Qu-Zhi Li and Han-Qing Zheng

1 Department of Physics Peking University,Beijing 100871,China

2 College of Physics,Sichuan University,Chengdu,Sichuan 610065,China

3 Collaborative Innovation Center of Quantum Matter,Beijing,China

Abstract It is demonstrated that for the isospin I=1/2 πN scattering amplitude,TI=1/2(s,t),are two accumulation points of poles on the second sheet of complex s plane,and are hence accumulation of singularities of TI=1/2(s,t).Foris the accumulation point of poles on the second sheet of the complex s plane.The proof is valid up to all orders of chiral expansions.

Keywords:dispersion relations,partial wave,analyticity

where dJis the standard Wigner d-function.Substituting equation(6)into equation(7),then using the relation between the Wigner d-function and the Legendre polynomial

one gets

with

where F stands for A or B.

(1)In the region s ∈(cR,sR),the S-matrixSJs

BP神經(jīng)網(wǎng)絡實質上是一種采用反向傳播學習算法的多層前饋網(wǎng)絡。從結構上講，BP網(wǎng)絡是一種分層型網(wǎng)絡，由輸入層、隱層和輸出層組成。層與層之間采用全互連方式，同一層單元之間不存在相互連接。

The sign of the infinity is independent of the angular momentum J.Things will be different,however,when s tends to cL.It turns out thattends toandt ends to ±(- 1)J+12∞.Taking the definition of Smatrix equation(15),and the fact that 2iρ(s)is negative at s=cR,cL,conclusions can be drawn that:5The emergence of S matrix zeros due to kinematical reasons is known,and χPT amplitudes can be consistently embedded into a unitary S matrix element.See for example the discussion in[4].

The kinematic factor ρ(s)is defined as

The scalar function AIand BImay be calculated by chiral perturbation theory at low energies.4In the region[sL,sR]chiral expansions are expected to work well.Here,we present the

which satisfy the optical theorem for partial waves,

A modification of the dispersion representation for function f defined in[1]in each channel may be needed accordingly,similar to what has been discussed in S11channel[1].Conclusions are similar in all channels:the contribution from the virtual pole to the phase shift is always exactly canceled by the additional contribution from the dispersion integral in f,when vL=cL(vR=cR).Taking for example the case that there exists only one virtual pole vLon the left.In this situation,

月球是片不毛之地。當然，月球上有幾輛月球車、一些高爾夫球、一面國旗、幾只尿袋、一張家庭照片。但月球上的大多數(shù)地方是空空蕩蕩的。然而，假如一家名叫iSpace的公司得償所愿，地球最近的太空鄰居（大概）很快就會成為一片喧鬧之地，變成一座充斥了工人和游客的工業(yè)之城。夢想家們稱其為“月球谷”。9月25日，那些夢想家宣布了月球之旅的第一小步，聲明SpaceX公司的獵鷹9號火箭將在2020和2021年運載iSpace公司的軌道飛行器-著陸器和月球車到月球。

1 2,

The parity eigenstates can be constructed by the linear combinations of helicity amplitudes

±()must contain a zero6This argument has been actually used a long time ago in[5].We thank one referee who brings our attention to this paper.,whiledoes not need to have.

(2)In the region s ∈(sL,cL),bothandcontain a zero for J=1/2,5/2,9/2,…,while bothandcontain a zero for J=3/2,7/2,11/2,….Or in other words,for I=1/2(I=3/2),there exists a virtual pole vL∈(sL,cL)in each partial wave amplitude with even(odd)angular momentum.

Taking a few examples,in S31channel there is no virtual pole,while in p waves,

· P11channel contains a virtual pole vR∈(cR,sR),as well as the nucleon bound state;

· P33channel contains a virtual pole in vL∈(sL,cL).

· P13channel contains a virtual pole in vR∈(cR,sR);

上述教學方法可靈活應用，利用藥學、臨床藥學、中藥學多專業(yè)不同學生的知識框架基礎，開展同堂討論，各抒己見，充分利用各自的專業(yè)優(yōu)勢，實現(xiàn)共同進步、共同發(fā)展?？傊?，實例式、啟發(fā)式、PBL式、比較法、互動教學及翻轉課堂教學等教學方法的實施，可激發(fā)學生學習興趣，全面提升藥用高分子材料學的教學質量。

一時間,苞米、葵花盤長了翅膀似的飛向徐進步,徐進步顧上顧不了下,狼狽地躥到了幾個籮筐后面。無辜挨打的男知青們也跟著東躲西藏。

一是開展安全生產(chǎn)考核，實化水行政主管部門安全生產(chǎn)監(jiān)管職責。為嚴格落實流域機構和省級水行政主管部門安全監(jiān)管職責，有效預防和減少生產(chǎn)安全事故，不斷提高水利安全生產(chǎn)管理水平，水利部決定從2013年開始啟動水利安全生產(chǎn)監(jiān)管工作考核。組織12個考核組對7個流域機構和32個省級水行政主管部門進行了考核，考核范圍不僅包括流域和省廳安全生產(chǎn)監(jiān)管部門本身，還包括其管理范圍內的水利運行管理單位和在建水利工程。通過考核，典型引導，實現(xiàn)了相互督促、交流和借鑒，有力地促進了流域和地方水利安全生產(chǎn)監(jiān)管職責的落實和工作水平的提高。

whereSvLrepresents the‘S matrix’of the newly found virtual pole vL,while Sidepicts all other known poles.7For more details about the production representation,one can refer to[6—8].Such an Scutis real and negative when s ∈(sL,cL),8Sphy(sL)=+1 according to equation(15).This is because sL is the branch point caused by the u channel continuous absorptive singularities,T(sL)itself is regular.For resonances Si=+1,for bound state or virtual state Si=-1,when s=sL.Particularly is negative when s ∈(sL,vL)and positive when s ∈(vL,cL).so the ‘spectral

一是加快河湖長制立法步伐。從法律層面明確河湖長制組織體系構架、各級河湖長權責利及有關部門聯(lián)動等保障機制，實現(xiàn)河湖長制工作由行政手段推動向法治剛性約束為主轉變，為各級河湖長履職盡責、考責、問責提供法律支撐。鑒于目前省人大已將《湖北省河湖長制工作條例》列入加強長江經(jīng)濟帶環(huán)境保護治理類規(guī)劃項目，納入優(yōu)先立法計劃，下一步應采取積極措施加快推進。

數(shù)據(jù)的整理及分析軟件為Microsoft Office Excel 2013及SPSS 25.0軟件。各組間盜血程度及病變鎖骨下動脈收縮期峰值、對側椎動脈收縮期峰值的比較用非參數(shù)檢驗。合并椎動脈狹窄性病變組與對照組束臂試驗結果的比較用卡方檢驗。以P＜0.05為差異有統(tǒng)計學意義。

Hence,according to equation(28),as J →∞,the leading contribution ofis10The contribution from chiral corrections will not diverge,since the contribution itself is regular when s ∈(sL,sR),and notice that |Pl(x)|＜1 when x ∈[-1,+1]for arbitrary l—which is proved using the Laplace formula of Legendre function.

One further proves that the accumulation of zeros at cLoccurs and that s=cLis an accumulation of singularities of T3/2(s,t)on the second sheet of the s plane.

Acknowledgments

The authors would like to thank Wei-Nian Zhang at Sichuan University,and Wei-Da Zheng for helpful discussions.This work is supported in part by National Nature Science Foundations of China under contract numbers 11975028 and 10925522.