Gallery — Math

Mathematical Induction paper

Group Isomorphisms

Simultaneous information and energy transfer (SIET) is attracting much attention as an effective method to provide green energy supply for mobiles. However, low power level of harvested energy from RF spectrum limits application of this technique. Thanks to improvement of sensitivity and efficiency of RF energy harvesting circuit as well as dense deployment of small cell base stations, SIET becomes more practical. In this paper, we propose a unified receiver model for SIET in LTE-A small cell base station networks, formulate a feasibility problem with Poisson point process model and analyze the feasibility for a special and practical scenario. The results show that it is feasible for mobiles to charge the secondary battery with harvested energy from BSs, but it is still impractical to directly charge the primary battery or operate without any battery at all.

A logic/math puzzle and solution.

A theorem I wrote describing how improper integrals of some functions can be expressed as proper integrals of inverses of these functions, with constraints to the integrand function.

A proof of a number being divisible by 4

A revised 6.046 Problem Set template which meets all of the submission format requirements and also has no template warnings/errors.

The Sine Rule

Sample Homework for Derivatives