9,738 research outputs found
Transformations of Heun's equation and its integral relations
We find transformations of variables which preserve the form of the equation
for the kernels of integral relations among solutions of the Heun equation.
These transformations lead to new kernels for the Heun equation, given by
single hypergeometric functions (Lambe-Ward-type kernels) and by products of
two hypergeometric functions (Erd\'elyi-type). Such kernels, by a limiting
process, also afford new kernels for the confluent Heun equation.Comment: This version was published in J. Phys. A: Math. Theor. 44 (2011)
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Prepose: privacy, security, and reliability for gesture-based programming
With the rise of sensors such as Microsoft Kinect, gesture-based interfaces have become practical. However, to recognize such gestures, applications need access to users' depth and video, exposing sensitive data about individuals and their environment. Prepose, a domain-specific language for building gesture recognizers, combined with a system architecture that protects privacy, security, and reliability with untrusted applications, addresses these threats
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