Weak KKM theorems in generalized finitely continuous space with applications

Some new weak Knaster-Kuratouski-Mazurkiewicz （KKM） theorems are proved under the noncompact situation in the generalized finitely continuous space （GFC-space） without any convexity. As applications, the minimax inequalities of the Ky Fan type are also given under some suitable conditions. The results unify and generalize some known results in recent literatures.     

Some bounded results of θ(t)-type singular integral operators

Let B be a Banach space in UMD with an unconditional basis. The boundedness of the θ(t)-type singular integral operators in L _B ^p (R ⁿ), (1≤p<+∞) and H _B ¹ (R ⁿ) spaces are discussed. Foundation item: the Education Commission of Shandong Province (J98P51) Biography: Zhao Kai (1960-)     

基于H∞范数的输电塔结构动力优化

目前输电塔结构设计主要基于静力及拟静力工况,以用钢量(总质量)为经济指标进行静力优化,忽略了动力荷载的频率特性。为解决输电塔结构动力优化问题,提出了基于H∞范数的优化方法。该方法以系统传递函数的H∞范数为优化目标,采用遗传算法对角钢截面进行优化。在计算H∞范数时,用串联多质点模型模拟塔架结构以简化计算。同时,引入惩罚函数来调整个体的适应度,从而保证优化结果满足静力工况,不出现杆件失稳且不增加用钢量。以一个实际输电塔结构作为算例进行优化计算,结果表明,该动力优化方法显著降低了输电塔的地震响应,同时保证结构满足静力工况且总质量不超过满应力优化法的用钢量。该方法不需要求解时域响应,计算效率较高。     

THE ANALYSES OF THE THREE-DIMENSIONAL STRESS STRUCTURE NEAR THE CRACK TIP OF MODE I CT SPECIMENS IN ELASTICPLASTIC STATE(Ⅰ)—THE ANALYSES OF CONSTRAINT PARAMETERS AND FRACTURE PARAMETERS

In the present paper, three dimensional analyses of some general constraint parameters and fracture parameters near the crack tip. of Mode I CT specimens in two different thicknesses are carried out by employing ADINA program. The results reveal that the constraints along the thickness direction are obviously separated into two parts: the keeping similar high constraint field (Z₁) and rapid reducing constraints one (Z₂). The two fields are experimentally confiremed to correspond to the smooth region and the shear lip on the fracture face respectively. So the three dimensional stress structure of Mode I specimens can be derived through discussing the two fields respectively. The distribution of the Crack Tip Opening Displacement (CTOD) along the thickness direction and the three dimensional distribution of the void growth ratio (V_g) near the crack tip are also obtained. The two fracture parameters are in similar trends along the thickness direction, and both of them can reflect the effect of thickness and that of the loading level to a certain degree.     

Linear viscoelasticity of thermoassociative chitosan-g-poly(N-isopropylacrylamide) copolymer

Chitosan-g-poly(N-isopropylacrylamide) (chitosan-g-PNIPAM) was synthesized and characterized rheologically in aqueous solutions. The copolymer solution exhibits a thermoassociative behavior in which its elastic response dramatically increases when temperature is above the critical temperature or the association temperature, T _assoc. The copolymer at low concentration shows typical solution property. When the temperature is increased up to the critical temperature, the copolymer exhibits a gel-like characteristic due to the formation of physical cross-links between chitosan backbones through the self-aggregation of PNIPAM side chains. At high concentration, the system exhibits a weak elastic response due to the entanglement of the copolymer at 25°C. As temperature is raised above T _assoc, the system shows a strong elastic behavior due to the formation of additional physical cross-links via the aggregation of PNIPAM side chains. Chitosan-g-PNIPAM offers an attractive associating behavior in aqueous solution at temperature close to the body temperature, thus providing potential applications in pharmaceutical and medical industries.     

Robust H∝ filtering for discrete-time impulsive systems with uncertainty

This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then, a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities （LMIs）. Finally, a numerical example is presented to show effectiveness of the obtained result.     

Maximal elements and generalized games involving condensing mappings in locally FC-uniform spaces and applications （II）

This paper is a continuum of the preceding paper of author. Some new systems of generalized vector quasi-equilibrium problems involving condensing mappings are introduced and studied in locally FC-uniform spaces. By applying the existence theorem of maximal elements of condensing set-valued mappings in locally FC-uniform spaces obtained by author in the preceding paper, some new existence theorems of solutions for the systems of generalized vector quasi-equilibrium problems are proved in locally FC-uniform spaces. These results improve and generalize some known results in literature to locally FC-uniform spaces. Project supported by the Natural Science Foundation of Sichuan Education Department of China (No. 2003A081 and SZD0406)     

Anisotropy of Seismic Attenuation in Fractured Media: Theory and Ultrasonic Experiment

This is a study on anisotropy of seismic attenuation in a transversely isotropic (TI) model, which is a long-wavelength equivalent of an isotropic medium with embedded parallel fractures. The model is based on Schoenberg’s linear-slip theory. Attenuation is introduced by means of a complex-valued stiffness matrix, which includes complex-valued normal and tangential weaknesses. To study the peculiarities of seismic attenuation versus wave-propagation direction in TI media, numerical modeling was performed. The model-input data were the complex-valued weaknesses found from the laboratory ultrasonic experiment made with a Plexiglas plate-stack model, oil-saturated (wet) and air-filled (dry). The laboratory experiment and the numerical modeling have shown that in the vicinity of the symmetry axis, in the wet model, P-wave attenuation is close to S-wave attenuation, while in the dry model, P-wave attenuation is much greater than S-wave attenuation. Moreover, the fluid fill affects the P-wave attenuation pattern. In the dry (air-saturated) model, the attenuation pattern in the vicinity of the symmetry axis exhibits steeper slope and curvature than in the wet (oil-saturated) model. To define the slope or the curvature, a QVO gradient was introduced, which was found to be proportional to the symmetry-axis Q _S/Q _P-ratio, which explains the differences between dry and wet models. Thus, depending on the Q _S/Q _P-ratio, the QVO gradient can serve as an indicator of the type of fluid in fractures, because the QVO gradient is greater in gas-saturated than in liquid-saturated rocks. The analysis of P-wave attenuation anisotropy in seismic reflection and vertical seismic profiling data can be useful in seismic exploration for distinguishing gas from water in fractures.     

Combining magnetic resonance measurements with numerical simulations – Extracting blood flow physiology information relevant to the investigation of intracranial aneurysms in the circle of Willis

Cerebral aneurysms in the region of the circle of Willis have an incidence of 3–6% in western populations and involve the risk of rupture with subsequent subarachnoidal bleeding. The patient specific blood flow patterns are of substantial importance for understanding the pathogenesis of the lesions and may eventually contribute to deciding on the most efficient treatment procedure for a specific patient.A non-invasive method for performing in vivo measurements on blood velocity is 4D phase-contrast magnetic resonance angiography (PC-MRA), on the basis of which a flow field with all its parameters can be simulated. We are using this approach to investigate the hemodynamic parameters in the circle of Willis and, by analyzing the values at common locations of aneurysms, trying to find potential parameters to predict the development of aneurysms. Methodologically, we are acquiring the artery geometry with 3D-time-of-flight magnetic resonance (TOF) measurements and the blood velocity in the feeding arteries with 4D PC-MRA measurements in a healthy volunteer. These measurements are combined with computational fluid dynamics (CFD) to describe detailed hemodynamic patterns within the circle of Willis.     

History-dependent systems

By reformulating a history-dependent system as an evolution equation on a fixed space we arrive at two distinct interpretations of such systems. The evolution equation on a Frechet space corresponding to a history-dependent system is proved to be well posed. The connection between history-dependent systems and continua with microstructure is discussed.     

Degree of branching of polypropylene measured from Fourier-transform rheology

In this study, linear and branched polypropylenes (PP) were compared under medium strain amplitude oscillatory shear (usually strain amplitude range from 10 to 100%) with Fourier-transform rheology (FT rheology). On a log–log diagram, the third relative intensity (I ₃/I ₁), which is a parameter to represent nonlinearity, shows a linear relationship with the strain amplitude in the range of medium strain amplitude. The slope of I ₃/I ₁ of linear PP with various molecular weight and molecular weight distribution was 2 as most constitutive equations predict, while that of branched PP was 1.64, which is lower than that of linear PP. When the linear and branch PP were blended, the slope of I ₃/I ₁ was proportional to the composition of the branch PP. Therefore, it is suggested that the degree of branching can be defined in terms of the slope of I ₃/I ₁ under medium amplitude oscillatory shear.