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Full-Text Articles in Physical Sciences and Mathematics
A Note On Eulerian Numbers And Toeplitz Matrices, Tian-Xiao He, Peter J.-S. Shiue
A Note On Eulerian Numbers And Toeplitz Matrices, Tian-Xiao He, Peter J.-S. Shiue
Mathematical Sciences Faculty Research
This note presents a new formula of Eulerian numbers derived from Toeplitz matrices via Riordan array approach.
Fundamental Results On S-Closures, William D. Taylor
Fundamental Results On S-Closures, William D. Taylor
Mathematical Sciences Faculty Research
This paper establishes the fundamental properties of the s-closures, a recently introduced family of closure operations on ideals of rings of positive characteristic. The behavior of the s-closure of homogeneous ideals in graded rings is studied, and criteria are given for when the s-closure of an ideal can be described exactly in terms of its tight closure and rational powers. Sufficient conditions are established for the weak s-closure to equal to the s-closure. A generalization of the Briancon-Skoda theorem is given which compares any two different s-closures applied to powers of the same ideal.
Towards A Novel Generalized Chinese Remainder Algorithm For Extended Rabin Cryptosystem, Justin Zhan, Peter J. Shiue, Shen C. Huang, Benjamin J. Lowe
Towards A Novel Generalized Chinese Remainder Algorithm For Extended Rabin Cryptosystem, Justin Zhan, Peter J. Shiue, Shen C. Huang, Benjamin J. Lowe
Mathematical Sciences Faculty Research
This paper proposes a number of theorems and algorithms for the Chinese Remainder Theorem, which is used to solve a system of linear congruences, and the extended Rabin cryptosystem, which accepts a key composed of an arbitrary finite number of distinct primes. This paper further proposes methods to relax the condition on the primes with trade-offs in the time complexity. The proposed algorithms can be used to provide ciphertext indistinguishability. Finally, this paper conducts extensive experimental analysis on six large data sets. The experimental results show that the proposed algorithms are asymptotically tight to the existing decryption algorithm in the …
Finite Element Analysis Of An Arbitrary Lagrangian–Eulerian Method For Stokes/Parabolic Moving Interface Problem With Jump Coefficients, Rihui Lan, Michael J. Ramirez, Pengtao Sun
Finite Element Analysis Of An Arbitrary Lagrangian–Eulerian Method For Stokes/Parabolic Moving Interface Problem With Jump Coefficients, Rihui Lan, Michael J. Ramirez, Pengtao Sun
Mathematical Sciences Faculty Research
In this paper, a type of arbitrary Lagrangian–Eulerian (ALE) finite element method in the monolithic frame is developed for a linearized fluid–structure interaction (FSI) problem — an unsteady Stokes/parabolic interface problem with jump coefficients and moving interface, where, the corresponding mixed finite element approximation in both semi- and fully discrete scheme are developed and analyzed based upon one type of ALE formulation and a novel H1- projection technique associated with a moving interface problem, and the stability and optimal convergence properties in the energy norm are obtained for both discretizations to approximate the solution of a transient Stokes/parabolic interface problem …