The name is absent



dHc  _

daj (t)

1
aj(t)

+ λ(t) = 0, j = 1, . . . , n2

(7)

dλ

л - ρλ =

dH
dx

= 2n1c1x(t) + 2n2c2x(t) + λ(t)

b-

2x(t)
(x2(t) + 1)2,

(8)

dHc _
dλ(t)

a(t) -

x2(t)
bx(t) + (x2(t) + 1)2

(9)

From (6) and (7),

λ(t)


1
ai(t)


1
aj(t)


i = 1,...,n1, j = 1,...,n2,


which implies


ai(t) = aj (t) ∀i = 1, . . . , n1 , j = 1, . . . , n2


(10)

(11)


Moreover:

λ(t)


1
ai(t)


i = 1, . . . ,n1 implies n1ai(t) =


ni
λ(t)


and therefore

n1                                                  n2

= n1ai(t), and by similar argument     = n2aj (t),

i=1                                           j=1

which means that

n1           n2

a(t) =     ai(t) +     aj(t) i = 1,...,n1, j = 1,...,n2          (12)

i=1        j=2

and

a(t) = n1ai(t) + n2aj(t) i = 1, . . . , n1, j = 1, . . . , n2              (13)

Note that λ can be expressed as a function of a via the following reasoning:

λ(t)


1
ai(t)


i = 1, . . . ,n1 and λ(t)


1

aj(t)


j = 1, . . . ,n2


⇒      ai(t)λ(t) = -1 i = 1, . . . , n1 and aj (t)λ(t) = -1 j = 1, . . . , n2

n1                                   n2

⇒ λ(t)    ai(t) = -n1 and λ(t)    aj (t) = -n2

i=1                              j=1

Adding the two together:

λ(t) ∑ ai(t) + λ(t) ∑ aj (t) = -(n + П2)
i=1              j=1



More intriguing information

1. A multistate demographic model for firms in the province of Gelderland
2. Forecasting Financial Crises and Contagion in Asia using Dynamic Factor Analysis
3. The name is absent
4. Sex differences in the structure and stability of children’s playground social networks and their overlap with friendship relations
5. EMU: some unanswered questions
6. Solidaristic Wage Bargaining
7. Regional science policy and the growth of knowledge megacentres in bioscience clusters
8. The name is absent
9. Regulation of the Electricity Industry in Bolivia: Its Impact on Access to the Poor, Prices and Quality
10. Poverty transition through targeted programme: the case of Bangladesh Poultry Model