A Computational Quadruple Laplace Transform for the Solution of Partial Differential Equations

In this paper, we proposed new results in quadruple Laplace transform and proved some properties concerned with quadruple Laplace transform. We also developed some applications based on these results and solved homogeneous as well as non-homogeneous partial differential equations involving four variables. The performance of quadruple Laplace transform is shown to be very encouraging by concrete examples. An elementary table of quadruple Laplace transform is also provided.

On-chip classification of micro-particles using laser light scattering and machine learning

The rapid detection of microparticles exhibits a broad range of applications in the field of science and technology. The proposed method differentiates and identifies the 2 μm and 5 μm sized particles using a laser light scattering. The detection method is based on measuring forward light scattering from the particles and then classifying the acquired data using support vector machines. The device is composed of a microfluidic chip linked with photosensors and a laser device using optical fiber. Connecting the photosensors and laser device using optical fibers makes the device more diminutive in size and portable. The prepared sample containing microspheres was passed through the channel, and the surrounding photosensors measured the scattered light. The time-domain features were evaluated from the acquired scattered light, and then the SVM classifier was trained to distinguish the particle’s data. The real-time detection of the particles was performed with an overall classification accuracy of 96.06%. The optimum conditions were evaluated to detect the particles with a minimum concentration of 0.2 μg/m L. The developed system is anticipated to be helpful in developing rapid testing devices for detecting pathogens ranging between 2 μm to 10 μm.