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 of phacoemulsification in patients with previous trabeculectomy

AIM: To observe the clinical effect of transparent corneal incision phacoemulsification in cataract patients who had undergone different kinds of glaucoma filtration surgeries.<p>METHODS: Totally 43 cases(50 eyes), in which 23 patients with primary angle-closure glaucoma(group A, 26 eyes)and 20 patients with primary open angle glaucoma(group B, 24 eyes), all had undergone glaucoma filtration surgery for more than 6 months. Visual acuity, intraocular pressure, slit lamp, gonioscope, corneal endothelial cell counts, <i>etc</i>., were done before surgery.And transparent corneal incision phacoemulsification combined with artificial lens implantation operation were preformed, postoperative follow-up of 3 to 12 months, visual acuity, intraocular pressure, corneal endothelial cell counts and vision field, <i>etc</i>. were observed and recorded.<p>RESULTS: The visual acuity of 50 eyes(100%)increased with different degree postoperatively, 41 eyes(82%)with postoperative visual acuity ≥0.3; average preoperative intraocular pressure: group A 18.08±5.08mmHg(1mmHg=0.133kpa), group B 14.48±3.52mmHg; Postoperative follow-up average intraocular pressure: group A 13.65±3.51mmHg, group B 14.28±3.41 mmHg, intraocular pressure changed significantly pre and post-operation in group A(<i>P</i><0.05), there was no significant difference between pre and post-operation in group B(<i>P</i>>0.05); Postoperative intraocular pressure of 1 eye in group A and 3 eyes in group B rose within three days post-operation, the intraocular pressure fluctuated between 21-33mmHg, with drug therapy and drug withdral when intraocular pressure epistrophy; Intraocular pressure was stable in the follow-up process.Corneal endothelial cell density: pre-operation group A was 2 293.57±352.24(cells/mm²), group B 2 658.14±458.69(cells/mm²), post- operation group A 2 175.95±379.16(cells/mm²), group B 2 442.97±477.30(cells/mm²), cell loss rate: 5.13% in group A, and 8.10% in group B. Postoperative visual acuity was related to vision field damage in patients, the more visual field damage, the longer the duration. <p>CONCLUSION: Visual function restore is stable in transparent corneal incision phacoemulsification in cataract patients who underwent glaucoma filtration surgeries; the intraocular pressure can be controlled effectively, and can further reduce the intraocular pressure of angle-closure glaucoma. Preoperative comprehensive evaluation of the affected eye and appropriate technique selection are benefit to the improvement of operation effect and the reduction of complications

Constraints on running vacuum models with the baryon-to-photon ratio

We study the influence of running vacuum on the baryon-to-photon ratio in running vacuum models (RVMs). When there exists a non-minimal coupling between photons and other matter in the expanding universe, the energy-momentum tensor of photons is no longer conserved, but the energy of photons could remain conserved. We discuss the conditions for the energy conservation of photons in RVMs. The photon number density and baryon number density, from the epoch of photon decoupling to the present day, are obtained in the context of RVMs by assuming that photons and baryons can be coupled to running vacuum, respectively. Both cases lead to a time-evolving baryon-to-photon ratio. However the evolution of the baryon-to-photon ratio is strictly constrained by observations. It is found that if the dynamic term of running vacuum is indeed coupled to photons or baryons, the coefficient of the dynamic term must be extremely small, which is unnatural. Therefore, our study basically rules out the possibility that running vacuum is coupled to photons or baryons in RVMs.Comment: 25 pages, 3 figures, 5 tables, minor correction, references adde