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H'-splittings of Seifert Manifolds with Boundary

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Acta Mathematica Sinica,English Series 2023年第4期39卷 695-706页

作者： Yan XU feng chun lei feng Ling LI School of Mathematical Sciences Dalian University of TechnologyDalian 116024P.R.China

It is known that each compact connected orient able 3-manifold M with boundary admits an H’-splitting H1∪FH2,where F is a compact connected orientable surface properly embedded in M and splits M into two handlbodies H_(1) and H_(2).In this paper,we show that a non-completely L-reducible and minimal H’-splitting surface for a compact connected irreducible orientable anannular Seifert 3-manifold with boundary is horizontal,and give a necessary and sufficient condition for an amalgamation of two compact connected orientable 3-manifolds along a compact connected surface to be a Seifert manifold with boundary,and describe a characteristic of some H’-splittings to denote a Seifert 3-manifold with *** a compact connected orientable Seifert manifold M with a semi-bundle structure M_(1)∪_(F)M_(2),we give an upper bound of the genus of the base surface.

关键词： Seifert manifold H'-splitting vertical or horizontal surface amalgamated 3-manifold

SD-splittings for Some Bordered 3-Manifolds

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Acta Mathematica Sinica,English Series 2006年第5期22卷 1481-1484页

作者： feng chun lei Yang LI Department of Mathematics Harbin Institute of Technology Harbin 150001 P. R. China

In the present paper, we characterize the bordered 3-manifolds with genus 1 D-splittings and SD-splittings. We also describe a minimal genus SD-splitting for a handlebody and surface × I.

关键词： handlebody SD-splitting genus of SD-splitting

Some Sufficient Conditions for Tunnel Numbers of Connected Sum of Two Knots Not to Go Down

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Acta Mathematica Sinica,English Series 2011年第11期27卷 2229-2244页

作者： Guo Qiu YANG feng chun lei School of Astronautics Harbin Institute of Technology Harbin 150001 P. R. China Department of Mathematics Harbin Institute of Technology Harbin 150001 P. R. China School of Mathematical Sciences Dalian University of Technology Dalian 116024 P. R. China

In this paper, we show the following result： Let Ki be a knot in a closed orientable 3- manifold Mi such that （Mi,Ki） is not homeomorphic to （S^2 × S^1,x0 × S^1）, i = 1,2. Suppose that the Euler Characteristic of any meridional essential surface in each knot complement E（Ki） is less than the difference of one and twice of the tunnel number of Ki. Then the tunnel number of their connected sum will not go down. If in addition that the distance of any minimal Heegaard splitting of each knot complement is strictly more than 2, then the tunnel number of their connected sum is super additive. We further show that if the distance of a Heegaard splitting of each knot complement is strictly bigger than twice the tunnel number of the knot （twice the sum of the tunnel number of the knot and one, respectively）, then the tunnel number of connected sum of two such knots is additive （super additive, respectively）.

关键词： Tunnel number Heegaard splitting Heegaard distance meridional surface

A Khovanov Type Link Homology with Geometric Interpretation

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Acta Mathematica Sinica,English Series 2016年第4期32卷 393-405页

作者： Mei Li ZHANG feng chun lei School of Mathematical Sciences Dalian University of Technology Department of Basis Dalian Naval Academy

We study a Khovanov type homology close to the original Khovanov homology theory from Frobenius *** homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric *** homology has also geometric descriptions by introducing the genus generating *** prove that Jones Polynomial is equal to a suitable Euler characteristic of the homology *** an application,we compute the homology groups of（2,k）-torus knots for every k ∈ N.

关键词： Frobenius system TQFT Khovanov homology

A Lower Bound for the Heegaard Genera of Annulus Sum

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Journal of Mathematical Research and Exposition 2011年第4期31卷 578-586页

作者： feng Ling LI feng chun lei School of Mathematical Sciences Dalian University of Technology Liaoning 116024 P. R. China

Let Mi, i = 1,2, be a compact orientable 3-manifold, and Ai an incompressible annulus on a component Fi of OMi. Suppose A1 is separating on F1 and A2 is non-separating on F2. Let M be the annulus sum of M1 and M2 along A1 and A2. In the present paper, we give a lower bound for the genus of the annulus sum M in the condition of the Heegaard distances of the submanifolds M1 and M2

关键词： genus distance annulus.

Distance of Edges in the Curve Complex of a Surface

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Journal of Mathematical Research and Exposition 2011年第6期31卷 1092-1096页

作者： Xiu Ying SHI feng chun lei The College of Continuing Education Chifeng UniversityInner Mongolia 024000P.R.China School of Mathematical Sciences Dalian University of TechnologyLiaoning 116024P.R.China

Let S be a closed orientable surface of genus g ≥ 2,and C（S）the curve complex of *** the paper,we introduce the concepts of 2-path between edges in C（S）,which can be regarded as an analogue to the edge path betwe... 详细信息

关键词： curve complex distance of vertices 2-path between edges 2-diameter of C(S).

Spatially Resolved N2（A3Σ＋u, ν=0） Decay Studies in the Pulsed Direct-Current Nitrogen Discharge using the Laser-Induced-Fluorescence Technique

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Chinese Physics Letters 2014年第3期31卷 107-110页

作者： feng chun-lei YANG Hong-Liang GAO Liang DING Hong-bin School of Physics and Optoelectronic Engineering Key Laboratory of Materials Modification by Laser Ion and Electron Beams Dalian University of Technology Dalian 116024

We focus on the investigation of the spatial distribution and temporal evolution of N2（A3Σ＋u, ν=0） in a very early afterglow of a pulsed dc nitrogen discharge. The results indicate that a fast quenching process of N2（A3Σ＋u, ν=0） exists in the very early afterglow. We study the dependence of this fast quenching process on the discharge pressure 20–40 torr. It seems that this fast quenching behavior of N2（A3Σ＋u, ν=0） found in our experiment can be ascribed to the combined action of pooling reaction and collisions with N atoms through N2（A3Σ＋u）＋N2（A3Σ＋u）→ N2＊＋N2（N2＊=N2（B3Πg, C3Πu, C＇3Πu, C＂5Πu）） and N2（A3Σ＋u）＋N（4S）→N（2P）＋N2, respectively. Meanwhile, the decay studies of N2（A3Σ＋u, ν=0） near the anode and cathode infer that the production of N（4S） atoms does not distribute uniformly along the axis of the discharge gap at relatively low pressure, and this effect becomes gradually inconspicuous with the increasing discharge pressure.

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Multiscale observation in wide-spatial radar surveillance based on coherent FDA design

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Science China(Information Sciences) 2024年第2期67卷 232-252页

作者： lei YU feng HE Yi SU College of Electronics Science National University of Defense Technology

Wide-spatial radar surveillance missions are challenging tasks, requiring an increased power budget and agility in transmission aimed at extracting information from multiple targets in different environments. These requirements necessitate high transmitting degrees of freedom(DOF) to achieve the objective of multiscale observation for specific tasks in specialized regions of interest. Herein, we exploit the multiscale observation ability in wide-spatial radar surveillance based on frequency diverse array(FDA)radar. The proposed method facilitates spatial anisotropic control of multiple radar resources, including the transmitting waveforms, beampattern, and bandwidth. By utilizing a coherent FDA radar, we offer principles for the selection of baseband waveforms, in addition to the quantitative design of the beampattern gain and optimal bandwidth from the perspective of detection. The feasibility of the proposed method is validated through numerical experiments, thus indicating the potential in wide-spatial radar surveillance. Moreover,this work can be regarded as a preliminary attempt to gauge the efficacy of the computational array, a novel academic concept.

关键词： multi-scale observation wide-spatial surveillance frequency diverse array (FDA) beampattern synthesis frequency diversity gain computational array

Coupled conditional nonlinear optimal perturbations and their application to ENSO ensemble forecasts

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Science China Earth Sciences 2024年第3期67卷 826-842页

作者： Wansuo DUAN lei HU Rong feng LASG Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China University of Chinese Academy of Sciences Beijing 100049China

Limitations are existed in current ensemble forecasting initial perturbation methods for describing the interactions among various spheres of the Earth system. In this study, a new method is proposed, namely, the coupled conditional nonlinear optimal perturbation(C-CNOP) method, which incorporates multisphere interactions much appropriately. The El Nino-Southern Oscillation(ENSO) is a typical ocean-atmosphere “coupling”(or “interaction”) phenomenon. The C-CNOP method is applied to ensemble forecasting of ENSO. It is demonstrated that the C-CNOP method can generate coupled initial perturbations(CPs) that appropriately consider initial ocean-atmosphere coupling uncertainty for ENSO ensemble forecasts. Results reveal that the CPs effectively improve the ability of ENSO ensemble-mean forecasts in both temporal variability of Nio3.4 sea surface temperature anomalies(SSTAs) and spatial variability of ENSO mature-phase SSTAs. Notably, despite the weakest ocean-atmosphere coupling strength in the tropical Pacific occurring during the boreal spring and summer, CPs still capture the uncertainties of this weak coupling when ENSO predictions are initialized at these seasons. This performance of CPs significantly suppresses the rapid increase of ENSO prediction errors due to the high ocean-atmosphere coupling instability during these seasons, and thus effectively extends the lead time of skillful ENSO forecasting. Hence, the C-CNOP method is a suitable initial perturbation approach for ENSO ensemble forecast that can describe initial ocean-atmosphere coupling uncertainty. It is expected that the CCNOP method plays a significant role in predictions of other high-impact climate phenomena, and even future Earth system predictions.

关键词： Ensemble forecast Multisphere interaction Initial perturbations ENSO