CPMG echo amplitudes with arbitrary refocusing angle: explicit expressions, asymptotic behavior, approximations

Exact explicit analytical expression for echoes in the Carr–Purcell–Meiboom–Gill sequence with arbitrary excitation and refocusing angles and resonance offset of RF pulses was obtained, employing the generating functions formalism developed earlier by authors. Asymptotic form and analytical approximation for echoes were derived in an elegant way and analyzed in details. In particular, it was shown that depending on T₁, T₂ and parameters of the pulse sequence, oscillatory behavior of echoes can take place. Accuracy of asymptotic forms and approximations were tested by comparison with exactly calculated echo amplitudes. Besides, it was shown, that the generating function approach can be applied to the consideration of terminated pulse sequences, when after-pulses echoes are registered.     

量子系统保结构计算新进展

本文主要介绍量子系统保结构计算最新进展情况,分以下几部分内容:哈密顿系统的辛算法、适合于量子系统的哈密顿量显含时间的辛算法、A2B模型分子和双原子分子系统的经典轨迹辛算法计算、双原子分子CO在激光场中的经典轨迹的辛算法计算及其振动和解离、定态Schr dinger方程的辛形式及求解定态Schr dinger方程本征值问题的辛 打靶法、含时Schr dinger方程的保结构算法及其在激光原子物理中的应用、伪分立态模型、强激光与原子相互作用的渐近边界条件、"非齐线性正则方程"的辛算法及其在计算强激光场中一维原子的多光子电离和高次谐波发射中的应用以及Heisenberg方程的保结构计算等等。     

Remarks on Higgs inflation

We discuss models where the Higgs boson of the electroweak standard model plays the role of the inflaton. We focus on the question of the violation of perturbative unitarity due to the coupling of the Higgs boson either to the Ricci scalar or to the Einstein tensor and discuss the background dependence of the unitarity bounds. Our conclusion is that the simplest model which restricts itself to the standard model Higgs boson without introducing further degrees of freedom has a serious problem. However, in the asymptotically safe gravity scenario, the Higgs boson of the standard model could be the inflaton and no physics beyond the standard model is required to explain both inflation and the spontaneous breaking of the electroweak symmetry of the standard model.     

Asymptotics for the Tail Probability of Random Sums with a Heavy-Tailed Random Number and Extended Negatively Dependent Summands

Let {X,X_k:k≥1} be a sequence of extended negatively dependent random variables with a common distribution F satisfying EX 0.Let r be a nonnegative integer-valued random variable,independent of {X,X_k:k≥1}.In this paper,the authors obtain the necessary and sufficient conditions for the random sums S_r =(?)X_n to have a consistently varying tail when the random number t has a heavier tail than the summands,i.e.,(P(Xx))/(P(r x))→0as x→∞     

ASYMPTOTIC PROPERTIES OF THE MOMENT CONVERGENCE FOR NA SEQUENCES

It is well-known that the complete convergence theorem for i.i.d. random variables has been an active topic since the famous work done by Hsu and Robbins [6]. Chow [4]obtained a moment version of Hsu and Robbins series. However, the series tends to infinity whenever ∈ goes to zero, so it is of interest to investigate the asymptotic behavior of the series as ∈ goes to zero. This note gives some limit theorems of the series generated by moments for NA random variables.     

Quasi-likelihood analysis for nonsynchronously observed diffusion processes

We consider nonsynchronous sampling of parameterized stochastic regression models, which contain stochastic differential equations. Constructing a quasi-likelihood function, we prove that the quasi-maximum likelihood estimator and the Bayes type estimator are consistent and asymptotically mixed normal when the sampling frequency of the nonsynchronous data becomes large.     

Approximation algorithms for constructing some required structures in digraphs

We consider a new problem of constructing some required structures in digraphs, where all arcs installed in such required structures are supposed to be cut from some pieces of a specific material of length L. Formally, we consider the model: a digraph D = (V, A; w), a structure S and a specific material of length L, where w: A → R⁺, we are asked to construct a subdigraph D′ from D, having the structure S, such that each arc in D′ is constructed by a part of a piece or/and some whole pieces of such a specific material, the objective is to minimize the number of pieces of such a specific material to construct all arcs in D′.     

Exponential stability of uniform Euler–Bernoulli beams with non-collocated boundary controllers

We study the stability of a robot system composed of two Euler–Bernoulli beams with non-collocated controllers. By the detailed spectral analysis, we prove that the asymptotical spectra of the system are distributed in the complex left-half plane and there is a sequence of the generalized eigenfunctions that forms a Riesz basis in the energy space. Since there exist at most finitely many spectral points of the system in the right half-plane, to obtain the exponential stability, we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half-plane. Hence the Riesz basis property ensures that the system is exponentially stable. Finally we give some simulation for spectra of the system.