A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimentional case in certain discrete version respectively. These results are in fact the intrinsic reason that the numerical experiments indicate that such finite element algorithms are accurate in practice.Comment: 7 pages, 3 figure

Clinical observation on the effect of resection of eyelid tumor and stage Ⅰ recovery

AIM: To investigate clinical effects of local resection of eyelid tumors and pathological examination or frozen section examination as well as the stage I recovery.<p>METHODS: For all 92 cases 92 eyes of eyelid tumor patients who underwent local resection, reconstruction in stage Ⅰ and routine pathological examination(37 cases of suspected malignant tumors using frozen section examination. If it was malignant, excision by Moths surgery). Using free palate mucosa autograft in stage I or reconstruction by Hughes surgery combined with eye flaps repaired eyelid defects.<p>RESULTS: The postoperative pathological diagnosis: 52 cases were benign tumors, and 40 cases malignant tumors. All cases of eye flaps and hard palate mucosa grafts were survived. Followed up for more than 6mo, no tumor were recurred. The appearance and function of eyelid were satisfactory.<p>CONCLUSION: In this group of cases, nearly half of eyelid tumors are malignant tumors. It should be treated and operated as early as possible. For suspected malignant tumors, we use frozen section examination to confirm its properties in order to excision cleanly in stage Ⅰ, reducing the recurrence and metastasis. According to the eyelid defect after resection, we could do repair operation in stage Ⅰ. The inner larger defect is repaired by using hard palate mucosa transplantation or Hughes surgery. The outer layer of the eyelid defect is repaired by using eye flap glide, the free flap, the kite flap, the simple suture, <i>etc</i>. It should be careful when using the hard palate mucosa transplantation in the upper eyelid defect

Luttinger-volume violating Fermi liquid in the pseudogap phase of the cuprate superconductors

Based on the NMR measurements on Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ (La-Bi2201) in strong magnetic fields, we identify the non-superconducting pseudogap phase in the cuprates as a Luttinger-volume violating Fermi liquid (LvvFL). This state is a zero temperature quantum liquid that does not break translational symmetry, and yet, the Fermi surface encloses a volume smaller than the large one given by the Luttinger theorem. The particle number enclosed by the small Fermi surface in the LvvFL equals the doping level $p$, not the total electron number $n_e=1-p$. Both the phase string theory and the dopon theory are introduced to describe the LvvFL. For the dopon theory, we can obtain a semi-quantitative agreement with the NMR experiments.Comment: The final version in PR

Light anti-nuclei production in pp collisions at s\sqrt{s}=7 and 14 TeV

A dynamically constrained coalescence model based on the phase space quantization and classical limit method was proposed to investigate the production of light nuclei (anti-nuclei) in non-single diffractive (NSD) pp collisions at $\sqrt{s}$=7 and 14 TeV. This calculation was based on the final hadronic state in the PYTHIA and PACIAE model simulations, the event sample consisted of 1.2$\times 10^8$ events in both simulations. The PACIAE model calculated $\bar D$ yield of 6.247$\times 10^{-5}$ in NSD pp collisions at $\sqrt{s}$=7 TeV is well comparing with the ALICE rough datum of 5.456$\times 10^{-5}$. It indicated the reliability of proposed method in some extent. The yield, transverse momentum distribution, and rapidity distribution of the $\bar D$, $^3{\bar{He}}$, and $_{\bar\Lambda} ^3{\bar H}$ in NSD pp collisions at $\sqrt{s}$=7 and 14 TeV were predicted by PACIAE and PYTHIA model simulations. The yield resulted from PACIAE model simulations is larger than the one from PYTHIA model. This might reflect the role played by the parton and hadron rescatterings.Comment: 5 pages, 2 figure