The Planck Length and the Constancy of the Speed of Light in Five Dimensional Spacetime Parametrized with Two Time Coordinates

In relativity and quantum field theory, the vacuum speed of light is assumed to be constant;the range of validity of general relativity is determined by the Planck length. However, there has been no convincing theory explaining the constancy of the light speed. In this paper, we assume a five dimensional spacetime with three spatial dimensions and two local time coordinates giving us a hint about the constancy of the speed of light. By decomposing the five dimensional spacetime vector into four-dimensional vectors for each time dimension and by minimizing the resulting action, for a certain class of additional time dimensions, we observe the existence of a minimal length scale, which we identify as the Planck scale. We derive an expression for the speed of light as a function of space and time and observe the constancy of the vacuum speed of light in the observable universe.

REAL-TIME THREE-DIMENSIONAL ECHOCARDIOGRAPHY FOR QUANTIFYING LEFT VENTRICULAR MASS

To test the accuracy of real-time three-dimensional echocardiography (RT3DE) imaging system for evaluating left ventricular mass (LVM) in phantom and excised canine heart. Methods Ten left ventricular (LV) wall phantoms made of two rubber-bursas, ten excised canine hearts underwent RT3DE and two-dimensional echocardiography (2DE). In RT3DE "full volume" imaging, the myocardial volume was mea-sured using 2,4,8, and 16-plane method with the analysis software of RT3DE. Mass was then calculated by multiplying the resulting myocardial volume by specific density of myocardial tissue. In 2DE the masses were measured by area-length meth-od. The true LV wall phantom mass was measured by water displacement and the canine LVM was weighed by anatomy, which served as a reference standard. We compared RT3DE or 2DE with true mass. Results In LV wall phantoms, RT3DE correlated with true masses strongly (r = 0.813-0.994) and weakly correlated between 2DE and true masses (r = 0.628). In excised canine hearts, there is an excellent correlation between RT3DE and true masses (r = 0.764-0.991), while 2DE value showed a lesser correlation (r = 0.514). There are no difference between RT-3DE and true masses (P > 0.05) but different between 2DE and true masses (P < 0.05). In different planes, there was no difference between 8-plane and 16-plane (P > 0.05) but different between 8-plane and 2, 4-plane (P < 0.05). Conclusion RT3DE can accurately quantify LVM and provide a new tool to evaluate LV function. For LVM by RT3DE, 8-plane measurement method is the best choice for accuracy and convenience.

Real-time Three-dimensional Echocardiographic Assessment of Left Ventricular Remodeling Index in Patients with Hypertensive Heart Disease and Coronary Artery Disease

Left ventricular remodeling index （LVRI） was assessed in patients with hypertensive heart disease （HHD） and coronary artery disease （CAD） by real-time three-dimensional echocardiography （RT3DE）. RT3DE data of 18 patients with HHD, 20 patients with CAD and 22 normal controis （NC） were acquired. Left ventricular end-diastolic volume （EDV） and left ventricular end-diastolic epicardial volume （EDVepi） were detected by RT3DE and two-dimensional echocardiography Simpson biplane method （2DE）. LVRI （left ventricular mass/EDV） was calculated and compared. The results showed that LVRI measurements detected by RT3DE and 2DE showed significant differences inter-groups （P〈0.01）. There was no significant difference in NC group （P〉0.05）, but significant difference in HHD and CAD intra-group （P〈0.05）. There was good positive correlations between LVRI detected by RT3DE and 2DE in NC and HHD groups （t=0.69, P〈0.01; r=0.68, P〈0.01）, but no significant correlation in CAD group （r=0.30, P〉0.05）. It was concluded that LVRI derived from RT3DE as a new index for evaluating left ventricular remodeling can provide more superiority to LVRI derived from 2DE.

QUANTITATIVE ASSESSMENT OF MYOCARDIAL PERFUSION DEFECTS WITH REAL-TIME THREE-DIMENSIONAL MYOCARDIAL CONTRAST ECHOCARDIOGRAPHY

Objective To evaluate the feasibility and accuracy of measurement of myocardial perfusion defects with intravenous contrast-enhanced real-time three-dimensional echocardiography (CE-RT3DE). Methods RT3DE was performed in 21 open-chest mongrel dogs undergoing acute ligation of the left anterior descending artery (LAD, n=14) or distal branch of the left circumflex artery (LCX, n=7). A perfluorocarbon microbubble contrast agent was injected intravenously to assess the resulting myocardial perfusion defects with Philips Sonos-7500 ultrasound system. Evans blue dye was injected into the occluded coronary artery for subsequent anatomic identification of underperfused myocardium. In vitro anatomic measurement of myocardial mass after removal of the animal’s heart was regarded as the control. Blinded off-line calculation of left ventricular mass and perfusion defect mass from RT3DE images were performed using an interactive aided-manual tracing technique.Results Total left ventricular (LV) myocardial mass ranged from 38.9 to 78.5 (mean±SD: 60.0±10.1) g. The mass of perfusion defect ranged from 0 to 21.4 (mean±SD: 12.0±5.0) g or 0 to 27% of total LV mass (mean±SD: 19%±6%). The RT3DE estimation of total LV mass (mean±SD: 59.8±9.9 g) strongly correlated with the anatomic measurement (r=0.98; y=2.01+0.96x). The CE-RT3DE calculation of the mass of underperfused myocardium (mean±SD: 12.3±5.3 g) also strongly correlated with the anatomic measurement (r=0.96; y=-0.10+1.04x) and when expressed as percentage of total LV mass (r=0.95; y=-0.20+1.04x). Conclusions RT3DE with myocardial contrast opacification could accurately estimate underperfused myocardial mass in dogs of acute coronary occlusion and would play an important role in quantitative assessment of myocardial perfusion defects in patients with coronary artery disease.

Real-time Three-Dimensional Color Doppler Flow Imaging： An Improved Technique for Quantitative Analysis of Aortic Regurgitation

The recently introduced real-time three-dimensional color Doppler flow imaging （RT-3D CDFI） technique provides a quick and accurate calculation of regurgitant jet volume （RJV） and fraction. In order to evaluate RT-3D CDFI in the noninvasive assessment of aortic RJV and regurgitant jet fraction （RJF） in patients with isolated aortic regurgitation, real-time three-dimensional echocardiographic studies were performed on 23 patients with isolated aortic regurgitation to obtain LV end-diastolic volumes （LVEDV）, end-systolic volumes （LVESV） and RJV, and then RJF could be calculated. The regurgitant volume （RV） and regurgitant fraction （RF） calculated by two-dimensional pulsed Doppler （2D-PD） method served as reference values. The results showed that aortic RJV measured by the RT-3D CDFI method showed a good correlation with the 2D-PD measurements （r= 0.93, Y=0.89X＋ 3.9, SEE= 8.6 mL, P〈0.001 ）; the mean （SD） difference between the two methods was - 1.5 （9.8） mL. % RJF estimated by the RT-3D CDFI method was also correlated well with the values obtained by the 2D-PD method （r=0.88, Y=0.71X＋ 14.8, SEE= 6.4 %, P〈0. 001）; the mean （SD） difference between the two methods was -1.2 （7.9） %. It was suggested that the newly developed RT-3D CDFI technique was feasible in the majority of patients. In patients with eccentric aortic regurgitation, this new modality provides additional information to that obtained from the two-dimensional examination, which overcomes the inherent limitations of two-dimensional echocardiography by depicting the full extent of the jet trajectory. In addition, the RT-3D CDFI method is quick and accurate in calculating RJV and RJF.

Evaluation of Right Ventricular Volume and Systolic Function by Real-time Three-dimensional Echocardiography

The optimal plane for measurement of the right ventricular (RV) volumes by real-time three-dimensional echocardiography (RT3DE) was determined and the feasibility and accuracy of RT3DE in studying RV systolic function was assessed. RV “Full volume” images were acquired by RT3DE in 22 healthy subjects. RV end-diastolic volumes (RVEDV) and end-systolic volumes (RVESV) were outlined using apical biplane, 4-plane, 8-plane, 16-plane offline separately. RVSV and RVEF were calculated. Meanwhile tricuspid annual systolic excursion (TASE) was measured by M-mode echo. LVSV was outlined by 2-D echo according to the biplane Simpson's rule. The results showed: (1) There was a good correlation between RVSV measured from series planes and LVSV from 2-D echo (r=0.73; r=0.69; r=0.63; r=0.66, P<0.25—0.0025); (2) There were significant differences between RVEDV in biplane and those in 4-, 8-, 16-plane (P<0.001). There was also difference between RV volume in 4-plane and that in 8-plane (P<0.05), but there was no significant difference between RV volume in 8-plane and that in 16-plane (P>0.05); (3) Inter-observers and intro-observers variability analysis showed that there were close agreements and relations for RV volumes (r=0.986, P<0.001; r=0.93, P<0.001); (4) There was a significantly positive correlation of TASE to RVSV and RVEF from RT3DE (r=0.83; r=0.90). So RV volume measures with RT3DE are rapid, accurate and reproducible. In view of RV's complex shape, apical 8-plane method is better in clinical use. It may allow early detection of RV systolic function.

Evaluation of Atrial Septal Defect Using Real-time Three-dimensional Echocardiography:Comparison with Surgical Findings

The present study evaluated the application of three dimensional echocardigraphy （3DE） in the diagnosis of atrial septal defect （ASD） and the measurement of its size by 3DE and compared the size with surgical findings. Two-dimensional and real-time three dimensional echocardiography （RT3DE） was performed in 26 patients with atrial septal defect, and the echocardiographic data were compared with the surgical findings. Significant correlation was found between defect diameter by RT3DE and that measured during surgery （r=0.77, P〈0.001）. The defect area changed significantly during cardiac cycle. Percentage change in defect size during cardiac cycle ranged from 6%-70%. Our study showed that the size and morphology of atrial septal defect obtained with RT3DE correlate well with surgical findings. Therefore, RT3DE is a feasible and accurate non-invasive imaging tool for assessment of atrial septal size and dynamic changes.

Quasi-real time inversion method of three-dimensional epicenter coordinate, trigger time, and magnitude based on CORS

This study explores the quasi-real time inversion principle and precision estimation of three-dimensional coordinates of the epicenter, trigger time and magnitude of earthquakes with the aim to improve traditional methods, which are flawed due to missing information or distortion in the seismograph records. The epicenter, trigger time and magnitude from the Lushan earthquake are inverted and analyzed based on high-frequency GNSS data. The inversion results achieved a high precision, which are consistent with the data published by the China Earthquake Administration. Moreover, it has been proven that the inversion method has good theoretical value and excellent application prospects.

Splitting Based Scheme for Three-dimensional MHD with Dual Time Stepping

A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.

Guaranteed Cost Consensus for High-dimensional Multi-agent Systems With Time-varying Delays

Guaranteed cost consensus analysis and design problems for high-dimensional multi-agent systems with time varying delays are investigated. The idea of guaranteed cost con trol is introduced into consensus problems for high-dimensiona multi-agent systems with time-varying delays, where a cos function is defined based on state errors among neighboring agents and control inputs of all the agents. By the state space decomposition approach and the linear matrix inequality(LMI)sufficient conditions for guaranteed cost consensus and consensu alization are given. Moreover, a guaranteed cost upper bound o the cost function is determined. It should be mentioned that these LMI criteria are dependent on the change rate of time delays and the maximum time delay, the guaranteed cost upper bound is only dependent on the maximum time delay but independen of the Laplacian matrix. Finally, numerical simulations are given to demonstrate theoretical results.

Design of Discrete-time Repetitive Control System Based on Two-dimensional Model

This paper presents a novel design method for discrete-time repetitive control systems （RCS） based on two-dimensional （2D） discrete-time model. Firstly, the 2D model of an RCS is established by considering both the control action and the learning action in RCS. Then, through constructing a 2D state feedback controller, the design problem of the RCS is converted to the design problem of a 2D system. Then, using 2D system theory and linear matrix inequality （LMI） method, stability criterion is derived for the system without and with uncertainties, respectively. Parameters of the system can be determined by solving the LMI of the stability criterion. Finally, numerical simulations validate the effectiveness of the proposed method.

Real-time Three-dimensional Echocardiography in Assessment of Congenital Double Orifice Mitral Valve

The application of real-time three-dimensional echocardiography （RT 3DE） in the diagnosis of double orifice mitral valve （DOMV） was explored. Five cases of DOMV were examined by using 2-dimensional echocardiography （2DE） and RT 3DE. The spatial morphology of malformed mitral valve and its change in hemodynamics were observed. DOMV associated with partial atrioventricular septal defect was found in 3 cases （in which 2 cases had cleft mitral valve） and isolated DOMV in 2 cases; and moderate to severe mitral regurgitation was detected in 3 cases, and mild mitral regurgitation in 1, and no regurgitation in 1 case; 1 case had complicated rhumatic heart disease. Three cases were preoperatively discovered by 2DE, while 2 missed （1 case was discovered postoperatively）. Four cases were diagnosed by RT 3DE preoperatively, and 1 case was diagnosed postoperatively （not examined by RT 3DE preoperatively）. It was suggested that RT 3DE is a reliable technique in the diagnosis of DOMV; it permitted comprehensive and noninvasive assessment of mitral valve and may supplement 2D TTE in the assessment of DOMV.

Preliminary Clinical Study of Real-time Three-dimensional Echo-cardiographic Volume-time Curve in Evaluating Left Ventricular Diastolic Function

The volume-time curve change in patients with normal left ventricular （LV） diastolic function and diastolic dysfunction was evaluated by real-time three-dimensional echocardiography （RT3DE）. LV diastolic dysfunction was defined by E＇〈A＇ in pulse-wave tissue Doppler for inter-ventricular septal （IVS） of mitral annulus. In 24 patients with LV diastolic dysfunction, including 12 patients with delayed relaxation （delayed relaxation group） and 12 patients with pseudo-normal function （pseudo-normal group） and 24 normal volunteers （control group）, data of full-volume image were acquired by real-time three-dimensional echocardiography and subjected to volume-time curve analysis. EDV （end-diastolic volume）, ESV （end-systolic volume）, LVEF （left ventricular ejection fraction）, PER （peak ejection rate）, PFR （peak filling rate） from RT3DE were examined in the three groups. Compared to the control group, PFR （diastolic filling index of RT3DE） was significantly reduced in the delayed relaxation group and pseudo-normal group （P〈0.05）. There were no significant differences in EDV, ESV, LVEE PER （P〉0.05）. It is concluded that PFR, as a diastolic filling index of RT3DE, can reflect the early diastolic function and serve as a new non-invasive, quick and accurate tool for clinical assessment of LV diastolic function.

New Exact Traveling Wave Solutions of (2 + 1)-Dimensional Time-Fractional Zoomeron Equation

In this paper, the new mapping approach and the new extended auxiliary equation approach were used to investigate the exact traveling wave solutions of (2 + 1)-dimensional time-fractional Zoomeron equation with the conformable fractional derivative. As a result, the singular soliton solutions, kink and anti-kink soliton solutions, periodic function soliton solutions, Jacobi elliptic function solutions and hyperbolic function solutions of (2 + 1)-dimensional time-fractional Zoomeron equation were obtained. Finally, the 3D and 2D graphs of some solutions were drawn by setting the suitable values of parameters with Maple, and analyze the dynamic behaviors of the solutions.

Two-Dimensional Terahertz Time-Domain Spectroscopy and Its Applications

In this work, we review the developing progress of two-dimensional terahertz time-domain spectroscopy（THz-TDS） and its diverse applications, including analyzing the polarization of THz radiation from a laser-induced plasma source and studying the corresponding physical mechanism, and characterizing the optical properties of crystals, etc.

USING TWO-DIMENSIONAL TIME RESOLVED LIGHT SCATTERING TO STUDY THE CURE REACTION INDUCED PHASE SEPARATION PROCESS OF EPOXY-AMINE-POLYETHERSULFONE BLEND WITH SECONDARY PHASE SEPARATION

The generalized two-dimensional correlation analysis based on time-resolved light scattering patterns （2D TRLS） has been employed to study the phase separation process of an epoxy-amine-polyethersulfone blend in which the secondary phase separation takes place. The results of the 2D TRLS provided more detailed information that was not readily observed in the 1D TRLS patterns. （i） During the first process of phase separation, the sequential order of coarsening in size of the domains among the larger and smaller ones has been reversed between the diffusion regime and the hydrodynamic regime. （ii） The change of the larger domains in size, due to the hydrodynamic flow in the late stage of the first phase separation process, keeps on taking place earlier than that of the new domains appeared in the secondary phase separation process. （iii） During the secondary phase separation process the size growth of the smaller domains takes place earlier than that of the larger ones, probably due to the assumption that the coarsening mode could decrease the interface tension more quickly.

Special Relativity in Three-Dimensional Space-Time Frames

In Newton’s classical physics, space and time are treated as absolute quantities. Space and time are treated as independent quantities and can be discussed sepa-rately. With his theory of relativity, Einstein proved that space and time are de-pendent and must be treated inseparably. Minkowski adopted a four-dimensional space-time frame and indirectly revealed the dependency of space and time by adding a constraint for an event interval. Since space and time are inseparable, a three-dimensional space-time frame can be constructed by embedding time into space to directly show the interdependency of space and time. The formula for time dilation, length contraction, and the Lorenz transformation can be derived from graphs utilizing this new frame. The proposed three-dimensional space-time frame is an alternate frame that can be used to describe motions of objects, and it may improve teaching and learning Special Relativity and provide additional insights into space and time.

Multi-dimensional ambiguity function for subarray-based space-time coding radar

Space-time coding radar has been recently proposed and investigated.It is a radar framework which can perform transmit beamforming at the receiver.However,the range resolution decreases when the number of the transmit element increases.A subarray-based space-time coding(sub-STC)radar is explored to alleviate the range resolution reduction.For the proposed radar configuration,an identical waveform is transmitted and it introduces a small time offset in different subarrays.The multidimensional ambiguity function of sub-STC radar is defined by considering resolutions in multiple domains including the range,Doppler,angle and probing direction.Analyses on properties of the multi-dimensional ambiguity function of the sub-STC radar with regard to the spatial coverage,resolution performance and low sidelobes are also given.Results reveal that the range resolution and low sidelobes performance are improved with the proposed approach.

Two-dimensional gel electrophoresis and surface-enhanced laser desorption ionization-time of flight-mass spectrometry for detection of protein expression profiles in the hippocampus following closed brain injury

Gene expression profile changes in brain regions following traumatic brain injury at the gene level cannot sufficiently elucidate gene expression time, expression amount, protein post-translational processing or modification. Therefore, it is necessary to quantitatively analyze the gene expression profile using proteomic techniques. In the present study, we established a rat model of closed brain injury using Marmarou＇s weight-drop device, and investigated hippocampal differential protein expression using two-dimensional gel electrophoresis and surface-enhanced laser desorption ionization-time of flight-mass spectrometry. A total of 364 protein peaks were detected on weak cation exchange-2 protein chips, including 37 differential protein peaks. 345 protein peaks were detected on immobilized metal affinity capture arrays-Cu, including 12 differential protein peaks Further examination of these differential proteins revealed that glucose-regulated protein and proteasome subunit alpha type 3 expression were significantly upregulated post-injury. These results indicate that brain injury can alter protein expression in the hippocampus, and that glucose-regulated protein and proteasome subunit alpha type 3 are closely associated with the occurrence and development of traumatic brain injury.