Physical Sciences and Mathematics Commons^™

Signal Flow Graph Approach To Efficient Dst I-Iv Algorithms, Sirani M. Perera

Sirani Mututhanthrige Perera

In this paper, fast and efficient discrete sine transformation (DST) algorithms are presented based on the factorization of sparse, scaled orthogonal, rotation, rotation-reflection, and butterfly matrices. These algorithms are completely recursive and solely based on DST I-IV. The presented algorithms have low arithmetic cost compared to the known fast DST algorithms. Furthermore, the language of signal flow graph representation of digital structures is used to describe these efficient and recursive DST algorithms having (n􀀀1) points signal flow graph for DST-I and n points signal flow graphs for DST II-IV.

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Distance-Varying Assortativity And Clustering Of The International Trade Network, Angela Abbate, Luca De Benedictis, Giorgio Fagiolo, Lucia Tajoli

Luca De Benedictis

Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

Brandon Russell

Power-Law Scaling Of Extreme Dynamics Near Higher-Order Exceptional Points, Q. Zhong, Demetrios N. Christodoulides, M. Khajavikhan, K. G. Makris, Ramy El-Ganainy

Ramy El-Ganainy

We investigate the extreme dynamics of non-Hermitian systems near higher-order exceptional points in photonic networks constructed using the bosonic algebra method. We show that strong power oscillations for certain initial conditions can occur as a result of the peculiar eigenspace geometry and its dimensionality collapse near these singularities. By using complementary numerical and analytical approaches, we show that, in the parity-time (PT) phase near exceptional points, the logarithm of the maximum optical power amplification scales linearly with the order of the exceptional point. We focus in our discussion on photonic systems, but we note that our results apply to other …

The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

Sandy Avila

No abstract provided.

Global Stability For A 2n+1 Dimensional Hiv Aids Epidemic Model With Treatments, Olusegun M. Otunuga

Olusegun Michael Otunuga

Motion Planning For Educational Robots, Ronald I. Greenberg, Jeffery M. Karp

Ronald Greenberg

This paper considers various simple ways of navigating in a 2-dimensional territory with a two-wheeled robot of a type typical in educational robotics. We determine shortest paths under various modes of operation and compare.

An Interval Arithmetic Newton Method For Solving Systems Of Nonlinear Equations, Ronald I. Greenberg, Eldon R. Hansen

Ronald Greenberg

We introduce an interval Newton method for bounding solutions of systems of nonlinear equations. It entails three sub-algorithms. The first is a Gauss-Seidel type step. The second is a real (non-interval) Newton iteration. The third solves the linearized equations by elimination. We explain why each sub-algorithm is desirable and how they fit together to provide solutions in as little as 1/3 to 1/4 the time required by a commonly used method due to Krawczyk.

Reproducible Research For Computing In Science & Engineering, Lorena A. Barba, George K. Thiruvathukal

George K. Thiruvathukal

The editors of the new track for reproducible research outline the parameters for future peer review, submission, and access, highlighting the magazine’s previous work in this field and some of the challenges still to come.

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