Methods for solving fuzzy assignment problems and fuzzy travelling salesman problems with different membership functions

Mukherjee and Basu proposed a new method for solving fuzzy assignment problems. In this paper, some fuzzy assignment problems and fuzzy travelling salesman problems are chosen which cannot be solved by using the fore-mentioned method. Two new methods are proposed for solving such type of fuzzy assignment problems and fuzzy travelling salesman problems. The fuzzy assignment problems and fuzzy travelling salesman problems which can be solved by using the existing method, can also be solved by using the proposed methods. But, there exist certain fuzzy assignment problems and fuzzy travelling salesman problems which can be solved only by using the proposed methods. To illustrate the proposed methods, a fuzzy assignment problem and a fuzzy travelling salesman problem is solved. The proposed methods are easy to understand and apply to find optimal solution of fuzzy assignment problems and fuzzy travelling salesman problems occurring in real life situations.     

Model reduction of nonlinear systems with external periodic excitations via construction of invariant manifolds

A methodology for determining reduced order models of periodically excited nonlinear systems with constant as well as periodic coefficients is presented. The approach is based on the construction of an invariant manifold such that the projected dynamics is governed by a fewer number of ordinary differential equations. Due to the existence of external and parametric periodic excitations, however, the geometry of the manifold varies with time. As a result, the manifold is constructed in terms of temporal and dominant state variables. The governing partial differential equation (PDE) for the manifold is nonlinear and contains time-varying coefficients. An approximate technique to find solution of this PDE using a multivariable Taylor-Fourier series is suggested. It is shown that, in certain cases, it is possible to obtain various reducibility conditions in a closed form. The case of time-periodic systems is handled through the use of Lyapunov-Floquet (L-F) transformation. Application of the L-F transformation produces a dynamically equivalent system in which the linear part of the system is time-invariant; however, the nonlinear terms get multiplied by a truncated Fourier series containing multiple parametric excitation frequencies. This warrants some structural changes in the proposed manifold, but the solution procedure remains the same. Two examples; namely, a 2-dof mass-spring-damper system and an inverted pendulum with periodic loads, are used to illustrate applications of the technique for systems with constant and periodic coefficients, respectively. Results show that the dynamics of these 2-dof systems can be accurately approximated by equivalent 1-dof systems using the proposed methodology.     

Generic routing and wavelength assignment algorithm for a wavelength-routed WDM network

In this paper, we have developed a simple mathematical model which is used for the calculation of blocking probability of network. A generic routing and wavelength assignment algorithm has also been proposed for the optimization and minimization of blocking probability. The implementation of the proposed model has less complexity and the computation used in this model is quite efficient. This paper suggests an optimum path and assigns wavelength to that path, as a solution to routing and wavelength assignment problem to have least blocking probability. This model can be implemented on different network topologies. Further, the model is also used to evaluate the blocking performance of a 6-node simple network topology and hence used to improve its performance on the basis of blocking probability.     

An adaptive reservation scheme for optical network

In this paper, the various Optical Burst Switching (OBS) reservation schemes have been examined in order to reduce data loss caused by either channel scheduling or resources. A novel multi-service OBS edge node with synchronized bandwidth reservation mechanism (SRM) has been proposed, which enables high-speed network transport nodes to dynamically reserve bandwidth needed for active data burst flows. The performance of the proposed mechanism is evaluated by means of NS-2 simulation. The results show that the packet delay is kept within the constraint for each traffic flow and the performance metrics such as burst loss rate, throughput and fairness are remarkably improved.     

Formation of Gallium-induced nanostructures on single crystal HOPG surface

The room temperature growth of gallium atoms on the highly oriented pyrolytic graphite (HOPG) surface has been performed. The gallium atoms were deposited by thermal evaporation method in an ultra high vacuum system at a base pressure 5 × 10⁻¹⁰ torr. The X-ray photo electron spectroscopy (XPS) studies had been performed to confirm the presence of gallium atoms on HOPG surface. Scanning tunneling spectroscopy (STM) technique was employed to study the surface morphology of the clean HOPG surface and gallium covered HOPG surfaces which recognize the formation of gallium induced nanostructures. The deconvoluted XPS core level spectra of C (1s) and Ga (3d) demonstrate the possible interaction between substrate and the adsorbate atoms. The STM analysis revealed that the gallium deposition on HOPG led to significant change in the surface morphology. It was observed that the Ga atoms adsorbed as layer structure on HOPG surface for low coverage while quasi one-dimensional chain like nanostructure (1 ± 0.2 nm) has been formed for higher Ga coverage. The nanostructured surfaces induced by Ga deposition are found to be stable and could be used as a template for the growth of metallic nanostructures.     

Diffusion of water in molecular magnet Cu(0.75)Mn(0.75)[Fe(CN)6]·7H2O

Here we report the dynamical behaviour of water in Prussian blue analogue (PBA) Cu(0.75)Mn(0.75)[Fe(CN)(6)]·7H(2)O molecular magnet in the temperature range 260-360 K as studied using the quasielastic neutron scattering technique. While significant quasielastic broadening is observed in the hydrated sample, no broadening was observed in the dehydrated one. Data analysis showed that the observed quasielastic broadening in Cu(0.75)Mn(0.75)[Fe(CN)(6)]·7H(2)O corresponds to the dynamics of the non-coordinated water molecules at the 32f site and the coordinated water molecules at the 24e site, existing in the cavities created by the absence of Fe(CN)(6) units. The non-coordinated water molecules at 8c interstitial sites do not contribute to the broadening, suggesting that they are immobile at least within the time window of the spectrometer used. Behaviour of the elastic incoherent structure factor is consistent with the model where the water molecules undergo translational diffusion localized within the cavity of 5.1 ?. While all the non-coordinated water molecules at the 32f site are dynamic over the entire range of temperatures, the coordinated ones at the 24e site become progressively dynamic with temperature. The water molecules were found to undergo hindered (~1.16 × 10(-5) cm(2) s(-1) at 300 K) diffusion compared to bulk water and the diffusivity followed Arrhenius behaviour within the measured temperature range with an activation energy of 1.26 kcal mol(-1).     

Dielectric shielded nanoscale patch laser resonators

Dielectric shielded nanoscale patch laser resonators are introduced. Low-index dielectric shield layers surrounding a high-index core are shown to significantly reduce both metal and radiation losses. Structures suitable for both optical and electrical pumping and smaller than the vacuum wavelength in all three dimensions are shown to have a low enough threshold gain to lase at room temperature. Shifting the gain medium core provides control over the radiation pattern of the resonator and enables coupling of the laser light into a waveguide, opening opportunities for chipscale integration.     

Optical and hydrophobic properties of co-sputtered chromium and titanium oxynitride films

The chromium and titanium oxynitride films on glass substrate were deposited by using reactive RF magnetron sputtering in the present work. The structural and optical properties of the chromium and titanium oxynitride films as a function of power variations are investigated. The chromium oxynitride films are crystalline even at low power of Cr target (≥60 W) but the titanium oxynitride films are amorphous at low target power of Ti target (≤90 W) as observed from glancing incidence X-ray diffraction (GIXRD) patterns. The residual stress and strain of the chromium oxynitride films are calculated by sin² ψ method, as the average crystallite size decreases with the increase in sputtering power of the Cr target, higher stress and strain values are observed. The chromium oxynitride films changes from hydrophilic to hydrophobic with the increase of contact angle value from 86.4° to 94.1°, but the deposited titanium oxynitride films are hydrophilic as observed from contact angle measurements. The changes in surface energy were calculated using contact angle measurements to substantiate the hydrophobic properties of the films. UV-vis and NIR spectrophotometer were used to obtain the transmission and absorption spectra, and the later was used for determining band gap values of the films, respectively. The refractive index of chromium and titanium oxynitride films increases with film packing density due to formation of crystalline chromium and titanium oxynitride films with the gradual rise in deposition rate as a result of increase in target powers.     

On some new m-spotty Lee weight enumerators

One of the objectives of coding theory is to ensure reliability of the computer memory systems that use high-density RAM chips with wide I/O data (e.g. 16, 32, 64 bits). Since these chips are highly vulnerable to m-spotty byte errors, this goal can be achieved using m-spotty byte error-control codes. This paper introduces the m-spotty Lee weight enumerator, the split m-spotty Lee weight enumerator and the joint m-spotty Lee weight enumerator for byte error-control codes over the ring of integers modulo ? (? ≥  2 is an integer) and over arbitrary finite fields, and also discusses some of their applications. In addition, MacWilliams type identities are also derived for these enumerators.