scholarly journals A Simple Proof of Regularity for $C^{1,\alpha}$ Interface Transmission Problems

2021 ◽  
Vol 37 (1) ◽  
pp. 22-30
Author(s):  
Hongjie Dong
2013 ◽  
Vol 36 (1-2) ◽  
pp. 165-170 ◽  
Author(s):  
Ira M. Gessel
Keyword(s):  

The Galerkin approximation to the Navier–Stokes equations in dimension N , where N is an infinite non-standard natural number, is shown to have standard part that is a weak solution. This construction is uniform with respect to non-standard representation of the initial data, and provides easy existence proofs for statistical solutions.


2000 ◽  
Vol 23 (8) ◽  
pp. 579-584
Author(s):  
J. G. O'Hara

We establish a representation forqin the second-order linear quasi-differential equation(py′)′+qy=0. We give a number of applications, including a simple proof of Sturm's comparison theorem.


1988 ◽  
Vol 105 (4) ◽  
pp. 279-285 ◽  
Author(s):  
P. Mani-Levitska

2020 ◽  
pp. 1-13
Author(s):  
Yang Mei

Because the teaching methods of Chinese teaching in higher vocational colleges are improper and the problems in the teaching process cannot be found in time, the teaching effect is not good and there are many difficulties in the teaching process of teachers. According to actual needs, based on complex evolution and improved neural network algorithms, this paper builds a Chinese online teaching system in high vocational colleges. After communication with users and social research, the model function module is determined, and the system performance is improved through the mapping optimization model to eliminate data transmission problems in the system operation, and the realization process of the system function module is shown in the form of a diagram. In addition, this paper designs a control experiment to verify the performance of the model and uses the traditional algorithm model as a control to start the test teaching and uses statistical methods to compare the teaching effects. The research results show that the teaching system constructed in this paper has certain advantages over the traditional model.


2012 ◽  
Vol 55 (2) ◽  
pp. 507-511
Author(s):  
Takahiko Nakazi ◽  
Takanori Yamamoto

AbstractLet H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.


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