JxFk(x)dx о 0, (28)
respectively, and to verify afterwards that the optimal weight functions Fk satisfy the stronger
conditions (6) and (7).
Without loss of generality we may represent the functions Fk by their Fourier flexible
form
∞∞
Fk(x) α αo,k + ∑ αj,kcos(2jπx) + ∑ βj,ksin(2jπx)
Then by some tedious but straightforward calculations it can be shown that:
Lemma 6. The conditions (27), (28), (8), (9), and (10) now read as:
Fk(χ)dχ α αok - 0

;(χ)dχ - -F-∑ β
2π J=1 J
ffFk(x )Fm (y )min(x, y ) dxdy
8π2

÷Σ
J=1
βJ,kβJ,
0 if k ≠ m ,
∞
F(x ) [Fm (y ) dydx = -r- Σ
4 4 4 П 7=1
β
J, kt^J, m
Vj-1
∞
Σ
j=1
β
J,m J,k
[Fk(x )Fm (x ) dx = ʌ
∞
V α..α.
X-7 j, k j,
Ij'1
ʌ
-∞
÷ βjkβ rnt
0 if k ≠ m .
Combining (1) and the results of Lemma 6, we have
16
More intriguing information
1. The quick and the dead: when reaction beats intention2. The name is absent
3. The name is absent
4. Effects of a Sport Education Intervention on Students’ Motivational Responses in Physical Education
5. Top-Down Mass Analysis of Protein Tyrosine Nitration: Comparison of Electron Capture Dissociation with “Slow-Heating” Tandem Mass Spectrometry Methods
6. SOME ISSUES CONCERNING SPECIFICATION AND INTERPRETATION OF OUTDOOR RECREATION DEMAND MODELS
7. Commitment devices, opportunity windows, and institution building in Central Asia
8. Human Rights Violations by the Executive: Complicity of the Judiciary in Cameroon?
9. AN ANALYTICAL METHOD TO CALCULATE THE ERGODIC AND DIFFERENCE MATRICES OF THE DISCOUNTED MARKOV DECISION PROCESSES
10. THE AUTONOMOUS SYSTEMS LABORATORY