ON MEROMORPHIC SOLUTIONS OF A TYPE OF SYSTEM OF COMPOSITE FUNCTIONAL EQUATIONS

In this article, we mainly investigate the growth and existence of meromorphic solutions of a type of systems of composite functional equations, and obtain some interesting results. It extends some results concerning functional equations to the systems of functional equations.

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.

ON MATRIX AND DETERMINANT IDENTITIES FOR COMPOSITE FUNCTIONS

We present some matrix and determinant identities for the divided differences of the composite functions, which generalize the divided difference form of Faa di Bruno＇s formula. Some recent published identities can be regarded as special cases of our results.

EXTENDED LEVENBERG-MARQUARDT METHOD FOR COMPOSITE FUNCTION MINIMIZATION

In this paper, we propose an extended Levenberg-Marquardt （ELM） framework that generalizes the classic Levenberg-Marquardt （LM） method to solve the unconstrained minimization problem min ρ（r（x））, where r ： Rn→ Rm and ρ ： Rm → R. We also develop a few inexact variants which generalize ELM to the cases where the inner subproblem is not solved exactly and the Jaeobian is simplified, or perturbed. Global convergence and local superlinear convergence are established under certain suitable conditions. Numerical results show that our methods are promising.

Centrifugal casting processes of manufacturing in situ functionally gradient composite materials of Al-19Si-5Mg alloy

Cylindrical components of in situ functionally gradient composite materials of Al-19Si-5Mg alloy were manufactured by centrifugal casting. Microstructure characteristics of the manufactured components were observed and the effects of the used process factors on these characteristics were analyzed. The results of observations shows that, in thickness, the components possess microstructures accumulating lots of Mg2Si particles and a portion of primary silicon particles in the inner layer, a little MgzSi and primary silicon particles in the outer layer, and without any Mg2Si and primary silicon particle in the middle layer. The results of the analysis indicate that the rotation rate of centrifugal casting, mould temperature, and melt pouring temperature have evidently affected the accumulation of the second phase particles. Also, the higher the centrifugal rotation rate, mould temperature, and melt pouring temperature are, the more evident in the inner layer the degree of accumulation of Mg2Si and primary silicon particles is.

Characteristics of two Al based functionally gradient composites reinforced by primary Si particles and Si/in situ Mg_2Si particles in centrifugal casting

Two kinds of Al based functionally gradient composite tubes reinforced by primary Si particles alone and primary Si/in situ Mg2Si particles jointly were successfully prepared by centrifugal casting,and their structural and mechanical characters were compared.It is found that the composite reinforced with primary Si particles takes a characteristic of particles distribution both in the inner and outer layers.However,composite reinforced with primary Si/Mg2Si particles jointly takes a characteristic of particles distribution only in the inner layer and shows a sudden change of particles distribution across the section of inner and outer layers.The hardness and wear resistance of Al-19Si-5Mg tube in the inner layer are greatly higher than that in the other layers of Al-19Si-5Mg tube and Al-19Si tube.Theoretical analysis reveals that the existence of Mg2Si particles is the key factor to form this sudden change of gradient distribution of two kinds of particles.Because Mg2Si particles with a lower density have a higher centripetal moving velocity than primary Si particles,in a field of centrifugal force,they would collide with primary Si particles and then impel the later to move together forward to the inner layer of the tube.

Development of functionally graded aluminium composites using centrifugal casting and influence of reinforcements on mechanical and wear properties

Functionally graded Al/B_4C, Al/Si C, Al/Al_2O_3 and Al/TiB_2 composites with constant 12%(mass fraction) of reinforcement were fabricated by centrifugal casting and hollow cylindrical components were obtained. Microstructural characteristics were investigated at outer surface of all composites and segregation of reinforcement particles was observed. Graded property of the composites with different reinforcements was investigated through hardness and tensile measurements. Results revealed that the outer peripheries of all composites exhibit higher hardness except in Al/B_4C composite and the outer zones of all composites show higher tensile strength. Abrasive wear test was conducted on the outer peripheries of all composites and Al/TiB_2 composite exhibits less wear rate.

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.

Characterization of aluminum based functionally graded composites developed via friction stir processing

Al/SiC functionally graded material(FGM) was developed through a novel multi-step friction stir processing(FSP) method. Si C particles with a mean size of 27.5 μm were embedded in the groove on the 6082-Al plate. To create a graded structure over a predefined value, FSP was carried out with three tools with different pin lengths and with varying volume fractions of SiC particles. The structure was formed by passing tools with 1-3 passes with a constant rotational and traveling speeds of 900 r/min and 20 mm/min, respectively. The experiments were conducted at room temperature. Microstructural features of functionally graded(FG) samples were examined by using scanning electron microscopy(SEM) and 3D light microscopy. Mechanical properties in terms of wear resistance and microhardness were thoroughly assessed. The results indicate that the increase in FSP pass number causes more uniform SiC particle dispersion. The microhardness values were impacted by the number of passes and improved by 51.54% for Pass 3 when compared to as-received 6082-Al. Wear resistance of Al/SiC FG samples was found to increase as a result of the addition of SiC particles.

Co-electrodeposition and properties evaluation of functionally gradient nickel coated ZrO_2 composite coating

For the first time,functionally electroless nickel plated ZrO2(NCZ)graded Ni-NCZ composite coating has been successfully co-electrodeposited from a bath with gradually increasing of stirring rate.Studies showed that co-electrodeposition in a bath with stirring rate of250r/min results in the maximum co-electrodeposited particle content and the best particle distribution.To produce NCZ graded Ni-NCZ composite coating,the stirring rate was continuously increased from0to250r/min.The electroplated coating had a continuous gradient increasing of co-electrodeposited NCZ content from substrate towards the surface.The results showed that with increasing the co-electrodeposited NCZ particles content in Ni matrix,microhardness increases from interface towards the surface of the coating.Little crystallite size of Ni matrix and higher co-electrodeposited hard particles content were recognized as the reasons of microhardness increasing.Bend test revealed that the functionally graded composite coating shows more excellent adhesion to the substrate compared with the ordinary distributed Ni-NCZ on the same substrate.This result is attributed to lower mechanical mismatch between coating and substrate in the functionally graded composite coating with respect to the uniformly distributed one.The results of wear resistance measurements reveal that wear resistance of functionally graded Ni-NCZ is higher than that of ordinary distributed composite coating.

“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.

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.

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.

Density Functional Theory of Composite Fermions

We construct a density functional theory for two-dimensional electron （hole） gases subjected to both strong magnetic fields and external potentials. In particular, we are focused on regimes near even-denominator filling factors, in which the systems form composite fermion liquids. Our theory provides a systematic and rigorous approach to determine the properties of ground states in a fractional quantum Hall regime that is modified by artificial structures. We also propose a practical way to construct an approximated functional.

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.

Surface Functionalized Carbon Nanofibers and Their Effect on the Dispersion and Tribological Property of Epoxy Nanocomposites

Surface functionalization of carbon nanofibers（CNFs） was carried out, i e, CNFs were firstly oxidized and then the surface was silanized by 3-Aminopropyltriethoxysilane（APTES） via an assembly method. A new kind of high wear resistance s-CNFs/epoxy composite was fabricated by in-situ reaction. FTIR spectroscopy was used to detect the changes of the functional groups produced by silane on the surface of CNFs. The tribological properties and microstructures of modified and unmodified CNFs/epoxy composites were studied, respectively. The expremental results indicate that APTES is covalently linked to the surface of CNFs successfully and improves the dispersion of CNF in epoxy matrix. The friction coefficients and the wear rates of s-CNFs/epoxy composites are evidently lower than those of u-CNFs/epoxy composites under the same loads. Investigations also indicate that abrasive wear is the main wear mechanism for u-CNFs/epoxy composite, with slight adhesive wear for s-CNFs/epoxy composite under the same sliding wear condition.

The effect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates

The purpose of the present study is to examine the impact of initial geometric imperfection on the nonlinear dynamical characteristics of functionally graded carbon nanotube-reinforced composite(FG-CNTRC) rectangular plates under a harmonic excitation transverse load. The considered plate is assumed to be made of matrix and single-walled carbon nanotubes(SWCNTs). The rule of mixture is employed to calculate the effective material properties of the plate. Within the framework of the parabolic shear deformation plate theory with taking the influence of transverse shear deformation and rotary inertia into account, Hamilton’s principle is utilized to derive the geometrically nonlinear mathematical formulation including the governing equations and corresponding boundary conditions of initially imperfect FG-CNTRC plates. Afterwards, with the aid of an efficient multistep numerical solution methodology, the frequency-amplitude and forcing-amplitude curves of initially imperfect FG-CNTRC rectangular plates with various edge conditions are provided, demonstrating the influence of initial imperfection,geometrical parameters, and edge conditions. It is displayed that an increase in the initial geometric imperfection intensifies the softening-type behavior of system, while no softening behavior can be found in the frequency-amplitude curve of a perfect plate.

The Influence of Plant Diversity and Functional Composition on Ecosystem Stability of Four Stipa Communities in the Inner Mongolia Plateau

The main purpose of this study was to examine the effects of plant species diversity and functional composition (the identity of the plant functional groups) on ecosystem stability of Stipa, communities in the Inner Mongolia Plateau. The research work was based on a 12-year study (from 1984 to 1995) of species abundance, diversity, and primary productivity of four Stipa communities, i.e. S. baicalensis Roshev., S. grandis P. Smirn., S, krylovii Roshev., and S. klemenzii Roshev. respectively. The Shnnon-Wiener index was used as a measurement of plant diversity, while functional composition was used to differentiate the functional groups that were included in the communities. The plant species of four Stipa communities were classified into functional groups based on the differences in life forms and ecological groups, which influence their performance in resource requirements, seasonality of growth, tolerance to water stress, and life history. Plant species were classified into five functional groups based on their differences in life form, shrubs and half shrubs, perennial bunch grasses, perennial rhizome grasses, forbs, annuals and biennials. Based on their differences in water requirement these species were classified into four functional groups: xerads, intermediate xerads, intermediate mesophytes, and mesophytes. The results showed: 1) Plant species diversity stabilized ecosystem processes. Shannon-Wiener index were 2.401 4, 2.172 0, 1.624 8, 0.354 3 from S. baicalensis community to S. grandis, S. krylovii and S. klemenzii community, respectively. The dynamics of the aboveground net primary productivity (ANPP) for a 12-year's period showed a reverse pattern, the coefficients of variation of the four communities were 21.94%, 20.63%, 29.21% and 39.72% respectively. 2) The Life form functional group component of diversity was a greater determinant of the ecosystem processes than the species component of diversity. The effects of perennial bunch grasses, perennial rhizome grasses and forbs on community stability were highly significant. 3) The ecological group component of diversity was also a great determinant of the ecosystem processes. The effects of xerads, intermediate xerads, and mesophytes on community stability were also very strong.

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.