GROUP THEORY METHODFOR ENUMERATION OFOUTERPLANAR GRAPHS

In this paper we give an enumeration formula of the outerplanar graphs by means of graph compression, group theory and combinatorial numbers. Some simple examples are exhibited for illustrating the method. The computational results are shown in the table at the end of this paper.

Theory and Method of Mineral Resource Prediction Based on Synthetic Information

Metallogenic prognosis of synthetic information uses the geological body and the mineral resource body as a statistical unit to interpret synthetically the information of geology, geophysics, geochemistry and remote sensing from the evolution of geology and puts all the information into one entire system by drawing up digitalized interpretation maps of the synthetic information. On such basis, different grades and types of mineral resource prospecting models and predictive models of synthetic information can be established. Hence, a new integrated prediction system will be formed of metallogenic prognosis (qualitative prediction), mineral resources statistic prediction (determining targets) and mineral resources prediction (determining resources amount).

Design Theory and Method of Complex Products:A Review

Design is a high-level and complex thinking activity of human beings,using existing knowledge and technology to solve problems and create new things.With the rise and development of intelligent manufacturing,design has increasingly reflected its importance in the product life cycle.Firstly,the concept and connotation of complex product design is expounded systematically,and the different types of design are discussed.The four schools of design theory are introduced,including universal design,axiomatic design,TRIZ and general design.Then the research status of complex product design is analyzed,such as innovative design,digital design,modular design,reliability optimization design,etc.Finally,three key scientific issues worthy of research in the future are indicated,and five research trends of“newer,better,smarter,faster,and greener”are summarized,aiming to provide references for the equipment design and manufacturing industry.

The theory and method research on the double evaluation of land and space:A survey

By reviewing the theories and methods of resource and environmental carrying capacity evaluation and suitability evaluation of land and space development,it provides theoretical and technical support for rational layout and optimization of land and space development pattern.From the aspects of resource carrying capacity,environmental carrying capacity,the importance of ecological protection,the suitability of agricultural production,and the suitability of urban construction,we sort out domestic and foreign documents.The evaluation of resource carrying capacity has changed from single-factor evaluation to multi-factor comprehensive evaluation.At present,the optimization of land use pattern based on the“three-generation”space is still under exploration,it is not enough to systematize and summarize the thought of optimizing the spatial pattern of the national territory.The theoretical framework,model,method and index of“dual evaluation”of territorial space need to be improved continuously,it also needs the scientific analysis and cognition from the natural direction to the human location direction and the spatial equilibrium state as the new driving force.

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications (NM-TMA) publishes high-quality original research papers on the construction,analysis and application of numerical methods for solving scientific problems.Important research and expository papers devoted to the numerical solution of mathematical problems arising in all areas of science and technology are expected.The journal originates from the journal Numerical Mathematics:A Journal of Chinese Universities (English Edition).

Numerical Mathematics Theory,Methods and Applications

Aims and Scope: Numerical Mathematics:Theory, Methods and Applications(NM-TMA) publishes high-quality original

THE RATIONALISM THEORY AND ITS FINITE ELEMENT ANALYSIS METHOD OF SHELL STRUCTURES

In this paper, a kind of rationalism theory of shell is established which is of different mechanic characters in tension and in compression, and the finite element numerical analysis method is also described.

The Theory and Methods Research on Ecological Quality Control of Enterprises

So far, most theories of economics and management are under the same premise that the natural resources are never exhausted and regenerated repeatedly. The magic of technology brought by industrial revolution endowed human with power that they can do anything they want. It also turns natural resources into industrial energy and enhances the development of human society and civilization. Human uses direct comparison of input and output and the satisfaction degree of demands to measure the production activities, the economic benefit and management performance, regardless of the change of ecology that serves as the natural resources. However, since the ecological environment has been changing worse recently and natural disaster happened frequently human's dream of conquering the nature has been broken.

RESEARCH ON THE THEORY AND METHODS OF COMPREHENSIVE EVALUATION OF REGIONAL COAL RESOURCES

consists of forecasting for the total reserves of regional mineral resources and evaluation,compreIn general,based on evaluated objects and factors involved,evaluation of mineral resources hensive evaluation of regional mineral resources, and economic and technical evaluation of deposits. Here a region can be a country, a province, or a mining area, while a deposit is mainly related to a single type of mineral, although it can contain more than one types of minerals. In the past, to assess mineral resources was primarily to evaluate and forecast the total reserves of regional mineral resources. With the advancement of science, technology, and economy, the evaluation of mineral resources has developed from forecasting the reserves of them to comprehensively evaluating them on the basis of numerous factors.

Density Functional Theory Study on the Adsorption of Dioxygen on Small Pt-Pd Clusters

The electronic and physical properties of PtmPdn （m＋n≤5） metal clusters and their interactions with dioxygen have been studied by using hybrid density functional B3LYP method. The total energies, atomization energies, vibration frequencies, and charge distributions were reported. The Pt-Pt bridge site modified by Pd atoms was found to be the most active site for the dissociation of dioxygen, which was mainly due to the change of electronic structures of the Pt atoms in bimetallic Pt-Pd clusters.

Regioselectivity Study on Propylene Polymerization Catalyzed by Neutral Salicyladiminato Pd(II) Model Complex with DFT Method

Many attempts have been made to control the regioselectivity for olefin poly- merization by varying the structures of ligands in catalysts. The regioselectivity of propylene polymerization was investigated by replacing a nitrogen atom in the Pd(II) diimine catalyst with an oxygen atom from density functional theory method at the B3LYP/LANL2DZ level. The results show that the 1,2-insertion becomes a rival mechanism to the 2,1-insertion when the nitrogen atom is replaced by the oxygen atom leading to an asymmetric environment in the catalyst, and that the steric effect in the asymmetrical catalyst plays an important part in the polymerization. The insertion barrier from 2-O is much higher than that from 2-N. A pyramid transition state was characterized for the catalyst to convert 2-O back to 2-N through internal rotation. The propylene prefers to coordinate at the opposite side of O in the catalyst. This is the driving force for the internal rotation. The results are significant for isotactic and syndiotactic polymerization.

Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory

This paper deals with off-diagonal operator matrices and their applications in elasticity theory. Two kinds of completeness of the system of eigenvectors are proven, in terms of those of the compositions of two block operators in the off-diagonal operator matrices. Using these results, the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed. Moreover, we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation.

Bolt support mechanism based on elastic theory

Mechanical model of anchorage surrounding rock considering tray effect was established based on elastic theory,in order to study the mechanism of bolt supporting.Elastic solutions of normal force at point in the interior of a semi-infnite solid were obtained by means of classical displacement function method in elasticity.The factors which influence stress of bolted surrounding rock,such as the length of bolt and tray effect,were analyzed.The absolute value of stress along bolt axes decreased rapidly with an increase in radical distance and the maximum appeared near ends of bolt.With increasing radical distance,the value of radical stress changed from positive to negative roughly and then increased to zero,with maximum at the middle of bolt.The evolution of hoop stress as radical distance increasing was similar with stress along bolt axes.With an increase in depth,the radical effect ranges of all normal stress components were reduced.These suggest that the effect from tray on stress along bolt axes of bolted surrounding rock could be neglected,except near surface of surrounding rock.

Powell dynamic identification of displacement parameters of indeterminate thin-walled curve box based on FCSE theory

The FCSE controlling equation of pinned thinwalled curve box was derived and the indeterminate problem of continuous thin-walled curve box with diaphragm was solved based on flexibility theory. With Bayesian statistical theory,dynamic Bayesian error function of displacement parameters of indeterminate curve box was founded. The corresponding formulas of dynamic Bayesian expectation and variance were deduced. Combined with one-dimensional Fibonacci automatic search scheme of optimal step size,the Powell optimization theory was utilized to research the stochastic identification of displacement parameters of indeterminate thin-walled curve box. Then the identification steps were presented in detail and the corresponding calculation procedure was compiled. Through some classic examples,it is obtained that stochastic performances of systematic parameters and systematic responses are simultaneously deliberated in dynamic Bayesian error function. The one-dimensional optimization problem of the optimal step size is solved by adopting Fibonacci search method. And the Powell identification of displacement parameters of indeterminate thin-walled curve box has satisfied numerical stability and convergence,which demonstrates that the presented method and the compiled procedure are correct and reliable.During parameters鈥？iterative processes,the Powell theory is irrelevant with the calculation of finite curve strip element（FCSE） partial differentiation,which proves high computation effciency of the studied method.

Theories and Methods of Landscape Architecture Heritage Protection

This paper firstly made an overview of foreign and domestic theories and methods of landscape architecture heritage protection.It studied the landscape architecture heritage from policies and regulations,investment management,talent cultivation,and popular science education.Then,it discussed problems of landscape architecture heritage protection in China:lack of legislation,weak awareness of heritage resources,overdevelopment of heritage resources,and vacancy in management and monitoring of heritage resources.Finally,it came up with recommendations that competent authorities of Chinese government should attach greater importance to heritage management,talent cultivation,and fund input,integrate with advanced management methods of developed countries,and exploring a landscape architecture heritage protection and management mode suitable for national conditions of China at levels of thought,methods,and technology.

Prediction of Aqueous Solubility for 209 Polychlorinated Diphenyl Ethers from Molecular Structural Parameters by DFT Method

Optimized calculations of 209 polychlorinated diphenyl ethers （PCDEs） and diphenyl ethers were carried out at the B3LYP/6-31G^＊ level with the Gaussian 98 program. Based on the theoretical linear solvation energy relationship （TLSER） model, the obtained structural parameters were taken as theoretical descriptors to establish the novel QSPR model for predicting aqueous solubility （-lgSw） of PCDEs. The model obtained in this work contains two variables： mean molecular polarizability （a） and the most positive partial charge on a hydrogen atom （qH^＋）, of which RE = 0.9606 and SD = 0.32. And the results of cross-validation test also show that the model exhibits optimum stability and better predictive power. Moreover, the predictive power of the new model is better than that of MCIs method.

Studies on the Quantitative Structure-activity Relationship of Substituted Biphenyls by Density Function Theory (DFT)

Geometrical configurations of 16 substituted biphenyls were computed at the B3LYP/6-311G^＊＊ level with Gaussian 98 program. Based on linear solvation energy theory, lgKow as well as the structural and thermodynamic parameters obtained at this level was taken as theoretical descriptors, and corresponding equation predicting the toxicity of Daphnia magna （-lgEC5o） was thus obtained, in which three parameters were contained, i.e., n-octanol/water partition coefficients （lgKow）, dipole moment of the molecules（ μ） and entropy （S°）. For this equation, R^2 = 0.9582, q^2 = 0.8921 and SD = 0.102. The absolute t-scores of three variables are larger than the standard one in the confidence range of 95%, which confirms the creditability and stability of this model.

Complete leaky mode coupling in dual-core photonic crystal fibre based on the coupled-mode theory

This paper theoretically investigates the dependence of leaky mode coupling between inner core fundamental mode and outer core defect mode on phase and loss matching in pure silica dual-core photonic crystal fibres with the multi-pole method. The complete mode coupling can take place when both the phase and loss matching conditions are satisfied at the avoided anti-crossing wavelength. It shows the influences of cladding structure parameters including the diameters of cladding air holes d1, diameters of outer core holes d2 and hole to hole pitch A on the characteristics of leaky modes coupling. The coupled-mode theory is used to analyse the mode transition characteristics and the complete coupling can be clearly indicated by comparing the real and imaginary parts of propagation constant of the leaky modes.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.