RICCATI-TYPE RESULT FOR MEROMORPHIC SOLUTIONS OF SYSTEMS OF COMPOSITE FUNCTIONAL EQUATIONS

By use of Nevanlinna value distribution theory,we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation,the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth.

Fast First-Order Methods for Minimizing Convex Composite Functions

Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.

Nonlinear vibration of functionally graded graphene platelet-reinforced composite truncated conical shell using first-order shear deformation theory

In this study,the first-order shear deformation theory(FSDT)is used to establish a nonlinear dynamic model for a conical shell truncated by a functionally graded graphene platelet-reinforced composite(FG-GPLRC).The vibration analyses of the FG-GPLRC truncated conical shell are presented.Considering the graphene platelets(GPLs)of the FG-GPLRC truncated conical shell with three different distribution patterns,the modified Halpin-Tsai model is used to calculate the effective Young’s modulus.Hamilton’s principle,the FSDT,and the von-Karman type nonlinear geometric relationships are used to derive a system of partial differential governing equations of the FG-GPLRC truncated conical shell.The Galerkin method is used to obtain the ordinary differential equations of the truncated conical shell.Then,the analytical nonlinear frequencies of the FG-GPLRC truncated conical shell are solved by the harmonic balance method.The effects of the weight fraction and distribution pattern of the GPLs,the ratio of the length to the radius as well as the ratio of the radius to the thickness of the FG-GPLRC truncated conical shell on the nonlinear natural frequency characteristics are discussed.This study culminates in the discovery of the periodic motion and chaotic motion of the FG-GPLRC truncated conical shell.

“Toolbox”for the Processing of Functional Polymer Composites

Functional polymer composites(FPCs)have attracted increasing attention in recent decades due to their great potential in delivering a wide range of functionalities.These functionalities are largely determined by functional fillers and their network morphology in polymer matrix.In recent years,a large number of studies on morphology control and interfacial modification have been reported,where numerous preparation methods and exciting performance of FPCs have been reported.Despite the fact that these FPCs have many similarities because they are all consisting of functional inorganic fillers and polymer matrices,review on the overall progress of FPCs is still missing,and especially the overall processing strategy for these composites is urgently needed.Herein,a"Toolbox"for the processing of FPCs is proposed to summarize and analyze the overall processing strategies and corresponding morphology evolution for FPCs.From this perspective,the morphological control methods already utilized for various FPCs are systematically reviewed,so that guidelines or even predictions on the processing strategies of various FPCs as well as multi-functional polymer composites could be given.This review should be able to provide interesting insights for the field of FPCs and boost future intelligent design of various FPCs.

A Mini-review for the Application of Bacterial Cellulose-based Composites

Countries are duly focusing more on biomass resources because of the increasing oil crisis.Owing to their excellent properties,such as natural characteristics,good mechanical performance,and outstanding chemical properties,cellulose-based materials are highly valued as promising bioderived nanomaterials,especially bacterial cellulose(BC).The main advantage lies in eliminating the problem of removing lignin and hemicellulose from woody cellulose.Moreover,the use of BC reduces the consumption of wood,the excessive use of which aggravates global warming.Herein,we summarize the applications of BC composites in filter,medical,and conductive materials,and other fields.This review contributes to further expand the applications of this renewable polymer.

Vibration characteristics of piezoelectric functionally graded carbon nanotube-reinforced composite doubly-curved shells

This paper presents an analytical solution for the free vibration behavior of functionally graded carbon nanotube-reinforced composite(FG-CNTRC) doubly curved shallow shells with integrated piezoelectric layers. Here, the linear distribution of electric potential across the thickness of the piezoelectric layer and five different types of carbon nanotube(CNT) distributions through the thickness direction are considered. Based on the four-variable shear deformation refined shell theory, governing equations are obtained by applying Hamilton's principle. Navier's solution for the shell panels with the simply supported boundary condition at all four edges is derived. Several numerical examples validate the accuracy of the presented solution. New parametric studies regarding the effects of different material properties, shell geometric parameters, and electrical boundary conditions on the free vibration responses of the hybrid panels are investigated and discussed in detail.

Plant functional trait diversity and structural diversity co-underpin ecosystem multifunctionality in subtropical forests

Tree species diversity is assumed to be an important component in managing forest ecosystems because of effects on multiple functions or ecosystem multifunctionality.However,the importance of tree diversity in determining multifunctionality in structurally complex subtropical forests relative to other regulators(e.g.,soil microbial diversity,stand structure,and environmental conditions)remains uncertain.In this study,effects of aboveground(species richness and functional and structural diversity)and belowground(bacterial and fungal diversity)biodiversity,functional composition(community-weighted means of species traits),stand structure(diameter at breast height and stand density),and soil factors(pH and bulk density)on multifunctionality(including biomass production,carbon stock,and nutrient cycling)were examined along a tree diversity gradient in subtropical forests.The community-weighted mean of tree maximum height was the best predictor of ecosystem multifunctionality.Functional diversity explained a higher proportion of the variation in multifunctionality than that of species richness and fungal diversity.Stand structure-played an important role in modulating the effects of tree diversity on multifunctionality.The work highlights that species composition and maximizing forest structural complexity are effective strategies to increase forest multifunctionality while also conserving biodiversity in the management of multifunctional forests under global environmental changes.

Isogeometric nonlocal strain gradient quasi-three-dimensional plate model for thermal postbuckling of porous functionally graded microplates with central cutout with different shapes

This study presents the size-dependent nonlinear thermal postbuckling characteristics of a porous functionally graded material(PFGM) microplate with a central cutout with various shapes using isogeometric numerical technique incorporating nonuniform rational B-splines. To construct the proposed non-classical plate model, the nonlocal strain gradient continuum elasticity is adopted on the basis of a hybrid quasithree-dimensional(3D) plate theory under through-thickness deformation conditions by only four variables. By taking a refined power-law function into account in conjunction with the Touloukian scheme, the temperature-porosity-dependent material properties are extracted. With the aid of the assembled isogeometric-based finite element formulations,nonlocal strain gradient thermal postbuckling curves are acquired for various boundary conditions as well as geometrical and material parameters. It is portrayed that for both size dependency types, by going deeper in the thermal postbuckling domain, gaps among equilibrium curves associated with various small scale parameter values get lower, which indicates that the pronounce of size effects reduces by going deeper in the thermal postbuckling regime. Moreover, we observe that the central cutout effect on the temperature rise associated with the thermal postbuckling behavior in the presence of the effect of strain gradient size and absence of nonlocality is stronger compared with the case including nonlocality in absence of the strain gradient small scale effect.

Couple stress-based nonlinear primary resonant dynamics of FGM composite truncated conical microshells integrated with magnetostrictive layers

The size-dependent geometrically nonlinear harmonically soft excited oscillation of composite truncated conical microshells(CTCMs)made of functionally graded materials(FGMs)integrated with magnetostrictive layers is analyzed.It is supposed that the FGM CTCMs are subjected to mechanical soft excitations together with external magnetic fields.An analytical framework is created by a microstructuredependent shell model having the 3rd-order distribution of shear deformation based on the modified couple stress(MCS)continuum elasticity.With the aid of the discretized form of differential operators developed via the generalized differential quadrature technique,a numerical solution methodology is introduced for obtaining the couple stress-based amplitude and frequency responses related to the primary resonant dynamics of the FGM CTCMs.Jump phenomena due to the loss of the first stability branch and falling down to the lower stable branch can be seen in the nonlinear primary resonance of the FGM CTCMs.It is demonstrated that the hardening type of nonlinearity results in bending the frequency response to the right side,and the MCS type of size effect weakens this pattern.Moreover,for higher material gradient indexes,the hardening type of nonlinearity is enhanced,and the MCS-based frequency response bends more considerably to the right side.

Conformal Human–Machine Integration Using Highly Bending‑Insensitive,Unpixelated,and Waterproof Epidermal Electronics Toward Metaverse

Efficient and flexible interactions require precisely converting human intentions into computer-recognizable signals,which is critical to the breakthrough development of metaverse.Interactive electronics face common dilemmas,which realize highprecision and stable touch detection but are rigid,bulky,and thick or achieve high flexibility to wear but lose precision.Here,we construct highly bending-insensitive,unpixelated,and waterproof epidermal interfaces(BUW epidermal interfaces)and demonstrate their interactive applications of conformal human–machine integration.The BUW epidermal interface based on the addressable electrical contact structure exhibits high-precision and stable touch detection,high flexibility,rapid response time,excellent stability,and versatile“cut-and-paste”character.Regardless of whether being flat or bent,the BUW epidermal interface can be conformally attached to the human skin for real-time,comfortable,and unrestrained interactions.This research provides promising insight into the functional composite and structural design strategies for developing epidermal electronics,which offers a new technology route and may further broaden human–machine interactions toward metaverse.

A Model of Fuzzy Normal Distribution

Nowadays fuzzy concepts are frequently used as statistical parameters, while the traditional normal distribution can only accept determinate variable. In order to design a practical model for fuzzy statistic events, this paper combines the fuzzy number, like “may-occur”, “very-likely-occur”, “rarely-occur”, to optimize the normal distribution probability density function, to provide a significant method in statistics.

Superior anti-corrosion and self-healing bi-functional polymer composite coatings with polydopamine modified mesoporous silica/graphene oxide

In this article,graphene oxide(GO)and benzotriazole-loaded mesoporous silica nanoparticles(BTA/MSNs)are combined on micro scale through the in situ polymerization of polydopamine(PDA),preparing a selfhealing bi-functional GO(fGO)used as nano-fillers for anti-corrosion enhancement of waterborne epoxy(WEP)coatings.Scanning electronic microscopy(SEM)images show that the BTA/MSNs are uniformly distributed on the surface of high aspect ratio GO nanosheets to endow GO nanocontainer characteristics.UV-vis profiles demonstrate that fGO has p H-controlled release function.Modulus at lowest frequency is generally used for comparing the corrosion resistance of organic coatings.Modulus at lowest frequency(1.42×10^(5)Ωcm^(2))after 30 days immersion in 3.5 wt.%Na Cl solution revealed 2 orders of magnitude higher that of blank WEP(1.17×10^(7)Ωcm^(2)).With artificial cracks on its coatings,fGO/WEP had no obvious rust compared with blank WEP after 240 h of immersion.We anticipate that self-healing and physical barrier bi-functional nanocontainers improve the traditional anticorrosion coating efficiency with better,longer-lasting performance for shipping,oil drilling or bridge maintenance.

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control(AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance.To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control(ILC), a new boundary layer function is proposed by employing MittagLeffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function(CEF)containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Analytical transient phase change heat transfer model of wearable electronics with a thermal protection substrate

As thermal protection substrates for wearable electronics,functional soft composites made of polymer materials embedded with phase change materials and metal layers demonstrate unique capabilities for the thermal protection of human skin.Here,we develop an analytical transient phase change heat transfer model to investigate the thermal performance of a wearable electronic device with a thermal protection substrate.The model is validated by experiments and the finite element analysis(FEA).The effects of the substrate structure size and heat source power input on the temperature management efficiency are investigated systematically and comprehensively.The results show that the objective of thermal management for wearable electronics is achieved by the following thermal protection mechanism.The metal thin film helps to dissipate heat along the in-plane direction by reconfiguring the direction of heat flow,while the phase change material assimilates excessive heat.These results will not only promote the fundamental understanding of the thermal properties of wearable electronics incorporating thermal protection substrates,but also facilitate the rational design of thermal protection substrates for wearable electronics.

Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic Equations

A novel canonical Euler splitting method is proposed for nonlinear compositestiff functional differential-algebraic equations, the stability and convergence of themethod is evidenced, theoretical results are further confirmed by some numerical experiments.Especially, the numerical method and its theories can be applied to specialcases, such as delay differential-algebraic equations and integral differential-algebraicequations.

A deep feed-forward neural network for damage detection in functionally graded carbon nanotube-reinforced composite plates using modal kinetic energy

This paper proposes a new Deep Feed-forward Neural Network(DFNN)approach for damage detection in functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.In the proposed approach,the DFNN model is developed based on a data set containing 20000 samples of damage scenarios,obtained via finite element(FE)simulation,of the FG-CNTRC plates.The elemental modal kinetic energy(MKE)values,calculated from natural frequencies and translational nodal displacements of the structures,are utilized as input of the DFNN model while the damage locations and corresponding severities are considered as output.The state-of-the art Exponential Linear Units(ELU)activation function and the Adamax algorithm are employed to train the DFNN model.Additionally,in order to enhance the performance of the DFNN model,the mini-batch and early-stopping techniques are applied to the training process.A trial-and-error procedure is implemented to determine suitable parameters of the network such as the number of hidden layers and the number of neurons in each layer.The accuracy and capability of the proposed DFNN model are illustrated through two distinct configurations of the CNT-fibers constituting the FG-CNTRC plates including uniform distribution(UD)and functionally graded-V distribution(FG-VD).Furthermore,the performance and stability of the DFNN model with the consideration of noise effects on the input data are also investigated.Obtained results indicate that the proposed DFNN model is able to give sufficiently accurate damage detection outcomes for the FG-CNTRC plates for both cases of noise-free and noise-influenced data.

Strain heterogeneity,cooccurrence network,taxonomic composition and functional profile of the healthy ocular surface microbiome

Background:There is growing evidence indicating that the microbial communities that dwell on the human ocular surface are crucially important for ocular surface health and disease.Little is known about interspecies interactions,functional profiles,and strain heterogeneity across individuals in healthy ocular surface microbiomes.Methods:To comprehensively characterize the strain heterogeneity,cooccurrence network,taxonomic composition and functional profile of the healthy ocular surface microbiome,we performed shotgun metagenomics sequencing on ocular surface mucosal membrane swabs of 17 healthy volunteers.Results:The healthy ocular surface microbiome was classified into 12 phyla,70 genera,and 140 species.The number of species in each healthy ocular surface microbiome ranged from 6 to 47,indicating differences in microbial diversity among individuals.The species with high relative abundances and high positivity rates were Streptococcus pyogenes,Staphylococcus epidermidis,Propionibacterium acnes,Corynebacterium accolens,and Enhydrobacter aerosaccus.A correlation network analysis revealed a competitive interaction of Staphylococcus epidermidis with Streptococcus pyogenes in ocular surface microbial ecosystems.Staphylococcus epidermidis and Streptococcus pyogenes revealed phylogenetic diversity among different individuals.At the functional level,the pathways related to transcription were the most abundant.We also found that there were abundant lipid and amino acid metabolism pathways in the healthy ocular surface microbiome.Conclusion:This study explored the strain heterogeneity,cooccurrence network,taxonomic composition,and functional profile of the healthy ocular surface microbiome.These findings have important significance for the future development of probiotic-based eye therapeutic drugs.

Development and applications of functional gene microarrays in the analysis of the functional diversity,composition,and structure of microbial communities

Functional gene arrays(FGAs)are a special type of microarrays containing probes for key genes involved in microbial functional processes,such as biogeochemical cycling of carbon,nitrogen,sulfur,phosphorus,and metals,biodegradation of environmental contaminants,energy processing,and stress responses.GeoChips are considered as the most comprehensive FGAs.Experimentally established probe design criteria and a computational pipeline integrating sequence retrieval,probe design and verification,array construction,data analysis,and automatic update are used to develop the GeoChip technology.GeoChip has been systematically evaluated and demonstrated to be a powerful tool for rapid,specific,sensitive,and quantitative analysis of microbial communities in a high-throughput manner.Several generations of GeoChip have been developed and applied to investigate the functional diversity,composition,structure,function,and dynamics of a variety of microbial communities from different habitats,such as water,soil,marine,bioreactor,human microbiome,and extreme ecosystems.GeoChip is able to address fundamental questions related to global change,bioenergy,bioremediation,agricultural operation,land use,human health,environmental restoration,and ecological theories and to link the microbial community structure to environmental factors and ecosystem functioning.

Using functional trait diversity to infer community assembly mechanisms:an exclosure experiment as an example

Aims The Qinghai-Tibetan Plateau has a mean altitude exceeding 4000 m and covers about 2.5 million km2.More than 60%of this area is alpine grassland.Exclosures have been widely used in this region to study the sustainable use of grassland resources.We used patterns of functional trait diversity to infer the effects of exclosures on com-munity assembly in alpine meadows.Methods We studied functional diversity using five traits under grazing and three enclosed(exclosure)plots(3,8,and 18 years old)in an alpine meadow on the Qinghai-Tibetan Plateau.We quantified the strength of the community assembly processes by comparing the observed functional trait diversity with a null model that assumes random community assembly.Important findings We found evidence for deterministic assembly processes for plant communities in exclosures.The changes in CWM of the five traits from grazing land to 18-year exclosure indicated that environmen-tal filtering occurred due to the exclosures.Multivariate functional diversity(MFDis and MPDses),and functional diversity of individual traits,including that of leaf area,leaf weight and aboveground bio-mass(FDis of leaf area,leaf weight,and aboveground biomass),increased gradually from grazing land to the 18-year exclosure,and the values of the 18-year exclosure were significantly greater than null expectation.This can be interpreted to indicate that exclosures resulted in greater competitive interaction between species.These results suggest that the effect of exclosures on community assembly is more deterministic than stochastic in this meadow.

Dielectric Properties of SiC_f/PyC/SiC Composites After Oxidation

In this paper,the SiC fiber-reinforced SiC matrix composites with a 0.15μm thick pyrocarbon interphase(noted as SiC/PyC/SiC) were prepared by chemical vapor infiltration(CVI).The SiCf/PyC/SiC were oxidized in air at950 "C for 50 h.The dielectric properties after this high temperature oxidation were investigated in X-band from room temperature(RT) to 700℃.Results suggested that:ε′ of the SiC_f/PyC/SiC after oxidation increased at first then decreased with temperature elevating;ε″ increased with temperature raising in the temperature range studied.