BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and sev...BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.展开更多
The purpose of this review is to provide a definitive account of small intestinal mucosal structure and interpretation. The coeliac lesion has been well known, but not well described to date and this review aims to id...The purpose of this review is to provide a definitive account of small intestinal mucosal structure and interpretation. The coeliac lesion has been well known, but not well described to date and this review aims to identify the interpretative difficulties which have arisen over time with the histological assessment of coeliac disease. In early coeliac interpretation, there were significant inaccuracies, particularly surrounding intraepithelial lymphocyte counts and the degree of villous flattening which occurred in the tissue. Many of these interpretive pitfalls are still encountered today, increasing the potential for diagnostic errors. These difficulties are mostly due to the fact that stained 2-dimensional sections can never truly represent the 3-dimensional framework of the intestinal tissue under investigation. Therefore, this review offers a critical account occasioned by these 2-dimensional interpretative errors and which, in our opinion, should in general be jettisoned. As a result, we leave a framework regarding the true 3-dimensional knowledge of mucosal structure accrued over the 70-year period of study, and one which is available for future reference.展开更多
In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient condit...In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.展开更多
Marijuana use as well as abuse is a significant public health and public safety concern in the United States and using hair to identify marijuana users and abusers has been gaining acceptance in a number of venues inc...Marijuana use as well as abuse is a significant public health and public safety concern in the United States and using hair to identify marijuana users and abusers has been gaining acceptance in a number of venues including workplace, court ordered, and substance abuse treatment monitoring. After the presentation of a fully validated 2-dimensional gas chromatography-tandem mass spectrometry method for the detection of 11-nor-9-carboxy-Δ9-tetrahydrocannabinol (THCA), the chief metabolite of the main psychoactive compound in marijuana, Δ9-tetrahydrocannabinol (THC), we evaluated the usefulness of fingernail clippings as an alternative specimen type to hair by the analysis of a set of 60 matched pairs of head hair and fingernail clippings. The limit of detection was 10 fg/mg, the limit of quantitation was 20 fg/mg, and the assay was linear from 20 fg/mg to 500 fg/mg. The intra- and inter-assay imprecision and bias studies at 4 different concentrations (50, 100, 500, and 1000 fg/mg) were acceptable where all % Target observations were within 16% of their expected concentrations and all %CV calculations were less than 13.5%. THCA was detectable in more fingernail specimens (53.3%) than hair specimens (46.7%) and the mean concentrations in nails were on average 4.9 times higher than in hair (1813 fg/mg and 364 fg/mg, respectively). The THCA concentrations in hair and nail were strongly associated (r = 0.974, P < 0.01, n = 60) and the association was significant. The study demonstrated that fingernail clippings are a suitable alternative specimen type to hair to monitor for marijuana use and abuse.展开更多
Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amor...Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amorphous 2-dimensional barcode is presented in this paper.The barcode uses encoding graph units to encode data.There are two key points in a 2-dimensional barcode:One is the encoding graph unit,the other is its encoding rules.Because encoding graph units of a 2-dimensional barcode are surrounded by other graphics,the units should be self-positioned and distinguished from other units.This paper presents an encoding graph unit generation algorithm,which is based on genetic algorithms.Encoding rules of the barcode are also given in this paper.Those rules include data encoding rules and encoding graph unit sequence arrangement rules.Data encoding rules are used to encode data to an encoding graph unit sequence.Encoding graph unit sequence arrangement rules are used to embed the unit sequence in the target picture.In addition to those rules,it also discussed the steps to restore encoding graph unit sequence from a picture.In the experiments section of this paper,an example is provided to encode a string and embed it in a car ad picture by the barcode.According to encoding rules of the barcode,those encoding graphic units can be scattered and embedded in a picture with other graphics,so amorphous 2-dimensional barcode has no fixed shape.Take advantage of this,designer can present a more elegant design to lay out barcodes with other graphic elements.展开更多
The elastic and functional coupling of heart and vessels makes the stroke work (SW) of the heart optimal. Speckle tracking imaging (STI) can evaluate the myocardial strain and function. We studied ventricular-vasc...The elastic and functional coupling of heart and vessels makes the stroke work (SW) of the heart optimal. Speckle tracking imaging (STI) can evaluate the myocardial strain and function. We studied ventricular-vascular coupling in 80 diabetic patients with different systolic function using STI. The patients were divided into two groups according to ejection fraction (EF): the diabetes mel- litus with normal EF (DMN) group and the diabetes mellitus with abnormal EF (DMA) group. Forty-two volunteers served as control group. The relative wall thickness (RWT), left ventricular mass index (LVMI), stroke volume (SV), SW, rate-pressure product (RPP), systemic vascular resis- tance index (SVRI), left ventricular end-systolic elastance (Ees), effective arterial elasticity (Ea) and ventricular-vascular coupling index (VVI) were measured and calculated by conventional echocardi- ography. The longitudinal strain (LS) at basement (LSBA), papillary muscle (LSvM) and cardiac apex (LSAv) was assessed with STI. It was found: (A) compared with control group, in DMN and DMA groups, LSBA, LSvM and LSAp decreased, and they were lower in DMA group. (B) VVI, RPP and SVRI increased, and they were higher in DMN group; Ees decreased, and it was lower in DMA group. (C) LSBA, LSpM, and LSAv had negative correlation with VVI. LSAp, RWT, LVMI and SW were independent predictors for VVI. The area under the receiver operating characteristic (ROC) curves was used for identification of DMA and DMN with LSBA, LSpM, and LSAp, and the area under the ROC of LSAp was the largest. This study supports that myocardial LS could reflect the ventricu- lar-vascular coupling. Different segments had an order to “respond to” the state of the coupling, and the cardiac apex might be the earliest.展开更多
Several 2-D displacement sensing methods are reviewed. As to the crossdiffraction grating, there is no absolute zero-reference. In regards to the optical fiber method,the output signal is affected greatly by the quali...Several 2-D displacement sensing methods are reviewed. As to the crossdiffraction grating, there is no absolute zero-reference. In regards to the optical fiber method,the output signal is affected greatly by the quality of the reflecting surface and it is hard to gethigh resolution. Considering the concentric-circle gratings, the displacement can only be gainedwith complicated calculating of the experiment data. Compared with the advantages and limitations ofthe methods above, a novel 2-D zero-reference mark is especially proposed and demonstrated. Thiskind of mark has an absolute zero-reference when used in pair, and the experimental result is simpleto dispose. By superimposing a pair of specially coded 2-D marks, the correct alignment position ofthe two marks can be detected by the maximum output of the sharp intensity peak. And each slope ofthe peak is of good linearity which can be used to achieve high resolution in positioning andalignment in two dimensions. Design and fabrication of such 2-D zero-reference marks are introducedin detail. The experiment results are agreed with the theoretical ones.展开更多
A new silicon micro flow sensor with multiple temperature sensing elements was proposed and numerically simulated in considering wide range flow measuring properties.The micro flow sensor has three pairs of temperatur...A new silicon micro flow sensor with multiple temperature sensing elements was proposed and numerically simulated in considering wide range flow measuring properties.The micro flow sensor has three pairs of temperature sensing elements with a central heater compared with typical sensor which has only a temperature sensing element on each side of a central heater.A numerical analysis of the micro flow sensor by Finite Difference Formulation for Heat Transfer Equation was performed.The nearest pair of temperature sensor showed very good linear sensitivity between 0 to 0.4m/s flow and saturated from 0.75m/s flow.However the furthest pair of temperature sensor showed some flow sensitivity even though the flow rate of 2.0m/s.Thus,this suggested new micro flow meter with multiple temperature sensing elements could be used as a thermal mass flow sensor which has accuracy sensitivity for very wide flow range.展开更多
We analyzed the SU(2)×SU(2)chiral model with mixed fundamental-adjoint action on the 2-dimensional(2-D)random lattice by using Monte-Carlo(M-C)simulation.The results sluw that the model behaves like the mixed SU(...We analyzed the SU(2)×SU(2)chiral model with mixed fundamental-adjoint action on the 2-dimensional(2-D)random lattice by using Monte-Carlo(M-C)simulation.The results sluw that the model behaves like the mixed SU(2)×SU(2)chiral model on the 2-D regular lattice,but the character of the phase transition seems to be different.展开更多
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ...This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.展开更多
Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamic...Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.展开更多
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ...For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.展开更多
The inherent catalytic anisotropy of two-dimensional(2D) materials has limited the enhancement of LiO_(2) batteries(LOBs) performance due to the significantly different adsorption energies on 2D and edge surfaces.Tuni...The inherent catalytic anisotropy of two-dimensional(2D) materials has limited the enhancement of LiO_(2) batteries(LOBs) performance due to the significantly different adsorption energies on 2D and edge surfaces.Tuning the adsorption strength in 2D materials to the reaction intermediates is essential for achieving high-performance LOBs.Herein,a MnS/MoS_(2) heterostructure is designed as a cathode catalyst by adjusting the adsorption behavior at the surface.Different from the toroidal-like discharge products on the MoS_(2) cathode,the MnS/MoS_(2) surface displays an improved adsorption energy to reaction species,thereby promoting the growth of the film-like discharge products.MnS can disturb the layer growth of MoS_(2),in which the stack edge plane features a strong interaction with the intermediates and limits the growth of the discharge products.Experimental and theoretical results confirm that the MnS/MoS_(2) heterostructure possesses improved electron transfer kinetics at the interface and plays an important role in the adsorption process for reaction species,which finally affects the morphology of Li_2O_(2),In consequence,the MnS/MoS_(2) heterostructure exhibits a high specific capacity of 11696.0 mA h g^(-1) and good cycle stability over 1800 h with a fixed specific capacity of 600 mA h g^(-1) at current density of100 mA g^(-1) This work provides a novel interfacial engineering strategy to enhance the performance of LOBs by tuning the adsorption properties of 2D materials.展开更多
The two-dimensional(2D)Janus monolayers are promising in spintronic device application due to their enhanced magnetic couplings and Curie temperatures.Van der Waals CrCl_(3) monolayer has been experimentally proved to...The two-dimensional(2D)Janus monolayers are promising in spintronic device application due to their enhanced magnetic couplings and Curie temperatures.Van der Waals CrCl_(3) monolayer has been experimentally proved to have an in-plane magnetic easy axis and a low Curie temperature of 17 K,which will limit its application in spintronic devices.In this work,we propose a new Janus monolayer Cr_(2)Cl_(3)S_(3) based on the first principles calculations.The phonon dispersion and elastic constants confirm that Janus monolayer Cr_(2)Cl_(3)S_(3) is dynamically and mechanically stable.Our Monte Carlo simulation results based on magnetic exchange constants reveal that Janus monolayer Cr_(2)Cl_(3)S_(3) is an intrinsic ferromagnetic semiconductor with TC of 180 K,which is much higher than that of CrCl_(3) due to the enhanced ferromagnetic coupling caused by S substitution.Moreover,the magnetic easy axis of Janus Cr_(2)Cl_(3)S_(3) can be tuned to the perpendicular direction with a large magnetic anisotropy energy(MAE)of 142eV/Cr.Furthermore,the effect of biaxial strain on the magnetic property of Janus monolayer Cr_(2)Cl_(3)S_(3) is evaluated.It is found that the Curie temperature is more robust under tensile strain.This work indicates that the Janus monolayer Cr_(2)Cl_(3)S_(3) presents increased Curie temperature and out-of-plane magnetic easy axis,suggesting greater application potential in 2D spintronic devices.展开更多
The catalytic descriptor with operational feasibility is highly desired towards rational design of high-performance catalyst especially the electrode/electrolyte solution interface working under mild conditions.Herein...The catalytic descriptor with operational feasibility is highly desired towards rational design of high-performance catalyst especially the electrode/electrolyte solution interface working under mild conditions.Herein,we demonstrate that the descriptorΩparameterized by readily accessible intrinsic properties of metal center and coordination is highly operational and efficient in rational design of single-atom catalyst(SAC)for driving electrochemical nitrogen reduction(NRR).Using twodimensional metal(M)-B_(x)P_(y)S_(z)N_m@C_(2)N as prototype SAC models,we reveal that^(*)N_(2)+(H~++e~-)→^(*)N_(2)H acts predominantly as the potential-limiting step(PLS)of NRR on M-B_(2)P_(2)S_(2)@C_(2)N and M-B_(1)P_(1)S_(1)N_(3)@C_(2)N regardless of the distinction in coordination microenvironment.Among the 28 screened M active sites,withΩvalues close to the optimal 4,M-B_(2)P_(2)S_(2)@C_(2)N(M=V(Ω=3.53),Mo(Ω=5.12),and W(Ω=3.92))and M-B_(1)P_(1)S_(1)N_(3)@C_(2)N(M=V(Ω=3.00),Mo(Ω=4.34),and W(Ω=3.32))yield the lowered limiting potential(U_(L))as-0.45,-0.54.-0.36,-0.58,-0.25,and-0.24 V,respectively,thus making them the promising NRR catalysts.More importantly,these SACs are located around the top of volcano-shape plot of U_(L) versusΩ,re-validatingΩas an effective descriptor for accurately predicting the high-activity NRR SACs even with complex coordination.Our study unravels the relationship between active-site structure and NRR performance via the descriptorΩ,which can be applied to other important sustainable electrocatalytic reactions involving activation of small molecules viaσ-donation andπ^(*)-backdonation mechanism.展开更多
Estimated ocean subsurface fields derived from satellite observations provide potential data sources for operational marine environmental monitoring and prediction systems.This study employs a statistic regression rec...Estimated ocean subsurface fields derived from satellite observations provide potential data sources for operational marine environmental monitoring and prediction systems.This study employs a statistic regression reconstruction method,in combination with domestic autonomous sea surface height and sea surface temperature observations from the Haiyang-2(HY-2)satellite fusion data,to establish an operational quasi-realtime three-dimensional(3D)temperature and salinity products over the Maritime Silk Road.These products feature a daily temporal resolution and a spatial resolution of 0.25°×0.25°and exhibit stability and continuity.We have demonstrated the accuracy of the reconstructed thermohaline fields in capturing the 3D thermohaline variations through comprehensive statistical evaluations,after comparing them against Argo observations and ocean analysis data from 2022.The results illustrate that the reconstructed fields effectively represent seasonal variations in oceanic subsurface structures,along with structural changes resulting from mesoscale processes,and the upper ocean’s responses to tropical cyclones.Furthermore,the incorporation of HY-2 satellite observations notably enhances the accuracy of temperature and salinity reconstructions in the Northwest Pacific Ocean and marginally improves salinity reconstruction accuracy in the North Indian Ocean when compared to the World Ocean Atlas 2018 monthly climatology thermohaline fields.As a result,the reconstructed product holds promise for providing quasi-real-time 3D temperature and salinity field information to facilitate fast decisionmaking during emergencies,and also offers foundational thermohaline fields for operational ocean reanalysis and forecasting systems.These contributions enhance the safety and stability of ocean subsurface activities and navigation.展开更多
Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-di...Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-dimensional layered ternary indium phosphorus sulfide(In_(2)P_(3)S_(9)) nanosheets are prepared.The layered structure and ternary composition of the In_(2)P_(3)S_(9) electrode result in impressive electrochemical performance,including a high reversible capacity of 704 mA h g^(-1) at 0.1 A g^(-1),an outstanding rate capability with 425 mA h g^(-1) at 5 A g^(-1),and an exceptional cycling stability with a capacity retention of88% after 350 cycles at 1 A g^(-1).Furthermore,sodium-ion full cell also affords a high capacity of 308 and114 mA h g^(-1) at 0.1 and 5 A g^(-1).Ex-situ X-ray diffraction and ex-situ high-resolution transmission electron microscopy tests are conducted to investigate the underlying Na-storage mechanism of In_(2)P_(3)S_(9).The results reveal that during the first cycle,the P-S bond is broken to form the elemental P and In_(2)S_(3),collectively contributing to a remarkably high reversible specific capacity.The excellent electrochemical energy storage results corroborate the practical application potential of In_(2)P_(3)S_(9) for sodium-ion batteries.展开更多
High-capacity nickel-rich layered oxides are promising cathode materials for high-energy-density lithium batteries.However,the poor structural stability and severe side reactions at the electrode/electrolyte interface...High-capacity nickel-rich layered oxides are promising cathode materials for high-energy-density lithium batteries.However,the poor structural stability and severe side reactions at the electrode/electrolyte interface result in unsatisfactory cycle performance.Herein,the thin layer of two-dimensional(2D)graphitic carbon-nitride(g-C_(3)N_(4))is uniformly coated on the LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)(denoted as NCM811@CN)using a facile chemical vaporization-assisted synthesis method.As an ideal protective layer,the g-C_(3)N_(4)layer effectively avoids direct contact between the NCM811 cathode and the electrolyte,preventing harmful side reactions and inhibiting secondary crystal cracking.Moreover,the unique nanopore structure and abundant nitrogen vacancy edges in g-C_(3)N_(4)facilitate the adsorption and diffusion of lithium ions,which enhances the lithium deintercalation/intercalation kinetics of the NCM811 cathode.As a result,the NCM811@CN-3wt%cathode exhibits 161.3 mAh g^(−1)and capacity retention of 84.6%at 0.5 C and 55°C after 400 cycles and 95.7 mAh g^(−1)at 10 C,which is greatly superior to the uncoated NCM811(i.e.129.3 mAh g^(−1)and capacity retention of 67.4%at 0.5 C and 55°C after 220 cycles and 28.8 mAh g^(−1)at 10 C).The improved cycle performance of the NCM811@CN-3wt%cathode is also applicable to solid–liquid-hybrid cells composed of PVDF:LLZTO electrolyte membranes,which show 163.8 mAh g^(−1)and the capacity retention of 88.1%at 0.1 C and 30°C after 200 cycles and 95.3 mAh g^(−1)at 1 C.展开更多
Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmet...Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.展开更多
When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, ...When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.展开更多
基金supported by a grant from the Shanghai Municipal Health Bureau(No.054041)
文摘BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.
文摘The purpose of this review is to provide a definitive account of small intestinal mucosal structure and interpretation. The coeliac lesion has been well known, but not well described to date and this review aims to identify the interpretative difficulties which have arisen over time with the histological assessment of coeliac disease. In early coeliac interpretation, there were significant inaccuracies, particularly surrounding intraepithelial lymphocyte counts and the degree of villous flattening which occurred in the tissue. Many of these interpretive pitfalls are still encountered today, increasing the potential for diagnostic errors. These difficulties are mostly due to the fact that stained 2-dimensional sections can never truly represent the 3-dimensional framework of the intestinal tissue under investigation. Therefore, this review offers a critical account occasioned by these 2-dimensional interpretative errors and which, in our opinion, should in general be jettisoned. As a result, we leave a framework regarding the true 3-dimensional knowledge of mucosal structure accrued over the 70-year period of study, and one which is available for future reference.
文摘In this paper, we obtain the strong law of large numbers for a 2-dimensional array of pairwise negatively dependent random variables which are not required to be identically distributed. We found the sufficient conditions of strong law of large numbers for the difference of random variables which independent and identically distributed conditions are regarded. In this study, we consider the limit as which is stronger than the limit as m× n→?∞ when m, n →?∞?are natural numbers.
文摘Marijuana use as well as abuse is a significant public health and public safety concern in the United States and using hair to identify marijuana users and abusers has been gaining acceptance in a number of venues including workplace, court ordered, and substance abuse treatment monitoring. After the presentation of a fully validated 2-dimensional gas chromatography-tandem mass spectrometry method for the detection of 11-nor-9-carboxy-Δ9-tetrahydrocannabinol (THCA), the chief metabolite of the main psychoactive compound in marijuana, Δ9-tetrahydrocannabinol (THC), we evaluated the usefulness of fingernail clippings as an alternative specimen type to hair by the analysis of a set of 60 matched pairs of head hair and fingernail clippings. The limit of detection was 10 fg/mg, the limit of quantitation was 20 fg/mg, and the assay was linear from 20 fg/mg to 500 fg/mg. The intra- and inter-assay imprecision and bias studies at 4 different concentrations (50, 100, 500, and 1000 fg/mg) were acceptable where all % Target observations were within 16% of their expected concentrations and all %CV calculations were less than 13.5%. THCA was detectable in more fingernail specimens (53.3%) than hair specimens (46.7%) and the mean concentrations in nails were on average 4.9 times higher than in hair (1813 fg/mg and 364 fg/mg, respectively). The THCA concentrations in hair and nail were strongly associated (r = 0.974, P < 0.01, n = 60) and the association was significant. The study demonstrated that fingernail clippings are a suitable alternative specimen type to hair to monitor for marijuana use and abuse.
基金This work was funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amorphous 2-dimensional barcode is presented in this paper.The barcode uses encoding graph units to encode data.There are two key points in a 2-dimensional barcode:One is the encoding graph unit,the other is its encoding rules.Because encoding graph units of a 2-dimensional barcode are surrounded by other graphics,the units should be self-positioned and distinguished from other units.This paper presents an encoding graph unit generation algorithm,which is based on genetic algorithms.Encoding rules of the barcode are also given in this paper.Those rules include data encoding rules and encoding graph unit sequence arrangement rules.Data encoding rules are used to encode data to an encoding graph unit sequence.Encoding graph unit sequence arrangement rules are used to embed the unit sequence in the target picture.In addition to those rules,it also discussed the steps to restore encoding graph unit sequence from a picture.In the experiments section of this paper,an example is provided to encode a string and embed it in a car ad picture by the barcode.According to encoding rules of the barcode,those encoding graphic units can be scattered and embedded in a picture with other graphics,so amorphous 2-dimensional barcode has no fixed shape.Take advantage of this,designer can present a more elegant design to lay out barcodes with other graphic elements.
基金supported by a grant from the Shanghai Health and Family Planning Commission,China(No.201440290)
文摘The elastic and functional coupling of heart and vessels makes the stroke work (SW) of the heart optimal. Speckle tracking imaging (STI) can evaluate the myocardial strain and function. We studied ventricular-vascular coupling in 80 diabetic patients with different systolic function using STI. The patients were divided into two groups according to ejection fraction (EF): the diabetes mel- litus with normal EF (DMN) group and the diabetes mellitus with abnormal EF (DMA) group. Forty-two volunteers served as control group. The relative wall thickness (RWT), left ventricular mass index (LVMI), stroke volume (SV), SW, rate-pressure product (RPP), systemic vascular resis- tance index (SVRI), left ventricular end-systolic elastance (Ees), effective arterial elasticity (Ea) and ventricular-vascular coupling index (VVI) were measured and calculated by conventional echocardi- ography. The longitudinal strain (LS) at basement (LSBA), papillary muscle (LSvM) and cardiac apex (LSAv) was assessed with STI. It was found: (A) compared with control group, in DMN and DMA groups, LSBA, LSvM and LSAp decreased, and they were lower in DMA group. (B) VVI, RPP and SVRI increased, and they were higher in DMN group; Ees decreased, and it was lower in DMA group. (C) LSBA, LSpM, and LSAv had negative correlation with VVI. LSAp, RWT, LVMI and SW were independent predictors for VVI. The area under the receiver operating characteristic (ROC) curves was used for identification of DMA and DMN with LSBA, LSpM, and LSAp, and the area under the ROC of LSAp was the largest. This study supports that myocardial LS could reflect the ventricu- lar-vascular coupling. Different segments had an order to “respond to” the state of the coupling, and the cardiac apex might be the earliest.
基金This project is supported by National Natural Science Foundation of China(No.50335050, No.50275140)Specialized Research Foundation for Doctoral Program of Higher Education (SRFDP) of China(No. 20030358020).
文摘Several 2-D displacement sensing methods are reviewed. As to the crossdiffraction grating, there is no absolute zero-reference. In regards to the optical fiber method,the output signal is affected greatly by the quality of the reflecting surface and it is hard to gethigh resolution. Considering the concentric-circle gratings, the displacement can only be gainedwith complicated calculating of the experiment data. Compared with the advantages and limitations ofthe methods above, a novel 2-D zero-reference mark is especially proposed and demonstrated. Thiskind of mark has an absolute zero-reference when used in pair, and the experimental result is simpleto dispose. By superimposing a pair of specially coded 2-D marks, the correct alignment position ofthe two marks can be detected by the maximum output of the sharp intensity peak. And each slope ofthe peak is of good linearity which can be used to achieve high resolution in positioning andalignment in two dimensions. Design and fabrication of such 2-D zero-reference marks are introducedin detail. The experiment results are agreed with the theoretical ones.
文摘A new silicon micro flow sensor with multiple temperature sensing elements was proposed and numerically simulated in considering wide range flow measuring properties.The micro flow sensor has three pairs of temperature sensing elements with a central heater compared with typical sensor which has only a temperature sensing element on each side of a central heater.A numerical analysis of the micro flow sensor by Finite Difference Formulation for Heat Transfer Equation was performed.The nearest pair of temperature sensor showed very good linear sensitivity between 0 to 0.4m/s flow and saturated from 0.75m/s flow.However the furthest pair of temperature sensor showed some flow sensitivity even though the flow rate of 2.0m/s.Thus,this suggested new micro flow meter with multiple temperature sensing elements could be used as a thermal mass flow sensor which has accuracy sensitivity for very wide flow range.
文摘We analyzed the SU(2)×SU(2)chiral model with mixed fundamental-adjoint action on the 2-dimensional(2-D)random lattice by using Monte-Carlo(M-C)simulation.The results sluw that the model behaves like the mixed SU(2)×SU(2)chiral model on the 2-D regular lattice,but the character of the phase transition seems to be different.
基金Project supported by the National Natural Science Foundation of China (Grant Nos.12275172 and 11905124)。
文摘This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.
基金Supported by the National Natural Science Foundation of China(12275172)。
文摘Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.
文摘For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.
基金supported by the National Natural Science Foundation of China (52173286, 52207249)Major basic research project of Natural Science Foundation of Shandong Province (ZR2023ZD12)+1 种基金the State Key Laboratory of Marine Resource Utilization in South China Sea (Hainan University) (MRUKF2023013)Open Program of Guangxi Key Laboratory of Information Materials (221024-K)。
文摘The inherent catalytic anisotropy of two-dimensional(2D) materials has limited the enhancement of LiO_(2) batteries(LOBs) performance due to the significantly different adsorption energies on 2D and edge surfaces.Tuning the adsorption strength in 2D materials to the reaction intermediates is essential for achieving high-performance LOBs.Herein,a MnS/MoS_(2) heterostructure is designed as a cathode catalyst by adjusting the adsorption behavior at the surface.Different from the toroidal-like discharge products on the MoS_(2) cathode,the MnS/MoS_(2) surface displays an improved adsorption energy to reaction species,thereby promoting the growth of the film-like discharge products.MnS can disturb the layer growth of MoS_(2),in which the stack edge plane features a strong interaction with the intermediates and limits the growth of the discharge products.Experimental and theoretical results confirm that the MnS/MoS_(2) heterostructure possesses improved electron transfer kinetics at the interface and plays an important role in the adsorption process for reaction species,which finally affects the morphology of Li_2O_(2),In consequence,the MnS/MoS_(2) heterostructure exhibits a high specific capacity of 11696.0 mA h g^(-1) and good cycle stability over 1800 h with a fixed specific capacity of 600 mA h g^(-1) at current density of100 mA g^(-1) This work provides a novel interfacial engineering strategy to enhance the performance of LOBs by tuning the adsorption properties of 2D materials.
基金the National Natural Science Foundation of China(Grant No.12104234)the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BK20210578,20KJB140004,and JSSCBS20210513)+4 种基金Y Pu acknowledges the National Natural Science Foundation of China(Grant Nos.61874060,U1932159,and 61911530220)Jiangsu Specially-Appointed Professor Program,the Natural Science Foundation of Jiangsu Province,China(Grant Nos.BK20181388 and 19KJA180007)the Overseas Researcher Innovation Program of Nanjing,NUPTSF(Grant No.NY217118)F Li Acknowledges the Natural Science Fund for Colleges and Universities in Jiangsu Province,China(Grant No.21KJD140005)the National Natural Science Foundation of China(Grant No.12304085).
文摘The two-dimensional(2D)Janus monolayers are promising in spintronic device application due to their enhanced magnetic couplings and Curie temperatures.Van der Waals CrCl_(3) monolayer has been experimentally proved to have an in-plane magnetic easy axis and a low Curie temperature of 17 K,which will limit its application in spintronic devices.In this work,we propose a new Janus monolayer Cr_(2)Cl_(3)S_(3) based on the first principles calculations.The phonon dispersion and elastic constants confirm that Janus monolayer Cr_(2)Cl_(3)S_(3) is dynamically and mechanically stable.Our Monte Carlo simulation results based on magnetic exchange constants reveal that Janus monolayer Cr_(2)Cl_(3)S_(3) is an intrinsic ferromagnetic semiconductor with TC of 180 K,which is much higher than that of CrCl_(3) due to the enhanced ferromagnetic coupling caused by S substitution.Moreover,the magnetic easy axis of Janus Cr_(2)Cl_(3)S_(3) can be tuned to the perpendicular direction with a large magnetic anisotropy energy(MAE)of 142eV/Cr.Furthermore,the effect of biaxial strain on the magnetic property of Janus monolayer Cr_(2)Cl_(3)S_(3) is evaluated.It is found that the Curie temperature is more robust under tensile strain.This work indicates that the Janus monolayer Cr_(2)Cl_(3)S_(3) presents increased Curie temperature and out-of-plane magnetic easy axis,suggesting greater application potential in 2D spintronic devices.
基金supported by the National Natural Science Foundation of China (21673137)。
文摘The catalytic descriptor with operational feasibility is highly desired towards rational design of high-performance catalyst especially the electrode/electrolyte solution interface working under mild conditions.Herein,we demonstrate that the descriptorΩparameterized by readily accessible intrinsic properties of metal center and coordination is highly operational and efficient in rational design of single-atom catalyst(SAC)for driving electrochemical nitrogen reduction(NRR).Using twodimensional metal(M)-B_(x)P_(y)S_(z)N_m@C_(2)N as prototype SAC models,we reveal that^(*)N_(2)+(H~++e~-)→^(*)N_(2)H acts predominantly as the potential-limiting step(PLS)of NRR on M-B_(2)P_(2)S_(2)@C_(2)N and M-B_(1)P_(1)S_(1)N_(3)@C_(2)N regardless of the distinction in coordination microenvironment.Among the 28 screened M active sites,withΩvalues close to the optimal 4,M-B_(2)P_(2)S_(2)@C_(2)N(M=V(Ω=3.53),Mo(Ω=5.12),and W(Ω=3.92))and M-B_(1)P_(1)S_(1)N_(3)@C_(2)N(M=V(Ω=3.00),Mo(Ω=4.34),and W(Ω=3.32))yield the lowered limiting potential(U_(L))as-0.45,-0.54.-0.36,-0.58,-0.25,and-0.24 V,respectively,thus making them the promising NRR catalysts.More importantly,these SACs are located around the top of volcano-shape plot of U_(L) versusΩ,re-validatingΩas an effective descriptor for accurately predicting the high-activity NRR SACs even with complex coordination.Our study unravels the relationship between active-site structure and NRR performance via the descriptorΩ,which can be applied to other important sustainable electrocatalytic reactions involving activation of small molecules viaσ-donation andπ^(*)-backdonation mechanism.
基金The China-ASEAN Marine Cooperation Foundationthe Fundamental Research Funds for the Central Universities under contract No.B210203041+1 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province under contract No.KYCX23_0657the opening project of the Key Laboratory of Marine Environmental Information Technology of Ministry of Natural Resources under contract No.521037412.
文摘Estimated ocean subsurface fields derived from satellite observations provide potential data sources for operational marine environmental monitoring and prediction systems.This study employs a statistic regression reconstruction method,in combination with domestic autonomous sea surface height and sea surface temperature observations from the Haiyang-2(HY-2)satellite fusion data,to establish an operational quasi-realtime three-dimensional(3D)temperature and salinity products over the Maritime Silk Road.These products feature a daily temporal resolution and a spatial resolution of 0.25°×0.25°and exhibit stability and continuity.We have demonstrated the accuracy of the reconstructed thermohaline fields in capturing the 3D thermohaline variations through comprehensive statistical evaluations,after comparing them against Argo observations and ocean analysis data from 2022.The results illustrate that the reconstructed fields effectively represent seasonal variations in oceanic subsurface structures,along with structural changes resulting from mesoscale processes,and the upper ocean’s responses to tropical cyclones.Furthermore,the incorporation of HY-2 satellite observations notably enhances the accuracy of temperature and salinity reconstructions in the Northwest Pacific Ocean and marginally improves salinity reconstruction accuracy in the North Indian Ocean when compared to the World Ocean Atlas 2018 monthly climatology thermohaline fields.As a result,the reconstructed product holds promise for providing quasi-real-time 3D temperature and salinity field information to facilitate fast decisionmaking during emergencies,and also offers foundational thermohaline fields for operational ocean reanalysis and forecasting systems.These contributions enhance the safety and stability of ocean subsurface activities and navigation.
基金Financial supports from the National Natural Science Foundation of China(22265018 and 21961019)the Key Project of Natural Science Foundation of Jiangxi Province(20232ACB204010)。
文摘Developing reliable and efficient anode materials is essential for the successfully practical application of sodium-ion batteries.Herein,employing a straightforward and rapid chemical vapor deposition technique,two-dimensional layered ternary indium phosphorus sulfide(In_(2)P_(3)S_(9)) nanosheets are prepared.The layered structure and ternary composition of the In_(2)P_(3)S_(9) electrode result in impressive electrochemical performance,including a high reversible capacity of 704 mA h g^(-1) at 0.1 A g^(-1),an outstanding rate capability with 425 mA h g^(-1) at 5 A g^(-1),and an exceptional cycling stability with a capacity retention of88% after 350 cycles at 1 A g^(-1).Furthermore,sodium-ion full cell also affords a high capacity of 308 and114 mA h g^(-1) at 0.1 and 5 A g^(-1).Ex-situ X-ray diffraction and ex-situ high-resolution transmission electron microscopy tests are conducted to investigate the underlying Na-storage mechanism of In_(2)P_(3)S_(9).The results reveal that during the first cycle,the P-S bond is broken to form the elemental P and In_(2)S_(3),collectively contributing to a remarkably high reversible specific capacity.The excellent electrochemical energy storage results corroborate the practical application potential of In_(2)P_(3)S_(9) for sodium-ion batteries.
基金supported by the National Key R&D Program of China(Grant No.2023YFB2503900)the National Natural Science Foundation of China(Grant No.52372203)+1 种基金the National Natural Science Foundation of China(Grant No.52202259)the Shandong Province Natural Science Foundation(ZR2022QE093).
文摘High-capacity nickel-rich layered oxides are promising cathode materials for high-energy-density lithium batteries.However,the poor structural stability and severe side reactions at the electrode/electrolyte interface result in unsatisfactory cycle performance.Herein,the thin layer of two-dimensional(2D)graphitic carbon-nitride(g-C_(3)N_(4))is uniformly coated on the LiNi_(0.8)Co_(0.1)Mn_(0.1)O_(2)(denoted as NCM811@CN)using a facile chemical vaporization-assisted synthesis method.As an ideal protective layer,the g-C_(3)N_(4)layer effectively avoids direct contact between the NCM811 cathode and the electrolyte,preventing harmful side reactions and inhibiting secondary crystal cracking.Moreover,the unique nanopore structure and abundant nitrogen vacancy edges in g-C_(3)N_(4)facilitate the adsorption and diffusion of lithium ions,which enhances the lithium deintercalation/intercalation kinetics of the NCM811 cathode.As a result,the NCM811@CN-3wt%cathode exhibits 161.3 mAh g^(−1)and capacity retention of 84.6%at 0.5 C and 55°C after 400 cycles and 95.7 mAh g^(−1)at 10 C,which is greatly superior to the uncoated NCM811(i.e.129.3 mAh g^(−1)and capacity retention of 67.4%at 0.5 C and 55°C after 220 cycles and 28.8 mAh g^(−1)at 10 C).The improved cycle performance of the NCM811@CN-3wt%cathode is also applicable to solid–liquid-hybrid cells composed of PVDF:LLZTO electrolyte membranes,which show 163.8 mAh g^(−1)and the capacity retention of 88.1%at 0.1 C and 30°C after 200 cycles and 95.3 mAh g^(−1)at 1 C.
基金Supported by the National Natural Science Foundation of China(12001424)the Natural Science Basic Research Program of Shaanxi Province(2021JZ-21)the Fundamental Research Funds for the Central Universities(2020CBLY013)。
文摘Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.
文摘When discovering the potential of canards flying in 4-dimensional slow-fast system with a bifurcation parameter, the key notion “symmetry” plays an important role. It is of one parameter on slow vector field. Then, it should be determined to introduce parameters to all slow/fast vectors. It is, however, there might be no way to explore for another potential in this system, because the geometrical structure is quite different from the system with one parameter. Even in this system, the “symmetry” is also useful to obtain the potentials classified by R. Thom. In this paper, via the coordinates changing, the possible way to explore for the potential will be shown. As it is analyzed on “hyper finite time line”, or done by using “non-standard analysis”, it is called “Hyper Catastrophe”. In the slow-fast system which includes a very small parameter , it is difficult to do precise analysis. Thus, it is useful to get the orbits as a singular limit. When trying to do simulations, it is also faced with difficulty due to singularity. Using very small time intervals corresponding small , we shall overcome the difficulty, because the difference equation on the small time interval adopts the standard differential equation. These small intervals are defined on hyper finite number N, which is nonstandard. As and the intervals are linked to use 1/N, the simulation should be done exactly.