This paper deals with the construction of anisotropic curl-free wavelets on the cube [0,1]3, which satisfies the specific boundary conditions. First, one constructs curl-free wavelets on the unit cube based on one dim...This paper deals with the construction of anisotropic curl-free wavelets on the cube [0,1]3, which satisfies the specific boundary conditions. First, one constructs curl-free wavelets on the unit cube based on one dimensional wavelets on the interval [0,1] with some boundary conditions. Then, the stability of the corresponding wavelets in curl-free space and the characterization of Sobolev spaces are studied. Finally, one gives a Helmholtz decomposition and the representation of curl and div operators in wavelet coordinates.展开更多
Numerous considerations deal with specialties of bioelectromagnetic effects, including the force-free and field-free interactions. The fact that bioelectromagnetic phenomena consist of effects without mechanical force...Numerous considerations deal with specialties of bioelectromagnetic effects, including the force-free and field-free interactions. The fact that bioelectromagnetic phenomena consist of effects without mechanical forces and even without measurable fields looks impossible in the simple considerations. However, the stochastic fluctuations cause surprising results, with scientifically proven bioelectromagnetism in field-free conditions. In the first steps, we show the scalar and vector potentials’ specialties instead of electric and magnetic fields defined by the well-known Maxwellian equations. The vanishing of the fields is connected to the potentials’ stochastic fluctuations, the noises control the “zero-ground”. The result shows a possibility of a wave that has no attenuation during its transmission through the material. In this meaning, the result is similar to the consequences of the scalar-wave (SW) considerations. The structural changes follow a particular noise spectrum (called pink-noise or 1/f noise), which keeps the entropy constant in a broad range of scaling magnification.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.11201094,11161014)the 863 Project of China(Grant No.2012AA011005)+2 种基金the Project of Guangxi Innovative Team(Grant No.2012jjGAG0001)the fund of Education Department of Guangxi Province(Grant Nos.201012M9094,201102ZD015,201106LX172)the fund of Guilin University of Electronic Technology(Grant No.Z20710)
文摘This paper deals with the construction of anisotropic curl-free wavelets on the cube [0,1]3, which satisfies the specific boundary conditions. First, one constructs curl-free wavelets on the unit cube based on one dimensional wavelets on the interval [0,1] with some boundary conditions. Then, the stability of the corresponding wavelets in curl-free space and the characterization of Sobolev spaces are studied. Finally, one gives a Helmholtz decomposition and the representation of curl and div operators in wavelet coordinates.
文摘Numerous considerations deal with specialties of bioelectromagnetic effects, including the force-free and field-free interactions. The fact that bioelectromagnetic phenomena consist of effects without mechanical forces and even without measurable fields looks impossible in the simple considerations. However, the stochastic fluctuations cause surprising results, with scientifically proven bioelectromagnetism in field-free conditions. In the first steps, we show the scalar and vector potentials’ specialties instead of electric and magnetic fields defined by the well-known Maxwellian equations. The vanishing of the fields is connected to the potentials’ stochastic fluctuations, the noises control the “zero-ground”. The result shows a possibility of a wave that has no attenuation during its transmission through the material. In this meaning, the result is similar to the consequences of the scalar-wave (SW) considerations. The structural changes follow a particular noise spectrum (called pink-noise or 1/f noise), which keeps the entropy constant in a broad range of scaling magnification.
