methods for solution of simultaneous linear equations

... domain finite methods for the numerical solution of time dependent Maxwell’s equations The two finite methods focused are FDTD and FETD methods The applications of the developed hybrid methods are ... mathematical properties of electromagnetic fields and Maxwell’s equations Finite methods are numerical techniques which seek solution of Maxwell’s equations in the differential form The finite methods focused ... analysis of passive microwave circuits and studies in dosimetry and tissue interaction CHAPTER TIME DOMAIN FINITE METHODS FOR SOLUTION OF MAXWELL’S EQUATIONS 2.1 Maxwell’s Equations The physics of...

Ngày tải lên: 14/09/2015, 11:39

... discuss the Itˆ formula, the Feymano Kac formula and the existence and uniqueness of solutions of SDEs These tools and results provide the basis for the application and numerical solution of stochastic ... definition of the strong error on the left hand side of (0.0.1) one notices that strong schemes provide pathwise approximations of the original solution X of the given SDE These methods are therefore ... efficient implementations of weak schemes For the approximation of the expected value of a function g of the solution X T at a final time T , there exist alternative numerical methods Under suitable...

Ngày tải lên: 19/02/2014, 22:20

... numbered then vertices of T2 and finally vertices of Tq The vertices of the same class are numbered in an arbitrary order Basic properties of optimal tours We now consider the problem of finding an optimal ... inverse direction i + 1, i, i - with e ≤ i - and i + ≤ n Proof The proof is similar to that of Proposition Proposition For n > an optimal tour of Problem B cannot pass through three successive vertices ... the altitude of its vertices Each pair of aggregate vertices is linked by an edge Applying the above solution we get an optimal tour for the new graph To obtain an optimal tour for the initial...

Ngày tải lên: 14/03/2014, 13:20

... and out of the process in various combinations * Butterworth, 4th order, with cut-offfrequency of 15 Hz ** Butterworth, 4th order, with cut-off frequency of Hz Page of 11 (page number not for citation ... Several methods were used for evaluation of the success of extraction of the volitional EMG The basic one was by visual inspection of the approximated signal which, despite not providing information ... Despite the many methods for the elimination of the ESinduced component, providing the volitional only EMG component, most of them not provide an evaluation of the accuracy of the extraction...

Ngày tải lên: 19/06/2014, 10:20

... for the electrical conductivity of water The concentrations of these ions are very small At −7 25°C, for pure water, there is a concentration of × 10 mole per liter of the hydronium ion and of ... essentially + + the concentration of the solute Therefore, for dilute solutions, {H } is equal to [H ] The existence of the hydronium ion is the basis for the definition of pH as originated by Sorensen ... portions of the sample Each of these portions is inoculated into a set of five replicate tubes For example, for the 10-mL portion, each of five fermentation tubes is inoculated with 10-mL portions of...

Ngày tải lên: 19/06/2014, 16:20

... end of crest to gage point B = axial length of converging section C = width of downstream end of flume D = width of upstream end of flume E = depth of flume F = length of throat G = length of diverging ... Beveled edge of crest of weir FIGURE 3.2 Schematic for derivation of weir formulas is, the contraction is suppressed This happens when the weir is extended fully across the width of the channel, ... of K for θ greater than 90° is 0.58 Therefore, θ 4.16 = 0.58  - tan ,  15 and θ tan = 13.45, θ = 171.49, say 171° Given available head of 0.2 m, provide a freeboard of 0.3 m; therefore,...

Ngày tải lên: 19/06/2014, 16:20

... flow radially into the side of the chamber circumscribing it, by conveying the flow forward by proper design of the impeller, and by a mix of forward and radial throw of the flow The pump that uses ... elevation of the eye of the impeller or centerline of the pump system; the second is the source tank below the eye of the impeller or centerline of the pump system The flow in flow pipes for the ... the pump At 20°C, Pv (vapor pressure of water) = 2.34 kN/m = 0.239 m of water Assume standard atmosphere of atm = 10.34 m of water Therefore, theoretical limit of pump cavitation = − (10.34 − 0.239)...

Ngày tải lên: 19/06/2014, 16:20

... because of formation of gases, makes solids rise resulting in inefficiency of the basin Thus, in practice, there is a practical range of values of 1.5 to 2.5 h based on the average flow for primary ... of combinations of the values of the elements of Vc[Xc] + Vu[Xc] can occur before the solids reach the critical section of the thickener This combination corresponds to the different speeds of ... the cross section of a grit removal unit consisting of four identical channels to remove grit for a peak flow of 80,000 m /d, an average flow 3 of 50,000 m /d and a minimum flow of 20,000 m /d There...

Ngày tải lên: 19/06/2014, 16:20

... Projected area of paddle blade Sum of projected areas of paddle blades Length of paddle blade Coefficient of drag Width of paddle blade The diameter of the impeller Diameter of vessel Distance of impeller ... length of the paddle blades of the longest compartment to that of the length of the paddle blades of the middle compartment is 2.6:2, and the ratio of the length of the paddle blades of the middle ... to each other, the rate of inflow of air corrected to its value at the surface of the vessel is then (Pi/Pa)Qi Thus, the number of bubbles n formed from a rate of inflow of air Qi is Pi Pi h  ...

Ngày tải lên: 19/06/2014, 16:20

... 0.022(q) 2.22 hd = 0.0133(q) for uniform sand, 1.0 mm diameter 2.10 for uniform anthracite, 1.0 mm diameter 2.10 for uniform anthracite, 1.6 mm diameter 2.10 for uniform anthracite, 2.0 mm diameter ... Proportionality constant for the inertial force Proportionality constant for the shear force Length of bed Expanded bed depth Filter yield Rate of mass inflow into bed Mass of cake per unit volume of filtrate ... and uniformity coefficient of a proposed filter −2 is to be 5(10 ) cm and 1.5, respectively, perform a sieve analysis to transform the run -of- bank sand of Figure 7.9 into a usable sand −2 Solution: ...

Ngày tải lên: 19/06/2014, 16:20

... function of the number of particles in solution Comparing the 1,000 mg/L concentrations of Na2SO4 and MgSO4, the osmotic pressure of the former is about to 1.4 times that of the latter In solution ... therefore, osmotic pressure depends on the number of particles in solution From this finding, osmotic pressure is, therefore, additive Determination of α mo and s The straight-line form of Equation ... pressure values of various solutes Some generalizations may be made from this table For example, comparing the osmotic pressures of 1,000 mg/L of NaCl and 1,000 mg/L of Na2SO4, the former has about...

Ngày tải lên: 19/06/2014, 16:20

... affinity of the solute to form into a solid An example of this operation is the making of ice from liquid water The formation of snow from water vapor in the atmosphere is also a process of crystallization ... performs an experiment for the purpose of determining the value of β of a particular wastewater The [Cos,w] of the wastewater after shaking the jar thoroughly is 7.5 mg/L The temperature of the ... viscosity of fluid Mass density of the gas phase (air) Mass density of fluid Surface tension of fluid PROBLEMS 9.1 9.2 The value of (KLa)20 for a certain industrial waste is 2.46 per hour and the value of...

Ngày tải lên: 19/06/2014, 16:20

... removed in the form of CaCO3 This is the reason for the use of the second chemical known as soda ash for the removal of the noncarbonate hardness of calcium Thus, another set of chemical reactions ... the number of reference species is moles of positive charges for each of these reactions Thus, the equivalent mass of calcium is Ca/2 and the number of equivalents of the MCa mass of calcium ... use of alkalinity in any of the softening equations, yet, in the literature, this parameter is used in softening calculations The reason is that the use of this parameter in softening is often...

Ngày tải lên: 19/06/2014, 16:20

... smallest Ksp value is the one that can form a dead end −5 for the carbonate equilibria reactions Mg forms MgCO3 with a Ksp of 10 Ca forms −9 CaCO3 with a Ksp of 4.8(10 ) Table 11.3 shows other carbonate ... smallest of the Ksp’s is that for Hg2CO3 Thus, considering all of the possible candidates that we have written, Hg2CO3 is the one that will form a dead end for the carbonate equilibria; however, of ... amount of calcium carbonate that precipitates is simply the equivalent of the calcium ion that precipitates, Cappt Because the number of moles of Cappt is equal to the number of moles of the...

Ngày tải lên: 19/06/2014, 16:20

... concentrations of each of these complex ions are determined by the pH of the solution In the application of the above equations in an actual coagulation treatment of water as in all applications of coagulants, ... be used Therefore, we now derive the formulas for estimating the volume of sludge produced in coagulation treatment of water Two sources of solids are available for the production of sludge: the ... chlorine Acidity—The capacity of a solution to absorb the effect of the addition of a base Alkalinity—The capacity of a solution to absorb the effect of the addition of an acid © 2003 by A P Sincero...

Ngày tải lên: 19/06/2014, 16:20

... reason for the high pH values for the removal of iron as Fe(OH)2 and for the removal of + manganese as Mn(OH)2 is the formation of the complex ions These ions are FeOH + − − and Fe (OH) for the ... means that the concentrations of each of these complex ions are determined by the pH of the solution In the application of the previous equations in an actual treatment of water, conditions must ... kilograms of lime used for the manganous reaction MNaOHMn = kilograms of caustic used for the manganous reaction M Cl2 Mn = kilograms of chlorine used for the manganous reaction MNaClOMn = kilograms of...

Ngày tải lên: 19/06/2014, 16:20

... than the range for the use of either alum or ferric salts 14.8 UNIT OPERATIONS FOR PHOSPHORUS REMOVAL The removal of phosphorus involves provision for the addition of chemicals both for adjusting ... liter of suspended solids in raw water Cubic meters of water treated Water of hydration of alum Activity coefficient of the calcium ion Activity coefficient of the hydrogen ion Activity coefficient of ... efficiency of removal of phosphorus Would this really happen? The answer would be yes, but this could be a good topic for applied research A concentration of zero for the calcium ion is, of course,...

Ngày tải lên: 19/06/2014, 16:20

... unit mass of BOD5 or mass of organisms or cells per unit mass of COD For the case of Ydn, the units used in practice are in terms of mass of the organisms or cells per unit of mass of the nitrate ... (productions) for Nitrosomonas of 0.04 to 0.29 milligrams of the bacteria per milligram of NH4–N destroyed and cell yields for Nitrobacter of 0.02 to 0.084 milligrams of the bacteria per milligrams of NO2–N ... rate of increase of the concentration of the organisms The first term on the right-hand side of Equation (15.71) is the rate of increase of microorganism that corresponds to the rate of decrease of...

Ngày tải lên: 19/06/2014, 16:20

... exchange capacity of the bed be (X/M )ult meq/g of bed The equivalents of ion displaced from the bed is equal to the equivalents of displacing ion in solution; therefore, the mass of bed material ... corresponding volume is 3.47/1000 = 0.0035 m For an interval of regeneration of h and assuming a rate of flow for the water treated of 75 m /d, the volume of water treated is 75/24(8) = 25 m Thus, ... 16.6.1 QUANTITY OF EXCHANGE MATERIALS Before discussing quantities of exchange materials, a method of expressing exchange capacity in terms of calcium carbonate is addressed This method of expressing...

Ngày tải lên: 19/06/2014, 16:20

... is formed, the gas must have already been forming, and that for the dichloramine to be formed, more HOCl is needed than is needed for the formation of the gas The reaction for the formation of ... the unit of disinfecting power of NaOCl is NaOCl/2 = 37.24 Therefore, the available chlorine of NaOCl is the ratio of the mass of chlorine to the mass of NaOCl that has the same unit of oxidizing ... Because the hydroxyl is involved, this would mean that chloroform formation is enchanced at high pH To prevent formation of the chloroform, all that is necessary © 2003 by A P Sincero and G A Sincero...

Ngày tải lên: 19/06/2014, 16:20