Fluorescence from the second excited singlet state of [18] annulenes

The emission spectra of the second excited singlet state of [18] annulene and of monofluoro [18] annulene (in a 3-methylpentane glass at 4 K) are reported. The large energy gap between the first and second excited singlet states inhibits fast internal conversion and favours the appearance of S₂ → S₀ emission. In addition, fluorescence from the S₁ state can be observed in monofluoro [13] annulene by exciting into the S₂ or directly into the S₁ absorption.     

Die Bildungsenthalpien einiger Siliciumtetrahalogenid—Pyridin-Addukte

The enthalpies of formation of the addition compounds F₄Si(py)₂, Cl₄Si(py)₂, Br₄Si(py)₂ and I₄Si(py)₄ have been measured calorimetrically by two different ways (see table 1). It was not possible to confirm enthalpy data published in^{7, 8}. The sequence SiF₄4～SiBr₄>SiI₄(?) is proposed for the acceptor power of the silicon tetrahalides towards pyridine.     

On Gaussian approximation of the strength of Daniels' bundle with brittle Weibull fibers

The paper deals with the classical fiber bundle model with brittle Weibull fibers and equal load sharing. This model is significant for the strength of fibrous materials and composites, and the generally random strength of quasi-brittle structures. The model is also relevant for the analysis of the reliability of various parallel systems (computer components, infrastructure etc.). An improved closed-form Gaussian approximation of the standard deviation of bundle strength is presented and compared with accurate solution calculated by recursive formula proposed by Daniels. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stages of melting of graphene model in two-dimensional space

Spontaneous melting of a perfect crystalline graphene model in 2D space is studied via molecular dynamics simulation. Model containing 10⁴ atoms interacted via long-range bond-order potential (LCBOP) is heated up from 50 to 8,450 K in order to see evolution of various thermodynamic quantities, structural characteristics and occurrence of various structural defects. We find that spontaneous melting of our graphene model in 2D space exhibits a first-order behaviour of the transition from solid 2D graphene sheet into a ring-like structure 2D liquid. Occurrence and clustering of Stone–Wales defects are the first step of melting process followed by breaking of C–C bonds, occurrence/growth of various types of vacancies and multi-membered rings. Unlike that found for melting of a 2D crystal with an isotropic bonding, these defects do not occur homogeneously throughout the system, they have a tendency to aggregate into a region and liquid phase initiates/grows from this region via tearing-like or crack-propagation-like mechanism. Spontaneous melting point of our graphene model occurs at T_m = 7,750 K. The validity of classical nucleation theory and Berezinsky–Kosterlitz–Thouless–Nelson–Halperin–Young (BKTNHY) one for the spontaneous melting of our graphene model in strictly 2D space is discussed.     

Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

This research aims to compare the performance of ARIMA as a linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We used the data collected from Yahoo Finance with daily frequency for the period from 1 January 2000 to 31 December 2019. By using a rolling window approach, we compared ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than the simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we compared their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE), and their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio, and adjusted information ratio). The main contribution of this research is to show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index) over the long term. These results are not sensitive to varying window sizes, the type of distribution, and the type of the GARCH model.     

On a characterization of analytic compactifications for ℂ* × ℂ*

Let M be a minimal compact surface, let Γ ⊂ M be a compact analytic sub-variety. Assume that X:= M \ Γ is Stein. Then we will show that X admits algebraic compactifications M _i (resp. non algebraic compactifications $ \mathbb{M}_i $ \mathbb{M}_i ) which are not birationally equivalent (resp. not bimeromorphically equivalent) iff X is biholomorphic to      

Regularized gap functions and error bounds for split mixed vector quasivariational inequality problems

In this paper, we consider a class of split mixed vector quasivariational inequality problems in real Hilbert spaces and establish new gap functions by using the method of the nonlinear scalarization function. Further, we obtain some error bounds for the underlying split mixed vector quasivariational inequality problems in terms of regularized gap functions. Finally, we give some examples to illustrate our results. The results obtained in this paper are new.     

Novel numerical techniques for the finite moment log stable computational model for European call option

Option pricing models are often used to describe the dynamic characteristics of prices in financial markets. Unlike the classical Black–Scholes (BS) model, the finite moment log stable (FMLS) model can explain large movements of prices during small time steps. In the FMLS, the second-order spatial derivative of the BS model is replaced by a fractional operator of order α which generates an α-stable Lévy process. In this paper, we consider the finite difference method to approximate the FMLS model. We present two numerical schemes for this approximation: the implicit numerical scheme and the Crank–Nicolson scheme. We carry out convergence and stability analyses for the proposed schemes. Since the fractional operator routinely generates dense matrices which often require high computational cost and storage memory, we explore three methods for solving the approximation schemes: the Gaussian elimination method, the bi-conjugate gradient stabilized method (Bi-CGSTAB) and the fast Bi-CGSTAB (FBi-CGSTAB) in order to compare the cost of calculations. Finally, two numerical examples with exact solutions are presented where we also use extrapolation techniques to achieve higher-order convergence. The results suggest that the proposed schemes are unconditionally stable and convergent, and the FMLS model is useful for pricing options.