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Geissler, E and J Van Courtland Moon, Eds (1999) Biological and Toxin Weapons: Research, Development and Use from the Middle Ages to 1945 Sipri Chemical & Biological Warfare Studies, No 18 New York: Oxford University Press Gleick, J (1999) Faster New York: Random House Gold, H (1996) Unit 731 Testimony New York: Charles E Tuttle Co Harris, R and J Paxman (2002) A Higher Form of Killing: The Secret History of Chemical and Biological Warfare New York: Random House Harris, S (2001) Factories of Death: Japanese Biological Warfare, 1932 45 and the American Cover-Up New York: Routledge International Institute for Strategic Studies wwwiissorg Kenakin, T (1997) Molecular Pharmacology Cambridge, MA: Blackwell Science MacKenzie, D (2002) Secret Gas Changes Face of Urban War NewSci entist 176(2367): 6 Mangold, T and J Goldberg (2002) Plague Wars: The Terrifying Reality of Biological Warfare New York: St Martin Grif n McClellan, J.

The linear combination of fn(x) should well represent the unknown f(x) in the domain. Substitute (2.2.2) into (2.2.1), we have

dx'G(x, x')fn(x') = c(x)

(2.2.3)

When a method is shared, you no longer need to create an object from the class before using the method So instead of using code that looks like this:

The unknown coefficients b1 , b2, ... , bN are to be determined. (2) Next a set of N weighting functions (testing functions) WI (x), W2 (x), ... , WN(X) is chosen. Multiply (2.2.3) by wm(x) and integrate over the domain

dxwm(x)

dx'G(x,x')fn(x') =

dxwm(x)c(x)

(2.2.4)

Dim prod as Product prod = New Product prod = prodCreate(1)

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and H Dorn (1999) Science and Technology in World His tory Baltimore: The Johns Hopkins University Press Miller, J, S Engelberg, and W Broad (2002) Germs: Biological Weapons and America s Secret War New York: Simon & Schuster Oliver, R (1999) The Coming Biotech Age: The Business of Bio-Materials New York: McGraw-Hill Porter, D (1997) The Greatest Bene t to Mankind New York: WW Norton and Co Ross, D (2002) Introduction to Molecular Medicine New York: Springer Verlag Shulman, S (2002) Of Oncomice and Men MIT Technology Review 105(7): 87 Stipp, D (2002) China s Biotech is Starting to Bloom Fortune 146(4): 126 34 Stix, G (2002) The Universal Biosensor Scienti c American 287(5): 37 9 Stock, G (2002) Redesigning Humans: Our Inevitable Genetic Future New York, Houghton Mif in Company Whitby, S (2002) Biological Warfare Against Crops New York, Palgrave Macmillan.

(2.2.5)

dxwm(x)c(x) = (wm,c)

(2.2.6) (2.2.7)

dxwm(x)

the code instead looks like this:

dx'G(x,x')fn(x') = (wm,Gfn)

(1, g) =

dx f(x) g(x)

(2.2.8)

White House Of ce of Management and Budget, The wwwwhitehouse gov/omb/budget/fy2003/budgethtml Zilinskas, R, Ed (1999) Biological Warfare: Modern Offense and De fense Boulder, CO: Lynne Rienner Publishers..

Dim prod as Product prod = ProductCreate(1)

Generally (2.2.5) is a full matrix equation. We note the following (1) Matrix solution: To solve a full matrix equation of order N by full matrix inversion (e.g., Gaussian elimination) requires O(N 3 ) number of operations. This increases rapidly with N. (2) Matrix filling: To calculate G mn , m, n = 1,2, ... , N can be computationally intensive because there are N 2 values of G mn . Also G mn can require the evaluation of a double integral as given in (2.2.7). The matrix filling can be more computationally intensive than matrix solution because G(x, x') can be of a complicated form. Also since there are N 2 elements of G mn , this can impose a large memory requirement. (3) The study of fn, n = 1,2, ... , N is also an important subject as the choice of fn must well represent the correct solution. Often they have to satisfy differentiation and continuity properties.

Basis functions can use full domain functions such as sines, cosines, special functions, polynomials, modal solutions, etc. A set that is useful for practical problem is the subsectional basis function. This means that each fn is only nonzero over a subsection of the domain of f. A common choice is the pulse function (Fig. 2.2.1a)

fn(x) =

(2.2.9)

where the interval a S x S b have been divided into N intervals with endpoints an and bn , n = 1,2, ... , N. Another choice is the triangle basis functions (Fig. 2.2.1b). In Fig. 2.2.1b we show fn(x) and fn+I(X). Note that fn(x) and fn+I(X) overlap.

Notice that the code does not create an instance and uses the class name (Product in this example) instead of the object variable name (prod) to call the method This is because a shared method cannot be accessed using an instance

dX'dY'{_ik1b~1)(PR)I~n+1)(r')

y') _

+ i k1 b~1)(PR)I(n+1)(r') af(x', y') af(x, y)}

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