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This paper is concerned with finding the optimal way of rearranging items in a warehouse from their initial positions to their desired final locations. Such a rearrangement may become necessary because of changes in the relative demand for each item, with the result that what were once fast-moving items at the 'front' end of the warehouse, are now only slow-moving ones that must be moved towards the 'rear.' Although the problem, as treated in this paper, is addressed to the rearrangement of items in a warehouse, many other applications come immediately to mind, such as the reorganization of the layout of open-plan orates and factories. The paper gives a two-stage algorithm that produces the sequence of item movements necessary to achieve the desired rearrangement and incur the minimum cost (or time) spent in the rearranging process; the result is optimal in the restricted case where the rearrangement must be done in a number of cycles each one being of a short time duration (the case, for example, if the warehouse were to remain operative during the rearrangement). [ABSTRACT FROM AUTHOR]

This paper discusses the optimal rate of advertising expenditure given the relationship between the rate of change of sales and the rate of expenditure. It is shown that we may assume that the marginal return of increased expenditure is never increasing. This is because when marginal returns increase there is always a "mixed" pattern in which two levels of expenditure are used, each for infinitesimally short intervals, with the property that the average cost for a given sales change is lower than with a fixed policy, and marginal returns are constant. If we assume that marginal returns do not increase, then, provided it is profitable to advertise, there exists an over-all optimal sales rate and an expenditure level, just sufficient to maintain it, with the following properties with respect to long-run discounted profits: (1) If sales even reach this level it is optimal to keep them there. (2) Starting from any other level, the optimal policy is to spend in such a way as to drive sales towards this level. The only requirements for these results are that the cost of achieving a given change in the sales rate be an increasing function of the sales rate and the rate of change of sales rate. It is also shown that the optimal sales rate to be maintained in the long run is not the rate which maximises the rate of gaining profit after advertising, unless the discount rate is zero. In practice, the mixed policy cannot be followed because discreet changes in expenditure levels cannot be made too frequently. When a mixed policy is optimal the best we can achieve is to use a cyclic policy in which we advertise for short intervals at each of the appropriate levels. A simple example calling for such a policy is when we have an advertising threshold below which expenditure has no effect, together with a relatively small market with low profit margins. Whether or not advertising thresholds exist requires psychological theory or controlled experimentation beyond the scope of this paper. [ABSTRACT FROM AUTHOR]

This paper simplifies and extends some previous work on domain restriction. With the help of an easy arithmetical result, two types of necessary and sufficient conditions are established for transitivity and quasi-transitivity under majority rule and transitivity under non-minority rule. [ABSTRACT FROM AUTHOR]

The author discusses the energy conversion in photosynthesis using a model that is constructed from a commercially available set of coupled pendula. He states that when one pendulum is set to oscillate, which is likened to the absorption of a photon, the resultant twisting of the string causes a periodic force to be used to the second at the same frequency. Since the two pendula are identical, they have similar central frequency of oscillation, which causes the second pendulum to oscillate back forth. As the second pendulum's oscillation increase, energy is drawn from the first until it is at rest and the second is oscillating with all the energy that was present in the oscillations of the first. This movement indicates the energy transfer.

The article focuses on the problem of long cycles in residential construction. According to the author, cycles are understood to be alternations of expansions and contractions. Ideally the duration of either one should not be less than one and one-half business cycles. Lord swings are generally periods of acceleration and retardation in growth. They would become cycles only after the elimination of secure trend. The causes of prolonged periods of expansion are now not difficult to find. They cannot be attributed to short-term factors alone because they were much too strong and decisively dominated more than one business cycle. The fundamental cause was the accumulated demand strongly reinforced by international and internal immigration. The statistical evidence of a study does not suggest the existence of building cycles in total residential construction. this construction activity can be most appropriately described by such terms as breaks in the series, vigorous expansions following the breaks, and changes of pace or at most changes in short trends.

The article reports on the cycle of chemical elements in the ecosystem. It notes that in the precipitation and in salt deposit there was an addition of chemical elements, while a loss of chemical elements from the ecosystem occurs through leaching, run-off, and grazing. It gives an account of the chemical element content in a 7½-year-old stand of gorse (Ulex Europaeus L.), the elements' quantities in the annual litter fall and throughfall, and the accession of chemical elements in rain. To present a picture of the circulation of the matter, data on these various facets are combined.

The article studies the seasonal periodicity in the growth and development of some forest trees in the rain forests in Nigeria. The climate is markedly seasonal at Ibadan, Nigeria, with distinct dry and rainy seasons, with six consecutive months each have less than 10 centimeter of rainfall, according to the author. Observations on seasonal periodicity were made during the period of 1957 to 1961 on a number of trees growing in the Botanical Garden of the University College in Ibadan. The trees, according to the author, are of natural occurrence, and had been growing under secondary forest conditions in the area before it was constituted into a botanical garden in 1949.

The article presents a study on the origin and development of the Festuco-Agrostidetum or the agrostis plant on an eroded sand. The article is substantiated with a discourse on the area being investigated, profile of the soil, samples of soil and the determined factors, the vegetation analysis, and a detailed description of the communities including the stages which the plant undergoes. The result is explored together with details on the plant's habitat, flora, competition and succession. It concludes that both stages exist while a series of dry years speeds up the retrogression and while the climate holds the balance, periodicity is inherent in the vegetation and associated with the lichen cycle.

The article investigates the factors that influence the periodicity of diatoms. Some of the factors considered, include seasonal variations in natural waters, like variation in nitrate content, silica content and hardness in lake waters as well as variation in the composition of soil drainage. The author also investigates the impact of water variation and salinity on diatom periodicity, in five bodies of water: lakes, rivers, ponds and seas. Findings show that lows salinity is closely correlated with high diatom numbers. Evidence also suggests that flood water has a significant impact on diatom periodicity by affecting the substances dissolved in the water, like nitrates, silica and oxygen.

Explores causes of vegetational cycles. Comparability of cycles of vegetation to cycles of erosion; Impact of the climate on the final stage; Characteristics of the original plant formation in any habitat; Succession of plant formation; Division of pioneer formations in moist climates.

Presents a study which focused on an elementary expression for computing the probability of a cyclical majority in the case of several alternatives. Proposition that the number of forward cycles must be equal to the number of backward cycles; Information on paradox weakening vectors; Linear expression of the existence of a paradox.