Relaying over power line communication (PLC) channels can considerably enhance the performance and reliability of PLC systems. This paper is dedicated to study and analyze the energy efficiency of multi-hop cooperative relaying PLC systems. Incremental decode-and-forward (IDF) relying is exploited to reduce the transmit power consumption. The PLC channel is assumed to experience log-normal fading with impulsive noise. The performances of single-hop and conventional DF relaying systems are also analyzed in terms of outage probability and energy efficiency for which analytical expressions are derived. Results show that using more relays can improve the outage probability performance; however, this is achieved at the expense of increased power consumption due to the increased static power of the relays, especially when the total source-to-destination distance is relatively small. Results also demonstrate that the IDF PLC system has better energy efficiency performance compared to the other schemes.

Taking the Iwaniec explicit formula as a starting point, we give a short proof of a more precise $\frac{2}{3}$ bound for the exponent in the error term of the Gallagher-type prime geodesic theorem for the modular surface.

Abstract This paper investigates the financial and social efficiency of microfinance institutions (“MFIs”) in Bosnia and Herzegovina, as well as the effects of the latest crisis on these “two-dimensional” efficiencies. Specifically, we analyze the efficiency of MFIs in Bosnia and Herzegovina (BiH) as a good case of a European, post-war country in transition with a developed micro-financial sector. The efficiency analysis relies on secondary data collected and investigated through Data Envelopment Analysis (DEA). The study covers data for the period commencing in 2008 and ending in 2015. In our empirical investigation, we find a suboptimal level of both financial and social efficiency among MFIs in BiH. However, financial efficiency is significantly higher than social efficiency, while small-sized MFIs over perform larger ones in both the financial and social dimensions. As a result of the crisis, MFIs recorded a declining trend in efficiency up to 2010, after which they began to show signs of slow recovery. However, our results suggest that MFIs prioritized financial over social goals in recovery period following the crisis.