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The purpose of this paper is to study the regions of parameter space of engineering design in which performance is sensitive to design parameters. Some of these parameters (for example, the dimensions and compositions of components) constitute the design, but others are intrinsic properties of materials or Nature. The paper is concerned with narrow regions of parameter space, “cliffs”, in which performance (some measure of the final state of a system, such as ignition or nonignition of a flammable gas, or failure or nonfailure of a ductile material subject to tension) is a sensitive function of the parameters. In these regions, performance is also sensitive to uncertainties in the parameters. This is particularly important for intrinsically indeterminate systems, those whose performance is not predictable from measured initial conditions and is not reproducible.

We develop models of ignition of a flammable mixture and of failure in plastic flow under tension. We identify and quantify cliffs in performance as functions of the design parameters. These cliffs are characterized by large partial derivatives of performance parameters with respect to the design parameters and with respect to the uncertainties in the model. We calculate and quantify the consequences of small random variations in the parameters of indeterminate systems.

We find two qualitatively different classes of performance cliffs. In one class, performance is a sensitive function of the parameters in a narrow range that separates wider ranges in which it is insensitive. In the other class, the final state is not defined for parameter values outside some range, and performance is a sensitive function of the parameters as they approach their limiting values. We find that sensitivity of performance to control (design) parameters implies that it is also sensitive to other parameters, some of which may not be known, and to uncertainties of the initial state that are not under the control of the designer. Near or on a cliff performance is degraded. It is also less predictable and less reproducible.

Frequently, design optimization or cost minimization leads to choices of engineering design parameters near cliffs. The sensitivity of performance to uncertainty that we find in those regimes implies that caution and extensive empirical experience are required to assure reliable functioning. Because cliffs are defined as behavior on the threshold of failure, this is a reflection of the trade-off between optimization and margin of safety, and implies the importance of ensuring that margins and uncertainties are quantified. The implications extend far beyond the model systems we consider to engineering systems in general.

Many of these considerations have been part of the informal culture of engineering design, but they were not formalized until the methodology of “Quantification of Margins and Uncertainty” was developed in recent years. Although this methodology has been widely used and discussed, it has only been published in a small number of reports (cited here), and never in a journal article or book. This paper may be its first formal publication, and also its first quantitative application to and illustration with explicit model problems.

HAVING discussed in the standard longhand notation the main ideas and methods for the calculation of redundant structures on the basis of forces as unknowns we now turn our attention to the matrix formulation of the analysis. Consider a system consisting of s structural elements with a total number n of redundancies which may be forces (stresses), moments or any generalized forces. We select a basic system by ‘cutting’ a number r of redundancies where r<n. Thus, the simple idea of a statically determinate basic system (r=n) is but a particular case of our investigations.

The purpose of this paper is to examine the extent to which a flexible exchange rate system is able to function given a least developed economy where financial markets are inactive and economic growth is low.

A theoretical general equilibrium model is developed to examine the determinacy of a flexible exchange rate system on a small open market economy on the verge of subsistence. Using data from Sudan, an empirical analysis is conducted to find support for the theoretical results.

The theoretical analysis finds that in economies on the verge of subsistence with inactive financial markets, a flexible exchange rate system is indeterminate and thus will not work. In support of the theoretical results, the empirical analysis indicates that the financial deepening of an economy has a significant positive impact on the determinacy of the exchange rate.

The robustness of the empirical results would be strengthened by examining the significance of financial deepening on exchange rates for additional economies with a large subsistence sector beyond Sudan.

A policy recommendation for economies on the verge of subsistence such as Sudan is to develop their financial institutions in order to increase their competitiveness in the exchange rate market. Moreover, future empirical studies on the impact of exchange rate changes should include monetary variables in order to reflect the degree of an economy's financial market advancement.

The paper illustrates that under conditions of subsistence, general equilibrium models of devaluation are determinant only when supply functions are based on absolute prices and not relative prices.

This paper aims to propose a new neural-based enhanced extreme learning machine (EELM) algorithm, used as an online adaptive estimation model, regarding undetermined system dynamics and containing internal/external perturbations.

The EELM structure bases on the single layer feed-forward neural (SLFN) model in which the hidden weighting coefficients are initiated in random and the weighting outputs of the SLFN are online modified using an online adaptive rule implemented from Lyapunov stability concept.

Four different benchmark uncertain chaotic system tests have been satisfactorily investigated for demonstrating the superiority of proposed EELM technique.

Authors confirm that this manuscript is original.

The first Principia Mathematica (1686) by Sir Isaac Newton with reference to natural philosophy and his system of the world has largely contributed to the first revolution in scientific thinking in modern times. It has created the conceptual basis of modern science in the classical tradition by providing the tools of analysis and the technique of reasoning in terms of stability—from—within or, as we would say today, the model of stable equilibrium conditions.

THE general theorems given in Sections 4 and 6 include, from the fundamental point of view, all that is required for the analysis of redundant structures. However, to facilitate practical calculations it is helpful to develop more explicit methods and formulae. To find these is the purpose of this Section.

A DSIR Sponsored Research Programme on the Development and Application of the Matrix Force Method and the Digital Computer. The present issue gives a summary of the basic theory of the matrix force method together with some necessary extensions for the fuselage problem. The equilibrium conditions for the idealized structure are then examined in detail and the relevant equations of equilibrium established in matrix form.

Industry′s claim to create wealth serves to legitimize the independence of its policies and actions. Yet such a creation process is delusory in an interdependent and indeterminate world grounded in quantum physics, ecology and chaos theory. Contemporary corporate annual reports are prepared from the perspective of discrete industrial entities driven by the dynamic of unlimited growth. Most pressures being applied to change these reports seek merely to complicate, by adding information, rather than to revise by removing organizational boundaries and restating core beliefs. Recent corporate environmental reports, for example, confuse and are of limited use to company analysts; they do little to aid the fundamental transition to sustainable industry. However, a conception of industry as a wealth appropriator within the ecosphere can help, and this understanding gives rise to a new direction for accounting, auditing and environmental reporting. Examples of first steps taken by Denmark in this new direction are given.

The article makes a comprehensive study of the development of social economic thought in the history of economic doctrines. Traces of social economic development are dated back to the Physiocrats and moral philosophers and reference is made to the early Arab works in the developments of these social economic doctrines. The social economic thought in the classical school of economic theory is critically studied. It is shown that with the advancement of economic theory in the hands of the neoclassical school and its latter‐day developments social economic doctrines receded from mainstream economics. The contemporary social economists in North America have fallen into the trap of these neoclassical approaches applied to the study of social economic phenomena. The article also shows that similar neoclassical and ethically neutral traces continue in the works of the mixed economy theorists, institutionalists, macroeconomists, monetarists, rational expectations hypothesists, public and social choice theorists of all types. Thus, the whole gamut of mainstream economics is shown to be trapped in an epistemological and methodological quandary as to how ethical phenomena are to be treated rationally in the framework of economic theory.

The purpose of this paper is to show that transmission of information and information storage or registration depends on structures. Structures emerge from coordinated sets of constraints. Complex systems depend on their structures to function. The temporal sequence of changes in the levels of the complex system determines its behavior. These three concepts are intimately linked with the environment. Environment, structure, function and behavior form a complex system–environment unit, which is the operational unit of existence for all open complex systems. Therefore, it becomes a point in the directional propagation of the cause, where stimulus environment becomes a Creaon, and then the Creaon becomes a Genon, becoming in turn the response to the experienced environment. The formation of structures is the main phenomenon of evolution. Evolution can also be accepted as free, in the sense that it does not cost additional deaths.

Mathematical and logical development of the structure and thermodynamics in complex systems.

Based on the above considerations, the authors are going to introduce two fundamental principles in Complex systems Theory: the Matthew Effect and the Principle of Sagan.

But as the authors’ purpose is to give a formal definition of a complex system from a totally theoretical point of view, they establish a relationship between concepts of General Systems Theory, Theory of the Environment, linguistics, Information Theory and thermodynamics.