Perturbative Power Counting,Lowest-Index Operators and Their Renormalization in Standard Model Effective Field Theory

We study two aspects of higher dimensional operators in standard model effective field theory.We first introduce a perturbative power counting rule for the entries in the anomalous dimension matrix of operators with equal mass dimension.The power counting is determined by the number of loops and the difference of the indices of the two operators involved,which in turn is defined by assuming that all terms in the standard model Lagrangian have an equal perturbative power.Then we show that the operators with the lowest index are unique at each mass dimension d,i.e.,(H~?H)~(d/2)for even d≥4,and(L~TεH)C(L~TεH)~T(H~?H)~((d-5)/2)for odd d≥5.Here H,L are the Higgs and lepton doublet,andε,C the antisymmetric matrix of rank two and the charge conjugation matrix,respectively.The renormalization group running of these operators can be studied separately from other operators of equal mass dimension at the leading order in power counting.We compute their anomalous dimensions at one loop for general d and find that they are enhanced quadratically in d due to combinatorics.We also make connections with classification of operators in terms of their holomorphic and anti-holomorphic weights.     

光子计数技术及其在弱光计量中的应用

从光子计数原理出发,介绍光子计数系统的构成,分析光电倍增管的脉冲幅度分布,并叙述光子计数技术在弱光计量中的实际应用。     

Two-Phase Image Segmentation by Nonconvex Nonsmooth Models with Convergent Alternating Minimization Algorithms

Two-phase image segmentation is a fundamental task to partition an image into foreground and background. In this paper, two types of nonconvex and nonsmooth regularization models are proposed for basic two-phase segmentation. They extend the convex regularization on the characteristic function on the image domain to the nonconvex case, which are able to better obtain piecewise constant regions with neat boundaries. By analyzing the proposed non-Lipschitz model, we combine the proximal alternating minimization framework with support shrinkage and linearization strategies to design our algorithm. This leads to two alternating strongly convex subproblems which can be easily solved. Similarly, we present an algorithm without support shrinkage operation for the nonconvex Lipschitz case. Using the Kurdyka-Łojasiewicz property of the objective function, we prove that the limit point of the generated sequence is a critical point of the original nonconvex nonsmooth problem. Numerical experiments and comparisons illustrate the effectiveness of our method in two-phase image segmentation.     

掺铒光纤激光器自混合理论与微振动位移测量

利用线形掺铒光纤激光器搭建了一种新型光纤传感测量系统来测量微振动位移.采用条纹计数法分析自混合干涉信号,实验显示扬声器的振幅与驱动电压成很好的线性关系.该实验装置结构简单、成本低.实验结果表明,用该传感系统来进行振动位移测量,信号稳定,方法简单、迅速.     

无机盐对非离子表面活性剂从水相到油相传质的影响研究

采用同位素示踪原子法研究了非离子表面活性剂在无机盐存在下从水相到油相传质的规律,发现无机盐强烈地影响非离子表面活性剂Ａｐ型和Ｓｐ型的传质行为,而且因无机盐性质的不同,表面活性剂结构的差异,传质行为亦会有很大的不同。中外,利用此技术研究解决了连续定量测定微量表活剂的问题,为系统研究表面传质问题开辟了一个新方法。     

On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds

We consider a new algorithm, an interior-reflective Newton approach, for the problem of minimizing a smooth nonlinear function of many variables, subject to upper and/or lower bounds on some of the variables. This approach generatesstrictly feasible iterates by using a new affine scaling transformation and following piecewise linear paths (reflection paths). The interior-reflective approach does not require identification of an activity set. In this paper we establish that the interior-reflective Newton approach is globally and quadratically convergent. Moreover, we develop a specific example of interior-reflective Newton methods which can be used for large-scale and sparse problems.Research partially supported by the Applied Mathematical Sciences Research Program (KC-04-02) of the Office of Energy Research of the U.S. Department of Energy under grant DE-FG02-86ER25013.A000, and in part by NSF, AFOSR, and ONR through grant DMS-8920550, and by the Advanced Computing Research Institute, a unit of the Cornell Theory Center which receives major funding from the National Science Foundation and IBM Corporation, with additional support from New York State and members of its Corporate Research Institute.Corresponding author.     

On the distribution of the number of packets in the fluid flow approximation of packet arrival streams

Fluid flow approximations are widely used for approximating models of communication systems where packet arrival streams are generated in a regular manner over certain intervals (constant rate). The appropriate mathematical model for describing those bursty arrival streams in the fluid flow framework are the well-known Markov modulated rate processes (MMRP). The paper deals with the distribution of the numberN(t) of packets in the interval [0,t] of MMRP. For two-state MMRPs and their superpositions we derive formulas for the distribution ofN(t) and its density. Further we give asymptotic results. The presented numerical results and simulation studies illustrate the goodness of the fluid flow approximation and show that the proposed numerical algorithms work well even in the case of multiplexing a large number of burst silence sources.This work was partially supported by a grant from the Deutsche Bundespost TELEKOM.     

Weierstrass型函数图象的分形维数

考虑函数f(x)=sum from i=1 to ∞(?)~(-1)φ((?) θ_n)和w(x)=sum from n=1 to ∞(?)φ_(?)((?)x θ_(?)),式中0<α<(?)是任意实数,在一定条件下,估计了函数f图象的Hausdorff维数的下界,并求得了w函数图象的Box维数和Packing维数。     

Reduction in etching time for fission tracks in diallyl phthalate resin

Diallyl phthalate (DAP) resin plates were irradiated with fission fragments, and then etched in a conventional aqueous solution of KOH or a PEW solution containing ethanol, water and KOH. Etched tracks were observed and counted by using an optical microscope. The PEW solution made the fission tracks etch-pits clearer in an incomparably shorter etching time. The large and round etch-pits developed on a smooth surface were convenient for optical automatic counting. These etching characteristics of DAP in a PEW solution are suitable for quantitative analysis of fissionable materials and neutron dosimetry.