Naturally ordered regular semigroups with an inverse monoid transversal

The notion of an inverse transversal of a regular semigroup is well-known. Here we investigate naturally ordered regular semigroups that have an inverse transversal. Such semigroups are necessarily locally inverse and the inverse transversal is a quasi-ideal. After considering various general properties that relate the imposed order to the natural order, we highlight the situation in which the inverse transversal is a monoid. The regularity of Green’s relations is also characterised. Finally, we determine the structure of a naturally ordered regular semigroup with an inverse monoid transversal.     

The Ruin Probability in the Presence of Extended Regular Variation and Optimal Investment

Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.     

Growth rates of total variations of snapshots of 1D linear wave equations with nonlinear right-end boundary conditions

This paper is concerned with the one-dimensional wave equation on a unit interval, where the left-end boundary condition (BC) is linear, while the right-end BC is general nonlinearity. We give the dynamical behavior of the Riemann invariants (u,v) of the wave equation in terms of the total variations, and show that chaotic vibration occurs when η enters a certain parameter range.     

Population models in almost periodic environments

We establish the basic theory of almost periodic sequences on ?₊. Dichotomy techniques are then utilized to find sufficient conditions for the existence of a globally attracting almost periodic solution of a semilinear system of difference equations. These existence results are, subsequently, applied to discretely reproducing populations with and without overlapping generations. Furthermore, we access evidence for attenuance and resonance in almost periodically forced population models.     

Quantitative Determination and Variation Trends of Six Alkaloids in Crude and Processed Corydalis Yanhusuo

A convenient, sensitive, and accurate analytical method using reversed-phase high-performance liquid chromatography coupled with ultraviolet-visible detection was investigated for the determination of 6 alkaloids (tetrahydrocoptisine, protopine, tetrahydropalmatine, coptisine, corydaline, and palmatine) in crude and processed samples of corydalis yanhusuo. The results revealed that the content of the alkaloids in crude corydalis yanhusuo samples varied from those of the processed samples. The concentrations of tetrahydrocoptisine, protopine, tetrahydropalmatine, coptisine, and corydaline were reduced after processing; however, the concentration of palmatine increased after processing. This method was established using a C₁₈ column (250 mm × 4.6 mm, 5 µm). The mobile phase, a mixture (19:81) of acetonitrile and a 0.6% solution of acetic acid (pH 3.5, adjusted using triethylamine), was used to elute the target compounds in the isocratic elution mode. The solvent flow rate was 1.0 mL/min, the column temperature was 35°C, and the detection wavelength was 280 nm. All of the calibration curves exhibited good linearity with R >0.9999. The inter- and intra-day precisions for all of the investigated components ranged from 0.10–2.64% RSD, and the recoveries were in the range of 97.3–102.5%. The validated method provides a new solution for analyzing the contents of crude and processed samples of corydalis yanhusuo.     

Stuffer‐free multiplex ligation‐dependent probe amplification based on conformation‐sensitive capillary electrophoresis: A novel technology for robust multiplex determination of copy number variation

Developing diagnostic tools based on the application of known disease/phenotype‐associated copy number variations (CNVs) requires the capacity to measure CNVs in a multiplex format with sufficient reliability and methodological simplicity. In this study, we developed a reliable and user‐friendly multiplex CNV detection method, termed stuffer‐free MLPA‐CE‐SSCP, that combines a variation of multiplex ligation‐dependent probe amplification (MLPA) with CE‐SSCP. In this variation, MLPA probes were designed without the conventionally required stuffer sequences. To separate the similar‐sized stuffer‐free MLPA products, we adopted CE‐SSCP rather than length‐dependent conventional CE analysis. An examination of the genomic DNA from five cell lines known to vary in X‐chromosome copy number (1–5) revealed that copy number determinations using stuffer‐free MLPA‐CE‐SSCP were more accurate than those of conventional MLPA, and the CV of the measured copy numbers was significantly lower. Applying our system to measure the CNVs on autosomes between two HapMap individuals, we found that all peaks for CNV targets showed the expected copy number changes. Taken together, our results indicate that this new strategy can overcome the limitations of conventional MLPA, which are mainly related to long probe length and difficulties of probe preparation.     

基于脉动变光程的分光光度法自标定检测磷酸盐

分光光度法应用于磷酸盐长期监测存在络合物对透光窗口附着污染的干扰问题.本研究采用新的脉动变光程的分光光度检测原理,提出自标定检测方法,开发了脉动可变光程的机械装置.利用此设备实现了水体磷酸盐检测的长期原位自标定.利用本方法与传统分光光度计进行长期监测对比实验,结果表明:本方法能够有效去除镜头附着污染等干扰因素影响,提高了检测结果的准确性与可靠性.     

原子运动与场频率变化操控下的场熵演化及量子态制备

在旋波近似下,同时考虑原子运动和光场频率随时间作正弦函数变化,研究了二能级原子与单模辐射场相互作用系统中场的量子约化熵的演化规律.运用数值计算的方法分别给出了在不考虑原子的运动和考虑原子的运动的情况下场熵随时间的演化曲线,讨论了原子运动、场模结构、场频率的幅值和角频率变化对场熵的影响.根据Schmidt分解定理,解析制备了光场与原子的纠缠态、光场偶数态及原子相干叠加态,获得了调控和制备上述量子态的系统参量.研究结果表明:场熵的演化受场频率变化的调制,场频率变化的幅值增大会削弱场与原子的相互作用,场熵演化的周期性与场频率变化一致|原子的运动导致了场熵演化周期加倍|在场频率变化的角频率一定的情形下,场熵演化规律与场模结构参量的奇偶性有关|无论原子运动与否,都可周期性制备场-原子的近似EPR态.     

Effect of spectrum processing procedure on the linearity of EPR dose reconstruction in tooth enamel

Electron Paramagnetic Resonance (EPR) spectroscopy with tooth enamel is a widely used method of dosimetry. The accuracy of EPR tooth dosimetry depends on the spectrum processing procedure, the quality of which, in its turn, relies on instrumental noise and the signals from impurities. This is especially important in low-dose evaluation. The current paper suggests a method to estimate the accuracy of a specific spectrum processing procedure. The method is based on reconstruction of the radiation-induced signal (RIS) from a simulated spectrum with known RIS intensity. The Monte Carlo method was used for the simulations. The model of impurity and noise signals represents a composite residual spectrum (CRS) obtained by subtraction of the reconstructed RIS and the native background signal (BGS) from enamel spectra measured in HMGU (Neuherberg, Germany) and IMP (Yekaterinburg, Russia). The simulated spectra were deconvoluted using a standard procedure. The method provides an opportunity to compare the simulated “true” RIS with reconstructed values. Two modifications of the EPR method were considered: namely, with and without the use of the reference Mn²⁺ signals. It was observed that the spectrum processing procedure induces a nonlinear dose response of the reconstructed EPR amplitude when the height of the true RIS is comparable with the amplitudes of noise-like random splashes of CRS. The area of nonlinearity is below the limit of detection (DL). The use of reference Mn²⁺ signals can reduce the range of nonlinearity. However, the impact of the intensities of CRS random signals on nonlinearity is two times higher than the one observed when the reference signals were not used. The reproducibility of the software response is also dependent on both the amplitude of the CRS and the use of a reference signal, and it is also two times more sensitive to the amplitude of the CRS. In most EPR studies, all of the data are used, even those for which the dose value is lower than the DL. This study shows that low doses evaluated with the help of linear dose–response can be significantly overestimated. It is recommended that linear dose response calibration curves be constructed using only data above the DL. Data below the DL should be interpreted cautiously.     

Quadratic variation of martingales in Riesz spaces

We derive quadratic variation inequalities for discrete-time martingales, sub- and supermartingales in the measure-free setting of Riesz spaces. Our main result is a Riesz space analogue of Austin?s sample function theorem, on convergence of the quadratic variation processes of martingales.