Some comments on fuzzy variables

Nahmias introduced the concept of a fuzzy variable as a possible axiomatic framework from which a rigorous theory of fuzziness may be constructed. In this paper we attempt to shed more light on fuzzy variables in analogy with random variables. In particular, we study the problem: if X₁, X₂,…,X_n are mutually unrelated fuzzy variables with common membership function μ and α₁, α₂,…,α_n are real numbers satisfying α_i ? o for every i and Σ_i=1ⁿα_i=1, when does does Z = Σ_{i = 1}ⁿα_iX_i have the same membership function μ?     

The vibrational spectra of (CH3)3SiX (S=H, F, Br) molecules, revisited Transferable scale factor sets for methylsilane derivatives

The joint experimental and theoretical study of the vibrational spectra of the molecular series (CH3)3SiX (with X=H, F and Br) is carried out. Data from newly recorded IR and Raman spectra for the bromo derivative, experimental data obtained previously for the remaining species, DFT theoretical calculations and the use of the SQMFF procedure have allowed us to propose common patterns and to unify criteria in their assignment. In addition, two sets of averaged scale factors for the B3LYP force field obtained with two different basis sets (6-31G* and DZP+diff) have been proposed for the common bulky moiety of that molecular series. These parameters were used successfully in order to reproduce the frequency of the bands assigned to the (CH3)3Si- group in the vibrational spectra of the corresponding silanolic and methoxy derivatives, i.e., trimethylsilanol and methoxytrimethylsilane, proving their transferability.     

Analysis of hormonal steroids in fish plasma and bile by coupling solid-phase extraction to GC/MS

An analytical procedure for the simultaneous determination of twelve endogenous steroids (testosterone, androstenedione, 17β-estradiol, estrone, pregnenolone, progesterone, dihydroandrostenedione, dihydrotestosterone, 11α-ketotestosterone, 17α-hydroxyprogesterone, 17α-hydroxypregnenolone, 17α,20β-dihydroxy-4-pregnen-3-one) in plasma and bile samples by solid-phase extraction (SPE) and gas chromatography/mass spectrometry (GC–MS) has been developed. After enzymatic hydrolysis for bile samples only, samples were concentrated and purified using two successive SPE (C₁₈ and NH₂) cartridges. Analytes were derivatized with a mixture of N-methyl-N-(trimethylsilyl)trifluoroacetamide (MSTFA) / mercaptoethanol / ammonium iodide (NH₄I) and determined by GC–MS in selective ion monitoring mode. For most of the steroids monitored, recoveries were in the range 90–120% in plasma and in the range 60–70% in bile, and the reproducibility was below 10% for the complete procedure. Limits of detection obtained ranged from 0.1 to 0.4 ng/g in fish plasma and from 1.6 to 14 ng/g in fish bile. The developed method was successfully applied to the determination of plasma steroids in flounders (Platichthys flesus) collected from two French estuaries.     

Fulop-Tsutsui interactions on quantum graphs

We examine scale invariant Fulop-Tsutsui couplings in a quantum vertex of a general degree n. We demonstrate that essentially same scattering amplitudes as for the free coupling can be achieved for two (n−1)-parameter Fulop-Tsutsui subfamilies if n is odd, and for three (n−1)-parameter Fulop-Tsutsui subfamilies if n is even. We also work up an approximation scheme for a general Fulop-Tsutsui vertex, using only n δ function potentials.     

Analysis of market efficiency for the Shanghai stock market over time

In this paper, we analyze market efficiency for the Shanghai stock market over time using a model-free method known as multifractal detrended fluctuation analysis. Through analyzing the change of scale behavior, we find that the price-limited reform improved the efficiency in the long term, but the influence in the short term was very minor. Employing the method of moving window, using three different measures we find that the Shanghai stock market became more and more efficient after the reform. We also implement the same procedure on volatility series and find the evidence of inefficiency.     

A note on scale functions and the time value of ruin for Lévy insurance risk processes

We examine discounted penalties at ruin for surplus dynamics driven by a general spectrally negative Lévy process; the natural class of stochastic processes which contains many examples of risk processes which have already been considered in the existing literature. Following from the important contributions of [Zhou, X., 2005. On a classical risk model with a constant dividend barrier. North Am. Act. J. 95-108] we provide an explicit characterization of a generalized version of the Gerber-Shiu function in terms of scale functions, streamlining and extending results available in the literature.     

Effects of fish farm loading on sea grass Posidonia oceanica at Vrgada Island (Central Adriatic): a nitrogen stable isotope study

Analyses of nitrogen stable isotopes in the marine sea grass Posidonia oceanica were used to investigate the influence of fish farming on the coastal ecosystem of Vrgada Island in the Murter Sea, Central Adriatic. The results show a statistically significant ¹⁵N enrichment (up to 4.7‰ at p?<?0.005) in P. oceanica leaf and shoot tissues from fish cage sites with respect to the unaffected offshore reference site of Lumbarda Reef Flat (Kornati Islands). Heavy nitrogen enrichment was also detected in other benthic organisms analysed during this study and is attributed to the absorption and assimilation of ¹⁵N-enriched fish farm derived nitrogen waste.     

Characterization of fish schooling behavior with different numbers of Medaka (Oryzias latipes) and goldfish (Carassius auratus) using a Hidden Markov Model

Fish that swim in schools benefit from increased vigilance, and improved predator recognition and assessment. Fish school size varies according to species and environmental conditions. In this study, we present a Hidden Markov Model (HMM) that we use to characterize fish schooling behavior in different sized schools, and explore how school size affects schooling behavior. We recorded the schooling behavior of Medaka (Oryzias latipes) and goldfish (Carassius auratus  ) using different numbers of individual fish (10–40), in a circular aquarium. Eight to ten 3 s video clips were extracted from the recordings for each group size. Schooling behavior was characterized by three variables: linear speed, angular speed, and Pearson coefficient. The values of the variables were categorized into two events each for linear and angular speed (high and low), and three events for the Pearson coefficient (high, medium, and low). Schooling behavior was then described as a sequence of 12 events (2×2×3$2\times 2\times 3$), which was input to an HMM as data for training the model. Comparisons of model output with observations of actual schooling behavior demonstrated that the HMM was successful in characterizing fish schooling behavior. We briefly discuss possible applications of the HMM for recognition of fish species in a school, and for developing bio-monitoring systems to determine water quality.     

On the Consistency of Prony's Method and Related Algorithms

Abstract

Modifications of Prony's classical technique for estimating rate constants in exponential fitting problems have many contemporary applications. In this article the consistency of Prony's method and of related algorithms based on maximum likelihood is discussed as the number of observations n → ∞ by considering the simplest possible models for fitting sums of exponentials to observed data. Two sampling regimes are relevant, corresponding to transient problems and problems of frequency estimation, each of which is associated with rather different kinds of behavior. The general pattern is that the stronger results are obtained for the frequency estimation problem. However, the algorithms considered are all scaling dependent and consistency is not automatic. A new feature that emerges is the importance of an appropriate choice of scale in order to ensure consistency of the estimates in certain cases. The tentative conclusion is that algorithms referred to as Objective function Reweighting Algorithms (ORA's) are superior to their exact maximum likelihood counterparts, referred to as Gradient condition Reweighting Algorithms (GRA's), especially in the frequency estimation problem. This conclusion does not extend to fitting other families of functions such as rational functions.     

A numerical study on extinction behaviour of laminar micro-diffusion flames

We conducted a numerical study on the fluid dynamic, thermal and chemical structures of laminar methane–air micro flames established under quiescent atmospheric conditions. The micro flame is defined as a flame on the order of one millimetre or less established at the exit of a vertically-aligned straight tube. The numerical model consists of convective–diffusive heat and mass transport with a one-step, irreversible, exothermic reaction with selected kinetics constants validated for near-extinction analyses. Calculations conducted under the burner rim temperature 300 K and the adiabatic burner wall showed that there is the minimum burner diameter for the micro flame to exist. The Damköhler number (the ratio of the diffusive transport time to the chemical time) was used to explain why a flame with a height of less than a few hundred microns is not able to exist under the adiabatic burner wall condition. We also conducted scaling analysis to explain the difference in extinction characteristics caused by different burner wall conditions. This study also discussed the difference in governing mechanisms between micro flames and microgravity flames, both of which exhibit similar spherical flame shape.