SIR Analysis Via Signal Fractions

High dimensional data analysis via the SIR/PHD approach

Solved via Continued Fractions

The purpose of this article is to provide criteria for the solvability of the Diophantine equation a2X2− bY 2 = c in terms of the simple continued fraction expansion of √ a2b, and to explore criteria for the solvability of AX2 − BY 2 = C for given A, B, C ∈ N in the general case. This continues work in [9]–[11].

Sustained oscillations via coherence resonance in SIR.

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic a...

Addition Theorems via Continued Fractions

We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for Bessel functions and confluent hypergeometric functions. We also derive several addition theorems for basic hypergeometric functions. Applications to the evaluat...

An Approach to Fractions Via Measurement

No matter how many diagrams they see of pizzas divided into slices, students have persistent difficulties with understanding fractions. What does a fraction mean? Where do the rules for fraction arithmetic come from? What does multiplication, or division, of fractions represent? What is the role of “proportional reasoning” in all this? What is the significance of the rational number system whic...