Hitting probabilities and the Hausdorff dimension of the inverse images of a class of anisotropic random fields

Let X = {X(t):t ∈ R~N} be an anisotropic random field with values in R~d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.     

Role of the Bridge in Photoinduced Electron Transfer in Porphyrin–Fullerene Dyads

The role of π‐conjugated molecular bridges in through‐space and through‐bond electron transfer is studied by comparing two porphyrin–fullerene donor–acceptor (D–A) dyads. One dyad, ZnP–Ph–C₆₀ (ZnP=zinc porphyrin), incorporates a phenyl bridge between D and A and behaves very similarly to analogous dyads studied previously. The second dyad, ZnP–EDOTV–C₆₀, introduces an additional 3,4‐ethylenedioxythienylvinylene (EDOTV) unit into the conjugated bridge, which increases the distance between D and A, but, at the same time, provides increased electronic communication between them. Two essential outcomes that result from the introduction of the EDOTV unit in the bridge are as follows: 1) faster charge recombination, which indicates enhanced electronic coupling between the charge‐separated and ground electronic states; and 2) the disappearance of the intramolecular exciplex, which mediates photoinduced charge separation in the ZnP–Ph–C₆₀ dyad. The latter can be interpreted as a gradual decrease in electronic coupling between locally excited singlet states of D and A when introducing the EDOTV unit into the D–A bridge.     

Study of blood collection and sample preparation for analysis of vitamin D and its metabolites by liquid chromatography–tandem mass spectrometry

The analysis of vitamin D status, with special emphasis on 25-hydroxyvitamin D and 1,25-dihydroxyvitamin D, is gaining interest in clinical studies due to the classical and non-classical effects attributed to this prohormone. In this research, the influence of the two steps preceding determination (viz. sample collection and preparation) on the quantitative analysis of vitamin D and its more important metabolites has been studied. Two preparation approaches, deproteination and solid-phase extraction (SPE), have been evaluated in terms of sensitivity to delimit their application, thus establishing that detection of 1,25-dihydroxyvitamin D cannot be addressed by protein precipitation. Concerning sample collection, serum and plasma reported high accuracy (above 83.3%) for vitamin D and metabolites, while precision, expressed as relative standard deviation, was below 12.9% for all analytes in both samples. Statistical analysis revealed that serum and plasma provided similar physiological levels for vitamin D₃, 24,25-dihydroxyvitamin D₃ and 25-hydroxyvitamin D₃, while significantly different levels were obtained for 1,25-dihydroxyvitamin D₃, always higher in plasma than in serum. Sample collection and treatment have proved to be significant in the analysis of vitamin D and its relevant metabolites.     

Infinite family of transmission irregular trees of even order

Distance between two vertices is the number of edges in a shortest path connecting them in a connected graph $G$. The transmission of a vertex $v$ is the sum of distances from $v$ to all the other vertices of $G$. If transmissions of all vertices are mutually distinct, then $G$ is a transmission irregular graph. It is known that almost no graphs are transmission irregular. Infinite families of transmission irregular trees of odd order were presented in Alizadeh and Klav?ar (2018). The following problem was posed in Alizadeh and Klav?ar (2018): do there exist infinite families of transmission irregular trees of even order? In this article, such a family is constructed.     

Molecular dynamics of the intramolecular 1, 3-dipolar ene reaction of a nitrile oxide and an alkene: non-statistical behavior of a reaction involving a diradical intermediate*

ABSTRACT

Potential energy surfaces and molecular dynamics of the intramolecular 1, 3-dipolar cycloaddition and ene reaction of a nitrile oxide with an alkene were performed in the gas phase and in dichloromethane with density functional theory. One hundred trajectories were propagated in the gas phase and in dichloromethane, respectively. Twenty percent of the trajectories in the gas phase involve bicyclic intermediate and the mean time gap is 472fs. A dynamically stepwise reaction is observed. In dichloromethane, more reactive trajectories were obtained and the time gap is larger than that in the gas phase.     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

基于LS -DYNA公路桥车桥耦合的车辆模型研究

研究公路桥梁在移动车辆荷载作用下的动力响应,建立合理的车辆模型非常重要。为更真实地体现桥梁在车载作用下的动力响应,基于LS-DYNA程序,结合常用重型车辆的结构特性及参数,对车辆的橡胶轮胎、轮胎内气体压力、车轮转动和车辆悬架系统进行模拟,使车辆模型更接近实际车辆。通过车辆轴重和动力特性初步验证车辆有限元模型的有效性;同时,以一座混凝土简支空心板梁桥为算例,验证车轮转动和车桥相互接触力,并将LS-DYNA计算结果与桥梁实测结果进行对比,进一步验证车辆有限元模型的有效性。研究结果表明,基于LS-DYNA建立的三维车辆有限元模型是可行的,可以用于研究车桥相互作用。