CENTER CONDITIONS AND BIFURCATION OF LIMIT CYCLES FOR A CLASS OF FIFTH DEGREE SYSTEMS

The center conditions and bifurcation of limit cycles for a class of fifth degree systems are investigated.Two recursive formulas to compute singular quantities at infinity and at the origin are given.The first nine singular point quantities at infinity and first seven singular point quantities at the origin for the system are given in order to get center conditions and study bifurcation of limit cycles.Two fifth degree systems are constructed.One allows the appearance of eight limit cycles in the neighborhood of infinity,which is the first example that a polynomial differential system bifurcates eight limit cycles at infinity.The other perturbs six limit cycles at the origin.

Study on Evaluation of Grassland Eco-system Coordination Based on Environment-Economy Coordination Degree Model

Based on the current studies,a reasonable evaluation index system was established by the development coordination of analysis systems.Furthermore,taking grassland resources in Nagchu Tibet as an example and according to the coordination degree evaluation model of the environmental economy system,a coordination degree evaluation index system of environmental economy was set up,and the coordination conditions of 11 counties in Nagchu district were analyzed by coordination function.

COMPLEX ISOCHRONICITY OF A SIXTH DEGREE SYSTEM

In this paper, we discuss the complex isochronicity of a sixth degree polynomial system. We first adopt a new algorithm to find necessary conditions for complex isochronicity, then prove the sufficient conditions using effective methods.

Degree of coupling and coordination of eco-economic system and the influencing factors： a case study in Yanchi County, Ningxia Hui Autonomous Region, China

Based on the statistical data, we analyzed and evaluated the degree of coupling and coordination of the eco-economic system in Yanchi County for the period spanning from 1983 to 2014. The eco-economic system can be divided into socioeconomic and ecological sub-systems and their relationship can reveal the interaction state between the two sub-systems and help the local government to establish a coordinated development mode. An index system was constructed to assess the development of the two sub-systems before the evaluation of the degree of coupling and coordination. The principal component regression analysis was adopted to quantitatively assess the influences of natural, economic and social factors on the degree of coupling and coordination of the eco-economic system. Results showed that, from 1983 to 2014, the development trends of both sub-systems were increasing with the ecological sub-system having more fluctuations. The degree of coupling and coordination of the eco-economic system in the study area increased gradually from 1983 to 2014, but experienced five different development stages from the verge of disorder to favorable coordination. The development of the local social and economic conditions was the most important factor influencing the degree of coupling and coordination. The second most important factor was the financial support from the local government. In addition, the environment protection policies also played undeniable roles. Due to the diversity of the influence factors, the government should take comprehensive measures to promote the sustainable development of the eco-economic system.

Model-Based Degree Estimation of Unbalance and Misalignment in Flexible Coupling-rotor System

The condition of rotor system must be assessed in order to develop condition-based maintenance for rotating machinery. It is determined by multiple variables such as unbalance degree, misalignment degree, the amount of bending deformation of the shaft, occurrence of shaft crack of rotor system and so on. The estimation of the degrees of unbalance and misalignment in flexible coupling-rotor system is discussed. The model-based approach is employed to solve this problem. The models of the equivalent external loads for unbalance and misalignment are derived and analyzed. Then, the degrees of unbalance and misalignment are estimated by analyzing the components of the equivalent external loads of which the frequencies are equal to the 1 and 2 times running frequency respectively. The equivalent external loads are calculated according to the dynamic equation of the original rotor system and the differences between the dynamical responses in normal case and the vibrations when the degree of unbalance or misalignment or both changes. The denoise method based on bandpass filter is used to decrease the effect of noise on the estimation accuracy. The numerical examples are given to show that the proposed approach can estimate the degrees of unbalance and misalignment of the flexible coupling-rotor system accurately.

Modified Two-Degrees-of-Freedom Internal Model Control for Non-Square Systems with Multiple Time Delays

A modified two-degrees-of-freedom( M-TDOF) internal model control( IMC) method is proposed for non-square systems with multiple time delays and right-half-plane( RHP) zeros. In this method,pseudo-inverse is introduced to design the internal model controller,and a desired closed-loop transfer function is designed to eliminate the unrealizable factors of the derived controller. In addition,set-point tracking and load-disturbance rejection of each process are separately controlled by two controllers. The simulation results show that in addition to high decoupling performance and robustness,the proposed control method also effectively improves loaddisturbance rejection and simultaneously optimizes the input tracking performance and disturbance rejection performance by selecting the parameters of controllers. Furthermore,the higher tolerance of model mismatch is achieved in this paper.

System Identification Modeling of Ship Manoeuvring Motion in 4 Degrees of Freedom Based on Support Vector Machines

Based on support vector machines, three modeling methods, i.e., white-box modeling, grey-box modeling and black-box modeling of ship manoeuvring motion in 4 degrees of freedom are investigated. With the whole-ship mathematical model for ship manoeuvring motion, in which the hydrodynamic coefficients are obtained from roll planar motion mechanism test, some zigzag tests and turning circle manoeuvres are simulated. In the white-box modeling and grey-box modeling, the training data taken every 5 s from the simulated 20°/20° zigzag test are used, while in the black-box modeling, the training data taken every 5 s from the simulated 15°/15°, 20°/20° zigzag tests and 15°, 25° turning manoeuvres are used; and the trained support vector machines are used to predict the whole 20°/20° zigzag test. Comparisons between the simulated and predicted 20°/20° zigzag tests show good predictive ability of the proposed methods. Besides, all mathematical models obtained by the proposed modeling methods are used to predict the 10°/10° zigzag test and 35° turning circle manoeuvre, and the predicted results are compared with those of simulation tests to demonstrate the good generalization performance of the mathematical models. Finally, the proposed modeling methods are analyzed and compared with each other in aspects of application conditions, prediction accuracy and computation speed. The appropriate modeling method can be chosen according to the intended use of the mathematical models and the available data needed for system identification.

Life-cycle cost model and evaluation system for power grid assets based on fuzzy membership degree

Life-cycle cost(LCC)theory can be effectively applied to improve the efficiency and quality of power plant equipment and asset management.However,specific aspects of the LCC calculation and evaluation model require further research for practical application.This paper proposes an LCC assessment model for the management of electric power plant equipment during its service life.A membership function method based on fuzzy logic is used to improve the allocation of modernization and overhaul projects to multiple equipment assets.An LCC assessment model and evaluation system for power equipment are proposed and successfully applied to the equipment and project management of a Guangzhou power plant in the China Southern Power Grid,providing a decision-making mechanism that facilitates efficient operation and optimal utilization of power plant equipment and assets.

Evolvement of the System Complexity Degree under Different Time Scalings:an Illustration of the Traffic Flow System

It is investigable how the system scaling affects the system complexity degree. The traffic flow system is taken in this paper as an illustration to study this question. First, the Lempel-Ziv algorithm is introduced for accurate depiction of the complexity degree of the traffic flow system. We gain 3 actual sequences and 20s period traffic flow sequences on the basis of the measure of the traffic flow data; we gain 5 traffic flow sequences whose periods are between 1-5min by simulating the traffic flow system. By calculating the complicacy of the 11 sequences, we obtain two hypothesis: the complicacies of the same system are different under different time scalings; negative correlation exists between the complicacy and the time scaling of the system.

Evaluation System for Farmers' Satisfaction Degree in the Green Energy Saving Rebuilding of Rural Residence

In view of the present situation of measuring a green residence just by energy saving and environmental protection,we propose that we should build the rural residence more from the farmer's view and set up an evaluation system based on farmers satisfaction.A total of 16 factors affecting the farmers' satisfaction degree of green energy saving rebuilding of rural residence are selected.Questionnaire survey on 110 peasant households is carried out under different situations in Guanzhong region in Shaanxi Province,so as to obtain the importance score of evaluation index.During constructing the evaluation system for farmers' satisfaction degree,Factor Analysis Method is used to classify the related influencing factors.Subjective analysis of Analytic Hierarchy Process and the objective analysis of Factor Analysis Method are combined together to determine the weights of factors at different grades.Then,the final evaluation model is obtained,which provides guidance for the further green energy saving rebuilding of rural residence in China.

The Theory of Membership Degree of Γ-Conclusion in Several n-Valued Logic Systems

Based on the analysis of the properties of Γ-conclusion by means of deduction theorems, completeness theorems and the theory of truth degree of formulas, the present papers introduces the concept of the membership degree of formulas A is a consequence of Γ (or Γ-conclusion) in Lukasiewicz n-valued propositional logic systems, Godel n-valued propositional logic system and the R0 n-valued propositional logic systems. The condition and related calculations of formulas A being Γ-conclusion were discussed by extent method. At the same time, some properties of membership degree of formulas A is a Γ-conclusion were given. We provide its algorithm of the membership degree of formulas A is a Γ-conclusion by the constructions of theory root.

GDOP’s Influence on Observable Degree of Multi-Antenna GPS/SINS Integrated Attitude Measuring System

GDOP’s influence on observable degree is studied by analyzing a multi-antenna GPS/SINS attitude measuring system. Firstly, the mathematical model of the attitude measuring system, whose observations are single-differences, is provided;Secondly, it is proved that the model can be studied by PWCS theory, and GDOP’s influence on observable degree is explained intuitively. Then, the variance of observable degree is studied by simulation while GDOP is different, and the result is analysed. Simulation results show that, the observable degree becomes worse with the increasing GDOP value. Therefore, while designing such kind of Kalman filter, the influence to observable degree which made by GDOP should be considered adequately.

Modifications in aroma characteristics of'Merlot'dry red wines aged in American,French and Slovakian oak barrels with different toasting degrees

Aging in oak barrels is widely used in enology which could bring flavor changes and aromatic complexity to wines.In the present study,the aroma compounds were analyzed from the‘Merlot’dry red wines,which were fermented in two types of fermenters(stainless steel tank and rotated oak barrel)and aged in six types of oak barrels(three geographic origins×two toasting degrees)for different time(0,3,6 and 9 months,respectively).Results showed that 30 volatiles were associated with barrels and increased during oak aging.The fermenters could influence the intensities of the toast,leathery,smoky,fruity,floral and caramel aromas.The concentration of whisky lactone,eugenol,cis-isoeugenol,and the intensities of the toast and spicy aromas were highest in the wines aged in American oak and were lowest in the wines aged in French oak barrels.The concentrations of guaiacol,syringol,trans-isoeugenol,furfural alcohol,vanilla,cis-whisky lactone enabled the medium toasting barrels to be distinguished from the light toasting ones.The compounds originating from the barrels could be used to distinguish the types of different barrels,but the other general grape-derived and fermentation-derived volatiles could not.The fermenters,oak species and toasting degrees of the barrels all had significant effects on the aroma profiles of the aged‘Merlot’dry red wines,but the influence of the geographic origin was not obvious.

Criteria for the Degree of Stability of the Linear Constant Systems

There are various applications of the stability theory of the first-order dynamical systems. And the stability of the non-linear control systems can be determined by its linear part. In practice, it is not enough to know the stability of the dynamical systems. Sometimes we must know the degree of stability of these systems. In this paper, we present some criteria for the degree of stability of the linear constant systems, by using the entries of the coefficient matrix A only.

Residential Electricity Consumption Behavior Mining Based on System Cluster and Grey Relational Degree

In order to improve the utilization of the residential electricity consumption data which contains the information on the user’s electricity consumption habits, a residential electricity consumption behaviors mining algorithm model is constructed. Firstly, according to the attribute, the collected data can be divided into the global data and the phase data, then the appropriate global variables are selected to mine the user’s electricity consumption patterns in the near future on the system clustering algorithm. Based on the theory of grey relational analysis, combing phase data with the power modes to analyze the potential characteristics of residential electricity consumption behaviors deeply that verify the ability of latest power mode to predict household electricity consumption situation in the coming few days and the effect of dominant phase variables on the peak load shifting. Finally, from the actual data of a certain family, the proposed data mining algorithm is testified that it can effectively explore the electricity consumption behavior habits and characteristics of the family.

Asymptotic dynamics of the alternate degrees of freedom for a two-mode system:An analytically solvable model

The composite systems can be non-uniquely decomposed into parts（subsystems）.Not all decompositions（structures） of a composite system are equally physically relevant.In this paper we answer on theoretical ground why it may be so.We consider a pair of mutually un-coupled modes in the phase space representation that are subjected to the independent quantum amplitude damping channels.By investigating asymptotic dynamics of the degrees of freedom,we find that the environment is responsible for the structures non-equivalence.Only one structure is distinguished by both locality of the environmental influence on its subsystems and a classical-like description.

Integrability of Hamiltonian Systems with Two Degrees of Freedom and Homogenous Potential of Degree Zero

We provide necessary conditions in order that the Hamiltonian systems with Hamiltonian ,?and one of the following potentials ?are integrable in the Liouville sense.

Green Synthesis and Physical and Chemical Characterization of Chitosans with a High Degree of Deacetylation, Produced by a Binary Enzyme System

Chitosan is a biopolymer obtained from chitin, where the N-acetylglucosamine monomer is in its deacetylated form; this polymer is useful for a wide variety of industrial applications. The properties and uses of chitosan depend on its physical and chemical characteristics, which result from the treatments used for its production. In this study, we report the preparation and characterization ofchitosan oligosaccharides by a green synthesis from crystalline shrimp chitin, using a sequential enzyme treatment by chitinase and chitin deacetylase. Chitinases were purified from grapes and used to rupture the crystalline shrimp chitin structure, modifying the crystallinity index from 57.6% to 15.9%. The resultant polymers were deacetylated using a recombinant chitin deacetylase from Saccharomyces cerevisiae, which was cloned and expressed in Pichia pastoris. The chitosans produced showed an estimated DA （degree of acetylation） of approximately 20%, and the molecular weights ranged from -7,600 to -3,700 after treatment in pH 3.0 and pH 6.0 for 10 min and 40 min, respectively. Physical and chemical characterization of the products indicated that enzyme fragmentation of chitin probably makes the acetamide groups more accessible to deacetylation, forming homogeneous polymers that are free of hazardous sub-products, have defined low molecular weights, and are highly deacetylated.

Study on Complex System Evaluation Method Based on PCA and Grey Relative Degree

The complexity and limited data samples in evaluation of complex system are obstacles for traditional evaluation method. Based on Grey relative degree theory and principal components analysis (PCA) method, a novel systemic evaluation method is put forward in this paper. Firstly, standardization method is modified for evaluation objective, and the method includes expression (2) and (3). Secondly, for few schemes of complex system, grey relative degree, expression (5), is substituted for relation coefficient. At last, validity of the method is verified by evaluating 3 schemes of a type of UUV.

Modelling rapid non-destructive test using light weight deflectometer on granular soils across different degrees of saturation

This study introduces an advanced finite element model for the light weight deflectometer(LWD),which integrates contact mechanics with fully coupled models.By simulating LWD tests on granular soils at various saturation levels,the model accurately reflects the dependence of the LWD modulus on dry density,water content,and effective stress.This model addresses and overcomes the limitations of previous finite element models for this specific problem.Simultaneously,this research presents the first experimentally validated fully coupled contact impact model.Furthermore,the research provides a comparative assessment of elastoplastic and nonlinear elastic models and contrasts an enriched node-tosegment method(developed in this study)with the more precise mortar technique for contact mechanics.These comparisons reveal unique advantages and challenges for each method.Moreover,the study underscores the importance of careful application of the LWD modulus,emphasising the need for sophisticated tools to interpret soil behaviour accurately.