Evolution equation of Lie type•Solid mechanics as a simple Lagrangian system.•Space of deformation tensors Sym+ as a configuration manifold.•Riemannian geometry of Sym+ and time-linearization of deformation processes.•Evolution equation of Lie type for finite deformations.•Riemannian ...
As shown in the equation above, the resonant frequency is only related to the constitutive parameters of the material and the aperture’s radiating impedance, while the specific shape and the positions of the apertures have no impacts on it. In other words, the antenna can be deformed into ...
Their topics include connections and differential analysis, the functional imperative, Bohr's correspondence, elementary particles in the jargon of abstract differential geometry, affine geometry and quantum, and quantized Einstein's equation. Differential Sheaves and Connections: A Natural Approach to Physic...
Functional equations in geometry of two sets 来自 Semantic Scholar 喜欢 0 阅读量: 22 作者: GG Mikhailichenko 摘要: We solve a functional equation connected with deformations of the canonical form of a metric function defining on one-dimensional manifolds the geometry of two sets (physical ...
In particular, the Biedenharn identity (I3) becomes a vector equation (mod 2), and the relation with Desargues' theorem is clarified. The advantage of this geometrical model is that the structure alone survives and all summations and complicated coefficients disappear. 展开 ...
Thegeometryof the cutting tool depends upon its intended function. 刀具的形状取决于它需要的功能. 期刊摘选 Quaternion definition andgeometrymeaning were described and quaternion movement equation was introduced. 阐述了四元数的定义、几何意义及四元数表示的运动学方程. ...
Lower estimates for the length of the second fundamental form of submanifolds Francisco G.S. Carvalho, ... Bruno V.M. Vieira February 2025 Research articleAbstract only A Souplet–Zhang type gradient estimate for the fast diffusion equation associated with the Witten Laplacian ...
The previous work on GIFT was done for problems of Laplace's Equation and Linear Elasticity. The main objective of this work is to further study the performance of GIFT for problems of bending and vibration of thin plates. The study consists in implementing GIFT for 3 different plates and ...
differential equation───[数]微分方程 双语使用场景 All the required elements of continuum mechanics, deformation theory anddifferential geometryare also covered.───连续统一体力学, 变形理论和不同几何学的全部被要求的要素也被包括. This type of differentiation is commonly used in classicaldifferential ...
Then, all primary objects defined for manifolds will be generalized to reach the level of noncommutative geometry via spectral triples, with the concrete analysis of the noncommutative torus which is a deformation of the ordinary one. The basics ingredients such as Dirac operators, heat equation ...