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/********************************************************************************** buildHW: constructs a lognormal Hull-White tree calibrated to the yield curve [in]: vector<double> zero : vector of zero rates double a : speed of mean reversion double volatility : volatility of short rate int N : number of time steps double T : time to maturity [out]: void **********************************************************************************/ void HullWhite::buildHW(vector<double> zero, double a, double volatility, int N, double T) { int i, j, k; int jmax; // max upward branch int jmin; // min downward branch double pu[20] = {0.0}; // up probabilities double pm[20] = {0.0}; // middle probabilities double pd[20] = {0.0}; // down probabilities double sum = 0.0; // sum of shifted discount Arrow-Debreu // securities double sum1 = 0.0; // sums of discount Arrow-Debreu // securities double sum2[20] = {0.0}; // sum of weighted discount Arrow-Debreu // securities double alpha[20] = {0.0}; // the value of r(i*dt) r*(i*dt) double alpha1[20][20]; // alpha value at node i, j double B[20] = {0.0}; // discount bond price at time step i double dt = T/N; // time step size double dr = volatility*sqrt(3*dt); // state step size jmax = (int) ceil(0.1835/(a*dt)); jmin = -jmax; B[0] = 1;



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The storage and production of fuels for fuel cells is currently under investigation by numerous research and development groups worldwide Its impact on the electric efficiency and profitability of any type of fuel cell system is probably as important as the fuel cell design itself Among the many proposed and investigated variants to supply hydrogen for the electrochemical oxidation process, the steam reforming concept has emerged as one of the most promising A fuel which can either easily be stored or is available at the fuel cell site for example gasoline, diesel fuel or natural gas undergoes a reaction with water vapor to produce hydrogen and several byproducts Often, this reforming product must be cleaned up before being fed into the fuel cell.

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The key issue with reforming is the supply of heat to the endothermic process and the demand for high temperatures in order to obtain high reaction rates and favorable chemical equilibria Whilst for low-temperature fuel cells this heat must be provided by external sources (eg, the direct oxidation of a part of the feed gas), hightemperature fuel cells such as the Solid Oxide Fuel Cell (SOFC) and Molten Carbonate Fuel Cell (MCFC) can act as a heat source for the reforming process This idea leads to a direct internal reforming (DIR) concept in which the endothermic reforming process is integrated into the fuel cell where the exothermic electrochemical reactions occur The interactions of both processes are based on their mass and energy coupling The use of mathematical models is probably the best way to gain a deeper understanding of the interactions of in-situ reforming and electrochemical oxidation.

default_properties.put( Context.INITIAL_CONTEXT_FACTORY, org.jnp.interfaces.NamingContextFactory ); default_properties.put( Context.PROVIDER_URL, localhost:1099 );

Some research groups working on the modeling of MCFC include the reforming reactions in their process models in different ways He and Chen [1] and Yoshiba et al [2] only consider the water gas shift reaction in a spatially distributed anode channel Due to its high rate, they assume the shift reaction to be in chemical equilibrium Lukas and Lee [3] and Park et al [4] also describe the water gas shift reaction in equilibrium, but in addition they include the steam reforming reaction of methane as an irreversible reaction with a finite reaction rate In particular, Park.

In order to select one object out of N objects, n = IdN bit of information is needed. 1dN is the logurithrnus dualis of N , i.e., the logarithm of N to the base 2. For example: In order to select one out of 1024 objects, Id 1024 = ld2" = 10 bit of information is required. Any information process, e.g., receiving a telegram may be regarded as answering a series of questions which allow alternative or multiple choice answers. It defines an information deficit, referred to as the entropy H , which is a positive quantity: (3.3-25)

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