A new BCR method for coupled operator equations with submatrix constraint

In the present work, a new biconjugate residual algorithm (BCR) is proposed in order to compute the constraint solution of the coupled operator equations, in which the constraint solution include symmetric solution, reflective solution, centrosymmetric solution and anti-centrosymmetric solution as special cases. When the studied coupled operator equations are consistent, it is proved that constraint solution can be convergent to the exact solutions if giving any initial complex matrices or real matrices. In addition, when the studied coupled operator equations are not consistent, the least norm constraint solution above can also be computed by selecting any initial matrices. Finally, some numerical examples are provided for illustrating the effectiveness and superiority of new proposed method.     

HHV和HVV耦合的有效拉氏量及费曼规则

首先包含Higgs粒子的六维算符用物理场来表示,然后给出包含HHV和HVV相互作用顶点的有效拉氏量,其中V=A,Z,W^±。最后,推导出每个六维算符和有效拉氏量的费曼规则。     

高阶多量子跃迁的一维直接检测——Raman磁共振方法

研究了异核AX₃自旋体系的初始态为最高阶量子相干态时的Raman磁共振谱.研究表明,唯有制备高阶多量子相干的初始态时才有可能对高阶多量子跃迁进行有效检测.积算符理论的精确性使得理论上准确地预言了Raman磁共振谱中各阶多量子跃迁频率、谱线强度,使得各阶多量子跃迁频率相互交错时仍有可能解析谱图.在Raman磁共振实验中采用了正负频偏交替变化采样的方法,对单量子信号进行压制,使其更有效地观察高阶多量子跃迁.     

EXPANSIONS OF STEP-TRANSITION OPERATORS OF MULTI-STEP METHODS AND ORDER BARRIERS FOR DAHLQUIST PAIRS

Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.     

Free moment measures and laws

In [3], it was shown that convex, almost everywhere continuous functions coordinatize a broad class of probability measures on ${\mathbb{R}}^n$ by the map $U?{\left(\mathrm{?}U\right)}_{\mathrm{\#}}{e}^{?U}dx$. We consider whether there is a similar coordinatization of non-commutative probability spaces, with the Gibbs measure $e^{?U}dx$ replaced by the corresponding free Gibbs law. We call laws parameterized in this way free moment laws. We first consider the case of a single (and thus commutative) random variable and then the regime of n non-commutative random variables which are perturbations of freely independent semi-circular variables. We prove that free moment laws exist with little restriction for the one dimensional case, and for small even perturbations of free semi-circle laws in the general case.     

Bilinear embedding in Orlicz spaces for divergence-form operators with complex coefficients

We prove a bi-sublinear embedding for semigroups generated by non-smooth complex-coefficient elliptic operators in divergence form and for certain mutually dual pairs of Orlicz-space norms. This generalizes a result by Carbonaro and Dragi?evi? from power functions to more general Young functions that still behave like powers. To achieve this, we generalize a Bellman function constructed by Nazarov and Treil.