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In this paper, we introduce the concept of a supporting set for a general system. We study basic properties of supporting sets for a general system, supporting sets for subsytems of a system, homomorphic images of supporting sets for a system, and supporting sets for free sums and direct sums of systems.

Several coefficients, called divergences, have been suggested in the statistical literature to reflect the fact that some probability distributions are “closer together” than others and consequently that it may be easier to distinguish between the distributions of one pair than between those of another. When comparing three biological populations, it is often interesting to measure how two of them “move apart” from the third. Deals with the statistical analysis of this problem by means of bivariate divergence statistics. Provides a unified study, depicting the behaviour and relative merits of traditional divergences, by using the (h,ø), divergence family of statistics introduced by Menéndez et al.

The concept of L‐fuzzy systems is introduced as a generalisation of that of general systems. A universal structure of a special kind of L‐fuzzy system is given, some mapping properties of L‐fuzzy systems are studied and a number of open questions posed.

Following Ma, Yonghao and Yi Lin's definition of a mathematical model of general systems in 1987, shows the class of all general systems with relation‐reversion mappings and that of all general systems with relation‐preserving mappings to be productive, co‐productive categories Answers two questions posed in earlier published papers and poses some more questions for solution.

The reducing transformation and global optimization technique called Alienor has been developed in the 1980s by Cherruault and Guillez. These methods are based on the approximating properties of α ‐dense curves. The aim of this work is to give a very large class of functions generating α ‐dense curves in a hyper‐rectangle of Rⁿ.

In the course of development of human communities towards industrially advanced societies of today, there have been changes not only in economic conditions in the majority of fields of human activity but also in the ways of providing for food, which went hand in hand with changes in living conditions. Large‐scale industrial production has brought about major changes in the way of life of the population. The development of industrial agglomerations results in a growing number of city dwellers, most of whom have no chance of producing foodstuffs of their own in kind. The distance between residential and industrial areas has been growing, the number of employed women has risen considerably. These are but a few factors affecting the way of boarding, particularly in households.

The paper aims to study the constraint solutions of the periodic coupled operator matrix equations by the biconjugate residual algorithm. The new algorithm can solve a lot of constraint solutions including Hamiltonian solutions and symmetric solutions, as special cases. At the end of this paper, the new algorithm is applied to the pole assignment problem.

When the studied periodic coupled operator matrix equations are consistent, it is proved that constraint solutions can converge to exact solutions. It is demonstrated that the solutions of the equations can be obtained by the new algorithm with any arbitrary initial matrices without rounding error in a finite number of iterative steps. In addition, the least norm-constrained solutions can also be calculated by selecting any initial matrices when the equations of the periodic coupled operator matrix are inconsistent.

Numerical examples show that compared with some existing algorithms, the proposed method has higher convergence efficiency because less data are used in each iteration and the data is sufficient to complete an update. It not only has the best convergence accuracy but also requires the least running time for iteration, which greatly saves memory space.

Compared with previous algorithms, the main feature of this algorithm is that it can synthesize these equations together to get a coupled operator matrix equation. Although the equation of this paper contains multiple submatrix equations, the algorithm in this paper only needs to use the information of one submatrix equation in the equation of this paper in each iteration so that different constraint solutions of different (coupled) matrix equations can be studied for this class of equations. However, previous articles need to iterate on a specific constraint solution of a matrix equation separately.

Describes Childreach – a US child‐focuses development organization which sponsors children and their families in developing countries – and a recent project in development education, “Buffalo banks and borewells: Childreach makes sense of development”, which involved creating and distributing educational newsletters on Third World and development issues. Lists the goals of the project and how they were addressed. Outlines what was gained from the exercise. Links this to the paradoxical situation in the USA whereby the public think money should go towards foreign aid but are reluctant to actually fork out any money themselves. Considers the role of trust and the concept of social capital, emphasizing that sponsors need to trust that their investment is making an important contribution to improving the life of the sponsored child and its family or community.

Cilia serves numerous biological functions in the human body. Malfunctioning of nonmotile or motile cilia will have different kinds of consequences for human health. More specifically, the directed and rhythmic beat of motile cilia facilitates the unidirectional flow of fluids that are crucial in both homeostasis and the development of ciliated tissues. In cilia-dependent hydrodynamic flows, tapering geometries look a lot like the structure of biological pathways and vessels, like airways and lymphatic vessels. In this paper, the Carreau fluid model through the cilia-assisted tapered channel (asymmetric) under the influence of induced magnetic field and convective heat transfer is investigated.

Lubrication theory is a key player in the mathematical formulation of momentum, magnetic field and energy equations. The formulated nonlinear and coupled differential equations are solved with the aid of the homotopy perturbation method (HPM). The graphical results are illustrated with the help of the computational software “Mathematica.”

The impact of diverse emerging physical parameters on velocity, induced magnetic field, pressure rise, current density and temperature profiles is presented graphically. It is observed that the cilia length parameter supported the velocity and current density profiles, while the Hartman number and Weissenberg number were opposed. A promising effect of emerging parameters on streamlines is also perceived.

The study provides novel aspects of cilia-driven induced magnetohydrodynamics flow of Carreau fluid under the influence of induced magnetic field and convective heat transfer through the asymmetric tapered channel.

The influence of the temperature discrepancy parameter and higher order of the time-derivative is discussed. Classical coupled and generalized hygrothermoelasticity models are recovered by considering the various special cases and illustrated graphically.

The theory of integral transformations has been used to study a new hygrothermal model that includes higher-order time derivatives with three-phase-lags and memory-dependent derivatives (MDD). This model considers the microscopic structure’s influence on a non-simple hygrothermoelastic infinitely long cylinder. The generalized Fourier and Fick’s law was adopted to derive the linearly coupled partial differential equations with higher-order time-differential with the two-phase lag model, including memory-dependent derivatives for the hygrothermal field. The investigation of microstructural interactions and the subsequent hygrothermal change has been undertaken as a result of the delay time and relaxation time translations.

These two-phase-lag models are also practically applicable in modeling nanoscale heat and moisture transport problems applied to almost all important devices. This work will enable future investigators to gain insight into non-simple hygrothermoelasticity with different phase delays of higher order in detail.

To the best of my knowledge, and after completing an intensive search of the relevant literature, the author could not learn any published research that presents a general solution for a higher-order time-fractional three-phase-lag hygrothermoelastic infinite circular cylinder with memory memory-dependent derivative.