三次Gauss和及二项指数和的混合均值

我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.     

Stochastic systems with memory and jumps

Stochastic systems with memory naturally appear in life science, economy, and finance. We take the modelling point of view of stochastic functional delay equations and we study these structures when the driving noises admit jumps. Our results concern existence and uniqueness of strong solutions, estimates for the moments and the fundamental tools of calculus, such as the Itô formula. We study the robustness of the solution to the change of noises. Specifically, we consider the noises with infinite activity jumps versus an adequately corrected Gaussian noise. The study is presented in two different frameworks: we work with random variables in infinite dimensions, where the values are considered either in an appropriate $L^p$-type space or in the space of càdlàg paths. The choice of the value space is crucial from the modelling point of view, as the different settings allow for the treatment of different models of memory or delay. Our techniques involve tools of infinite dimensional calculus and the stochastic calculus via regularisation.     

考虑塑性变形发展程度系数的RC梁开裂弯矩改进计算公式

针对RC梁开裂荷载计算方法尚未统一的现状，首先，结合18根RC梁试验数据对比了已有的6种RC梁开裂弯矩计算公式，发现开裂弯矩理论计算值与试验值的偏差大小和混凝土强度有关；然后，通过提出塑性变形发展程度系数k，推导新的RC梁开裂弯矩计算公式，并进一步基于k值和塑性影响系数计算值γ_k进行改进；最后，选取12根RC试验梁验证改进公式的准确性，证明改进公式的计算值与试验值吻合更好且偏于安全。     

Closed‐form approximations for spread options in Lévy markets

We provide new closed‐form approximations for the pricing of spread options in three specific instances of exponential Lévy markets, ie, when log‐returns are modeled as Brownian motions (Black‐Scholes model), variance gamma processes (VG model), or normal inverse Gaussian processes (NIG model). For the specific case of exchange options (spread options with zero strike), we generalize the well‐known Margrabe formula (1978) that is valid in a Black‐Scholes model to the VG model under a homogeneity assumption.     

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.     

On intensities of perturbed random measures on Hausdorff spaces

Abstract

This article studies classes of random measures on topological spaces perturbed by stochastic processes (a.k.a. modulated random measures). We render a rigorous construction of the stochastic integral of functions of two variables and showed that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. Mathematical formalism of integral-driven random measures and their stochastic intensities find numerous applications in stochastic models, physics, astrophysics, and finance that we discuss throughout the article.     

Modified Gauss rules for approximate calculation of some strongly singular integrals

The approach we follow consists in transforming the numerical evaluation of hyper-singular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are presented.     

Euler–Goursat-like formula via Laplace–Borel duality

The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities.     

Heavy‐Atom Tunneling Calculations in Thirteen Organic Reactions: Tunneling Contributions are Substantial,and Bell's Formula Closely Approximates Multidimensional Tunneling at ≥250 K

Multidimensional tunneling calculations are carried out for 13 reactions, to test the scope of heavy‐atom tunneling in organic chemistry, and to check the accuracy of one‐dimensional tunneling models. The reactions include pericyclic, cycloaromatization, radical cyclization and ring opening, and S_N2. When compared at the temperatures that give the same effective rate constant of 3×10⁻⁵ s⁻¹, tunneling accounts for 25–95 % of the rate in 8 of the 13 reactions. Values of transmission coefficients predicted by Bell's formula, κ_Bell , agree well with multidimensional tunneling (canonical variational transition state theory with small curvature tunneling), κ_SCT. Mean unsigned deviations of κ_Bell vs. κ_SCT are 0.08, 0.04, 0.02 at 250, 300 and 400 K. This suggests that κ_Bell is a useful first choice for predicting transmission coefficients in heavy‐atom tunnelling.