X-ray photoelectron spectroscopy: A new method for determination of copolymer composition,and monomer reactivity ratios and monomer sequence distribution therefrom

Copolymer compositions and reactivity ratios for the radical copolymerization of styrene with acrylonitrile have been determined by x-ray photoelectron spectroscopy (XPS). The results obtained by this technique were confirmed by elemental as well as ¹H-NMR (nuclear magnetic resonance) analysis. The monomer sequence distributions have also been calculated utilizing the monomer reactivity ratio values obtained by three different techniques viz., XPS, ¹H-NMR, and elemental analysis. The agreement between the monomer sequence distributions in the copolymer chain by these methods is very satisfactory. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 35: 2049–2056, 1997     

Scattering of oblique waves by bottom undulations in a two-layer fluid

Scattering of waves obliquely incident on small cylindrical undulations at the bottom of a two-layer fluid wherein the upper layer has a free surface and the lower layer has an undulating bottom, is investigated here assuming linear theory. There exists two modes of time-harmonic waves propagating at each of the free surface and the interface. Due to an obliquely incident wave of a particular mode, reflected and transmitted waves of both the modes are created in general by the bottom undulations. For small undulations, a simplified perturbation analysis is used to obtain first-order reflection and transmission coefficients of both the modes due to oblique incidence of waves of again both modes, in terms of integrals involving the shape function describing the bottom. For sinusoidal undulations, these coefficients are plotted graphically to illustrate the energy transfer between the waves of different modes induced by the bottom undulations.     

An inventory model for a deteriorating item with displayed stock dependent demand under fuzzy inflation and time discounting over a random planning horizon

An inventory model for a deteriorating item (seasonal product) with linearly displayed stock dependent demand is developed in imprecise environment (involving both fuzzy and random parameters) under inflation and time value of money. It is assumed that time horizon, i.e., period of business is random and follows exponential distribution with a known mean. The resultant effect of inflation and time value of money is assumed as fuzzy in nature. The particular case, when resultant effect of inflation and time value is crisp in nature, is also analyzed. A genetic algorithm (GA) is developed with roulette wheel selection, arithmetic crossover, random mutation. For crisp inflation effect, the total expected profit for the planning horizon is maximized using the above GA to derive optimal inventory decision. On the other hand when inflationary effect is fuzzy then the above expected profit is fuzzy in nature too. Since optimization of fuzzy objective is not well defined, the optimistic/pessimistic return of the expected profit is obtained using possibility/necessity measure of fuzzy event. Fuzzy simulation process is proposed to determine this optimistic/pessimistic return. Finally a fuzzy simulation based GA is developed and is used to maximize the above optimistic/pessimistic return to get optimal decision. The models are illustrated with some numerical examples and some sensitivity analyses have been presented.     

Optimal production inventory policy for defective items with fuzzy time period

In this paper, an optimal production inventory model with fuzzy time period and fuzzy inventory costs for defective items is formulated and solved under fuzzy space constraint. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is linearly stock dependent. The defective rate is taken as random, the inventory holding cost and production cost are imprecise. The fuzzy parameters are converted to crisp ones using credibility measure theory. The different items have the different imprecise time periods and the minimization of cost for each item leads to a multi-objective optimization problem. The model is under the single management house and desired inventory level and product cost for each item are prescribed. The multi-objective problem is reduced to a single objective problem using Global Criteria Method (GCM) and solved with the help of Fuzzy Riemann Integral (FRI) method, Kuhn–Tucker condition and Generalised Reduced Gradient (GRG) technique. In optimum results including production functions and corresponding optimum costs for the different models are obtained and then are presented in tabular forms.     

Numerical Approach of Multi-Objective Optimal Control Problem in Imprecise Environment

In this paper, realistic production-inventory models without shortages for deteriorating items with imprecise holding and production costs for optimal production have been formulated. Here, the rate of production is assumed to be a function of time and considered as a control variable. Also the demand is time dependent and known. The imprecise holding and production costs are assumed to be represented by fuzzy numbers which are transformed to corresponding interval numbers. Following interval mathematics, the objective function is changed to respective multi-objective functions and thus the single-objective problem is reduced to a multi-objective decision making(MODM) problem. The MODM problem is then again transformed to a single objective function with the help of weighted sum method and then solved using global criteria method, calculus method, the Kuhn–Tucker conditions and generalized reduced gradient(GRG) technique. The models have been illustrated by numerical data. The optimum results for different objectives are obtained for different types of production function. Numerical values of demand, production function and stock level are presented in both tabular and graphical forms     

Quantum Phase Diagram of a Frustrated Spin-1/2 Ferro-Antiferromagnetic Normal Ladder

In this work, we consider a frustrated two-leg spin-1/2 ladder composed of Heisenberg ferromagnetic and antiferromagnetic spin-1/2 chains, and nearest spins from different legs interact via Heisenberg type rung exchange interactions that can be either ferromagnetic or antiferromagnetic in nature. The competing exchange interactions in the system lead to five different quantum phases like ferromagnetic, non-collinear ferrimagnetic (NCF), , antiferromagnetic and dimer phases. The  quantum phase diagram is constructed for the Heisenberg spin-1/2 model and the phases are characterized using the correlation functions which are calculated by the density matrix renormalization group method. We also analyze the  stability of phase and calculate the pitch angle in the NCF phase.