The RSA is based on a trapdoor one-way function which is easy to compute but is most hard to revert without knowing the trapdoor. A cryptanalysis, presented in this paper, consists in finding a new decrypt key which plays the same role of the original trapdoor. To find this new decrypt key we must seek the maximum degree of ciphering function composition in a given modulus N. The maximum degree...

The cross-correlation matrix between equities comprises multiple interactions between traders with varying strategies and time horizons. In this paper, we use the Maximum Overlap Discrete Wavelet Transform (MODWT) to calculate correlation matrices over different time scales and then explore the eigenvalue spectrum over sliding time windows. The dynamics of the eigenvalue spectrum at different s...

We present a nonsmooth optimization technique for nonconvex maximum eigenvalue functions and for nonsmooth functions which are infinite maxima of eigenvalue functions. We prove global convergence of our method in the sense that for an arbitrary starting point, every accumulation point of the sequence of iterates is critical. The method is tested on several problems in feedback control synthesis.

Using finite element method (FEM), this study sought to investigate how the thickness and Young's modulus of cortical bone influenced stress distribution in bone surrounding a dental implant. The finite element implant-bone model consisted of a titanium abutment, a titanium fixture, a gold alloy retaining screw, cancellous bone, and cortical bone. The results showed that von Mises equivalent st...

The signless Laplacian separator of a graph is defined as the difference between the largest eigenvalue and the second largest eigenvalue of the associated signless Laplacian matrix. In this paper, we determine the maximum signless Laplacian separators of unicyclic, bicyclic and tricyclic graphs with given order.

The Laplacian spread of a graph is defined to be the difference between the largest eigenvalue and the second smallest eigenvalue of the Laplacian matrix of the graph. In this paper, we investigate Laplacian spread of graphs, and prove that there exist exactly five types of tricyclic graphs with maximum Laplacian spread among all tricyclic graphs of fixed order.

A second-order bundle method to minimize the maximum eigenvalue function François Oustry

Quick extraction of the largest modulus eigenvalues of a real antisymmetric matrix is important for some engineering applications. As neural network runs in concurrent and asynchronous manner in essence, using it to complete this calculation can achieve high speed. This paper introduces a concise functional neural network (FNN), which can be equivalently transformed into a complex differential ...

This note investigates the least eigenvalues of connected graphs with n vertices and maximum degree ∆, and characterizes the unique graph whose least eigenvalue achieves the minimum among all the connected graphs with n vertices and maximum vertex degree ∆ > n 2 .

This note investigates the least eigenvalues of connected graphs with n vertices and maximum degree ∆, and characterizes the unique graph whose least eigenvalue achieves the minimum among all the connected graphs with n vertices and maximum vertex degree ∆ > n 2 .