Direct analysis of anabolic steroids in urine using Leidenfrost phenomenon assisted thermal desorption-dielectric barrier discharge ionization mass spectrometry

Rapid detection of trace level anabolic steroids in urine is highly desirable to monitor the consumption of performance enhancing anabolic steroids by athletes. The present article describes a novel strategy for identifying the trace anabolic steroids in urine using Leidenfrost phenomenon assisted thermal desorption (LPTD) coupled to dielectric barrier discharge (DBD) ionization mass spectrometry. Using this method the steroid molecules are enriched within a liquid droplet during the thermal desorption process and desorbed all-together at the last moment of droplet evaporation in a short time domain. The desorbed molecules were ionized using a dielectric barrier discharge ion-source in front of the mass spectrometer inlet at open atmosphere. This process facilitates the sensitivity enhancement with several orders of magnitude compared to the thermal desorption at a lower temperature. The limits of detection (LODs) of various steroid molecules were found to be in the range of 0.05–0.1 ng mL⁻¹ for standard solutions and around two orders of magnitude higher for synthetic urine samples. The detection limits of urinary anabolic steroids could be lowered by using a simple and rapid dichloromethane extraction technique. The analytical figures of merit of this technique were evaluated at open atmosphere using suitable internal standards. The technique is simple and rapid for high sensitivity and high throughput screening of anabolic steroids in urine.     

STABILITY OF EQUILIBRIA OF NEMATIC LIQUID CRYSTALLINE POLYMERS

We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b*(6.7314863965), the only equilibrium state is isotropic and it is stable; when b*< b < 15/2, two anisotropic (prolate) equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state.     

卷积算子的Gibbs现象

本文建立了一般卷积算子在函数的第一类间断点处有Gibbs现象的刻画定理,并且给出了某些例子.     

Coquet-type formulas for the rarefied weighted Thue–Morse sequence

Newman proved for the classical Thue–Morse sequence, ((−1)^s(n))_n≥0, that for all N∈N with real constants satisfying c₂>c₁>0 and λ=log3/log4. Coquet improved this result and deduced , where F(x) is a nowhere-differentiable, continuous function with period 1 and η(N)∈{−1,0,1}. In this paper we obtain for the weighted version of the Thue–Morse sequence that for the sum a Coquet-type formula exists for every r∈{0,1,2} if and only if the sequence of weights is eventually periodic. From the specific Coquet-type formulas we derive parts of the weak Newman-type results that were recently obtained by Larcher and Zellinger.     

Regularity for obstacle problems without structure conditions

This paper deals with the Lipschitz regularity of minimizers for a class of variational obstacle problems with possible occurrence of the Lavrentiev phenomenon. In order to overcome this problem, the availment of the notions of relaxed functional and Lavrentiev gap is needed. The main tool used here is a crucial Lemma which reveals to be needed because it allows us to move from the variational obstacle problem to the relaxed-functional-related one. This is fundamental in order to find the solutions’ regularity that we intended to study. We assume the same Sobolev regularity both for the gradient of the obstacle and for the coefficients.     

关于猝灭问题的一些结果及其应用

本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。     

The nature of the bufferness phenomenon in weakly dissipative systems

We propose a mechanism for accumulating attractors in finite-dimensional weakly dissipative systems. The essence of this mechanism is that if a Hamiltonian or a conservative system with one and a half or more degrees of freedom is perturbed by small additional terms ensuring that it is dissipative, then under certain conditions, the number of its attractors appearing in small neighborhoods of different elliptic equilibriums or cycles of the nonperturbed system can increase without bound as the perturbations tend to zero. We consider meaningful examples from mechanics and radio physics: models of the bouncing ball dynamics, Fermi accelerations, the linear oscillator with impacts, and the self-excited oscillator with a discrete sequence of RLC circuits in the feedback circuit. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 447–466, March, 2006.     

消荧光现象与表面谐波产生

消荧光现象是激光与物质表面非线性相互作用的结果，这是一种普遍现象。在表面谐波产生的研究中，它常常被忽略。大量研究表明：表面谐波产生与消荧光现象，有着密切的内在联系。本文以消荧光观点详细讨论了表面谐波产生的机制，提出了表面谐波产生的消荧光模型。新机制可归纳为：（ａ）多光子受激吸收产生消荧光光斑，（ｂ）激光热效应等促进自发辐射转向准受激辐射，（ｃ）伴随荧光消失，部分产生荧光的激光能量转换为产生表面谐波