A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast dominat...A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast domination is a generalization of domination in which a set of broadcasting vertices emits signals of strength t that decrease by 1 as they traverse each edge, and we require that every vertex in the graph receives a cumulative signal of at least r from its set of broadcasting neighbors. In this paper, we extend the study of (t, r) broadcast domination to directed graphs. Our main result explores the interval of values obtained by considering the directed (t, r) broadcast domination numbers of all orientations of a graph G. In particular, we prove that in the cases r = 1 and (t, r) = (2, 2), for every integer value in this interval, there exists an orientation of G which has directed (t, r) broadcast domination number equal to that value. We also investigate directed (t, r) broadcast domination on the finite grid graph, the star graph, the infinite grid graph, and the infinite triangular lattice graph. We conclude with some directions for future study.展开更多
A continuous-time 7th-order Butterworth Gm-C low pass filter （LPF） with on-chip automatic tuning circuit has been implemented for a direct conversion DBS tuner in 0.35 μm SiGe BiCMOS technology. The filter＇s -3 dB...A continuous-time 7th-order Butterworth Gm-C low pass filter （LPF） with on-chip automatic tuning circuit has been implemented for a direct conversion DBS tuner in 0.35 μm SiGe BiCMOS technology. The filter＇s -3 dB cutoff frequency f0 can be tuned from 4 to 40 MHz. A novel on-chip automatic tuning scheme has been successfully realized to tune and Iock the filter＇s cutoff frequency. Measurement results show that the filter has -0.5 dB passband gain, ＋/- 5% bandwidth accuracy, 30 nV/Hz1/2 input referred noise, -3 dBVrms passband IIP3, and 27 dBVrms stopband IIP3. The I/Q LPFs with the tuning circuit draw 13 mA （with f0 = 20 MHz） from 5 V supply, and occupy 0.5 mm^2.展开更多
文摘A dominating set of a graph G is a set of vertices that contains at least one endpoint of every edge on the graph. The domination number of G is the order of a minimum dominating set of G. The (t, r) broadcast domination is a generalization of domination in which a set of broadcasting vertices emits signals of strength t that decrease by 1 as they traverse each edge, and we require that every vertex in the graph receives a cumulative signal of at least r from its set of broadcasting neighbors. In this paper, we extend the study of (t, r) broadcast domination to directed graphs. Our main result explores the interval of values obtained by considering the directed (t, r) broadcast domination numbers of all orientations of a graph G. In particular, we prove that in the cases r = 1 and (t, r) = (2, 2), for every integer value in this interval, there exists an orientation of G which has directed (t, r) broadcast domination number equal to that value. We also investigate directed (t, r) broadcast domination on the finite grid graph, the star graph, the infinite grid graph, and the infinite triangular lattice graph. We conclude with some directions for future study.
文摘A continuous-time 7th-order Butterworth Gm-C low pass filter （LPF） with on-chip automatic tuning circuit has been implemented for a direct conversion DBS tuner in 0.35 μm SiGe BiCMOS technology. The filter＇s -3 dB cutoff frequency f0 can be tuned from 4 to 40 MHz. A novel on-chip automatic tuning scheme has been successfully realized to tune and Iock the filter＇s cutoff frequency. Measurement results show that the filter has -0.5 dB passband gain, ＋/- 5% bandwidth accuracy, 30 nV/Hz1/2 input referred noise, -3 dBVrms passband IIP3, and 27 dBVrms stopband IIP3. The I/Q LPFs with the tuning circuit draw 13 mA （with f0 = 20 MHz） from 5 V supply, and occupy 0.5 mm^2.
