Abstract: In this paper we show that there are applications that transform the movement of a pendulum into movements in R3. This can be done using Euler top system of differential equations. On the constant level surfaces, Euler top system reduces to the equation of a pendulum. Those properties are also considered in the case of system of differential equations with delay argument and in the fr...

In this paper, we observe the behavior of complex roots of the generalized Euler polynomials Ẽn(x) of the second kind, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the generalized Euler polynomials Ẽn(x) of the second kind. Finally, we give a table for the solutions of the generalized Euler polynomials Ẽn...

Abstract In this paper we observe the behavior of complex roots of q-Euler numbers and polynomials Ẽ n,q (x) with weak weight α, using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of q-Euler numbers and polynomials Ẽ n,q (x) with weak weight α. Finally, we give a table for the solutions of q-Euler numbers and poly...

In this paper, we introduce a technique to find the cyclic path covering number of Euler graphs, by using the t-hypohamiltonian graphs. Also a special type of Euler graph in the name n-gon is also being introduced and a general result of cpcn of n-gon is also found. Finally an algorithm to find the cyclic path covering number of any Euler graph is being developed. AMS subject classification: 54...

The main object of this paper is to investigate the Apostol-Bernoulli polynomials and the Apostol-Euler polynomials. We first establish two relationships between the generalized Apostol-Bernoulli and Apostol-Euler polynomials. It can be found that many results obtained before are special cases of these two relationships. Moreover, we have a study on the sums of products of the Apostol-Bernoulli...

Euler Tour trees are due to Henzinger and King [1] and are an alternative to link-cut trees for representing dynamic trees. Euler tour trees are simpler and easier to analyze than link-cut trees, but do not naturally store aggregate information about paths in the tree. Euler tour trees are well suited for storing aggregate information on subtrees, which is a feature we will use in the next sect...

Following the pioneering work of Schapira, we consider topological Radon-type integral transforms on constructible Z-valued functions using the Euler characteristic as a measure. Contributions include: (1) application of the Schapira inversion formula to target localization and classification problems in sensor networks; (2) extension and application of the inversion formula to weighted Radon t...

We determine several necessary and sufficient conditions for a closed almost-complex orbifold Q with abelian local groups to admit a nonvanishing vector field. These conditions are stated separately in terms of the orbifold Euler-Satake characteristics of Q and the connected components of its twisted sectors, the Euler characteristics of the underlying topological spaces of Q and the components...

Diagrams in the Mind: Visual or Spatial? p. 1 Understanding Diagrams, and More: The Computer's View p. 2 Tutorials Diagrams: A Perspective from Logic (Invited Talk) p. 3 Drawing Euler Diagrams for Information Visualization (Invited Talk) p. 4 Graduate Student Symposium The Graduate Student Symposium of Diagrams 2010 (Invited Talk) p. 5 Euler and Venn Diagrams The Efficacy of Euler and Venn Diag...

For the standard one sector stochastic optimal growth model, we outline a new set of conditions for a policy function that satisfies the Ramsey-Euler equation to be optimal. An interior Ramsey-Euler policy function is optimal if (and only if) it is continuous or alternatively, if both consumption and investment are non-decreasing in output. One does not need to verify the transversality conditi...