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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 system.The homology is an invariant for oriented links up to isotopy by applying a tautological functor on the geometric complex.The homology has also geometric descriptions by introducing the genus generating operations.We prove that Jones Polynomial is equal to a suitable Euler characteristic of the homology groups.As an application,we compute the homology groups of（2,k）-torus knots for every k ∈ N.

关键词： Frobenius system TQFT Khovanov homology

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 S.In 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 betw... 详细信息

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

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

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

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

Exceptional points enhance sensing in silicon micromechanical resonators

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Microsystems & Nanoengineering 2024年第1期10卷 17-25页

作者： Man-Na Zhang lei Dong Li-feng Wang Qing-An Huang Key Laboratory of MEMS of the Ministry of Education Southeast UniversityNanjing 210096China

Exceptional points(EPs)have recently emerged as a new method for engineering the response of open physical systems,that is,systems that interact with the environment.The systems at the EPs exhibit a strong response to a small perturbation.Here,we show a method by which the sensitivity of silicon resonant sensors can be enhanced when operated at EPs.In our experiments,we use a pair of mechanically coupled silicon micromechanical resonators constituting a parity-time(PT)-symmetric dimer.Small perturbations introduced on the mechanically coupled spring cause the frequency to split from the EPs into the PT-symmetric regime without broadening the two spectrum linewidths,and this frequency splitting scales with the square root of the perturbation strength.The overall signal-tonoise ratio is still greatly enhanced,although the measured noise spectral density of the EP sensing scheme has a slight increase comparable to the traditional counterpart.Our results pave the way for resonant sensors with ultrahigh sensitivity.

关键词： resonant symmetric points

Attractor for the Extensible Beam Equation with Nonlocal Weak Damping on Time–Dependent Space

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Acta Mathematica Sinica,English Series 2024年第4期40卷 1115-1126页

作者： chun Xiang ZHAO feng Juan MENG Institute of Applied System Analysis Jiangsu UniversityZhenjiang 212013P.R.China School of Mathematics and Physics Jiangsu University of TechnologyChangzhou 213001P.R.China

In this article,we consider the long-time behavior of extensible beams with nonlocal weak damping:ε(t)u_(tt)+Δ^(2)u-m(‖▽u‖^(2))Δu+‖u_(t)‖^(p_(u_(t)))+f(u)=h,whereε(t)is a decreasing function vanishing at infinity.Within the theory of process on time-dependent spaces,we investigate the existence of the time-dependent attractor by using the Condition(C_(t))method and more detailed estimates.The results obtained essentially improve and complete some previous works.

关键词： Time-dependent attractor extensible beams equation nonlocal weak damping

Honokiol Prevents Intestinal Barrier Dysfunction in Mice with Severe Acute Pancreatitis and Inhibits JAK/STAT1 Pathway and Acetylation of HMGB1

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Chinese Journal of Integrative Medicine 2024年第6期30卷 534-542页

作者： LI Jie CHEN Ya-feng GAO lei LI Yi-jie feng Dian-xu Department of General Surgery Putuo HospitalShanghai University of Traditional Chinese MedicineShanghai200062China

Objective To investigate the effect of honokiol(HON)and the role of high-mobility group protein B1(HMGB1)on the pathogenesis of severe acute pancreatitis(SAP).Methods Thirty mice were numbered according to weight,and randomly divided into 5 groups using a random number table,including control,SAP,SAP and normal saline(SAP+NS),SAP and ethyl pyruvate(SAP+EP),or SAP+HON groups,6 mice in each group.Samples of pancreas,intestine,and blood were collected 12 h after SAP model induction for examination of pathologic changes,immune function alterations by enzyme linked immunosorbent assay(ELISA),and Western blot.In vitro experiments,macrophages were divided into 5 groups,the control,lipopolysaccharide(LPS),LPS+DMSO(DMSO),LPS+anti-HMGB1 monoclonal antibody(mAb),and LPS+HON groups.The tight connection level was determined by transmission electron microscopy and fluorescein isothiocyanate-labeled.The location and acetylation of HMGB1 were measured by Western blot.Finally,pyridone 6 and silencing signal transducer and activator of the transcription 1(siSTAT1)combined with honokiol were added to determine whether the Janus kinase(JAK)/STAT1 participated in the regulation of honokiol on HMGB1.The protein expression levels of HMGB1,JAK,and STAT1 were detected using Western blot.Results Mice with SAP had inflammatory injury in the pancreas,bleeding of intestinal tissues,and cells with disrupted histology.Mice in the SAP+HON group had significantly fewer pathological changes.Mice with SAP also had significant increases in the serum levels of amylase,lipase,HMGB1,tumor necrosis factor-α,interleukin-6,diamine oxidase,endotoxin-1,and procalcitonin.Mice in the SAP+HON group did not show these abnormalities(P<0.01).Studies of Caco-2 cells indicated that LPS increased the levels of occludin and claudin-1 as well as tight junction permeability,decreased the levels of junctional adhesion molecule C,and elevated intercellular permeability(P<0.01).HON treatment blocked these effects.Studies of macrophages indicated that LPS led to low nucle

关键词： severe acute pancreatitis intestinal barrier dysfunction honokiol high-mobility group protein B1 Januskinase signal transducerand activatorof transcription1