@article{chukwu_chukwu_2014, title={A Mathematical Solution to Boost the Positive Value of the Cumulative Balance of Payment of the USA}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_2}, abstractNote={Very recently the President of the USA, set up a bipartisan commission to generate strategies to boost the positive value of the Balance of Payment of the USA. A mathematical solution can be deduced from the following research monographs of the author, E. N. Chukwu. (1) E. N. Chukwu, Stability and Time Optimal Control of Hereditary Systems with Application to the Economic Dynamics of the US, 2nd edition, World Scientific, 2001, ISBN 981-02-4674-9. Singapore, New Jersey, London. (2) E. N. Chukwu, Differential Models and Neutral Systems for Controlling the Wealth of Nations, World Scientific, 2001, ISBN 9810243812, Singapore, New Jersey, London. (3) Optimal Control of the Growth of Wealth of Nations, Taylor and Francis, 2003, ISBN 0-415-26966-0, London, New York. (4) E. N. Chukwu, A Mathematical Treatment of Economic Cooperation and Competition Among Nations with Nigeria, USA, UK, China and Middle East Examples, Mathematics in Science and Engineering, v 203, Elsevier, 2005, ISBN-13978-0-444-51859-0, Amsterdam, The Netherlands. (5) E. N. Chukwu, The Omega Problem of all members of the United Nations, Atlantis Studies in Mathematics for Engineering and Science, v 7, World Scientific, pub. Date scheduled Summer 2010. (6) E. N. Chukwu, Stability and Time Optimal Control f Hereditary Systems, Academic Press, Boston, 1992.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={7–14} }
 @article{chukwu_chukwu_2014, title={Consequences}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_4}, abstractNote={Suppose at time t the coefficients $$ a_{ - 1i} ,a_{oi} ,a_{1i} $$ are fixed, and b ij , the coefficient of competition or cooperation for nation i and nation j is positive. If b ij is positive, the two nations are cooperating. If b ij is increased the net hereditary growth rate of GDP, $$ \frac{{dy_{i} (t)}}{dt} - a_{ - 1i} \frac{{dy_{i} (t - h)}}{dt} $$ is increased, i.e. the production of goods and services grows bigger. Cooperation enhances economic growth. Suppose b ij , the coefficient of competition is negative, decreasing competition will increase the net growth rate. Increasing competition will decrease the net growth rate.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={23–29} }
 @article{chukwu_chukwu_2014, title={Controllability Theory of the GDP of All Member States of the UN}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_5}, abstractNote={The function \(p\in L_{\infty}([\sigma,t],P), g \in L_{\infty}([\sigma,t],Q)\) are called the private firms’ control strategy and the governments’ (solidarity) strategy functions or controls respectively. The strategies p and g are used to steer initial value ψ ≡ x 0 of the nations’ gross domestic to a target x1 in time t1.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={31–37} }
 @book{chukwu_2014, title={Economic Dynamics of All Members of the United Nations, 2nd Edition}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8}, abstractNote={This book provides an enduring response to modern economic problems and the consequent crises, dealing with the economic modelling of nations and the forecasting of economic growth. The main arguments}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, EN}, year={2014}, pages={1–196} }
 @article{chukwu_chukwu_2014, title={Economic Plans, Programs Policies and Recommendation of 184 Nations}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_9}, abstractNote={In the previous chapter we studied economic growth by modeling through MATLAB regression the growth of gross domestic product, interest rate, employment, value of capital stock, prices, and cumulative balance of payment. It is now a common observation that there is a 30-year gain in the last century of longevity which is related to good health and generation of wealth. Dr. Robert Butler of the International Longevity Center who has studied this for over fifty years affirms this 30-year gain. Furthermore those nations that have a five-year advance in longevity compared to other countries actually have a greater GDP.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={147–154} }
 @inbook{chukwu_2014, title={Economic dynamics of all members of the United Nations second edition preface}, volume={10}, booktitle={Economic dynamics of all members of the united nations, 2nd edition}, author={Chukwu, E. N.}, year={2014}, pages={V-} }
 @article{chukwu_chukwu_2014, title={Employment and Gross Domestic Product Dynamics and Control of Interacting Nations}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_6}, abstractNote={In this chapter models of Gross Domestic Product and Employment of two interacting nations are derived. This system is a hereditary differential game of pursuit. It utilizes the principles of supply and demand and of rational expectations. A theory of interaction via net export is postulated. The net export function may include trade, debt repayment, etc. International employments can also be included. The UN and IMF data for two nations are used to validate the theory and test for the degree of cooperation and competition. MATLAB andMaple programs are exploited. The consequences of cooperation and competition are studied, and controllability questions answered. Once the system is proved controllable it can be made sufficiently cooperating, and sustained growth of GDP and employment can be guaranteed.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={39–64} }
 @article{chukwu_chukwu_2014, title={Full Employment: Private and Government Policies}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_1}, abstractNote={Employment is currently decaying in the United States of America. Policies of private firms and government to arrest the situation are now hotly debated. This paper is a readable reflection and extraction from Chukwu’s books, Stability and Time-Optimal Control of Hereditary Systems with Application to the Economic Dynamics of the USA,” 2nd Edition, World Scientific 2001 [1], and “The Omega Problem of all Members of the United Nations”, Atlantis Studies in Mathematics for Engineering and Science, Volume 6. Series editor, C. K. Chui, Stanford University, U.S.A. and World Scientific [2]. Reasonable and verifiable economic policies are deduced from Chukwu.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={1–5} }
 @article{chukwu_chukwu_2014, title={Full Hereditary Interacting Model of All Member States of the United Nations}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_3}, abstractNote={Aggregate demand zi is given by 
 
$$z_i = I_i + C_i + X_i + G_i,\quad i = 1,...,191,$$ 
 
(2.1) 
 
is the contribution to the country of yi interacting with countries of yj (j ≠ i) due to cooperation and competition.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={15–22} }
 @article{chukwu_chukwu_2014, title={Overview of Each Nations Economic State Dynamics and Control: Equations of GDP, Interest Rate, Employment, Value of Capital Stock, Prices, Cumulative Balance of Payment}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_7}, abstractNote={The economic state is x = [y, R, L, k, p, E). We now recall our earlier equations for interest rate [2, p. 29] – Stability and Time Optimal Control of Hereditary Systems with Applications to Economic Dynamics of the USA. Let M denote money supply (e.g., M1) 
 
$$\overline{L} = {\rm money\,demand} \approx {\rm Md}$$}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={65–115} }
 @article{chukwu_chukwu_2014, title={Program Results of Some Nations: Austria and France}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_10}, abstractNote={Just as in Botwana2.m policies can be deduced from the equation for y. It was executed by E. Chukwu. The raw data was taken from International Yearbook publications for 2003 and 2007. The equation q1(t) yield the government strategies and the equation r1(t) the representative firms strategy.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={155–186} }
 @article{chukwu_chukwu_2014, title={Program Results: Introduction}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_11}, abstractNote={In Sect. 10, Program Result for Some Nations: Austria and France, we display samples of what can be generated from the data, the programs and their execution from the contents of CD-Rom of the 141 nations.}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={187–188} }
 @article{chukwu_chukwu_2014, title={The Hereditary Model of GDP and Employment}, volume={10}, ISBN={["978-94-6239-075-1"]}, ISSN={["1875-7642"]}, DOI={10.2991/978-94-6239-076-8_8}, abstractNote={In this section we derive a hereditary model of gross domestic product, y, and employment L by invoking the “demand and supply principle”, and the “rational expectations hypothesis” which assumes that the expected values of economic variables are functions of the current and past values. Indeed let the aggregate demand function z i be given by 
 
$$z_i = I_i + C_i + X_i + G_i,\quad i = 1, 2$$ 
 
(7.1)}, journal={ECONOMIC DYNAMICS OF ALL MEMBERS OF THE UNITED NATIONS, 2ND EDITION}, author={Chukwu, Ethelbert Nwakuche and Chukwu, EN}, year={2014}, pages={117–145} }
 @article{chukwu_2005, title={Cooperation and competition in modeling the dynamics of gross-domestic products of nations}, volume={163}, ISSN={["0096-3003"]}, DOI={10.1016/j.amc.2003.12.141}, abstractNote={In this paper two major models of the gross-domestic product of four interacting nations are derived. One is an ordinary differential game of pursuit. The other is a hereditary one which utilizes the principle of rational expectations. A theory of interactions via net export is postulated. The UN and IMF data for a group of nations are used to validate it, and test for competition and cooperation MATLAB and MAPLE programs are used. The consequences of cooperation and competition are studied.}, number={2}, journal={APPLIED MATHEMATICS AND COMPUTATION}, author={Chukwu, EN}, year={2005}, month={Apr}, pages={991–1021} }
 @article{chukwu_bowers_2005, title={Instantaneous multiple-depth soil mechanical impedance sensing from a moving vehicle}, volume={48}, DOI={10.13031/2013.18492}, abstractNote={A three-depth soil mechanical impedance sensor was developed and tested within a laboratory soil bin. Soil 
mechanical impedance measurements were made on a continuous basis at three simultaneous depths of 178, 279, and 381 mm 
from one end of the soil bin to the other using three prismatic tips and three Omega LCF500 load cells. This article discusses 
how the sensor can be used for measuring the soil mechanical impedances that plant roots encounter during normal growth. 
The soil sensor also offers excellent opportunities to study the forces acting on soil-engaging implements and subsequent 
control of tillage tools. Compaction created from past tillage machinery operation and trafficking by heavy equipment 
sometimes forms “plowpans” in crop fields. These layers, as well as other naturally occurring dense soil layers that impede 
water infiltration and root penetration, can be located using the three-depth soil mechanical impedance sensor. The 
laboratory experiment for testing and verifying the device’s performance showed that the three-depth sensor can measure 
differences in soil mechanical impedance with depth and location and that these impedances correlate well with 
corresponding cone penetrometer measurements.}, number={3}, journal={Transactions of the ASAE}, author={Chukwu, E. and Bowers, C. G.}, year={2005}, pages={885–894} }
 @article{chukwu_2005, title={Sustainable global economic growth}, volume={63}, ISSN={["0362-546X"]}, DOI={10.1016/j.na.2004.09.021}, abstractNote={This survey highlights some recent advances on modeling the economic state of some nations of the world which are linked up in solidarity and competition or which are isolated. The problem of controllability, convergence, and permanence are explored. Some practical recent policy implications are deduced. Earth revolves around the sun in approximately circular orbit with radius r=a, completing a revolution in the time T=2π(a3/GM)1/2 which is one earth year; here M is the mass of the sun and G is the universal gravitational constant. The gravitational force of the sun on the earth is given by GMm/r2 where m is the mass of the earth. Therefore, if the earth “stood still” losing its orbital velocity, it will fall straight on a line into the sun in accordance with Newton's second law.Md2rdt2=-GMMr2. If this calamity occurred what fraction of the normal year T will it take for the earth to splash into the sun?” (Nagle, Saff, Snider) “Why did the earth stand still?” (Ndu Udo) “The symbol of Love and the earth's lover is the moon. With joy it dances around the earth in a circular orbit. When the inhabitants of the earth prefer hate and revenge to love, the moon stops to love, and stands still, losing its orbital velocity. It falls straight on a line into the earth in accordance with Newton's second law. The crash makes the earth stand still precipitating the Armageddon.” (Wisdom Goodness)}, number={5-7}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Chukwu, EN}, year={2005}, month={Nov}, pages={785–798} }
 @article{chukwu_2003, title={Goodness through optimal dynamics of the wealth of nations}, volume={4}, ISSN={["1468-1218"]}, DOI={10.1016/S1468-1218(02)00055-X}, abstractNote={In this paper, we survey the mathematical theory of competitive an co-operative systems that monitor national interactions and economic systems. The dynamics are described by ordinary differential equations, functional differential equations and coupled partial differential equations. Conditions are given which guarantee finite time extinction, finite time unbounded growth, and persistence. These conditions are already available in the literature (Proceedings of the First World Congress of Nonlinear Analysis, 1992 Vol I–IV 359–368 Gruyler, Berlin; Appl. Anal. 57 (1995) 3–4, pp. 309–323; Math. Biosci. 118 (1993) 197; In: T.G. Hallam, S.A. Levin (Eds.), Mathematical Ecology, Biomathematics, Vol. 17, Biomathematics, Springer, Berlin, Heidelberg, 1986; Convex Structures and Economic Theory, Academic Press, New York, 1968; SIAM J. Math. Anal. 18 (1987) 642; Introduction to Differential Equation, Prentice-Hall, Englewood Cliffs, NJ, 1987; SIAM J. Appl. Math. 36 (1979) 421; Proc. Nat. Acad. Sci. USA 68 (1971) 980; SIAM J. Math. Anal. 24 (1993) 1331; The Passionate God, Paulist Press, New York, 1981; Nonlinear Parabolic and Elliptic Equation, Plenum Press, New York, 1992; Economic Theory and Social Justice, MacMillan, London, UK, 1999; Extinction in finite time of solutions to nonlinear absorption–diffusion equations, personal communication). The theory is applied to national wealth that is carefully defined. It is shown that the wealth of co-operating nations can grow unbounded and competing ones become extinct. Using the principle of “trickle down of wealth” and incorporating a strategy of internally generated wealth due to improved health and education, we derive the dynamics of wealth.}, number={5}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Chukwu, EN}, year={2003}, month={Dec}, pages={653–666} }
 @book{chukwu_2003, title={Optimal control of the growth of wealth of nations}, ISBN={0415269660}, publisher={London; New York: Taylor & Francis}, author={Chukwu, E. N.}, year={2003} }
 @article{chukwu_2002, title={Control under scarcity of the growth of wealth of nations: with examples from Austria and the USA}, volume={23}, ISSN={["0267-5730"]}, DOI={10.1504/IJTM.2002.003033}, abstractNote={The author postulates formulae for aggregate demand and its components z = C + I + X + G - consumption, C, investment, I, net export, X and government outlay, G and aggregate supply, S. By MATLAB and regression, z is confronted with data from Austria and the USA to deduce the right dynamics, a differential game of pursuit which is equivalent to a control system with control constraints. Conditions for controllability are given and their policy implications explored.}, number={7-8}, journal={INTERNATIONAL JOURNAL OF TECHNOLOGY MANAGEMENT}, author={Chukwu, EN}, year={2002}, pages={675–690} }
 @article{chukwu_2002, title={International economic models as surveillance for the optimal control of the growth of wealth of nations}, volume={3}, ISSN={["1468-1218"]}, DOI={10.1016/S1468-1218(01)00014-1}, number={1}, journal={NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS}, author={Chukwu, EN}, year={2002}, month={Mar}, pages={75–84} }
 @book{chukwu_2001, title={Differential models and neutral systems for controlling the wealth of nations}, ISBN={9810243812}, DOI={10.1142/9789812791863}, abstractNote={Continuous delay models - motivation, economic dynamic model main results economic interpretation and fundamental economic principles economic hereditary models of Canada soft landing of key economic indicators with private and government controls under scarcity economic systems with delay in control the nonlinear theory of controllability of volterra neutral integrodifferential dynamics economic models of USA, Canada, UK, Germany and India model programmes and graphs optimal control of volterra integral neutral equations and of linear neutral equations nonlinear neutral systems controllable nonlinear neutral systems function space control of nonlinear interconnected economic systems of neutral type nonlinear mathematical controllability theory of the growth of wealth of nations oscillation construction of econometric meter and reform of global economic systems structure.}, publisher={Singapore; River Edge, N.J.: World Scientific}, author={Chukwu, E. N.}, year={2001} }
 @article{chukwu_2001, title={International economic models as surveillance for the optimal control of the growth of wealth of nations}, volume={47}, DOI={10.1016/s0362-546x(01)00483-7}, number={6}, journal={Nonlinear Analysis}, author={Chukwu, E. N.}, year={2001}, pages={3629–3639} }
 @book{chukwu_2001, title={Stability and time-optimal control of hereditary systems: With application to the economic dynamics of the US (2nd ed.)}, ISBN={9810246749}, DOI={10.1142/4745}, abstractNote={This monograph introduces the theory of stability and time-optimal control of hereditary systems, drawing upon a range of subjects for evidence and comparisons (biology - predator/prey dynamics; economics - dynamics of capital growth; engineering - aircraft stabilization and automatic steering).}, publisher={River Edge, NJ: World Scientific}, author={Chukwu, E. N.}, year={2001} }
 @article{chukwu_1999, title={Volterra integrodifferential neutral dynamics for the growth of wealth of nations: A controllability theory, with Canada example}, volume={5}, number={1-4}, journal={Journal of High Energy Physics}, author={Chukwu, E. N.}, year={1999}, pages={561–577} }
 @article{chukwu_1998, title={On the controllability of nonlinear economic systems with delay: The Italian example}, volume={95}, ISSN={["0096-3003"]}, DOI={10.1016/S0096-3003(97)10079-0}, abstractNote={The dynamic model of some key economic indicators – the gross national product, GNP, interest rate, R, employment, L, value of capital stock, k, prices, p, and cumulative balance of payment, E – are derived here from mathematical and economic principles. The model is described by a hereditary ordinary differential equation, a nonlinear delay differential pursuit game of neutral type. The quarry control-solidarity or government intervention consists of money supply, M, government budget, net expenditure, taxation, T, exchange rate, e, tariffs, foreign credit fo, distance between trading partners or trading arrangements d, or preferential arrangement. The pursuer control (private initiative) consists of autonomous private consumption, investment, net export, labor productivity, money wage rate w, autonomous money demand m, income autonomous consumption y10. Conditions are established for the variables of the economic indicators to be controllable from one initial function to a terminal function, in particular, employment, national income and prices can be controlled from one arbitrary vector function to another when the controls of the system are subject to scarcity, i.e., to constraints. Conditions for controllability are presented. Our model is tested with data on Italian economy. This paper opens up the hope that full employment, high income growth is compatible with low prices and low inflation, provided the control matrix has full rank, i.e., the existing controls are fully effectively used.}, number={2-3}, journal={APPLIED MATHEMATICS AND COMPUTATION}, author={Chukwu, EN}, year={1998}, month={Sep}, pages={245–274} }
 @article{chukwu_1998, title={Volterra integrodifferential neutral dynamics for the growth of wealth of nations: A controllability theory}, volume={29}, number={7}, journal={Indian Journal of Pure and Applied Mathematics}, author={Chukwu, E. N.}, year={1998}, pages={723–799} }
 @article{chukwu_1997, title={Control of nonlinear delay differential equations in W-2((1)) with economic applications}, volume={85}, ISSN={["0096-3003"]}, DOI={10.1016/S0096-3003(96)00108-7}, abstractNote={The control of economic system's growth with delay is formulated to illustrate Euclidean (En) and function space (W2(1)) controllability of a general nonlinear delay equation. Sufficient conditions are given, in terms of the control matrix, for controllability of the general nonlinear system. These conditions are shown to be necessary for W2(1) controllability. The theory is then applied to a simple dynamics of gross national product and interest rate. The concept of function space controllability is very appropriate: once the target is hit, it remains on a certain growing function for some time.}, number={1}, journal={APPLIED MATHEMATICS AND COMPUTATION}, author={Chukwu, EN}, year={1997}, month={Aug}, pages={17–59} }
 @article{chukwu_bowers_1997, title={Instantaneous multiple depth soil mechanical impedance sensing from a moving vehicle}, number={971077}, journal={Paper (American Society of Agricultural Engineers)}, author={Chukwu, E. and Bowers, C. G.}, year={1997}, pages={23} }
 @inbook{chukwu_1997, title={Nonlinear delay differential economic systems in W-2((1))}, booktitle={Advances in nonlinear dynamics}, publisher={Australia: Gordon and Breach}, author={Chukwu, E. N.}, editor={S. Sivasundaram and Martynyuk, A. A.Editors}, year={1997}, pages={157–170} }
 @article{chukwu_1997, title={Optimal control of the growth of wealth of nations: With Austria and USA examples}, volume={30}, ISSN={["0362-546X"]}, DOI={10.1016/S0362-546X(96)00246-5}, number={2}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Chukwu, EN}, year={1997}, month={Dec}, pages={1029–1041} }
 @article{chukwu_simpson_1997, title={The solution operator in W-p((1)) for systems of neutral type}, volume={29}, ISSN={["0362-546X"]}, DOI={10.1016/S0362-546X(96)00169-1}, number={10}, journal={NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS}, author={Chukwu, EN and Simpson, HC}, year={1997}, month={Nov}, pages={1173–1195} }