Billingsley's packing dimension

For a stochastic process on a finite state space, we define the notion of a packing measure based on the naturally defined cylinder sets. For any two measures , , corresponding to the same stochastic process, if

then we prove that

     

Estimation of dynamic properties of attractors observed in hollow copper electrode atmospheric pressure arc plasma system

Understanding of the basic nature of arc root fluctuation is still one of the unsolved problems in thermal arc plasma physics. It has direct impact on myriads of thermal plasma applications being implemented at present. Recently, chaotic nature of arc root behavior has been reported through the analysis of voltages, acoustic and optical signals which are generated from a hollow copper electrode arc plasma torch. In this paper we present details of computations involved in the estimation process of various dynamic properties and show how they reflect chaotic behavior of arc root in the system.     

Theory of nuclear quadrupole interactions in aluminum and copper metals in presence of muon

The electric field gradients at²⁷Al and⁶³Cu nuclei which are nearest neighbors to the muon in the face-centered cubic metals aluminum and copper, with muon at an octahedral interstitial site, are studied. The electron density fluctuations needed for the evaluation of the electronic, or valence, contributions to field gradients are taken from earlier investigations involving the spherical solid approximation. The enhancement factors a that have to be applied to the electric field-gradients obtained from these approximations, due to the departures of the electronic wave-functions from plane-wave character, and the incorporation of antishielding effects, have been obtained for both APW and OPW approaches to the conduction electron wave-functions and good agreement is found between the results by the two approaches. Size effects due to the lattice distortion associated with the presence of the muon are included through actual point ion summations using available calculated displacements of the ions surrounding the muon. The valence contributions are the dominant ones but the size effect contributions are also significant. The net field-gradient obtained for the²⁷Al site is significantly smaller than experiment while that for⁶³Cu is substantially larger than experiment. Possible sources that could lead to better agreement with experiment are discussed and it is concluded that major improvement is needed in the valence effect contributions in both metals.     

Chiral Schwinger model in curved space-time

We extend the method of path integrals to obtain the solution of the chiral Schwinger model in curved space-time and compare it with the flat space-time solution.     

Two-warehouse production model for deteriorating inventory items with stock-dependent demand under inflation over a random planning horizon

This paper develops a production-inventory model for a deteriorating item with stock-dependent demand under two storage facilities over a random planning horizon, which is assumed to follow exponential distribution with known parameter. The effects of learning in set-up, production, selling and reduced selling is incorporated. Different inflation rates for various inventory costs and time value of money are also considered. A hybrid genetic algorithm is designed to solve the optimization problem which is hard to solve with existing algorithms due to the complexity of the decision variable. To illustrate the model and to show the effectiveness of the proposed approach a numerical example is provided. A sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out.     

Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by , is a graph with the same set of vertices as G such that two vertices are adjacent in if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of and . The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

A mathematical model to characterise effects of liquid hold-up on bosh silicon transport in the dripping zone of a blast furnace

A first principle based mathematical model has been developed to characterise the effect of total liquid hold-up on the bosh silicon distribution behaviour in the dripping zone of a blast furnace. Two specific cases of hold-up behaviour have been investigated, namely, hold-up in the absence and in the presence of counter current gas flow conditions. The model exemplifies coupled phenomenon of chemical kinetics, transport processes and liquid hold-up to characterise the silicon behaviour in the dripping zone. The present modelling investigation shows that the bosh silicon level diminishes with the enhanced liquid hold-up in the dripping zone. Further, the influence of counter current gas flow on the hold-up is not significant. However, it has been observed that the liquid phase temperature reduces with increased liquid hold-up in dripping zone under steady state operating conditions. The model predictions of bosh silicon distribution have been validated with the published literatures (bulk values) and found to be in good agreement.     

Extremal graph characterization from the bounds of the spectral radius of weighted graphs

We consider weighted graphs, where the edge weights are positive definite matrices. The eigenvalues of a graph are the eigenvalues of its adjacency matrix. We obtain a lower bound and an upper bound on the spectral radius of the adjacency matrix of weighted graphs and characterize graphs for which the bounds are attained.