eta\in(0,1)$, $0<ab\xi\eta<1$, $\alpha \in(n-1, n]$ is a real number and $n\geq 3$, and $\mathbf{D}_{0+}^\alpha$ is the Riemann-Liouville's fractional derivative, and $f,g$ are continuous and semipositone. We derive an interval on $\lambda$ such that for any $\lambda$ lying in this interval, the semipositone boundary value problem has multiple positive solutions

Singular positone and semipositone boundary value problems of nonlinear fractional differential equations

We present some new existence results for singular positone and semipositone nonlinear fractional boundary value problem where μ &gt; 0, a, and f are continuous, α ∈ 3, 4 is a real number, and D α 0 is Riemann-Liouville fractional derivative. Throughout our nonlinearity may be singular in its dependent variable. Two examples are also given to illustrate the main results

Discrepancies among Pre-trained Deep Neural Networks: A New Threat to Model Zoo Reliability

Training deep neural networks (DNNs) takes significant time and resources. A practice for expedited deployment is to use pre-trained deep neural networks (PTNNs), often from model zoos.collections of PTNNs; yet, the reliability of model zoos remains unexamined. In the absence of an industry standard for the implementation and performance of PTNNs, engineers cannot confidently incorporate them into production systems. As a first step, discovering potential discrepancies between PTNNs across model zoos would reveal a threat to model zoo reliability. Prior works indicated existing variances in deep learning systems in terms of accuracy. However, broader measures of reliability for PTNNs from model zoos are unexplored. This work measures notable discrepancies between accuracy, latency, and architecture of 36 PTNNs across four model zoos. Among the top 10 discrepancies, we find differences of 1.23%-2.62% in accuracy and 9%ś131% in latency. We also find mismatches in architecture for well-known DNN architectures (e.g., ResNet and AlexNet). Our findings call for future works on empirical validation, automated tools for measurement, and best practices for implementation

Non-Markovian Dynamics of Entanglement for Multipartite Systems

Entanglement dynamics for a couple of two-level atoms interacting with independent structured reservoirs is studied using a non-perturbative approach. It is shown that the revival of atom entanglement is not necessarily accompanied by the sudden death of reservoir entanglement, and vice versa. In fact, atom entanglement can revive before, simultaneously or even after the disentanglement of reservoirs. Using a novel method based on the population analysis for the excited atomic state, we present the quantitative criteria for the revival and death phenomena. For giving a more physically intuitive insight, the quasimode Hamiltonian method is applied. Our quantitative analysis is helpful for the practical engineering of entanglement.Comment: 10 pages and 4 figure

Investigation of the evaluation system of SMEs’ industrial cluster management performance based on wireless network development

Abstract Today, with the rapid development of mobile Internet technology, the operation of enterprises is basically based on the mobile network platform. Therefore, the study of the evaluation system of SMEs’ industrial cluster management performance based on wireless network development is proposed. After briefly describing the relevant research of industrial cluster performance evaluation, the knowledge innovation of wireless network era is the core of SME industrial cluster management, and a set of industrial cluster management performance evaluation index system has been constructed. Based on this, a comprehensive evaluation method based on neural network algorithm is designed. In a subsequent experiment, it is demonstrated that this method can evaluate the level of cluster management performance