scholarly journals Deformation theory of 5-dimentional CR structures and the Rumin complex

2002 ◽  
Vol 50 (3) ◽  
pp. 517-550 ◽  
Author(s):  
Takao Akahori ◽  
Peter M. Garfield ◽  
John M. Lee
2021 ◽  
Vol 8 (1) ◽  
pp. 403-414
Author(s):  
Takao Akahori

Abstract Let (M, D) be a compact contact manifold with dim R M = 2n ≥ 5. This means that: M is a C ∞ differential manifold with dim R M = 2n ≥ 5. And D is a subbundle of the tangent bundle TM which satisfying; there is a real one form θ such that D = {X : X ∈ TM, θ(X) = 0}, and θ ^ Λ n−1(d ) ≠ 0 at every point of p of M. Especially, we assume that our D admits almost CR structure,(M, S). In this paper, inspired by the work of Matsumoto([M]), we study the difference of partially integrable almost CR structures from actual CR structures. And we discuss partially integrable almost CR structures from the point of view of the deformation theory of CR structures ([A1],[AGL]).


BioResources ◽  
2020 ◽  
Vol 15 (3) ◽  
pp. 7079-7099
Author(s):  
Jianying Chen ◽  
Guojing He ◽  
Xiaodong (Alice) Wang ◽  
Jiejun Wang ◽  
Jin Yi ◽  
...  

Timber-concrete composite beams are a new type of structural element that is environmentally friendly. The structural efficiency of this kind of beam highly depends on the stiffness of the interlayer connection. The structural efficiency of the composite was evaluated by experimental and theoretical investigations performed on the relative horizontal slip and vertical uplift along the interlayer between composite’s timber and concrete slab. Differential equations were established based on a theoretical analysis of combination effects of interlayer slip and vertical uplift, by using deformation theory of elastics. Subsequently, the differential equations were solved and the magnitude of uplift force at the interlayer was obtained. It was concluded that the theoretical calculations were in good agreement with the results of experimentation.


2020 ◽  
Vol 71 (7) ◽  
pp. 853-867
Author(s):  
Phuc Pham Minh

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions


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