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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.

Practical needs in geographical information systems (GIS) have led to the investigation of formal, sound and computational methods for spatial analysis. Since models based on topology of R² have a serious problem of incapability of being applied directly for practical computations, we have noticed that models developed on the raster space can overcome this problem. Because some models based on vector spaces have been effectively used in practical applications, we then introduce the idea of using the raster space as our platform to study spatial entities of vector spaces. In this paper, we use raster spaces to study not only morphological changes of spatial entities of vector spaces, but also equal relations and connectedness of spatial entities of vector spaces. Based on the discovery that all these concepts contain relativity, we then introduce several new concepts, such as observable equivalence, strong connectedness, and weak connectedness. Additionally, we present a possible method of employing raster spaces to study spatial relations of spatial entities of vector spaces. Since the traditional raster spaces could not be used directly, we first construct a new model, called pansystems model, for the concept of raster spaces, then develop a procedure to convert a representation of a spatial entity in vector spaces to that of the spatial entity in a raster space. Such conversions are called approximation mappings.

The purpose of this paper is to present the terms of grey numbers and its operations.

The definitions of elementary terms about grey numbers and its operations are presented one by one.

The reader could know the basic explanation about the important terms about grey numbers and its operations from this paper.

Many of the colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread the universal principles of grey system theory.

A group of n (> 1) peers are required to cooperate with each other in distributed applications on P2P overlay networks. A P2P group is distributed without a centralized controller and is scalable and heterogeneous. The purpose of this paper is to discuss how to realize a scalable group in P2P overlay networks.

In a group, messages have to be causally delivered to every peer. In order to realize a scalable group, messages are ordered by taking advantage of linear time (LT) and physical time (PT) since message length is O(1). Here, each peer has to hold information on the accuracy of physical clock of each peer and minimum delay time among every pair of peers. Since the size of the information is O(n²), it is difficult for each peer to hold the information and so the authors discuss a multi‐layered model to reduce the size of group information.

Through the evaluation studies, it is shown how the size of the group information can be reduced in a multi‐layered group compared with a traditional flat group.

In this paper, the authors discuss a multi‐layered group model for a scalable group, to reduce the size of group information; and also order messages by using both the linear time and physical time.

The purpose of this paper is to advance new rules about operations of grey numbers.

The paper first puts forward the definitions of basic element of grey number and general grey number. The operation axiom, operation rules of general grey numbers and a new algebraic system for general grey numbers are built based on the “kernel” and the degree of greyness of grey numbers.

Up to now, the operation of general grey numbers has been transformed to operation of real numbers; thus, the difficult problem for set up operation of general grey numbers has been solved to a certain degree.

The method exposed in the paper can be used to integrate information from a different source. The operation of general grey numbers could be extended to the case of grey algebraic equation, grey differential equation and grey matrix which includes general grey numbers. The operation system of general grey numbers also opened a new passageway for research on grey input‐output and grey programming, etc.

The new conception of a basic element of grey number and general grey number was given for the first time in this paper. The novel operation rules of general grey numbers were also constructed.

Provides a brief description of Spearman’s g which has become the cornerstone for most theories of intelligence and highlights the social, scientific and political controversy in which this is surrounded. Discusses the identification of g before covering the criticisms, the physiological manifestations and the practical and social implications together with education. Summarizes that this construct routinely accounts for more variance than all other cognitive factors combined and so holds a high position in any model of the structure of human cognitive abilities.

The purpose of this paper is to evaluate the possibility of a new biocatalyst prepared by kefir cells immobilization on grape stalks (GS) to reduce quickly and efficiently the Biochemical Oxygen Demand (BOD) and Chemical Oxygen Demand (COD) of the waste whey during its fermentation producing potable ethanol.

Many batch whey fermentations were carried out in order the effect of various conditions (pH, temperature) on 14C-labeled lactose uptake rate by the GS-immobilized kefir cells and consequently on fermentation rate as well as on ethanol production and whey BOD and COD reduction to be determined.

It has been illustrated that GS-biocatalyst was suitable for whey BOD and COD reduction by about 32 and 25 percent, respectively during whey alcoholic fermentation at 30°C and pH 5.5 in only ten hours, producing about 3.30 percent w/v of ethanol.

The findings of this research may enhance the existing literature on whey exploitation, for the first time focussing on the use of cheap and abundant GS as support for kefir immobilization during whey fermentation, which is potentially acceptable by industries in order to reduce fast and easily the whey polluting load and produce ethanol.

Many of the industrially important processes follow a complex reaction scheme and more than one reaction takes place simultaneously for these systems. Design and scale up of these processes are important but due to the nature of the system and high numbers of the affected parameters, modeling of the complex reactions becomes correspondingly difficult. The purpose of this paper is to develop a general model, which can simplify modeling of such (or similar) complex reactions.

Virtual model is a generalized novel approach for modeling of these complex reactions. In this model, the complex reactions have been imagined as a simple reaction. Now, kinetic and structural parameters of this simple reaction have been obtained by fitting the model relationships with the experimental data.

In this work, the ability of the virtual model has been validated using the experimental data pertinent to the reduction of molybdenum disulfide and cuprous sulfide by hydrogen in the presence of lime.

Virtual model is a generalized novel approach for modeling of these complex reactions. In this model, the complex reactions have been imagined as a simple reaction.

Two complementary 3D finite element formulations, with either the magnetic field or the magnetic vector potential as unknowns, are developed to deal with the modeling of eddy currents in electrical steel laminations. The magnetic flux through the flux gates of the conducting region is imposed via the boundary terms of the weak formulations, in a natural way thanks to the use of edge finite elements. The two formulations are applied to a simple 1D eddy current problem with analytical solution. As a practical 3D application example, a T‐joint region of an electrical steel lamination is considered.

The purpose of this paper is to reveal the multi‐scale relation between power law distribution and correlation of stock returns and to figure out the determinants underlying capital markets.

The multi‐scale relation between power law distribution and correlation is investigated by comparing the original series with the special series. The eliminating intraday trend series approach developed by Liu et al. is utilized to analyze the effects of power law decay change on correlation properties, and shuffling series originated by Viswanathan et al. for the impacts of special type of correlation on power‐law distribution.

It is found that the accelerating decay of power law has an insignificant effect on correlation properties of returns and the empirical results indicate that time scale may also be an important factor maintaining power law property of returns besides correlation. When time scale is under critical point, the effects of correlation are crucial, and the correlation of nonlinear long‐range presents the strongest influence. However, for time scale beyond critical point, the impact of correlation begins to diminish or even finally disappear and then the power law property shows complete dependence on time scale.

The 5‐min high frequency data of the Shanghai market as the empirical benchmark is insufficient to depict the relation over the entire time scale in the Chinese stock market.

The paper identifies the determinants of market dynamics to apply them to risk management through analysis of multi‐scale relations, and supports endeavors to introduce time parameter into further risk measures and control.

The paper provides the empirical evidence that time scale is one of the key determinants of market dynamics by analyzing the multi‐scale relation between power law distribution and correlation.