Universal series induced by approximate identities and some relevant applications

We prove the existence of series ∑a_nψ_n, whose coefficients (a_n) are in ∩_p>1?^p and whose terms (ψ_n) are translates by rational vectors in R^d of a family of approximations to the identity, having the property that the partial sums are dense in various spaces of functions such as Wiener’s algebra W(C₀,?¹), C_b(R^d), C₀(R^d), L^p(R^d), for every p∈[1,∞), and the space of measurable functions. Applying this theory to particular situations, we establish approximations by such series to solutions of the heat and Laplace equations as well as to probability density functions.     

Metal-Rich Phosphanediyl-and Arsanediyl-Clusters

Abstract

The reactions of primary silylphosphanes and -arsanes 1 with BuLi yield the three-dimensional M₂ER-aggregates 2 (E = P, As). We observed that the double lithiation of 1 in the presence of Li₂O results in the formation of the aggregates 3 and 4.     

Unbounded Energy Growth in Hamiltonian Systems with a Slowly Varying Parameter

We study Hamiltonian systems which depend slowly on time. We show that if the corresponding frozen system has a uniformly hyperbolic invariant set with chaotic behaviour, then the full system has orbits with unbounded energy growth (under very mild genericity assumptions). We also provide formulas for the calculation of the rate of the fastest energy growth. We apply our general theory to non-autonomous perturbations of geodesic flows and Hamiltonian systems with billiard-like and homogeneous potentials. In these examples, we show the existence of orbits with the rates of energy growth that range, depending on the type of perturbation, from linear to exponential in time. Our theory also applies to non-Hamiltonian systems with a first integral.     

UPLC-MS/MS detection of disaccharides derived from glycosaminoglycans as biomarkers of mucopolysaccharidoses

Mucopolysaccharidoses (MPSs) are a group of disorders resulting from primary defects in lysosomal enzymes involved in the degradation of glycosaminoglycans (GAGs). Depending on the specific enzyme defect, the catabolism of one or more GAGs is blocked leading to accumulation in tissues and biological fluids. GAG measurements are important for high-risk screening, diagnosis, monitoring treatment efficacy, and patient follow up. The dimethylmethylene blue (DMB) spectrophotometric method commonly used in most biochemical genetics laboratories relies on a non-specific total GAG analysis which has led to false positive results, and even false negative results (mainly for MPS III and IV patients). The main objective of our project was to devise and validate a reliable tandem mass spectrometry multiplex analysis for the urine quantitation of four GAGs (dermatan sulfate (DS), heparan sulfate (HS), keratan sulfate (KS), and chondroitin sulfate (CS)) for an eventual technological transfer to the clinic. The developed methodology is rapid (7 min) and our results showed good intraday and interday precision (RSDs ≤ 8.7%) and accuracy (Biases range: −12.0%–18.4%). Linearity was good (r² > 0.995) for DS, HS, CS, and KS calibration curves. In comparison with the DMB spectrophotometric method, this multiplex tandem mass spectrometry method allows GAG fractionation, thus a differentiation of MPS types, except for MPS I and II which are characterized by the same GAG profile. The devised method is a useful and reliable tool for diagnosis of MPS patients, as well as their monitoring and follow up, as shown by longitudinal studies.     

基于平面超材料的Fano谐振可调谐研究

基于两段相同金属分裂环谐振器构成的单层结构, 从理论及实验方面研究了平面超材料的可调谐Fano谐振. 实验测量了平面超材料对TE和TM入射波的电磁响应, 利用电磁波的入射角度控制Fano谐振的强度, 实现了谐振的开关特性, 谐振频率红移可达到21%. 基于有限元法给出了平面超材料的场分布, 强的正常色散表明平面超材料的电磁响应可类比经典电磁诱导透明现象, 仿真与实验结果相符合. 对称结构超材料Fano谐振的开/关特性为超材料性能的可调谐控制提供了有效途径.     

The law of large numbers for quantum stochastic filtering and control of many-particle systems

Theoretical and Mathematical Physics - There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing...