Stability of the Minkowski Measure of Asymmetry for Convex Bodies

Given a convex body $C\subset R^n$ (i.e., a compact convex set with nonempty interior), for $x\in$ {\it int}$(C)$, the interior, and a hyperplane $H$ with $x\in H$, let $H_1,H_2$ be the two support hyperplanes of $C$ parallel to $H$. Let $r(H, x)$ be the ratio, not less than 1, in which $H$ divides the distance between $H_1,H_2$. Then the quantity $${\it As}(C):=\inf_{x\in {\it int}(C)}\,\sup_{H\ni x}\,r(H,x)$$ is called the Minkowski measure of asymmetry of $C$. {\it As}$(\cdot)$ can be viewed as a real-valued function defined on the family of all convex bodies in $R^n$. It has been known for a long time that {\it As}$(\cdot)$ attains its minimum value 1 at all centrally symmetric convex bodies and maximum value $n$ at all simplexes. In this paper we discuss the stability of the Minkowski measure of asymmetry for convex bodies. We give an estimate for the deviation of a convex body from a simplex if the corresponding Minkowski measure of asymmetry is close to its maximum value. More precisely, the following result is obtained: Let $C\subset R^n$ be a convex body. If {\it As}$(C)\ge n-\varepsilon$ for some $0\le \varepsilon < 1/8(n+1),$ then there exists a simplex $S_0$ formed by $n+1$ support hyperplanes of $C$, such that $$(1+8(n+1)\varepsilon)^{-1}S_0\subset C\subset S_0,$$ where the homethety center is the (unique) Minkowski critical point of $C$. So $$d_{{\rm BM}}(C,S)\le 1+8(n+1)\varepsilon$$ holds for all simplexes $S$, where $d_{{\rm BM}}(\cdot,\cdot)$ denotes the Banach-Mazur distance.     

The impacts of the full returns policy on a supply chain with information asymmetry

In contrast to the existing return policies literature assuming that information is symmetrical between the manufacturer and the retailer, we study the full returns policy’s impact on supply chains with information asymmetry. We first study the case that the base level of the demand follows a discrete distribution with two states. We find that the retailer benefits from the full returns policy in all circumstances, while the manufacturer and the supply chain are better off under some conditions. We then consider the situation in which the base level of the demand is a type of AR(1) process.     

Analysis of π-mode Stopband in an Asymmetric Millimeter-Wave Helical Slow-Wave Structure

A simple closed form formula for the estimation of π-mode stopband in an azimuthally asymmetric helical slow-wave structure (SWS) was developed following coupled-mode analysis of multiple reflections of the degenerate space-harmonic modes from the support rod discontinuities. The method incorporates the effects of circuit loss, and accrues the accuracy of 3D electromagnetic analysis by allowing the use of dispersion characteristics obtainable from any standard electromagnetic modeling. The formula is simple and amenable to easy computation, even using a scientific calculator, and without resorting to exhaustive and time-intensive numerical computation, and at the same time, without sacrificing the accuracy in results. The analysis was benchmarked against published results and excellent agreement observed. The analysis was further used for demonstrating the stopband phenomenon for a typical millimeter-wave helical slow-wave structure. Compared to low frequency structures, the stopband phenomenon for a millimeter-wave structure was found to be more pronounced, and an interesting inference was drawn as to how asymmetry induced stopband might be made to advantage in combating π-mode instabilities in a millimeter-wave traveling-wave tube.     

Study of (∧) decay parameter in J/ψ→∧(∧)decay

The helicity amplitudes fot J/ψ→∧(∧)and the relevant background decays are presented for measuring the A decay parameter α+((∧)→(p)π)in J/ψ→∧(∧).The Monte Carlo(MC)simulations based on the helicity amplitudes information are carried out.The likelihood fit method to determine the A decay parameter is presented.Based on the MC generated sample,the sensitivity of the measurement for α+has been estimated,which shows that the J/ψ→∧(∧) channel can be used to measure the A decay parameter α+((∧)→(p)π+)well.     

Asymmetry in Negative Refraction of Nonlinear Waves

Recently, inwardly propagating waves （called antiwaves, AWs） in nonlinear oscillatory systems have attracted much attention. An interesting negative refraction phenomenon has been observed in a bidomain system where one medium supports forwardly propagating waves （normal waves, NWs） and the other AWs. In this paper we find that negative refraction （NR） in nonlinear media has an asymmetric property, i.e., NR can be observed only by applying wave source with proper frequency to one medium, but not the other. Moreover, NR appears always when the incident waves are dense and the refractional waves are sparse. This asymmetry is a particular feature for nonlinear NR, which can neither be observed in linear refraction processes （both positive and negative refractions） nor in nonlinear positive refraction. The mechanism underlying the asymmetry of nonlinear NR are fully understood based on the competition of nonlinear waves.     

Charmless Hadronic Decays B→VV in the Topcolor－Assisted Technicolor Model

Based on the effective Hamiltonian with the generalized factorization approach, we calculate the branching ratios and CP asymmetries of B→VV decays in the Topcolor-assisted Technicolor (TC2) model. Within the considered parameter space we find that: (a) for the penguin-dominated B→K^*+φ and K^*0φ decays, the new physics enhancements to the branching ratios are around 40%; (b) the measured branching ratios of B→K^*+φ and K^*0φ decays prefer the range of 3≤N_c^eff≤5; (c) the SM and TC2 model predictions for the branching ratio B(B⁺→ρ⁺ρ⁰) are only about half of the Belle's measurement; and (d) for most B→VV decays, the new physics corrections on their CP asymmetries are generally small or moderate in magnitude and insensitive to the variation of m_π and N_c^eff.     

点火靶驱动不对称性与表面粗糙度的模耦合模拟

使用二维辐射多群扩散流体力学程序LARED-S对点火靶内爆进行大规模数值模拟,同时考虑低阶辐射驱动不对称性和中高阶的表面粗糙度.计算结果表明：靶丸内爆流场不仅出现严重的低阶模面密度扰动,同时生成大幅度的尖钉与气泡结构;呈现明显的扰动模耦合效应,模耦合生成的扰动增长幅度与理论公式在一定时间内较好地吻合.在内爆减速阶段,扰动增长发展到强非线性阶段,模耦合效应使得扰动频谱分布变宽;同时芯部的涡流使得靶壳的尖钉弯曲,内爆流场出现明显的湍流混合现象.模耦合效应与湍流混合极大地降低了内爆性能,导致点火失败.     

Two-Photon Exchange Corrections to Single Spin Asymmetry of Neutron and 3He

In a simple hadronic model, the two-photon exchange contributions tothe single spin asymmetries for the nucleon and the ³He are estimated. The results show that the elastic contributions of two-photon exchange to the single spin asymmetries for the nucleon are rather small while those for the ³He are relativelylarge. Besides the strong angular dependence, the two-photon contributions to the single spin asymmetry for the ³He are very sensitive to the momentum transfer.     

基于角速率积分法的光纤陀螺标度因数不对称度测量方法

标度因数不对称度是评价光纤陀螺的一项重要指标,对其进行精确测量在高精度导航应用中具有重要意义。传统的测试方法受转台速率控制精度限制,很难精确测量小于1×10-6的不对称度。首次提出基于角速率积分的标度因数不对称度测量方法。该方法给定转台正反方向转动的角度,由固定在转台上的被测光纤陀螺进行角速率测量,并对输出值积分,从而得到标度因数不对称度。该方法基于转台位置控制,避免了转速不稳定及正反向转速不对称等因素造成的影响。还对可能引起测量误差的因素进行了分析。最后采用角速率积分法测得高精度光纤陀螺标度因数不对称度小于1×10-6。