BOSTON COMPUTER SOCIETY BENCHMARKS

The following benchmarks are used by the Boston Computer Society in their evaluation of Technical Word Processing systems (TWPs). Each benchmark is a fragment of text from a scientific publication.

Benchmark 1:

L. Tsang and J. A. Kong, Journal of Applied Physics, 51(7), July 1980, page 3471, equation ??.

W_{m_{1}n_{1}n_{2}}^{3β}(p_{1}, p_{2}) = U_{m_{1}n_{1}}^{3β}(p_{1}, p_{2}) + ∫_{0}^{∞} \frac{dp_{3}p_{3}^{2}}{8π^{3}} ∑_{n} ∑_{m} ∑_{α_{2}} ∑_{β_{2}} ∑_{n′} ∑_{n′′}(−1)^{m}

× (\frac{U_{m_{1}n_{1}}^{33}(p_{1}, p_{2})}{p_{3}^{2} − k^{2}}) z_{3m_{1}n_{1}}h_{n}(p_{3}, p_{2}) · a_{mn(m_{1}−m)n′n_{2}}^{α_{2}3}α_{−mn(−m_{1}+m)n′′n_{2}}^{β_{2}β}

× W_{(m_{1}−m)n′n′′}^{α_{2}β_{2}}(p_{3}, p_{2}).  (110)

Benchmark 2:

Athanasios Papoulis, Probability, Random Variables, and Stochastic Processes, second edition, McGraw-Hill, 1984, page 17.

Unions and intersections The sum or union of two sets A and B is a set whose elements are all elements of A or of B or of both (Fig. 2-3). This set will be written in the form

A + B or A ∪ B

The above operation is commutative and associative:

A + B = B + A (A + B) + C = A + (B + C)

We note that, if B ⊂ A, then A + B = A. From this it follows that

A + A = A A + {∅} = A I + A = I

The product or intersection of two sets A and B is a set consisting of all elements that are common to the sets A and B (Fig. 2-3). This set is written in the form

AB or A ∩ B

Benchmark 3: Richard P. Feynman, The Feynman Lectures in Physics, Addison-Wesley Publishing Co., 1965, Vol. 3, page 20-12, Table 20-1.

Physical Quantity Operator Coordinate Form
Energy  Ĥ  Ĥ = −\frac{h̄^{2}}{2m}∇^{2} + V (r)
Position  x̂  x
ŷ  y
ẑ  z
Momentum  p̂_{x}  P̂_{x} = \frac{h̄}{i} \frac{∂}{∂_{x}}
p̂_{y}  P̂_{y} = \frac{h̄}{i} \frac{∂}{∂_{y}}
p̂_{z}  P̂_{z} = \frac{h̄}{i} \frac{∂}{∂_{z}}

In this list, we have introduced the symbol P_{x} for the algebraic operator (h̄/i) ∂/∂x :

P̂_{x} = \frac{h̄}{i} \frac{∂}{∂_{x}}

Benchmark 4: William L. Brogan, Modern Control Theory, QPI Quantum Press Inc., Prentice Hall, 1984, page 240, Figure 9.11.

(u(t)) / •

◯ 2

+ − • x_3 2/9 + ◯

2

+ − • x_2 1/3

◯ + y(t)

◯ 5

+ − • x_1 2/9

−

Fig. 9.11 From Fig. 9.11,

[ ẋ_{1} ; ẋ_{2} ; ẋ_{3} ] = [ \begin{matrix}−5 & 0 & 0 \\ 0 & −2 & 1 \\ 0 & 0 & −2 \end{matrix} ] [ \begin{matrix}x_{1} \\ x_{2} \\ x_{3} \end{matrix} ] + [ \begin{matrix}1 \\ 0 \\ 1 \end{matrix} ] u and y = [−2/9 1/3 2/9]x

Benchmark 5:

Jerrold E. Marsden, Elementary Classical Analysis, W. H. Freeman and Co., 1974, page 234, proof of Theorem 2.

Proof: Define the function G : A ⊂ R^{n} × R^{m} → R^{n} × R^{m} by G(x, y) = (x, F (x, y)). Since F is of class C^{p}, and the identity mapping is of class C^{∞}, it follows that G is of class C^{p}. The matrix of partial derivatives of G (Jacobian matrix) is

( \begin{matrix}1 & 0 & ⋯ & 0 & 0 & ⋯ & 0 \\ 0 & 1 \\ ⋮ & & ... & ⋮ & ⋮ & & ⋮ \\ 0 & & ⋯ & 1 & 0 & ⋯ & 0 \\ \frac{∂F_{1}}{∂x_{1}} & & ⋯ & \frac{∂F_{1}}{∂x_{n}} & \frac{∂F_{1}}{∂y_{1}} & ⋯ & \frac{∂F_{1}}{∂y_{m}} \\ ⋮ & & & ⋮ & ⋮ & & ⋮ \\ \frac{∂F_{m}}{∂x_{1}} & & ⋯ & \frac{∂F_{m}}{∂x_{n}} & \frac{∂F_{m}}{∂y_{1}} & ⋯ & \frac{∂F_{m}}{∂y_{m}} \end{matrix} )

Benchmark 6:

Allen F. Henry, Nuclear Reactor Analysis, MIT Press, Cambridge, Mass, 21982, page 495, equation 11.4.19, subequations 4 and 5.

iB_{r} [ã_{kl}^{n}] ≡ \frac{1}{2}(h_{n−1} + h_{n}) ∫_{0}^{R} 2πr dr [ρ_{k}^{n_{∗}}(r)] \frac{d}{dr} [Ψ_{l}^{n}(r)] ,

[D_{r,kl}^{n}]^{−1} ≡ ∫_{0}^{R} 2πr dr ∫_{z_{n}− \frac{1}{2} h_{n}−1}^{z_{n}+ \frac{1}{2} h_{n}} [ρ_{k}^{n^{∗}}(r)] [D^{−1}(r, z)] [ρ_{l}^{n}(r)] ,

Benchmark 7:

· · · · · · · · · · · iΔ

· · · · · · -epμ

p p′ = 0 μ ν · · · · · · · = μ ν · · · · · · · · · · · · · 2ie^{2}g_{μν} FIG. 13. Feynman rules for the ϕ_{c} scalars.

Benchmark 8:

N CH_6 OH

N OH

CH_3

Ajmaline CH_3O HO CH

N N

CH CH_3

Quinine

Benchmark 9:

f\underline{z}(\underline{z}) f\underline{y}(\underline{y}) · e^{α^{β}}