Kyle Clarkson

University of British Columbia - Vancouver | UBC · Department of Computer Science

In this work we consider competitive strategies for the convex polygon inspection problem where a mobile agent must explore the exterior of a convex polygon in the plane without prior knowledge of the polygon's shape. The agent starts at a point exterior to the polygon and can see infinitely far in all directions; however, the polygon occludes its...

In today’s social media world we are provided with an impressive amount of data about users and their societal interactions. This offers computer scientists among others many new opportunities for research exploration. Arguably, one of the most interesting areas of work is that of predicting events and developments based on social media data and tr...

This paper is to study certain types of fractional differential and integral equations, such as θ ( x − x 0 ) g ( x ) = 1 Γ ( α ) ∫ 0 x ( x − ζ ) α − 1 f ( ζ ) d ζ , y ( x ) + ∫ 0 x y ( τ ) x − τ d τ = x + − 2 + δ ( x ) , and x + k ∫ 0 x y ( τ ) ( x − τ ) α − 1 d τ = δ ( m ) ( x ) in the distributional sense by Babenko’s approach and fractional cal...

The goal of this paper is to investigate the following Abel's integral equation of the second kind: y(t) + λ /Γα ∫t0 (t - τ)α-1y(τ)dτ = f (t), (t > 0) and its variants by fractional calculus. Applying Babenko's approach and fractional integrals, we provide a general method for solving Abel's integral equation and others with a demonstration of diff...

This paper begins to present relations among the convolutional definitions given by Fisher and Li, and further shows that the following fractional Taylor's expansion holds based on convolution \[ \frac{d^\lambda}{d x^\lambda} \theta (x) \phi(x) = \sum_{k = 0}^{\infty} \frac{\phi^{( k)}(0)\, x_+^{k - \lambda }}{\Gamma(k - \lambda + 1)} \quad \mbox{i...