By Ethelbert Nwakuche Chukwu
This publication offers an everlasting reaction to fashionable financial difficulties and the resultant crises, facing the commercial modelling of countries and the forecasting of monetary progress. the most arguments embodied represent the construction of jobs and the recovery of monetary development, utilizing the implicit attractiveness of study on differential types and impartial structures for controlling the wealth of nations.
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To prove global stability theorem, a Liapunov function of Volterra type, VðyÞ ¼ 191 X i¼1 Ci yi À yÃi À yÃi yi ln Ã ; yi is utilized. Thus for any initial value y0, the solution yðt; y0 Þ ! yÃ , as t ? We do not want to wait forever to attain the equilibrium. Target. y* can be attained and indeed attained in finite time by employing the government and private firms strategies gi(t) and pi(t). Thus any target can be attained in finite time in a cooperative system by applying government and private strategies which are subject to scarcity; and thus ‘‘the freedom of the market is placed in the services of human freedom in its totality’’ as pontificated by Pope John Paul II and affirmed by President Bush of the USA—a view reported in Chukwu [2, p.
We now reproduce Chukwu’s generalization of Hájek’s theorem to cover a hereditary nonlinear differential game. 5a, b) with respect to yt ðr; /Þ. Associated with it is a family of continuous linear operator T(t, r, /): C ? C, t C r, defined for all w [ C, by Tðt; r; /Þw ¼ zt ðr; wÞ; / 2 C: C = C[-h, 0], En), the space of continuous functions from [-h, 0] to En. r ð5:7Þ is given by xt ðr; /; p; qÞ ¼ yðr; /Þ À Zt Tðt; s; xs ðr; /; p; qÞy0 ðpðsÞ À qðsÞÞds; ð5:8Þ a where y(r, /) is a solution of d ½A0 yðtÞ À AÀ1 yðt À hÞ ¼ f ðt; yt Þ; dt t !
R; yr ¼ / 2 C: ð5:9Þ (see [1, p. 113]). 9) the following Theorem was formulated and cited in . 1 Assume 0 [ Q and P compact. There is complete capture everywhere at time t, for game d ½A0 xðtÞ À AÀ1 xðt À hÞ ¼ f ðt; xt Þ À pðtÞ þ qðtÞ dt if, and only if, the associated nonlinear control system of neutral type. ð5:10Þ 34 5 Controllability Theory of the GDP d ½A0 xðtÞ À AÀ1 xðt À hÞ ¼ f ðt; xt Þ À vðtÞ; dt vðtÞ 2 VðtÞ; ð5:11Þ VðtÞ Utþ1 ðÁ; xt ðr; /; u; 0Þ; tÞUt1 ð; xt ðr; /; n; qÞ; tÞPÃÀ ð5:12Þ Utþ1 ðÁ; xt ðr; u; 0Þ; tÞUt1 ðÁ; xt ðr; /; n; qÞð ; tÞQÞ is controllable at time t1.
Economic Dynamics of All Members of the United Nations by Ethelbert Nwakuche Chukwu