Stability Analysis of a Class of Nonlinear Fractional Differential Systems With Riemann-Liouville Derivative

Dear Editor,This letter investigates the stability of n-dimensional nonlinear fractional differential systems with Riemann-Liouville derivative.By using the Mittag-Leffler function,Laplace transform and the Gronwall-Bellman lemma,one sufficient condition is attained for the asymptotical stability of a class of nonlinear fractional differential systems whose order lies in(0,2).According to this theory,if the nonlinear term satisfies some conditions,then the stability condition for nonlinear fractional differential systems is the same as the ones for corresponding linear systems.Two examples are provided to illustrate the applications of our result.

TC-Fuse: A Transformers Fusing CNNs Network for Medical Image Segmentation

In medical image segmentation task,convolutional neural networks(CNNs)are difficult to capture long-range dependencies,but transformers can model the long-range dependencies effectively.However,transformers have a flexible structure and seldom assume the structural bias of input data,so it is difficult for transformers to learn positional encoding of the medical images when using fewer images for training.To solve these problems,a dual branch structure is proposed.In one branch,Mix-Feed-Forward Network(Mix-FFN)and axial attention are adopted to capture long-range dependencies and keep the translation invariance of the model.Mix-FFN whose depth-wise convolutions can provide position information is better than ordinary positional encoding.In the other branch,traditional convolutional neural networks(CNNs)are used to extract different features of fewer medical images.In addition,the attention fusion module BiFusion is used to effectively integrate the information from the CNN branch and Transformer branch,and the fused features can effectively capture the global and local context of the current spatial resolution.On the public standard datasets Gland Segmentation(GlaS),Colorectal adenocarcinoma gland(CRAG)and COVID-19 CT Images Segmentation,the F1-score,Intersection over Union(IoU)and parameters of the proposed TC-Fuse are superior to those by Axial Attention U-Net,U-Net,Medical Transformer and other methods.And F1-score increased respectively by 2.99%,3.42%and 3.95%compared with Medical Transformer.

Understanding the Predication Mechanism of Deep Learning through Error Propagation among Parameters in Strong Lensing Case

The error propagation among estimated parameters reflects the correlation among the parameters.We study the capability of machine learning of"learning"the correlation of estimated parameters.We show that machine learning can recover the relation between the uncertainties of different parameters,especially,as predicted by the error propagation formula.Gravitational lensing can be used to probe both astrophysics and cosmology.As a practical application,we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters(effective lens mass ML and Einstein radiusθ_(E))in accordance with the theoretical formula for the singular isothermal ellipse(SIE)lens model.The relation of errors of lens mass and Einstein radius,(e.g.,the ratio of standard deviations F=σ_(ML)/σ_(θ_(E)))predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model.As a proof-of-principle test,a toy model of linear relation with Gaussian noise is presented.We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise.Error propagation plays a crucial role in identifying the physical relation among parameters,rather than a coincidence relation,therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.

Anticorrosion Coatings from Poly(Aniline-co-2-Ethylaniline) Micro/Nanostructures

PANI copolymer micro/nanostructures with different surface wettability were obtained from the chemical oxidation copolymerization of aniline(Ani)with 2-ethyl aniline(EA)at diverse[EA]/[Ani+EA]molar ratios,by employing ammonium persulfate as an oxidant.The results revealed that the poly(aniline-co-2-ethyl aniline)(PANI-EA)copolymer micro/nanostructures exhibited satisfactory anticorrosion performance for carbon steel,and the corrosion protection efficiency increased with the increase of water repellent property.Poly(2-ethyl aniline)(PEA)showed the largest contact angle(CA=145°)and show the best corrosion protection for the carbon steel(h=87.29%).It is found that the superior anticorrosion property of PEA is attributed to its high hydrophobicity,low conductivity and low porosity.

Adaptive generalized projective synchronization of two different chaotic systems with unknown parameters

This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.

Two Contrary States of Human Soul

William Blake is a forerunner of the romantic poet of the 19th century. This paper tends to reveal the sharp contrast shown by poems in "Songs of Innocence" and "Songs of Experience". This may help people's understanding of what Blake said "the two contrary states of human soul."

Adaptive stabilization of an incommensurate fractional order chaotic system via a single state controller

In this paper, we investigate the stabilization of an incommensurate fractional order chaotic systems and propose a modified adaptive-feedback controller for the incommensurate fractional order chaos control based on the Lyapunov stability theory, the fractional order differential inequality and the adaptive control theory. The present controller, which only contains a single state variable, is simple both in design and in implementation. The simulation results for several fractional order chaotic systems are provided to illustrate the effectiveness of the proposed scheme.

The Existence of Positive Solutions of p-Laplacian Non-homogeneous Multi-point Boundary Value Problems

We study the following nonlinear m-point p-Laplacian boundary value problem with non-homogenous condition: (Φp(u′)′)+f(t, u, u′)=0, 0<t<1, u′(0)=0, u(1)-Σ m-2 i=1 kiu(ξi)=λ, where Φp(s)=|s|p-2 s, p>1, λ>0, ki≥0(i = 1, 2, ··· , m-2), 0<ξ1<ξ2< ··· <ξm-2<1,0 < Σm-2 i=1 ki<1. Under sufficient conditions, we show that there exists a positive number λ* such that the problem has at least one positive solution for 0 < λ < λ and no solution for λ > λ*. The proof is based on the Schauder fixed point theorem and upper-lower technics.

Adaptive lag synchronization and parameter identification of fractional order chaotic systems

This paper proposes a simple scheme for the lag synchronization and the parameter identification of fractional order chaotic systems based on the new stability theory. The lag synchronization is achieved and the unknown parameters are identified by using the adaptive lag laws. Moreover, the scheme is analytical and is simple to implement in practice. The well-known fractional order chaotic L/i system is used to illustrate the validity of this theoretic method.

Inverse problem of quadratic time-dependent Hamiltonians

Using an algebraic approach, it is possible to obtain the temporal evolution wave function for a Gaussian wavepacket obeying the quadratic time-dependent Hamiltonian(QTDH). However, in general, most of the practical cases are not exactly solvable, for we need general solutions of the Riccatti equations which are not generally known. We therefore bypass directly solving for the temporal evolution wave function, and study its inverse problem. We start with a particular evolution of the wave-packet, and get the required Hamiltonian by using the inverse method. The inverse approach opens up a new way to find new exact solutions to the QTDH. Some typical examples are studied in detail. For a specific timedependent periodic harmonic oscillator, the Berry phase is obtained exactly.

A single adaptive controller with one variable for synchronization of fractional-order chaotic systems

In this paper we investigate the synchronization of a class of three-dimensional fractional-order chaotic systems. Based on the Lyapunov stability theory and adaptive control technique, a single adaptive-feedback controller is developed to synchronize a class of fractional-order chaotic systems. The presented controller which only contains a single driving variable is simple both in design and in implementation. Numerical simulation and circuit experimental results for fractional-order chaotic system are provided to illustrate the effectiveness of the proposed scheme.

Adaptive synchronisation of fractional-order chaotic systems

A new stability theory of nonlinear dynamic systems is proposed, and a novel adaptive synchronisation method is presented for fractional-order chaotic and hyperchaotic systems based on the theory described in this paper. In comparison with previous methods, not only is the present control scheme simple but also it employs only one control strength, converges very fast, and it is also suitable for a large class of fractional-order chaotic and hyperchaotic systems. Moreover, this scheme is analytical and simple to implement in practice. Numerical and circuit simulations are used to validate and demonstrate the effectiveness of the method.

Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay

This paper is concerned with the adaptive synchronization of fractional-order complex-valued chaotic neural networks(FOCVCNNs)with time-delay.The chaotic behaviors of a class of fractional-order complex-valued neural network are investigated.Meanwhile,based on the complex-valued inequalities of fractional-order derivatives and the stability theory of fractional-order complex-valued systems,a new adaptive controller and new complex-valued update laws are proposed to construct a synchronization control model for fractional-order complex-valued chaotic neural networks.Finally,the numerical simulation results are presented to illustrate the effectiveness of the developed synchronization scheme.

Dynamic recombination of triplet excitons in polymer heterojunctions

The dynamic recombination of two triplet excitons with opposite spins in the heterojunction structure has been investigated using a nonadiabatic evolution method.We demonstrate that luminous composite states including the excited polaron and the biexciton can be formed efficiently via the triplet exciton-triplet exciton reaction in the heterojunction and therefore this reaction can enhance the electroluminescence efficiency considerably,which is consistent qualitatively with experimental observations.Meanwhile,we find that,although the heterojunctions are beneficial to the generation of luminescent particles,large band offset caused by the heterojunction structure is not helpful to improve the electroluminescence efficiency.In addition,the mechanism of the triplet exciton-triplet exciton reaction in heterojunction is different from that of two similar coupling chains.Our results may deepen the understanding of the electroluminescence mechanism in polymer light-emitting devices.

Biodiversity Sustainability Assessment of Principal Ecosystems in Hebei,China

Aiming at providing theoretical basis for effective protection of biodiversity, the study presents a cascade method which combines both qualitative and quantitative methods, incorporates basic data with RS（remote sense） technology, and ranks the ecosystems according to its ability of biodiversity sustainability in Hebei Province. The results indicate that the most important areas for protection in Hebei Province are forest and meadow ecosystems in some highlands around Xiaowutai Mountain, Wuling Mountain, North Hebei, Taihang Mountain and East Hebei; grass ecosystems in part of plateau area and North Hebei; and some scattered wetlands in the plain and inshore areas. This method is suitable for undertaking large-scale investigations especially when the data are not adequate or unevenly distributed spatially.

A phylogeny of the Passerida(Aves: Passeriformes)based on mitochondrial 12S ribosomal RNA gene

Background: Passerida is the largest avian radiation within the order Passeriformes. Current understanding of the high-level relationships within Passerida is based on DNA–DNA hybridizations; however, the phylogenetic relationships within this assemblage have been the subject of many debates.Methods: We analyzed the 12 S ribosomal RNA gene from 49 species of Passerida, representing 14 currently recognized families, to outline the phylogenetic relationships within this group.Results: Our results identified the monophyly of the three superfamilies in Passerida: Sylvioidea, Muscicapoidea and Passeroidea. However, current delimitation of some species is at variance with our phylogeny estimate. First, the Parus major, which had been placed as a distinct clade sister to Sylvioidea was identified as a member of the super family;second, the genus Regulus was united with the Sturnidae and nested in the Muscicapoidea clade instead of being a clade of Passerida.Conclusion: Our results were consistent with Johansson's study of the three superfamilies except for the al ocation of two families, Paridae and Regulidae.

Observe Chinese Culture from Chinese Idioms

Chinese idioms are the essence of the Chinese language, the crystallization of human wisdom and the important cartier of national culture. Through the structure, content and meaning of Chinese idioms, we can see various forms of the history and culture of the Han nationality. Observe national culture through the structure, content, meaning of Chinese idioms, namely the phenomenon of the linguistic phenomenon and culture phenomenon, we focus on elaborating Chinese idioms and cultural relationship between a Chinese idiom and Chinese culture.

Design and Application of English Learning System based on B/S Structure

This paper analyzes advantages and disadvantages of the current several popular computer-aided English learning software. combined with modem English teaching philosophy, proposed learning system with synchronization, interactivity, intelligence, and incentives in one of the English to students. System uses JavaEE framework to build, each module uses a low coupling between the way facilitate future extensions. The system can help students build confidence and motivate its progress.

Research on the coordination of the urbanization level and the economic development in China

At present, part of the local government officials who like to do grandiose things to impress people blindly promote the development of the real estate, resulting in the gap with the population migration, so many ghost towns are born. In addition, while building the local infrastructure of some of the districts, they also ignore the problem of the rational allocation of their own financial funds. Visibly, the implementation of the coordination between the two will help make China＇s urbanization level advancing in the health and right directions.