A sharp first order analysis of Feynman–Kac particle models,Part II: Particle Gibbs samplers

This article provides a new theory for the analysis of the particle Gibbs (PG) sampler (Andrieu et al., 2010). Following the work of Del Moral and Jasra (2017) we provide some analysis of the particle Gibbs sampler, giving first order expansions of the kernel and minorization estimates. In addition, first order propagation of chaos estimates are derived for empirical measures of the dual particle model with a frozen path, also known as the conditional sequential Monte Carlo (SMC) update of the PG sampler. Backward and forward PG samplers are discussed, including a first comparison of the contraction estimates obtained by first order estimates. We illustrate our results with an example of fixed parameter estimation arising in hidden Markov models.     

Dirichlet expression for <Emphasis Type="Italic">L</Emphasis>(1, <Emphasis Type="Italic">χ</Emphasis>) with general Dirichlet character

In the famous work of Dirichlet on class number formula, L(s, χ) at s = 1 has been expressed as a finite sum, where L(s, χ) is the Dirichlet L-series of a real Dirichlet character. We show that this expression with obvious modification is valid for the general primitive Dirichlet character χ.     

Electron spin polarisation in the photoreduction of xanthone in alcohol: effect of concentration and temperature

Time-resolved EPR studies of the hydrogen abstraction reaction of photoexcited xanthone in 2-propanol were carried out as a function of the concentration of xanthone and the sample temperature. The temperature was varied from 22°C to about ?30°C, and the concentration from about 0.2 to 4.0?mM. At low temperature or concentration, the observed spectra of the xanthone ketyl radical and the propan-2-olyl radical could be simulated as a superposition of a hyperfine-independent component due to the emissive triplet mechanism and a hyperfine-dependent component due to the S–T₀ radical pair mechanism. However, with an increase in the concentration of xanthone, the relative contribution of TM decreases, and, concomitantly, the net absorptive component of only the xanthone ketyl radical increases. As the spin polarisation mechanisms do not predict any concentration dependence, this unusual behaviour is explained by invoking the enhancement of the spin–lattice relaxation rates due to Heisenberg spin exchange occurring at high local concentrations of the radicals. The net absorptive signal is attributed to thermally equilibrated radicals. The observed temperature dependence of the spin polarisation behaviour is similarly explained. The origin of the net absorptive signal in the TREPR spectra of the acetone?2-propanol system is also attributed to thermally equilibrated radicals. The self-quenching mechanism of xanthone is proposed to be an electron-transfer reaction from an excited xanthone molecule to another xanthone in the ground state.     

Effect of citric acid and starch as emulsifier on phase formation and crystallite size of lanthanum oxide nanoparticles

Lanthanum oxide nanoparticles were synthesized via thermal decomposition method of the lanthanum nitrate in the presence of citric acid or starch as emulsifier. The effects of emulsifier and calcination temperature were investigated on the phase transformation and particle size distribution of the products. La₂O₃ nanoparticles were synthesized by drying lanthanum precursor and emulsifier solution, followed by calcination process at 600 and 900°C, respectively. Products were characterized by Fourier Transform Infrared (FT‐IR) spectroscopy, X‐ray diffraction (XRD), thermal analysis (TG/DTA) and nitrogen adsorption method (porous characteristics). The morphology of the samples analyzed using scanning electron microscopy (SEM). Average crystallite size of the products was calculated by XRD data and average particle size was measured from the TEM micrographs. Lanthanum dioxycarbonate in different forms of the tetragonal and monoclinic is crystallized in the presence of citric acid and starch during the calcination at 600°C, respectively. The hexagonal structure, however, is detected as the only crystalline phase formed by calcination at 900°C.     

Effects of silicon negative ion implantation in semi-insulating gallium arsenide

ABSTRACT

In the present work, effects of silicon negative ion implantation into semi-insulating gallium arsenide (GaAs) samples with fluences varying between 1?×?10¹⁵ and 4?×?10¹⁷?ions?cm^?2 at 100?keV have been described. Atomic force microscopic images obtained from samples implanted with fluence up to 1?×?10¹⁷?ion?cm^?2 showed the formation of GaAs clusters on the surface of the sample. The shape, size and density of these clusters were found to depend on ion fluence. Whereas sample implanted at higher fluence of 4?×?10¹⁷?ions?cm^?2 showed bump of arbitrary shapes due to cumulative effect of multiple silicon ion impact with GaAs on the same place. GXRD study revealed formation of silicon crystallites in the gallium arsenide sample after implantation. The silicon crystallite size estimated from the full width at half maxima of silicon (111) XRD peak using Debye-Scherrer formula was found to vary between 1.72 and 1.87?nm with respect to ion fluence. Hall measurement revealed the formation of n-type layer in gallium arsenide samples. The current–voltage measurement of the sample implanted with different fluences exhibited the diode like behavior.     

Manipulating sensitivities of planar oxadiazole-based high performing energetic materials

Nitrogen-rich energetic materials based on five-membered azoles, such as tetrazoles, triazoles, oxadiazoles, pyrazoles, and imidazoles, have garnered significant attention in recent years due to their environmental compatibility while maintaining high performance. These materials, including explosives, propellants, and pyrotechnics, are designed to release energy rapidly and efficiently while minimizing the release of toxic or hazardous byproducts and have attracted potential applications in the defense and space industries. The presence of extensive N C, N N, and NN high energy bonds in azoles provides high enthalpies of formation and facilitates intermolecular interactions through π-stacking which may help with reducing sensitivity to external stimuli. Now, we report on the synthesis and energetic properties of N-(5-(1H-tetrazol-5-yl)-1,3,4-oxadiazol-2-yl)nitramide ( 5 ) and its energetic salts. These new high nitrogen–oxygen-containing materials have attractive feature applications of insensitivity and increased performance.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Investigations on Timing Jitter by Chirp Selection of External Modulator in Return-to-Zero Optical Soliton Pulse Transmission at 10 Gb/s

Abstract

We investigate the chirp selection of externally modulated return-to-zero soliton pulse at 10 Gb/s for fiber optical communication system for the reduction in timing jitter. The chirp range (?5 to +5), as well as the effect of the post compensation, have been examined up to ten regenerated fiber spans in the link. Here, it is shown that the chirp value of the external modulator should be set to either 0 or ?1 to reduce timing jitter. Moreover, for more number of spans, it will be better to adopt other chirp values.     

Improved analysis of dispersion compensation using differential time delay for high-speed long-span optical link

Abstract

A dispersion-compensation technique using differential time delay has been analyzed for a high bit rate dispersive limited system using higher order dispersion terms. The technique is based on splitting the power spectrum into upper and lower parts, corresponding to the two modulation sidebands, and delaying one of these with respect to the other. RMS, phase deviation, dimension free chirp parameter, and figure of merit have been evaluated due to higher order dispersion terms for ideal and realistic optical communication systems. It has been shown that the transmission distance could be enhanced to fourfold, sixfold, and eightfold when the compensation has been performed using second-, third-, and fourth-order dispersion (20D, 30D, and 40D) terms.     

Sequential Monte Carlo Methods for Option Pricing

In this article, we provide a review and development of sequential Monte Carlo (SMC) methods for option pricing. SMC are a class of Monte Carlo-based algorithms, that are designed to approximate expectations w.r.t a sequence of related probability measures. These approaches have been used successfully for a wide class of applications in engineering, statistics, physics, and operations research. SMC methods are highly suited to many option pricing problems and sensitivity/Greek calculations due to the nature of the sequential simulation. However, it is seldom the case that such ideas are explicitly used in the option pricing literature. This article provides an up-to-date review of SMC methods, which are appropriate for option pricing. In addition, it is illustrated how a number of existing approaches for option pricing can be enhanced via SMC. Specifically, when pricing the arithmetic Asian option w.r.t a complex stochastic volatility model, it is shown that SMC methods provide additional strategies to improve estimation.