Bounded mean oscillation and bandlimited interpolation in the presence of noise

We study some problems related to the effect of bounded, additive sample noise in the bandlimited interpolation given by the Whittaker-Shannon-Kotelnikov (WSK) sampling formula. We establish a generalized form of the WSK series that allows us to consider the bandlimited interpolation of any bounded sequence at the zeros of a sine-type function. The main result of the paper is that if the samples in this series consist of independent, uniformly distributed random variables, then the resulting bandlimited interpolation almost surely has a bounded global average. In this context, we also explore the related notion of a bandlimited function with bounded mean oscillation. We prove some properties of such functions, and in particular, we show that they are either bounded or have unbounded samples at any positive sampling rate. We also discuss a few concrete examples of functions that demonstrate these properties.     

Resource constraint scheduling with a fractional shared resource

We consider a scheduling problem motivated by mining in remote off-grid areas. In this model, mines have pre-assigned mineral processing jobs and their own machine for executing these jobs. Each job also needs a certain amount of electricity in order to get completed. The electricity, on the other hand, is of limited supply and must be shared between the mines. We present a mathematical formulation of the problem and a Lagrangian relaxation based heuristic. Computational results which compares our heuristic with genetic algorithm and simulated annealing are also presented.     

Synthesis and antibacterial activity of some 5-hydroxy-5-trifluoromethyl-4,5-dihydropyrazol-1-thiocarboxamides, 3-trifluoromethylpyrazol-1-thiocarboxamides and 4-aryl-2-(5(3)-trifluoromethyl-1-pyrazolyl)thiazoles

5-Hydroxy-5-trifluoromethyl-4,5-dihydropyrazol-1-thiocarboxamides 3 and 3-trifluoromethylpyrazol-1-thiocarboxamides 4, regioselectively obtained by the condensation of trifluoromethyl-β-diketones with thiosemicarbazide under neutral and acidic conditions, on further reaction with phenacyl bromides 5 afforded 4-aryl-(5-trifluoromethyl-pyrazol-1-yl)thiazoles 6 and 4-aryl-(3-trifluoromethyl-pyrazol-1-yl)thiazoles 7, respectively. Five 4,5-dihydropyrazoles (3a–e) and two pyrazolylthiazoles (6a and 6c) were tested against one Gram-positive and one Gram-negative bacteria to assess their in vitro antibacterial activity. Compounds 3a, 3b and 3e showed moderate antibacterial activity against Gram-positive bacterium, Bacillus pumilus.     

Two body non-leptonic decaysB →Dπ with heavy quark and chiral symmetry

We have analysed the two body non-leptonic charmed-meson decays of heavyB meson based on the factorization assumption. The transition matrix elements and the corresponding decay widths are calculated in the heavy quark and chiral symmetry limit and the Isgur-Wise function present in the expression is determined by the wave function model of Aliet al. The results obtained are quite interesting and agree reasonably well with the experimental data.     

Exact formulation of stochastic EMQ model for an unreliable production system

The purpose of this paper is to present an exact formulation of stochastic EMQ model for an unreliable production system under a general framework in which the time to machine failure, corrective (emergency) and preventive (regular) repair times are assumed to be random variables. For exact financial implications of the lot-sizing decisions, the EMQ model is formulated based on the net present value (NPV) approach. Then, by taking limitation on the discount rate, the traditional long-run average cost model is obtained. The criteria for the existence and uniqueness of the optimal production time in both the models are derived under general failure and specific repair time distributions. Numerical examples are devoted to find the optimal production policies of the developed models and examine the sensitivity of the parameters involved. Computational results show that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach, though the performance level strongly depends on the pertinent failure and repair time distributions.     

Influence of branch content on the microstructure of blends of linear and octene-branched polyethylene: a MD simulation study

Microstructure of linear low-density polyethylene (LLDPE) with linear high-density polyethylene (HDPE) is investigated by molecular dynamics (MD) simulation. The branch content of LLDPE was varied from 10 to 60 branches/1000 C. An equimolar mixture of each of the two polymers is simulated in the NVT ensemble at 500 K and at average experimental densities of the two polymer melts. Initially, chains of LLDPE and HDPE were completely mixed and evolution of conformations with time was monitored. The blends were found to microphase separate when the branch content of LLDPE exceeded 30 branches/1000 C. At 40 branches/1000 C, the two polymers displayed partial microphase separation and complete microphase separation was observed at 60 branches/1000 C. Substantial short-range order and mismatch of molecular conformations is observed in the microphase-separated systems.     

Atom Capture by Nanotube and Scaling Anomaly

The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of a single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of such bound state. Binding of the polarizable atoms in the coupling constant interval η ²∈[0,1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in the literature.     

Asymptotic bounds on pion form factor

A technique recently developed for inelastic electron proton scattering is applied for inelastic electron pion scattering. It is found that all the derivatives of off-shell form factor of pion nears=m _π ² and for largeQ ² are bounded from above, provided that the dispersion relation for the form factor requires no more than one subtraction. The elastic pion form factor is bounded by [lnQ ²] ^c /Q ², wherec is any positive constant.     

Integration of Auditor Preferences and Sampling Objectives: A Polynomial Goal-Programming Perspective

The choice of an audit sample involves integration of diverse goals. Such integration must consider the preferences of the auditor towards costs as well as risks. Traditionally this problem has been formulated to determine minimal sample size and its allocation such that each of the goals is satisfied simultaneously or to the extent possible. However, these formulations do not consider trade-offs between goals, so that the sample may not reflect the auditor's preferences regarding sampling costs and risks. In this paper, we model such trade-offs by utilizing a polynomial goal-programming framework and utilize a practical case problem to illustrate the framework. Computational experience shows the technique to be feasible and inexpensive.