11B nuclear magnetic resonance study of boron nitride nanotubes prepared by mechano-thermal method

We reported ¹¹B nuclear magnetic resonance studies of boron nitride (BN) nanotubes prepared by mechano-thermal route. The NMR lineshape obtained at 192.493 MHz (14.7 T) was fitted with two Gaussian functions, and the ¹¹B nuclear magnetization relaxations were satisfied with the stretched–exponential function, exp[-(tlT₁)^(D+1)/6] (D: space dimension) at all temperatures. In addition, the temperature dependence of spin–lattice relaxation rates was well described by T_i^-1 = aT (a: constant, T: temperature) and could be understood in terms of direct phonon process. All the 11BNMR results were explained by considering the inhomogeneous distribution of the paramagnetic metal catalysts, such as α-Fe, Fe–N, and Fe₂ B, that were incorporated during the process of high-energy ball milling of boron powder and be synthesized during subsequent thermal annealing. X-ray powder diffraction as well as electron paramagnetic resonance (EPR) on BN nanotubes were also conducted and the results obtained supported these conclusions.

Modelling the cooling of coffee : insights from a preliminary study in Indonesia

This paper discusses an attempt to examine pre-service teachers’ mathematical modelling skills. A modelling project investigating relationships between temperature and time in the process of cooling of coffee was chosen. The analysis was based on group written reports of the cooling of coffee project and observation of classroom discussion. Findings showed that pre-service teachers were able to model the process of cooling of coffee as a decreasing exponential function. Difficulties with interpretation of the constant rate of cooling and reinterpretation of mathematical model were identified.

In-situ studies of X-ray diffraction line profiles from strained copper foils

The development of an in-situ tensometer is described along with preliminary results of x-ray line profiles from copper foils under tensile stress. The tensometer was designed and constructed on the high resolution diffraction instrument, Station 2.3 at the synchrotron radiation source (SRS) Daresbury Laboratory, and is capable of collecting data in either symmetric or asymmetric geometry including transmission and reflection modes. Experiments were carried out using 18 J..Lm thick copper foil up to strain levels of 5 % using both symmetric reflection and symmetric transmission diffraction. All profiles displayed diffraction broadening and asymmetry which increased with strain. In addition, the asymmetry observed in symmetric transmission was associated with extended tails on the low angle side of the profiles, but in symmetric reflection data the opposite asymmetry was observed. In the analysis, the measured profiles were fitted using the software TOPAS, a fundamental parameters approach to profile fitting. The instrumental profile function was characterised and modelled using annealed LaB6 powder. The diffraction broadening was then determined by refining the convolution of a Voigt function, an asymmetric exponential function and a fixed instrument function to reproduce the observed broadened profiles. The integral breadth and asymmetry results display a strong order dependence and increase almost linearly with strain. The results were interpreted by assuming crystallite size broadening in combination with dislocation broadening arising from fcc a/2( 110) {Ill } dislocations.

Relationships between inventory, sales and service in a retail chain store operation

Effective inventory management is critical to retailing success. Surprisingly, there islittle published empirical research examining relationships between retail inventory, sales andcustomer service. Based on a survey of 101 chain store units, this paper develops and tests aseries of hypotheses about retail inventory. Seventy-five percent of the store owners/managersresponded to the mail survey. As expected, significant positive relationships were found betweeninventory, service and sales. Specifically, support was found for the theory that inventory is afunction of the square root of sales. Also, greater product variety leads to higher inventory, andservice level is an exponential function of inventory. Finally, demand uncertainty was found tohave no apparent effect on inventory levels.

Exponential stabilization of neural networks with various activation functions and mixed time-varying delays

This paper presents some results on the global exponential stabilization for neural networks with various activation functions and time-varying continuously distributed delays. Based on augmented time-varying Lyapunov-Krasovskii functionals, new delay-dependent conditions for the global exponential stabilization are obtained in terms of linear matrix inequalities. A numerical example is given to illustrate the feasibility of our results.

Exponential stabilization of non-autonomous delayed neural networks via Riccati equations

This paper concerns with the problem of exponential stabilization for a class of non-autonomous neural networks with mixed discrete and distributed time-varying delays. Two cases of discrete time-varying delay, namely (i) slowly time-varying; and (ii) fast time-varying, are considered. By constructing an appropriate Lyapunov-Krasovskii functional in case (i) and utilizing the Razumikhin technique in case (ii), we establish some new delay-dependent conditions for designing a memoryless state feedback controller which stabilizes the system with an exponential convergence of the resulting closed-loop system. The proposed conditions are derived through solutions of some types of Riccati differential equations. Applications to control a class of autonomous neural networks with mixed time-varying delays are also discussed in this paper. Some numerical examples are provided to illustrate the effectiveness of the obtained results.