Finite-Time Optimal Control of Polynomial Systems Using Successive Suboptimal Approximations

It is shown in this paper that the finite-time optimal control of polynomial systems can be obtained by solving a sequence of optimal control problems for the linearized problem. The paper provides proof of convergence as well as illustration of the procedure by two examples.     

57Fe Mössbauer spectroscopic study of nanostructured zinc ferrite

Nanosize zinc ferrite particles, prepared by nitrate method, were investigated by XRD, TEM, ⁵⁷Fe Mössbauer spectroscopy and VSM. The average particle size in this system varies from 10 to 62 nm as the sintering temperature increases from 300°C to 1,000°C. The lattice parameters in this system are almost constant at a value of ～8.41 Å. The Mössbauer spectra of all the sintered samples show a single doublet. The Mössbauer hyperfine parameters show little change with the change of sintering temperature. The doublets are ascribed to the presence of superparamagnetism in this system, which is also corroborated by the VSM measurements.     

To analyse the performance of tapered and MMI assisted splitter on the basis of geographical parameters

A literal model using geometric examination was formulated to calculate the optimum width and length of multimode interference structure used in the 1 × 2 power splitter and plot electric field intensity for input and each output signal. Designing and simulation of the wavelength response of 1 × 2 splitter using Tapered and MMI assisted structure. Mechanism on the critical geographical parameters like length and width of MMI structure, separation distance between output ports ‘S’, arm angle ‘α’ which give the optimum power and electric field intensity for the considered necessary wavelength. Finite difference beam propagation methods have been used to simulate the conventional and tapered MMI device behaviour.     

A hybrid FVM–LBM method for single and multi‐fluid compressible flow problems

The lattice Boltzmann method (LBM) has established itself as an alternative approach to solve the fluid flow equations. In this work we combine LBM with the conventional finite volume method (FVM), and propose a non‐iterative hybrid method for the simulation of compressible flows. LBM is used to calculate the inter‐cell face fluxes and FVM is used to calculate the node parameters. The hybrid method is benchmarked for several one‐dimensional and two‐dimensional test cases. The results obtained by the hybrid method show a steeper and more accurate shock profile as compared with the results obtained by the widely used Godunov scheme or by a representative flux vector splitting scheme. Additional features of the proposed scheme are that it can be implemented on a non‐uniform grid, study of multi‐fluid problems is possible, and it is easily extendable to multi‐dimensions. These features have been demonstrated in this work. The proposed method is therefore robust and can possibly be applied to a variety of compressible flow situations. Copyright © 2009 John Wiley & Sons, Ltd.     

Degree of Approximation for Bivariate Chlodowsky–Szasz–Charlier Type Operators

We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the degree of approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky–Szasz–Charlier type and estimate the order of approximation in terms of mixed modulus of continuity.     

Kantorovich variant of a new kind of q‐Bernstein–Schurer operators

Ren and Zeng (2013) introduced a new kind of q‐Bernstein–Schurer operators and studied some approximation properties. Acu et al. (2016) defined the Durrmeyer modification of these operators and studied the rate of convergence and statistical approximation. The purpose of this paper is to introduce a Kantorovich modification of these operators by using q‐Riemann integral and investigate the rate of convergence by means of the Lipschitz class and the Peetre's K‐functional. Next, we introduce the bivariate case of q‐Bernstein–Schurer–Kantorovich operators and study the degree of approximation with the aid of the partial modulus continuity, Lipschitz space, and the Peetre's K‐functional. Finally, we define the generalized Boolean sum operators of the q‐Bernstein–Schurer–Kantorovich type and investigate the approximation of the Bögel continuous and Bögel differentiable functions by using the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the operators considered in the paper for the univariate case and the associated generalized Boolean sum operators to certain functions by means of graphics using Maple algorithms. Copyright © 2017 John Wiley & Sons, Ltd.     

Impact of information sharing and lead time on bullwhip effect and on-hand inventory

This work analyzes a two echelon (warehouse–retailer) serial supply chain to study the impact of information sharing (IS) and lead time on bullwhip effect and on-hand inventory. The customer demand at the retailer is assumed to be an autoregressive (AR(1)) process. Both the echelons use a minimum mean squared error (MMSE) model for forecasting lead time demand (LTD), and follow an adaptive base-stock inventory policy to determine their respective order quantities. For the cases of without IS and inter as well as intra echelon IS, expressions for the bullwhip effect and on-hand inventory for the warehouse are obtained, considering deterministic lead-time. The results are compared with the previous research work and an easy analysis of the various bullwhip effect expressions under different scenarios, is done to understand the impact of IS on the bullwhip effect phenomenon. It is shown that some part of bullwhip effect will always remain even after sharing both inter as well as intra echelon information. Further, with the help of a numerical example it is shown that the lead time reduction is more beneficial in comparison to the sharing of information in terms of reduction in the bullwhip effect phenomenon.     

Cyclic networks with general blocking and starvation

We introducegeneral starvation and consider cyclic networks withgeneral blocking and starvation (GBS). The mechanism of general blocking allows the server to process a limited number of jobs when the buffer downstream is full, and that of general starvation allows the server to perform a limited number of services in anticipation of jobs that are yet to arrive. The two main goals of this paper are to investigate how the throughput of cyclic GBS networks is affected by varying (1) the total number of jobsJ, and (2) the buffer allocationk=(k₁..., k_m) subject to a fixed total buffer capacityK=k ₁ +... + k_m. In particular, we obtain sufficient conditions for the throughput to be symmetric inJ and to be maximized whenJ=K/2. We also show that the equal buffer allocation is optimal under the two regimes of light or heavy usage. In order to establish these results, we obtain several intermediate structural properties of the throughput, using duality, reversibility, and concavity, which are of independent interest.Research supported in part by NSF Grant No. ECS-8919818.