STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅰ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro_financial system: balance, stable periodic, fractal, Hopf_bifurcation, the relationship between parameters and Hopf_bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro_economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.

STUDY FOR THE BIFURCATION TOPOLOGICAL STRUCTURE AND THE GLOBAL COMPLICATED CHARACTER OF A KIND OF NONLINEAR FINANCE SYSTEM(Ⅱ)

Based on the work discussed on the former study, this article first starts from the mathematical model of a kind of complicated financial system, and analyses all possible things that the model shows in the operation of our country's macro_financial system: balance, stable periodic, fractal, Hopf_bifurcation, the relationship between parameters and Hopf_bifurcation, and chaotic motion etc. By the changes of parameters of all economic meanings, the conditions on which the complicated behaviors occur in such a financial system, and the influence of the adjustment of the macro_economic policies and adjustment of some parameter on the whole financial system behavior have been analyzed. This study will deepen people's understanding of the lever function of all kinds of financial policies.

TOPOLOGICAL STRUCTURE OF RENORM ALIZATION CONSTANTS I N QUANTUM FIELD THEORY AT SHORT DISTANCE KUNMING COLLABRATION OF MULTIHADRON DYNAMIOS

The anomalous dimensions of the quantum fields are the Hausdorff dimensiongrad. The present candidate of the renormalization constant is the generalized Cantor discontinuum. The Hausdorff dimensiongrad of the Minkowski space time is based upon the point set with σ-length on light cone.

Topological structure effect on far-infrared spectra in a GaAs/InAs nanoring

On the basis of the growth mechanism of a GaAs/InAs nanoring, we propose a fine model which reflects the confinement details of real nanoring. Through calculations of the two-electron energy and far-infrared （FIR） spectra, we find that the ring topological structure and electron-electron interaction have great influence on the FIR spectra. The two unknown transition peaks in the experiment are determined theoretically. The theoretical results are in good agreement with the experiments.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅰ)- EXPERIMENTAL MODEL AND TOPOLOGICAL FLOW PATTERNS ON BOTH ENDWALLS AND BLADE SURFACES

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in the transverse section, and by appling topology theory, the structures on both endwalls and blade surfaces were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

TOPOLOGICAL STRUCTURE OF THE SINGULAR POINTS OF THE THIRD ORDER PHASE LOCKED LOOP EQUATIONS WITH THE CHARACTER OF DETECTED PHASE BEING g(φ)=(1+k)sinφ/(1+kcosφ)

In this paper, we study the topological structure of the singular points of the third order phase locked loop equations with the character of detected phase being g(?) =(1+k)sin?/1+kcos?.

COEFFICIEN TCONDITIONS OF LOCALLY TOPOLOGICAL STRUCTURE FOR NONLINEAR HOMOGENEOUS SYSTEM WITH ZERO CHARACTERISTIC ROOTS

In this paper, we discuss the locally topological structure for nonlinear homogeneous n-degree system with zero characteristic roots, and give a criteria by the coefficients of the polynonmials.

Topological Structure of Vortex Solution in Jackiw-Pi Model

By using φ-mapping method,we discuss the topological structure of the self-duality solution in Jackiw-Pimodel in terms of gauge potential decomposition.We set up relationship between Chern-Simons vortex solution andtopological number,which is determined by Hopf index and Brouwer degree.We also give the quantization of flux inthis ease.Then,we study the angular momentum of the vortex,which can be expressed in terms of,the flux.

LOCAL TOPOLOGICAL STRUCTURE OF THE PLANE CUBIC SYSTEM IN THE UNDETERMINED SIGN CASE

In this paper we discuss the topological structure near the singular point O (0,0) of the plane cubic system in the undetermined sign case, and give their coefficient conditions.

Topological structure bifurcation of temperature field of deformable drop in Marangoni migration

The unsteady processes of the Marangoni migration of deformable liquid drops are simulated numerically in a wider range of Marangoni number(up to Ma = 500) in the present work.A steady terminal state can always be reached,and the scaled terminal velocity is a monotonic function decreasing with increasing Marangoni number,which is generally in agreement with corresponding experimental data.The topological structure of flow field in the steady terminal state does not change as the Marangoni number increases,while bifurcation of the topological structure of temperature field occurs twice at two corresponding critical Marangoni numbers.A third critical value of Marangoni number also exists,beyond which the coldest point jumps from the rear stagnation to inside the drop though the topological structure of the temperature field does not change.It is found that the inner and outer thermal boundary layers may exist along the interface both inside and outside the drop if Ma>70.But the thickness decreases with increasing Marangoni number more slowly than the prediction of potential flow at large Marangoni and Reynolds numbers.

Topological structure of Gauss-Bonnet-Chern theorem and -branes

By making use of the C-mapping topological current theory, this paper shows that the Gauss Bonnet Chern density （the Euler-Poincare characteristic x（M） density） can be expressed in terms of a smooth vector field φ and take the form of δ（φ）, which means that only the zeros of φ contribute to x（M）. This is the elementary fact of the Hopf theorem. Furthermore, it presents that a new topological tensor current of p-branes can be derived from the Gauss-Bonnet-Chern density. Using this topological current, it obtains the generalized Nambu action for multi p-branes.

THE TOPOLOGICAL OPTIMIZATION FOR TRUSS STRUCTURES WITH STRESS CONSTRAINTS BASED ON THE EXIST-NULL COMBINED MODEL

A new exist-null combined model is proposed for the structural topology optimization. The model is applied to the topology optimization of the truss with stress constraints. Satisfactory computational result can be obtained with more rapid and more stable convergence as compared with the cross-sectional optimization. This work also shows that the presence of independent and continuous topological variable motivates the research of structural topology optimization.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅱ)- TOPOLOGICAL FLOW PATTERN AND VORTEX STRUCTURE IN THE TRANSVERSE SECTION OF A BLADE CASCADE

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in transverse section, and by appling topology theory, the topological structures and vortex structure in the transverse section of a blade cascade were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex, and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

TOPOLOGICAL STRUCTURES OF VORTEX AND HELICITY ANALYSIS

The topological structures of the vortex filaments and vortex tubes with an exact solution of a straight spiral vortex tube are discussed. It is found that there are some confusions about the calculation of the helicity of a knotted vortex filament and some linked vortex filaments by using different methods. How to unify these methods is explained and the right results are given. (Edited author abstract) 5 Refs.

Experimental observation of multiple topological nodal structure in LaSb_(2)

Unconventional fermions in the immensely studied topological semimetals are the source for rich exotic topological properties.Here,using symmetry analysis and first-principles calculations,we propose the coexistence of multiple topological nodal structure in LaSb_(2),including topological nodal surfaces,nodal lines and in particular eightfold degenerate nodal points,which have been scarcely observed in a single material.Further,utilizing angle-resolved photoemission spectroscopy,we confirm the existence of nodal surfaces and eightfold degenerate nodal points in LaSb_(2).The intriguing multiple topological nodal structure might play a crucial role in giving rise to the large linear magnetoresistance.Our work renews the insights into the exotic topological phenomena in LaSb_(2).

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

Study on local topology model of low/high streak structures in wall-bounded turbulence by tomographic time-resolved particle image velocimetry

The relationship between the in the logarithmic law （log-law） region of bursting event and the low/high-speed streak a turbulent boundary layer is investigated. A tomographic time-resolved particle image velocimetry （TRPIV） system is used to measure the instantaneous three-dimensional-three-component （3D-3C） velocity field. The momentum thickness based Reynolds number is about 2 460. The topological information in the log-law region is obtained experimentally. It is found that the existence of the quadrupole topological structure implies a three-pair hairpin-like vortex packet, which is in connection with the low/high-speed streak. An idealized 3D topological model is then proposed to characterize the observed hairpin vortex packet and low/high-speed streak.

Topological analysis of plasma flow control on corner separation in a highly loaded compressor cascade

In this paper, flow behavior and topology structure in a highly loaded compressor cascade with and without plasma aerodynamic actuation （PAA） are investigated. Streamline pattern, total pressure loss coefficient, outlet flow angle and topological analysis are considered to study the effect and mechanism of the plasma flow control on corner separation. Results presented include the boundary layer flow behavior, effects of three types of PAA on separated flows and performance parameters, topology structures and sequences of singular points with and without PAA. Two separation lines, reversed flow and backflow exist on the suction surface. The cross flow on the endwall is an important element for the comer separation. PAA can reduce the undertuming and overturning as well as the total pressure loss, leading to an overall increase of flow turning and enhancement of aerodynamic performance. PAA can change the topology structure, sequences of singular points and their corresponding separation lines. Types II and III PAA are much more efficient in controlling comer separation and enhancing aerodynamic performances than type I.

The ICM method with objective function transformed by variable discrete condition for continuum structure

ICM （Independent Continuous Mapping） method can solve topological optimization problems with the minimized weight as the objective and subjected to displacement constraints. To get a clearer topological configuration, by introducing the discrete condition of topological variables and integrating with the original objective, an optimal model with multi-objectives is formulated to make the topological variables approach 0 or 1 as near as possible, and the model reduces the effect of deleting rate on the result. The image-filtering method is employed to eliminate the checkerboard patterns and mesh dependence that occurred in the topology optimization of a continuum structure. The computational efficiency is enhanced through selecting quasi-active displacement constraints and a design region. Numerical examples indicate that this algorithm is robust and practicable, though the number of iterations is slightly increased with respect to the original algorithm.

Three-dimensional spatial structure of the macro-pores and flow simulation in anthracite coal based on X-ray μ-CT scanning data

The three-dimensional(3 D) structures of pores directly affect the CH4 flow.Therefore,it is very important to analyze the3 D spatial structure of pores and to simulate the CH4 flow with the connected pores as the carrier.The result shows that the equivalent radius of pores and throats are 1-16 μm and 1.03-8.9 μm,respectively,and the throat length is 3.28-231.25 μm.The coordination number of pores concentrates around three,and the intersection point between the connectivity function and the X-axis is 3-4 μm,which indicate the macro-pores have good connectivity.During the single-channel flow,the pressure decreases along the direction of CH4 flow,and the flow velocity of CH4 decreases from the pore center to the wall.Under the dual-channel and the multi-channel flows,the pressure also decreases along the CH4 flow direction,while the velocity increases.The mean flow pressure gradually decreases with the increase of the distance from the inlet slice.The change of mean flow pressure is relatively stable in the direction horizontal to the bedding plane,while it is relatively large in the direction perpendicular to the bedding plane.The mean flow velocity in the direction horizontal to the bedding plane(Y-axis) is the largest,followed by that in the direction horizontal to the bedding plane(X-axis),and the mean flow velocity in the direction perpendicular to the bedding plane is the smallest.