Support vector regression for warranty claim forecasting

Forecasting the number of warranty claims is vitally important for manufacturers/warranty providers in preparing fiscal plans. In existing literature, a number of techniques such as log-linear Poisson models, Kalman filter, time series models, and artificial neural network models have been developed. Nevertheless, one might find two weaknesses existing in these approaches: (1) they do not consider the fact that warranty claims reported in the recent months might be more important in forecasting future warranty claims than those reported in the earlier months, and (2) they are developed based on repair rates (i.e., the total number of claims divided by the total number of products in service), which can cause information loss through such an arithmetic-mean operation.To overcome the above two weaknesses, this paper introduces two different approaches to forecasting warranty claims: the first is a weighted support vector regression (SVR) model and the second is a weighted SVR-based time series model. These two approaches can be applied to two scenarios: when only claim rate data are available and when original claim data are available. Two case studies are conducted to validate the two modelling approaches. On the basis of model evaluation over six months ahead forecasting, the results show that the proposed models exhibit superior performance compared to that of multilayer perceptrons, radial basis function networks and ordinary support vector regression models.     

Temperature-Controlled Stereodivergent Synthesis of 2,2′-Biflavanones Promoted by Samarium Diiodide

In this work, the first example of a radical stereodivergent reaction directed towards the stereoselective synthesis of both (R*,R*)- and (R*,S*)-2,2′-biflavanones promoted by samarium diiodide is reported. Control experiments showed that the selectivity of this reaction was exclusively controlled by the temperature. It was possible to generate a variety of 2,2′-biflavanones bearing different substitution patterns at the aromatic ring in good-to-quantitative yields, being both stereoisomers of the desired compounds obtained with total or high control of selectivity. A mechanism that explains both the generation of the corresponding 2,2′-biflavanones and the selectivity is also discussed. The structure and stereochemistry determination of each isomer was unequivocally elucidated by single-crystal X-ray diffraction experiments.     

Some results on linear nabla Riemann-Liouville fractional difference equations

In this paper, we establish some criteria for boundedness, stability properties, and separation of solutions of autonomous nonlinear nabla Riemann-Liouville scalar fractional difference equations. To derive these results, we prove the variation of constants formula for nabla Riemann-Liouville fractional difference equations.     

Concise Synthesis of (+)-[13C4]-Anatoxin-a by Dynamic Kinetic Resolution of a Cyclic Iminium Ion

An asymmetric total synthesis of [¹³C₄]-anatoxin-a ([¹³C₄]- 1 ) has been developed from commercially available ethyl [¹³C₄]-acetoacetate ([¹³C₄]- 15 ). The unique requirements associated with isotope incorporation inspired a new, robust, and highly scalable route, providing access to 0.110 g of this internal standard for use in the detection and precise quantification of anatoxin-a in freshwater. A highlight of the synthesis is a method that leverages a cyclic iminium ion racemization to achieve dynamic kinetic resolution in an enantioselective Morita–Baylis–Hillman (MBH) cyclization.     

The fastest,simplified method of Lyapunov exponents spectrum estimation for continuous-time dynamical systems

Nonlinear Dynamics - Classical method of Lyapunov exponents spectrum estimation for a n-th-order continuous-time, smooth dynamical system involves Gram–Schmidt orthonormalization and...     

Fission fragment mass yields of Th to Rf even-even nuclei

Fission properties of the actinide nuclei are deduced from theoretical analysis. We investigate potential energy surfaces and fission barriers and predict the fission fragment mass yields of actinide isotopes. The results are compared with experimental data where available. The calculations were performed in the macroscopic-microscopic approximation with the Lublin-Strasbourg Drop (LSD) for the macroscopic part, and the microscopic energy corrections were evaluated in the Yukawa-folded potential. The Fourier nuclear shape parametrization is used to describe the nuclear shape, including the non-axial degree of freedom. The fission fragment mass yields of the nuclei considered are evaluated within a 3D collective model using the Born-Oppenheimer approximation.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.     

On measures integrating all functions of a given vector lattice

LetE be a vector lattice of real-valued functions defined on a setX, and (E):={{f1}:fE}. Among others, it is shown that, under some additional assumptions onE, every measure that integrates all functionsfE is (E)--smooth iffX is (E)-complete. An application of this general result to various topological situations yields some new measure-theoretic characterizations of realcompact, Borel-complete andN-compact spaces, respectively.     

Operator Khintchine inequality in non-commutative probability

   Abstract. For the operator , where belongs to the Schatten class and where are non-commutative random variables with mixed moments satisfying a specific condition, we prove the following Khintchine inequality We find the optimal constants in the case when are the q-Gaussian and circular random variables. Moreover, we show that the moments of any probability symmetric measure appear as the optimal constants for some random variables. Received November 6, 1998 / in final form June 8, 2000 / Published online December 8, 2000