‎An  oriented perfect path double cover (OPPDC) of a‎ ‎graph $G$ is a collection of directed paths in the symmetric‎ ‎orientation $G_s$ of‎ ‎$G$ such that‎ ‎each arc‎ ‎of $G_s$ lies in exactly one of the paths and each‎ ‎vertex of $G$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎Maxov{'a} and Ne{v{s}}et{v{r}}il (Discrete‎ ‎Math‎. ‎276 (2004) 287-294) conjectured that ...

New methodologies are designed to reduce the time complexity of an implicit discrete-time differentiator and simulation implement it. They rely on Horner’s method Shaw-Traub algorithm. The algorithms compared for differentiators order 3, 7, 10. Half-Horner Full-Horner methods showed best performance complexity.

In this article the elementary mathematical methods are used to prove Beal’s Conjecture, Fermat’s Collatz Conjecture and Goldbach Conjecture.

The widely acclaimed animated movie, Kung Fu Panda, provides an interesting resource for teaching concepts of motivation including Intrinsic and Extrinsic Motivation, Self-efficacy, Self-fulfilling Prophecy Vroom’s Expectancy Theory. This article clip-by-clip examples that exhibit these along with discussion prompts probable answers facilitate engagement understanding among students. Time stamp...

* Both authors are affiliated with the Department of Finance, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong. The second author is also affiliated with the University of British Columbia. We would like to thank K. C. Chan, Sudipto Dasgupta, Vojislav Maksimovic, Anjan Thakor, Sheridan Titman, and the seminar participants at the Hong Kong University of Science...

A distinguishing r-labeling of a digraph G is a mapping λ from the set of vertices of G to the set of labels {1, . . . , r} such that no nontrivial automorphism of G preserves all the labels. The distinguishing number D(G) of G is then the smallest r for which G admits a distinguishing r-labeling. From a result of Gluck (David Gluck, Trivial set-stabilizers in finite permutation groups, Can. J....

by the mordell-weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎there is no known algorithm for finding the rank of this group‎. ‎this paper computes the rank of the family $ e_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

let $g$ be a finite group and let $text{cd}(g)$ be the set of all‎ ‎complex irreducible character degrees of $g$‎. ‎b‎. ‎huppert conjectured‎ ‎that if $h$ is a finite nonabelian simple group such that‎ ‎$text{cd}(g) =text{cd}(h)$‎, ‎then $gcong h times a$‎, ‎where $a$ is‎ ‎an abelian group‎. ‎in this paper‎, ‎we verify the conjecture for‎ ${f_4(2)}.$‎

We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).