A Geometric Approach to Graph Isomorphism

Author(s):  
Pawan Aurora ◽  
Shashank K. Mehta
Author(s):  
S. Buonchristiano ◽  
C. P. Rourke ◽  
B. J. Sanderson

1984 ◽  
Vol 45 (C6) ◽  
pp. C6-87-C6-94
Author(s):  
H. Reinhardt ◽  
R. Balian ◽  
Y. Alhassid

1989 ◽  
Vol 17 (2) ◽  
pp. 86-99 ◽  
Author(s):  
I. Gardner ◽  
M. Theves

Abstract During a cornering maneuver by a vehicle, high forces are exerted on the tire's footprint and in the contact zone between the tire and the rim. To optimize the design of these components, a method is presented whereby the forces at the tire-rim interface and between the tire and roadway may be predicted using finite element analysis. The cornering tire is modeled quasi-statically using a nonlinear geometric approach, with a lateral force and a slip angle applied to the spindle of the wheel to simulate the cornering loads. These values were obtained experimentally from a force and moment machine. This procedure avoids the need for a costly dynamic analysis. Good agreement was obtained with experimental results for self-aligning torque, giving confidence in the results obtained in the tire footprint and at the rim. The model allows prediction of the geometry and of the pressure distributions in the footprint, since friction and slip effects in this area were considered. The model lends itself to further refinement for improved accuracy and additional applications.


2021 ◽  
Vol 11 (9) ◽  
pp. 4011
Author(s):  
Dan Wang ◽  
Jindong Zhao ◽  
Chunxiao Mu

In the field of modern bidding, electronic bidding leads a new trend of development, convenience and efficiency and other significant advantages effectively promote the reform and innovation of China’s bidding field. Nowadays, most systems require a strong and trusted third party to guarantee the integrity and security of the system. However, with the development of blockchain technology and the rise of privacy protection, researchers has begun to emphasize the core concept of decentralization. This paper introduces a decentralized electronic bidding system based on blockchain and smart contract. The system uses blockchain to replace the traditional database and uses chaincode to process business logic. In data interaction, encryption techniques such as zero-knowledge proof based on graph isomorphism are used to improve privacy protection, which improves the anonymity of participants, the privacy of data transmission, and the traceability and verifiable of data. Compared with other electronic bidding systems, this system is more secure and efficient, and has the nature of anonymous operation, which fully protects the privacy information in the bidding process.


2012 ◽  
Vol 11 (1) ◽  
pp. 1-24
Author(s):  
Emil Saucan ◽  
Eli Appleboim ◽  
Yehoshua Y. Zeevi
Keyword(s):  

2021 ◽  
pp. 1-15
Author(s):  
Jaewoon Kwon ◽  
Keunjun Choi ◽  
Frank C. Park

2021 ◽  
Vol 51 (3) ◽  
Author(s):  
Maurice A. de Gosson

AbstractWe define and study the notion of quantum polarity, which is a kind of geometric Fourier transform between sets of positions and sets of momenta. Extending previous work of ours, we show that the orthogonal projections of the covariance ellipsoid of a quantum state on the configuration and momentum spaces form what we call a dual quantum pair. We thereafter show that quantum polarity allows solving the Pauli reconstruction problem for Gaussian wavefunctions. The notion of quantum polarity exhibits a strong interplay between the uncertainty principle and symplectic and convex geometry and our approach could therefore pave the way for a geometric and topological version of quantum indeterminacy. We relate our results to the Blaschke–Santaló inequality and to the Mahler conjecture. We also discuss the Hardy uncertainty principle and the less-known Donoho–Stark principle from the point of view of quantum polarity.


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