An Algorithm for Computing the Singularity of the Generic Germ of a Pencil of Plane Curves

Abstract

We give an algorithm that describes the singularity of all but finitely-many germs in a pencil generated by two arbitrary germs of plane curve.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

Boolean operations on rasterized shapes represented by chain codes using space filling curves

This paper introduces a new algorithm for Boolean operations on rasterized geometric shapes that are represented with chain codes. The algorithm works in three steps. Firstly, the chain code symbols are transformed in the Hilbert space, where the overlaid chain code symbols are recognised. After that, a suitable starting cell is determined. Finally, the walk-about through the sequence of the initial chain code symbols is performed to obtain the sequence of chain code symbols representing the shape of the required Boolean operation. The algorithm is demonstrated on Freeman chain code in four directions. The time and space complexity of the proposed algorithm is linear, which was proven theoretically and confirmed by experiments.     

Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

A new method for the automated selection of the number of components for deconvolving overlapping chromatographic peaks

Mathematical deconvolution methods can separate co-eluting peaks in samples for which (chromatographic) separation fail. However, these methods often heavily rely on manual user-input and interpretation. This is not only time-consuming but also error-prone and automation is needed if such methods are to be applied in a routine manner.     

LiBr分子基态光谱常数和分子常数研究

采用高精度的量子化学从头计算多参考组态相互作用方法和相关一致基, 计算了LiBr分子基态的光谱常数和势能曲线. 为获得更准确的结果, 计算中还考虑了二阶Douglas-Kroll-Hess相对论修正对LiBr分子基态的平衡键长、谐振频率和离解能影响. 将计算得到的势能曲线拟合为Murrell-Sorbie解析势能函数形式, 并进一步计算得到LiBr分子基态的其它光谱常数,ωeχe, αe, Be, D0. 比较发现它们与实验值符合的非常好. 通过求解核运动径向Schrodinger方程, 找到了LiBr分子基态的全部振动态. 还计算了每一个振动态的振动能级、经典转折点和惯性转动常数, 这些结果与已有的实验值一致.     

Model selection based on Lorenz and concentration curves,Gini indices and convex order

In order to determine an appropriate amount of premium, statistical goodness-of-fit criteria must be supplemented with actuarial ones when assessing performance of a given candidate pure premium. In this paper, concentration curves and Lorenz curves are shown to provide actuaries with effective tools to evaluate whether a premium is appropriate or to compare two competing alternatives. The idea is to compare the premium income for sub-portfolios gathering low risks (identified as low by means of the premiums under consideration) to the true one, or equivalently, to the actual losses. Numerical illustrations performed on hypothetical data and real ones demonstrate the usefulness of the proposed approach.     

An anisotropic area-preserving flow for convex plane curves

This paper will deal with an anisotropic area-preserving flow which keeps the convexity of the evolving curve and the limiting curve converges to a homothety of a symmetric smooth strictly convex plane curve.     

Effect of europium doping levels on photoluminescence and thermoluminescence of strontium yttrium oxide phosphor

The present paper deals with the effect of europium (Eu³⁺) doping concentration (0.1–2.5 mol%) on photoluminescence (PL) and thermoluminescence (TL) of strontium yttrium oxide (SrY₂O₄) phosphor. The sample was prepared by the modified solid state reaction method, which is the most suitable method for large-scale production. The prepared phosphor sample was characterized by using X-ray Diffraction (XRD), field emission gun scanning electron microscopy, fourier transform infrared spectroscopy, high resolution transmission electron microscopy, photoluminescence, thermoluminescence and commission internationale de I׳Eclairage techniques. The PL emission was observed in the range of 410–630 nm for the SrY₂O₄ phosphor doped with Eu³⁺. Excitation spectrum was found at 254 and 325 nm, sharp peaks were found around 593, 615 and 625 nm with high intensity. From the XRD data, using Scherrer׳s formula, calculated average crystallite size of Eu³⁺ doped SrY₂O₄ phosphor is around 32 nm. Thermoluminescence study was carried out for the phosphor with UV and gamma irradiation. The TL response of SrY₂O₄:Eu³⁺ phosphor for two different radiations was compared and studied in detail. The present phosphor can act as a single host for white light emission in display devices. The detailed process and possible mechanisms for PL and TL are studied and discussed. For the variable concentration of Eu³⁺ on PL studies the PL intensity increases with increasing the concentration of dopant and the concentration quenching found after 2 mol% of Eu³⁺ the optimized concentration was 2 mol%, which is suitable for the display device application. In TL glow curve the optimized concentration was 1 mol% for the UV irradiated sample and 0.2 mol% of Eu³⁺ for the gamma irradiated sample and beta irradiated sample for 10 Gy dose. The kinetic parameters were calculated by the computerized glow curve deconvolution (CGCD) technique.