Three positive solutions to initial-boundary value problems of nonlinear delay differential equations

In this paper, we consider the existence of triple positive solutions to the boundary value problem of nonlinear delay differential equation $$\left\{ \begin{array}{lll} (\phi(x'(t)))^{\prime} + a(t)f(t,x(t),x'(t),x_{t})=0, \ \ 0 < t<1,\\ x_{0}=0,\\ x(1)=0, \end{array}\right.$$ where $\phi: \mathbb{R} \rightarrow \mathbb{R}$ is an increasing homeomorphism and positive homomorphism with $\phi(0)=0,$ and $x_t$ is a function in $C([-\tau,0],\mathbb{R})$ defined by $x_{t}(\sigma)=x(t+\sigma)$ for $-\tau \leq \sigma\leq 0.$ By using a fixed-point theorem in a cone introduced by Avery and Peterson, we provide sufficient conditions for the existence of triple positive solutions to the above boundary value problem. An example is also presented to demonstrate our result. The conclusions in this paper essentially extend and improve the known results

Hierarchical Metadata Information Constrained Self-Supervised Learning for Anomalous Sound Detection Under Domain Shift

Self-supervised learning methods have achieved promising performance for anomalous sound detection (ASD) under domain shift, where the type of domain shift is considered in feature learning by incorporating section IDs. However, the attributes accompanying audio files under each section, such as machine operating conditions and noise types, have not been considered, although they are also crucial for characterizing domain shifts. In this paper, we present a hierarchical metadata information constrained self-supervised (HMIC) ASD method, where the hierarchical relation between section IDs and attributes is constructed, and used as constraints to obtain finer feature representation. In addition, we propose an attribute-group-center (AGC)-based method for calculating the anomaly score under the domain shift condition. Experiments are performed to demonstrate its improved performance over the state-of-the-art self-supervised methods in DCASE 2022 challenge Task 2

The non-gibberellic acid-responsive semi-dwarfing gene uzu affects Fusarium crown rot resistance in barley

BACKGROUND: Studies in Arabidopsis show that DELLA genes may differentially affect responses to biotrophic and necrophic pathogens. A recent report based on the study of DELLA-producing reduced height (Rht) genes in wheat and barley also hypothesized that DELLA genes likely increased susceptibility to necrotrophs but increased resistance to biotrophs. RESULTS: Effects of uzu, a non-GA (gibberellic acid)-responsive semi-dwarfing gene, on Fusarium crown rot (FCR) resistance in barley were investigated. Fifteen pairs of near isogenic lines for this gene were generated and assessed under two different temperature regimes. Similar to its impacts on plant height, the semi-dwarfing gene uzu also showed larger effects on FCR severity in the high temperature regime when compared with that in the low temperature regime. CONCLUSIONS: Results from this study add to the growing evidence showing that the effects of plant height on Fusarium resistances are unlikely related to DELLA genes but due to direct or indirect effects of height difference per se. The interaction between these two characteristics highlights the importance of understanding relationships between resistance and other traits of agronomic importance as the value of a resistance gene could be compromised if it dramatically affects plant development and morphology

Variance-constrained dissipative observer-based control for a class of nonlinear stochastic systems with degraded measurements

The official published version of the article can be obtained from the link below.This paper is concerned with the variance-constrained dissipative control problem for a class of stochastic nonlinear systems with multiple degraded measurements, where the degraded probability for each sensor is governed by an individual random variable satisfying a certain probabilistic distribution over a given interval. The purpose of the problem is to design an observer-based controller such that, for all possible degraded measurements, the closed-loop system is exponentially mean-square stable and strictly dissipative, while the individual steady-state variance is not more than the pre-specified upper bound constraints. A general framework is established so that the required exponential mean-square stability, dissipativity as well as the variance constraints can be easily enforced. A sufficient condition is given for the solvability of the addressed multiobjective control problem, and the desired observer and controller gains are characterized in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite programming method. Finally, a numerical example is presented to show the effectiveness and applicability of the proposed algorithm.This work was supported in part by the Distinguished Visiting Fellowship of the Royal Academy of Engineering of the UK, the Royal Society of the UK, the GRF HKU 7137/09E, the National Natural Science Foundation of China under Grant 61028008, the International Science and Technology Cooperation Project of China under Grant 2009DFA32050, and the Alexander von Humboldt Foundation of Germany