Abstract: Fiber Bragg Grating (FBG) structure is an periodically modulated optical fiber. It acts as a selective filter of wavelength whose reflected peak is called Bragg wavelength and it depends on the period of the fiber and the refractive index. The simulation of FBG is based on solving the Coupled Mode Theory equation by using the Transfer Matrix Method which is carried out using MATLAB. It is found that spectral reflectivity is shifted when the change of temperature and strain is uniform. Under non-uniform temperature or strain perturbation, the spectrum is both shifted and destroyed. In case of transverse loading, reflectivity spectrum is split into two peaks, the first is specific to X axis, and the second belongs to Y axis. FBGs are used in civil engineering to detect perturbations applied to buildings.
Abstract: In modern financial mathematics, valuing derivatives such as options is often a tedious task. This is simply because their fair and correct prices in the future are often probabilistic. This paper examines three different Stochastic Differential Equation (SDE) models in finance; the Constant Elasticity of Variance (CEV) model, the Balck-Karasinski model, and the Heston model. The various Martingales option price valuation formulas for these three models were obtained using the replicating portfolio method. Also, the numerical solution of the derived Martingales options price valuation equations for the SDEs models was carried out using the Monte Carlo method which was implemented using MATLAB. Furthermore, results from the numerical examples using published data from the Nigeria Stock Exchange (NSE), all share index data show the effect of increase in the underlying asset value (stock price) on the value of the European Put Option for these models. From the results obtained, we see that an increase in the stock price yields a decrease in the value of the European put option price. Hence, this guides the option holder in making a quality decision by not exercising his right on the option.
Abstract: The interaction between the charge degrees of freedom
for itinerant antiferromagnets is investigated in terms of generalized
charge stiffness constant corresponding to nearest neighbour t-J
model and t1-t2-t3-J model. The low dimensional hole doped
antiferromagnets are the well known systems that can be described
by the t-J-like models. Accordingly, we have used these models
to investigate the fermionic pairing possibilities and the coupling
between the itinerant charge degrees of freedom. A detailed
comparison between spin and charge couplings highlights that
the charge and spin couplings show very similar behaviour in
the over-doped region, whereas, they show completely different
trends in the lower doping regimes. Moreover, a qualitative
equivalence between generalized charge stiffness and effective
Coulomb interaction is also established based on the comparisons
with other theoretical and experimental results. Thus it is obvious
that the enhanced possibility of fermionic pairing is inherent
in the reduction of Coulomb repulsion with increase in doping
concentration. However, the increased possibility can not give rise to
pairing without the presence of any other pair producing mechanism
outside the t-J model. Therefore, one can conclude that the t-J-like
models themselves solely are not capable of producing conventional
momentum-based superconducting pairing on their own.
Abstract: The thermal conductivity of thermal insulation materials are measured by Heat Flow Meter (HFM) apparatus. The components of uncertainty are complex and difficult on routine measurement by modelling approach. In this study, uncertainty of thermal conductivity measurement was estimated by single laboratory validation approach. The within-laboratory reproducibility was 1.1%. The standard uncertainty of method and laboratory bias by using SRM1453 expanded polystyrene board was dominant at 1.4%. However, it was assessed that there was no significant bias. For sample measurement, the sources of uncertainty were repeatability, density of sample and thermal conductivity resolution of HFM. From this approach to sample measurements, the combined uncertainty was calculated. In summary, the thermal conductivity of sample, polystyrene foam, was reported as 0.03367 W/m·K ± 3.5% (k = 2) at mean temperature 23.5 °C. The single laboratory validation approach is simple key of routine testing laboratory for estimation uncertainty of thermal conductivity measurement by using HFM, according to ISO/IEC 17025-2017 requirements. These are meaningful for laboratory competent improvement, quality control on products, and conformity assessment.