C. Discrete Mathematics: Proof Techniques and Mathematical Structures. World Scientific Pub. Co., 1999. 19. Polya, G. How to Solve It: A New Aspect of Mathematical Methods. Ishi Press, 2009. 20. Rodgers, N. Learning to Reason: an Introduction to Logic, Sets and Relations. Wiley & Sons...
Main article: Elementary proof An elementary proof is a proof which only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. For some time it was thought that certain theorems, like the prime number theorem, co...
Our techniques are based on determinant properties and they are obtained by induction.doi:10.48550/arXiv.0712.0362Kouachi SaidAbdelmalek SalemRebiai BelgacemmathematicsKouachi Said, Abdelmalek Salem, Rebiai Belgacem A Mathematical Proof of Dodgson's Algo- rithm, arXiv:0712.0362...
Chapter 1 Logic and Proof Section 1.3 Techniques of Proof l
Researchers have tried employing some cryptography techniques to alleviate these challenges. However, many researchers tried to come out of the privacy issues through anonymity and achieve anonymity through identity-based, pseudonyms-based, group signature-based, and ring signature-based schemes. ...
Our scheme, called Cuproof for conveniency, is established on the techniques of Bulletproofs and Lagrange’s three-square theorem given in [17]. Our protocol can be used to construct a range proof for arbitrary range. The argument of our scheme has low computation complexity. The main differen...
To address these challenges, further advancements in privacy-preserving techniques and data encryption on the blockchain are necessary. Zero-knowledge proofs are interactive verification protocols [11]. In this protocol, based on predefined actions, a verifier can be convinced that a prover possesses ...
Theorem 1 (Marton’s conjecture)Let be non-empty with . Then there exists a subgroup of with such that is covered by at most translates of , for some absolute constant . We established this result with , although it has since been improved to ...
“Paulie, people have been trying to prove that conjecture for ninety years. Whoever finally does will be some grad student in their twenties, using techniques that don’t exist yet.” “We were close, Gina. I know it.” She meets his eye, and holds the glance a long time before reply...
The underlying concept of this study is that applying data mining techniques by combination of the already discovered biomarkers of response to SRL and patient clinical phenotype we would achieve a better stratification of the patients than using single markers. Accordingly, here we provide the ...