Complex Function Approximation Based on Multi-ANN Approach

This paper presents a multi-ANN approximation approach to approximate complex non-linear function. Comparing with single-ANN methods the proposed approach improves and increases the approximation and generalization ability, and adaptability greatly in learning processes of networks. The simulation results have been shown that the method can be applied to the modeling and identification of complex dynamic control systems.

A Comparative Analysis of Syntactic Complexity in Applied Linguistics Abstracts Written by Chinese Novice Writers and Native English Advanced Writers

The rhetorical structure of abstracts has been a widely discussed topic, as it can greatly enhance the abstract writing skills of second-language writers. This study aims to provide guidance on the syntactic features that L2 learners can employ, as well as suggest which features they should focus on in English academic writing. To achieve this, all samples were analyzed for rhetorical moves using Hyland’s five-rhetorical move model. Additionally, all sentences were evaluated for syntactic complexity, considering measures such as global, clausal and phrasal complexity. The findings reveal that expert writers exhibit a more balanced use of syntactic complexity across moves, effectively fulfilling the rhetorical objectives of abstracts. On the other hand, MA students tend to rely excessively on embedded structures and dependent clauses in an attempt to increase complexity. The implications of these findings for academic writing research, pedagogy, and assessment are thoroughly discussed.

Performance study of a complex thermal barrier functional coating with an electro-spark deposited burn-resistant layer

It is necessary to develop burn-resistant and thermal barrier complex functional coatings on the titanium alloys surface due to the poor high temperature performance for titanium materials and the problem of“titanium fire”which is easily happened.MTU Aero Engines GmbH has developed a complex functional coating which has great performance of burn resistant and sealing,the coatings has already been applied on compressor blades and casing for aero-engines and showed great performance.In this study,the complex functional coating which is composed of an electro-spark deposited amorphous Ti40Zr25Ni3 burn-resistant layer and a high-energy plasma spraying prepared YSZ thermal barrier layer was prepared on titanium alloys surface.Then the heat insulation ability,burn resistant performance and the bonding strength were investigated.The experimental results showed that the interface between the coating and the matrix was typical metallurgical bonded,and the average bonding strength was 36.335 MPa;when the temperature of the flame on the one side of the specimen reached 600℃,the average insulated temperature of the coating samples was 70.67℃;when the flame temperature was 350℃,the titanium samples without the complex functional coatings were burned,while the samples with the coating showed great performance of burn resistant even when the temperature was 750℃.This indicates that the new functional coating has good heat-insulating and burn-resistant performance.

Density Functional Theory Study on La Complex with Schiff-base as Building Block

Quantum density functional theory （DFT） results are reported for the building block [LaL^1（NO3）] of La complex [LaL^1（NO3）]NO3·5H2O （L^1 = （CH3）2CHCH2CH（NCHC4H3O）COO^-）. The structure was optimized and the calculation results show that the lanthanum ion is coordinated by one nitrogen atom and three oxygen atoms of L^1 and two oxygen atoms of nitrate ion. The bond length of La-N is 0.2637 nm and the average length of La-O is 0.2526 nm, which are consistent with the literatures. In addition, the stabilities, electronic structural characteristics and IR spectra of the complex have been analyzed, which describe the coordination of lanthanum ion with other atoms in detail.

Resolution of Grandi’s Paradox as Extended to Complex Valued Functions

Grandi’s paradox, which was posed for a real function of the form 1/(1+ x), has been resolved and extended to complex valued functions. Resolution of this approximately three-hundred-year-old paradox is accomplished by the use of a consistent truncation approach that can be applied to all the series expansions of Grandi-type functions. Furthermore, a new technique for improving the convergence characteristics of power series with alternating signs is introduced. The technique works by successively averaging a series at different orders of truncation. A sound theoretical justification of the successive averaging method is demonstrated by two different series expansions of the function 1/(1+ ex ) . Grandi-type complex valued functions such as 1/(i + x) are expressed as consistently-truncated and convergence-improved forms and Fagnano’s formula is established from the series expansions of these functions. A Grandi-type general complex valued function is introduced and expanded to a consistently truncated and successively averaged series. Finally, an unorthodox application of the successive averaging method to polynomials is presented.

Function of Rural Settlement Complex Ecosystem in Mountain Area:A Case Study of Raosi Village of Zuogong County,Tibet

Using energy analysis,the quantifying evaluation and study method on production, living and ecology functions and their sustainability of rural settlement ecosystem in mountain area is established with these energy index such as export of labor and products, export of water resource, internal energy reserve, energy consumption for human living, net energy of ecosystem function and net internal reserve. Taking rural settlement Raosi Village in Hengduan Mountains as a case study, and on the basis of the synthetic research into the ecological process of the complex ecosystem, the study shows that energy costs of production, human living and ecology functions are separately taking 1.36%, 13.59% and 85. 05% of the gross ecosystem functions, and the exertions of production and human living functions are close to a high-point state on the present using level of energy in the settlement. The study also shows that the most important function of a rural settlement in mountain area is its ecological rather productive function.

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization （FPS） in drive–response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.

Density Functional Studies on Isonicotinato Lead(II) Complex [Pb(C_5H_4NCOO)_2]

The title compound of isonicotinato lead（Ⅱ） [Pb（C5H4NCOO）2] has been optimized at B3LYP/LANL2DZ level of theory and calculated results show that the lead（Ⅱ） ion adopts 4-coordinate geometry. Atomic charge distributions indicate that during forming the title compound, each isonicotinic acid ion transfers -0.452 e to lead（Ⅱ） ion. The electronic spectra calculations show that there exist two absorption bands and the electronic transitions are mainly derived from the contribution of intraligand π→π^＊ transition and ligand-to-metal charge transfer （LMCT） transition. The thermodynamic properties of the title compound at different temperatures have been calculated and corresponding relations between property and temperature have also been obtained. The calculation of the second order optical nonlinearity was carried out, and the molecular hyperpolarizability was 3.62365^＊10^-30 esu.

Preparation and Characterization of Carboxyl Functionalized Fluorescent Mesoporous Silica Nanoparticles Containing 8-Hydroxyquinolinate Zinc Complexes

Fluorescent mesoporous silica nanoparticles functionalized with carboxyl group(Znq-CMSCOOH) were successfully synthesized by in situ formation route of 8-hydroxyquinolinate zinc complexes in channels of mesoporous silica nanoparticles and post-grafting of carboxyl group on the surface. Moreover,the particle size and structural properties of Znq-CMS-COOH were characterized by transmission electron microscopy(TEM),field emission scanning electron microscopy(FE-SEM),dynamic light scattering(DLS),Fourier transform infrared spectroscopy(FT-IR),UV-vis spectrometer, fluorescence spectrometer and nitrogen adsorption-desorption measurements. The obtained results suggest that the Znq-CMS-COOH presents the uniform spherical shape with the mean diameter of about 85 nm and the obvious wormhole arrangement mesoporous. In addition, the Znq-CMS-COOH possesses green fluorescence with the emission peaks at 495 nm. So the Znq-CMS-COOH, which is beneficial to further modification and tracing, might be a great potential carrier for applying in drug delivery system in the future.

Modified Function Projective Synchronization of Complex Networks with Multiple Proportional Delays

This paper deals with the modified function projective synchronization problem for general complex networks with multiple proportional delays. With the existence of multiple proportional delays, an effective hybrid feedback control is designed to attain modified function projective synchronization of networks. Numerical example is provided to show the effectiveness of our result.

CONSTRUCTION SPACE HARMONIC FUNCTIONS IN POLYN0MIAL FORM AND SPHERICAL FUNCTIONS BY COMPLEX-FUNCTIONAL

In this paper, applying the theory of complex-functional, not only the spaceharmonic functions in polynomial form. but aIso the spherical functions are obtained.

SOME PROPERTIES OF HOLOMORPHIC CLIFFORDIAN FUNCTIONS IN COMPLEX CLIFFORD ANALYSIS

In this article, we mainly develop the foundation of a new function theory of several complex variables with values in a complex Clifford algebra defined on some subdomains of C^n＋l, so-called complex holomorphic Cliffordian functions. We define the complex holomorphic Cliffordian functions, study polynomial and singular solutions of the equation D△^mf= 0, obtain the integral representation formula for the complex holo-morphic Cliffordian functions with values in a complex Clifford algebra defined on some submanifolds of C^n＋1, deduce the Taylor expansion and the Laurent expansion for them and prove an invariance under an action of Lie group for them.

SPACES OF ANALYTIC FUNCTIONS REPRESENTED BY DIRICHLET SERIES OF TWO COMPLEX VARIABLES

We consider the space X of all analytic functionsof two complex variables s1 and s2, equipping it with the natural locally convex topology and using the growth parameter, the order of f as defined recently by the authors. Under this topology X becomes a Frechet space Apart from finding the characterization of continuous linear functionals, linear transformation on X, we have obtained the necessary and sufficient conditions for a double sequence in X to be a proper bases.

MEASURING OF COMPLEX STRUCTURE TRANSFER FUNCTION AND CALCULATING OF INNER SOUND FIELD

In order to measure complex structure transfer function and calculate inner sound field, transfer function of integration is mentioned. By establishing virtual system, transfer function of integration can be measured and the inner sound field can also be calculated. In the experiment, automobile body transfer function of integration is measured and experimental method of establishing virtual system is very valid.

Electron Transfer Reaction between M-C_6H_6 and M^+-C_6H_6 Complexes in the Gas Phase: Density Functional Theory Study

DFT/BLYP method is used to theoretically investigate the electron transfer (ET) reactions between M (Li, Na, Mg)-C_6H_6 and M+-C_6H_6 complexes in the gas phase. The geometry optimization of the precursor complexes and the transition state in the process of ET reaction was performed at 6-31G basis set level. The activation energy. the coupling matrix element and the rate constant of the ET reaction are calculated at semi-quantitative level.

Impact of coupling function on stability of synchronization for complex dynamical networks

In this paper, the coupling function of the complex dynamical networks was generalized, and the conditions for the stability of synchronization were given. We illustrate the impact of coupling function on the synchronization of complex dynamical networks, that is, the coupling strength can not assure the stability of synchronization when the coupling function is linear. However we can modulate coupling function to achieve stability of synchronization without changing coupling strength.

A Distributional Representation of Gamma Function with Generalized Complex Domian

In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.

Hash function construction using weighted complex dynamical networks

A novel scheme to construct a hash function based on a weighted complex dynamical network （WCDN） generated from an original message is proposed in this paper. First, the original message is divided into blocks. Then, each block is divided into components, and the nodes and weighted edges are well defined from these components and their relations. Namely, the WCDN closely related to the original message is established. Furthermore, the node dynamics of the WCDN are chosen as a chaotic map. After chaotic iterations, quantization and exclusive-or operations, the fixed-length hash value is obtained. This scheme has the property that any tiny change in message can be diffused rapidly through the WCDN, leading to very different hash values. Analysis and simulation show that the scheme possesses good statistical properties, excellent confusion and diffusion, strong collision resistance and high efficiency.

Syntheses,Spectral Characterization of the Nickel(Ⅱ) Complexes of Macrocyclic Dioxotetraamine and the Effect of the Functional Pendant Arms on their Properties

A series of new macrocyclic dioxo 13 aneN 4 bearing various functional pendants, 2 methylfuran (LF), 2 methylthiophene (LT), 2 methylpyridine (LP), have been synthesized and characterized, where dioxo 13 aneN 4 is 1,4,7,10 tetraazacyclotridecane 11,13 dione. The solution behaviours of the nickel(Ⅱ) complexes have been studied by Uv vis, cyclic voltammetric techniques. The red shifts were observed for the absorption band maxima of the electronic spectra from NiLR 1 to NiLR 2 (R=2 methylfuran, 2 methylthiophene, 2 methylpyridine). The value of E 1/2 of the NiLR 2 is less than NiLR 1 and both of them are lower than that of the nickel(Ⅱ) complex of the unsubstituted ligand, and these reasons are discussed.