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Two solution concepts for a FMP problem are suggested. The first one makes use of level sets of the fuzzy set of feasible alternatives. The second solution is based on the concept of Pareto maximum in vector optimization. It is shown that both solutions are equivalent in a sense that they give the same fuzzy value of a function maximized. It is suggested that if a decision‐maker is to choose a single element, then his choice must be based not only on the membership value of this element in the solution fuzzy set but also on the corresponding value of the function maximized. In this respect the situation is similar to that typical for vector optimization. The approach suggested in this paper is further used for analysing games with fuzzy sets of strategies of the players. A fuzzy equilibrium solution is introduced, which can provide a base for an agreement between the players.

It is well known that the laws of Leimkuhler, Mandelbrot, Lotka and the verbal formulation of Bradford's law are equivalent. In this note we prove an analogous framework of laws in which now the law of Zipf occurs instead of Mandelbrot's law. Laws in this group are Brookes' law and the graphical formulation of Bradford's law. We show that both groups of laws are very different in the sense that they are not even equal asymptotically for high rankings.

The analysis of multi‐stage distribution has been carried out along three dimensions, depending on the characteristics of the particular problem. These are location, transportation and inventory and while simple problems can be successfully solved using any one of the three approaches, it is fair to say that the analysis of a complex distribution system has been limited by computer storage and the time required by the search and optimising procedures. In this paper we develop a simple inventory‐type model and test it on a small set of data. The results are encouraging and the model can easily be extended to handle a more realistic size of problem.

It is shown that the clearances between the journals of a shaft and the bearings in which it runs may give rise to a species of unbalance and that unless this unbalance is corrected by a counter unbalance in the shaft or loads carried by it, steady motion is impossible in certain ranges of speed. The treatment presented is concerned with conditions for steady circular motion rather than with transient disturbances.

IN a recent paper, Morris discussed the conditions for steady circular motion of a shaft, allowing for the clearances between the journals of the shaft and the bearings in which it runs. Morris found that a certain degree of unbalance was necessary in order that steady circular motion should be possible, and that the system was very sensitive to small changes of unbalance under certain conditions.

The study aims to carry out predictive modeling based on publicly available COVID-19 data for the duration April 01, 2020 to June 20, 2020 pertaining to India and five of its most infected states: Maharashtra, Tamil Nadu, Delhi, Gujarat and Rajasthan.

The study leverages the susceptible, infected, recovered and dead (SIRD) epidemiological framework for predictive modeling. The basic reproduction number R0 is derived by an exponential growth method using RStudio package R0. The differential equations reflecting the SIRD model have been solved using Python 3.7.4 on the Jupyter Notebook platform. For visualization, Python Matplotlib 3.2.1 package is used.

The study offers insights on peak-date, peak number of COVID-19 infections and end-date pertaining to India and five of its states.

The results subtly indicate toward the amount of effort required to completely eliminate the infection. It could be leveraged by the political leadership and industry doyens for economic policy planning and execution.

The emergence of a clear picture about COVID-19 lifecycle is impossible without integrating data science algorithms and epidemiology theoretical framework. This study amalgamates these two disciplines to undertake predictive modeling based on COVID-19 data from India and five of its states. Population-specific granular and objective assessment of key parameters such as reproduction number (R0), susceptible population (S), effective contact rate (ß) and case-fatality rate (s) have been used to generate a visualization of COVID-19 lifecycle pattern for a critically affected population.

This paper is devoted to the analysis of metal forming with assumption of rigid‐plastic behaviour with strain hardening. As opposed to the classical rate problem formulation based on Markov's principle and the explicit scheme, a more satisfactory incremental approach is deduced from Moreau's catching up algorithm. This implicit scheme, although more complicated, gives better results concerning convergence and numerical stability. Using an internal variable representing the strain hardening, an incremental strain energy density is defined which leads to a principle of minimum of the total incremental strain energy. In the numerical approximation using finite elements, the non‐linear equilibrium equations are solved by classical Newton's method. An approximation of Coulomb's criterion is used in order to represent friction with a rigid foundation. The simple compression test is simulated and shows that the implicit scheme is faster than the explicit one.

Evaluating capital investments for additions or modifications to warehouses, for replacement of equipment or for entirely new facilities is a complex activity which involves numerous financial, competitive and other considerations. The financial aspect of capital investments is addressed and it is shown how ten different investment criteria can be brought to bear on the capital investment issue. The ten investment criteria consist of five primary criteria and five secondary criteria. The primary criteria are payback period in years, non‐discounted rate of return on investment, internal rate of return, Baldwin rate of return, and benefit cost ratio. All ten criteria are described and suggestions are made when each criterion is appropriate.

A computer model based on the fractional step method is presented for modelling density coupled mass transport in groundwater. Although several models utilising the fractional step method had been developed previously, all were based on the Eulerian solution approach. The model developed by the authors uses the Langrangian approach which has some inherent advantages and disadvantages. The problems associated with the implementation of the fractional step method and techniques by which they were overcome are discussed. The performance of the model is examined and results obtained for standard problems are compared with those from other computer packages.