The investigation of determining solutions for the Diophantine equation  over the Gaussian integer ring for the specific case of  is discussed. The discussion includes various preliminary results later used to build the resolvent theory of the Diophantine equation studied. Our findings show the existence of infinitely many solutions. Since the analytical method used here is based on simple algebraic properties, it can be easily generalized to study the behavior and the conditions for the existence of solutions to other Diophantine equations, allowing a deeper understanding, even when no general solution is known.

Nd:YAG laser pulses of 9 nanosecond pulse duration and operating wavelength at 1.06 μm, were utilized to drill high thermal conductivity and high reflectivity aluminum and copper foils. The results showed a dependence of drilled holes characteristics on laser power density and the number of laser pulses used. Drilled depth of 74 ϻm was obtained in aluminum at 11.036×108 W/cm2 of laser power density. Due to its higher melting point, copper required higher laser power density and/or larger number of laser pulses to melt, and a maximum depth of 25 μm was reached at 13.46×108 W/cm2 using single laser pulse.

<p>Energy and memory limitations are considerable constraints of sensor nodes in wireless sensor networks (WSNs). The limited energy supplied to network nodes causes WSNs to face crucial functional limitations. Therefore, the problem of limited energy resource on sensor nodes can only be addressed by using them efficiently. In this research work, an energy-balancing routing scheme for in-network data aggregation is presented. This scheme is referred to as Energy-aware and load-Balancing Routing scheme for Data Aggregation (hereinafter referred to as EBR-DA). The EBRDA aims to provide an energy efficient multiple-hop routing to the destination on the basis of the quality of the links between the source and destination. In