Let NSymm be the Hopf algebra of noncommutative symmetric functions over the integers. In this paper a description is given of its Lie algebra of primitives over the integers, Prim(NSymm), in terms of recursion formulas. For each of the primitives of a basis of Prim(NSymm), indexed by Lyndon words, there is a recursively given divided power series over it. This gives another proof of the theore...

In this paper capacity withholding in an oligopolistic electricity market that all Generation Companies (GenCos) bid in a Cournot model is analyzed and the capacity withheld index, the capacity distortion index and the price distortion index are obtained and formulated. Then a new index, Distortion-Withheld Index (DWI), is proposed in order to measure the potential ability of market for capacit...

Despite the importance of crystalline lens power in ocular development, schematic refractive index values used to calculate lens power have been validated for children. We measured refractive error and ocular component dimensions in 519 schoolchildren, calculating lens power using phakometrically measured lens radii and three different refractive index profiles: (1) Gullstrand-Emsley schematic ...

In this work we examine power measures used in the analysis of voting games to quantify power. We consider both weighted and non-weighted voting games giving simple examples of each. The power indices considered are the Shapley-Shubik [8] index, the Banzho index [1], the Penrose [7] index and Coleman [2] indices. We apply them to speci c examples taken from recent Canadian parliaments and to th...

The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

we propose a new ring resonator side-coupled m-z interferometer all-optical switch throughthe pumped nonlinear directional coupler. by controlling pump power p to lead the coupler reflectivityr approaching to 1, the resonator finesse will be enhanced dramatically, and then the minimumswitching power in silica-based practice devices can be obtained. as a sample, we use a nonlinearcoupler made by...

Power MOSFETs based on superjunction technology have become the industry norm in high-voltage switching converters. They offer lower RDS(on) simultaneously with reduced gate and output charges, which allows for more efficient switching at any given frequency. Prior to the availability of superjunction MOSFETs the dominant design platform for high-voltage devices was based on planar technology. ...

In this paper we analyze ternary bicooperative games, which are a refinement of the concept of a ternary voting game introduced by Felsenthal and Machover. Furthermore, majority voting rules based on the difference of votes are simple bicooperative games. First, we define the concepts of the defender and detractor swings for a player. Next, we introduce the Banzhaf power index and the normalize...

In the most recent heuristic methods, the high potential buses for capacitor placement are initially identified and ranked using loss sensitivity factors (LSFs) or power loss index (PLI). These factors or indices help to reduce the search space of the optimization procedure, but they may not always indicate the appropriate placement of capacitors. This paper proposes an efficient approach for t...

The management of power systems has become more difficult than earlier because power systems are operated closer to security limits, environmental constraints restrict the expansion of transmission network, the need for long distance power transfer has increased and fewer operators are engaged in the supervision and operation of power systems. Voltage stability has become a major concern in man...