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D. Gernert conjectured that the sum of two largest eigenvalues of the adjacency matrix of any simple graph is at most the number of vertices of the graph. This can be proved, in particular, for all regular graphs. Gernert's conjecture was recently disproved by one of the authors [4], who also provided a nontrivial upper bound for the sum of two largest… (More)

- Javad Ebrahimi, Seyed Hossein Hosseinian, Gevorg B. Gharehpetian
- 2010

—A new evolutionary algorithm known as the shuffled frog leaping algorithm is presented in this paper, to solve the unit commitment (UC) problem. This integer-coded algorithm has been developed to minimize the total energy dispatch cost over the scheduling horizon while all of the constraints should be satisfied. In addition, minimum up/down-time… (More)

—In this paper, a new topology for cascaded multilevel converter based on submultilevel converter units and full-bridge converters is proposed. The proposed topology significantly reduces the number of dc voltage sources, switches, IGBTs, and power diodes as the number of output voltage levels increases. Also, an algorithm to determine dc voltage sources… (More)

We present a polynomial time algorithm for mul ticasting rate h to N receivers over deterministic networks. Our algorithm requires intermediate network nodes to perform coding operations over vectors of a finite length L, through multiplication with L x L binary coding matrices that play the same role as coding coefficients over graphs. Our code design… (More)

—In vector network coding, the source multi-casts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying them with L × L coding matrices that play a similar role as coding coefficients in scalar coding. Vector network coding generalizes scalar coding, and thus offers a wider range… (More)

The unit distance graph R is the graph with vertex set R 2 in which two vertices (points in the plane) are adjacent if and only if they are at Euclidean distance 1. We prove that the circular chromatic number of R is at least 4, thus improving the known lower bound of 32/9 obtained from the fractional chromatic number of R. 1. Introduction. The unit… (More)

A new procedure is presented for the determination of low concentrations of lead and cadmium in water samples. Ligand assisted pseudo-stir bar hollow fiber solid/liquid phase microextraction using sol-gel sorbent reinforced with carbon nanotubes was combined with differential pulse anodic stripping voltammetry for simultaneous determination of cadmium and… (More)

—We here summarize some recent advances in the study of linear deterministic networks, recently proposed as approximations for wireless channels. This work started by extending the algebraic framework developed for multicasting over graphs in [1] to include operations over matrices and to admit both graphs and linear deterministic networks as special cases.… (More)

A long-standing open question in information theory is to characterize the unicast capacity of a wireless relay network. The difficulty arises due to the complex signal interactions induced in the network, since the wireless channel inherently broadcasts the signals and there is interference among transmissions. Recently, Avestimehr, Diggavi and Tse… (More)