GREEN FUNCTION ON TWO-PHASE SATURATED MEDIUM BY CONCENTRATED FORCE IN TWO-DIMENSIONAL DISPLACEMENT FIELD

The Green function on two-phase saturated medium by concentrated force has a broad and important use In seismology, seismic engineering, soil mechanics, geophysics, dynamic foundation theory and so on. According to the Green function on two-phase saturated medium by concentrated force in three-dimentional displacement field obtained by Ding Bo-yang et al., it gives out the Green function in two-dimensional displacement field by infinite integral method along x(3)-direction derived by De Hoop and Manolis. The method adopted in the thesis is simpler. The result will be simplified to the boundary element method of dynamic problem.

Assessment of Left Atrial Function by Full Volume Real-time Three-dimensional Echocardiography and Left Atrial Tracking in Essential Hypertension Patients with Different Patterns of Left Ventricular Geometric Models

Objective To evaluate left atrial function in essential hypertension patients with different patterns of left ventricular geometric models by real-time three-dimensional echocardiography(RT-3DE)and left atrial tracking(LAT).Methods One hundred and thirty-three patients with essential hypertension were divided into four groups according to criteria proposed by Ganau et al:36 patients in normal pattern group(I),34 patients in concentric remodelling pattern group(II),33 patients in concentric hypertrophy pattern group(III),and 30patients in eccentric hypertrophy pattern group(IV).Thirty-two healthy volunteers were enrolled in this study.RT-3DE and LAT were used to obtain the volume-time and emptying fraction curves,and then the maximal volume,minimal volume,stroke volume,presystolic volume,ejection fraction,systolic filling rate,early diastolic emptying rate and late diastolic emptying rate of the left atrium were measured.Conduit volume and passive emptying volume of the left atrium were calculated.Results Left atrial indexes,conduit volume,passive emptying volume,and early diastolic emptying rate decreased,while the other indices increased in the group I compared with the control group(all P<0.05).Compared with the control group,I and II groups,the left atrial volume parameters manifested change in the group III and group IV(all P<0.01).Left atrial ejection fraction measured by RT-3DE or LAT,and late diastolic emptying rate were lower in the group IV compared with the group III(all P<0.05).There was no difference in left atrial conduit volume,passive emptying volume,and early diastolic left atrial emptying rate between the group II and group I(all P>0.05).There was a positive correlation between RT-3DE and LAT in evaluating left atrial function.Conclusions Left atrial booster pump function decreases in the eccentric hypertrophy pattern.Left atrial conduit function is unchanged in the normal pattern and the concentric remodelling pattern groups.RT-3DE and LAT technology can be used for quantitative evaluation of left atrial volume and function.

Three-dimensional visualization of the functional fascicular groups of a long-segment peripheral nerve

The three-dimensional（3D） visualization of the functional bundles in the peripheral nerve provides direct and detailed intraneural spatial information. It is useful for selecting suitable surgical methods to repair nerve defects and in optimizing the construction of tissue-engineered nerve grafts. However, there remain major technical hurdles in obtaining, registering and interpreting 2D images, as well as in establishing 3D models. Moreover, the 3D models are plagued by poor accuracy and lack of detail and cannot completely reflect the stereoscopic microstructure inside the nerve. To explore and help resolve these key technical problems of 3D reconstruction, in the present study, we designed a novel method based on re-imaging techniques and computer image layer processing technology. A 20-cm ulnar nerve segment from the upper arm of a fresh adult cadaver was used for acetylcholinesterase（ACh E） staining. Then, 2D panoramic images were obtained before and after ACh E staining under the stereomicroscope. Using layer processing techniques in Photoshop, a space transformation method was used to fulfill automatic registration. The contours were outlined, and the 3D rendering of functional fascicular groups in the long-segment ulnar nerve was performed with Amira 4.1 software. The re-imaging technique based on layer processing in Photoshop produced an image that was detailed and accurate. The merging of images was accurate, and the whole procedure was simple and fast. The least square support vector machine was accurate, with an error rate of only 8.25%. The 3D reconstruction directly revealed changes in the fusion of different nerve functional fascicular groups. In conclusion. The technique is fast with satisfactory visual reconstruction.

On Multiplicative Generators of n-Dimensional Overlap Functions

In this paper, inspired by the multiplicative generators of overlap functions, we mainly propose the concepts of multiplicative generator pairs of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We present the condition under which the pair (g, h) can multiplicatively generate an n-dimensional overlap function Og,h. we focus on the homogeneity and idempotency property on multiplicatively generated n-dimensional overlap functions.

TIME-HARMONIC DYNAMIC GREEN'S FUNCTIONS FOR ONE-DIMENSIONAL HEXAGONAL QUASICRYSTALS

Quasicrystals have additional phason degrees of freedom not found in conventional crystals. In this paper, we present an exact solution for time-harmonic dynamic Green＇s function of one-dimensional hexagonal quasicrystals with the Laue classes 6/mh and 6/mhmm. Through the introduction of two new functions φ and ψ, the original problem is reduced to the determination of Green＇s functions for two independent Helmholtz equations. The explicit expressions of displacement and stress fields are presented and their asymptotic behaviors are discussed. The static Green＇s function can be obtained by letting the circular frequency approach zero.

Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals

Two-dimensional function photonic crystals, in which the dielectric constants of medium columns are the functions of space coordinates , are proposed and studied numerically. The band gaps structures of the photonic crystals for TE and TM waves are different from the two-dimensional conventional photonic crystals. Some absolute band gaps and semiDirac points are found. When the medium column radius and the function form of the dielectric constant are modulated, the numbers, width, and position of band gaps are changed, and the semi-Dirac point can either occur or disappear. Therefore,the special band gaps structures and semi-Dirac points can be achieved through the modulation on the two-dimensional function photonic crystals. The results will provide a new design method of optical devices based on the two-dimensional function photonic crystals.

The Structure of Reflective Function of Higher Dimensional Differential System

In this article, we discuss the structure of reflective function of the higher dimensional differential systems and apply the results to study the existence of periodic solutions of these systems.

Comment on “Band gaps structure and semi-Dirac point of two-dimensional function photonic crystals” by Si-Qi Zhang et al.

Recently, Zhang et al. （Chin. Phys. B 26 024208 （2017）） investigated the band gap structures and semi-Dirac point of two-dimensional function photonic crystals, and the equations for the plane wave expansion method were induced to obtain the band structures. That report shows the band diagrams with the effects of function coefficient k and medium column ra under TE and TM waves. The proposed results look correct at first glance, but the authors made some mistakes in their report. Thus, the calculated results in their paper are incorrect. According to our calculations, the errors in their report are corrected, and the correct band structures also are presented in this paper.

Three-dimensionally ordered macroporous cross-linked polystyrene incorporating functional group via hydrophilic spacer arm

A versatile and effective method for incorporating functional groups on the pore wall of three-dimensionally ordered macroporous cross-linked polystyrene（3DOM CLPS） by hydrophilic spacer arm has been investigated.The 3DOM CLPS with pore size 865 nm was prepared by sacrifice template method.The hydrophilic spacer arm（polyethylene glycol,molecular weight is 600） was grafted to the 3DOM CLPS via nucleophilic substitution reaction.The other side of active hydroxyl can be further converted into a lot of other functional groups.In this report,the chelating ligand 2-mercaptobenzothiazole（MBZ） group was introduced on the end of the PGE chain to evidence the versatile functionalization approach.The functionalized ordered macroporous materials were characterized by FT-IR,element analyzer,SEM.The results reveal that the pores were successfully bonded with 2-mercaptobenzothiazole groups via hydrophilic spacer arms and the original morphology of ordered macroporous materials were remained after functionalization.The MBZ group density is 0.052 mmol/m^2.The functionalized 3DOM CLPS are expected to application as heavy metal ions adsorbent.

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.

STUDY OF RECOGNITION TECHNIQUE OF RADAR TARGET'S ONE-DIMENSIONAL IMAGES BASED ON RADIAL BASIS FUNCTION NETWORK

This paper studies the problem applying Radial Basis Function Network(RBFN) which is trained by the Recursive Least Square Algorithm(RLSA) to the recognition of one dimensional images of radar targets. The equivalence between the RBFN and the estimate of Parzen window probabilistic density is proved. It is pointed out that the I/O functions in RBFN hidden units can be generalized to general Parzen window probabilistic kernel function or potential function, too. This paper discusses the effects of the shape parameter a in the RBFN and the forgotten factor A in RLSA on the results of the recognition of three kinds of kernel function such as Gaussian, triangle, double-exponential, at the same time, also discusses the relationship between A and the training time in the RBFN.

Evaluation of Right Ventricular Global Longitudinal Function in Patients with Tetralogy of Fallot by Two-dimensional Ultrasound Speckle Tracking Imaging

Quantification of right ventricular(RV)volume and function remains a challenge because of RV complex geometry by conventional echocardiography.The purpose of this study was to assess RV global longitudinal function in patients with tetralogy of Fallot(TOF)by 2-dimensional ultrasound speckle tracking imaging(STI).Thirty-eight patients with TOF were enrolled in this study and divided into child group(n=25)and adult group(n=13)according to age.Thirty-eight age-and sex-matched normal subjects were selected as c...

Assessment of Regional Left Ventricular Myocardial Function in Rats after Acute Occlusion of Left Anterior Descending Artery by Two-dimensional Speckle Tracking Imaging

This study evaluated the change in regional left ventricular myocardial function in rats following acute occlusion of the left anterior descending coronary artery （LAD） by using two-dimensional speckle tracking imaging （2D-STI）. Sixty Wistar rats were randomly divided into two groups, a myocardial infarction （MI） group, in which 50 rats were subjected to LAD occlusion for 30–45 min, and a sham-operated （SHAM） group that contained 10 rats serving as control. Echo-cardiography was performed at baseline and 1, 4 and 8 week（s） after the operation. High frequency two-dimensional images of left ventricular short axis at papillary muscle level were recorded. Peak systolic radial strain （PRS） and circumferential strain （PCS） were measured in the mid-ventricle in short-axis view by using EchoPAC workstation. Left ventricular internal diameter at diastole （LVIDd） and systole （LVIDs）, fractional shortening （FS）, ejection fraction （EF） and left ventricular mass （LVM） were measured by anatomical M-model echocardiography. Infarct size was measured using triphenyl tetrazolium chloride （TTC） staining 1 week and 8 weeks after the operation. Fibrosis of left ventricu-lar myocardium was displayed using Van Gieson staining 1 week after the infarction. In terms of the TTC staining results, the left ventricle fell into three categories： infarcted, peri-infarcted and remote myocardial regions. Compared with those at baseline and in the SHAM group, （1） PRS and PCS in the infarcted, peri-infarcted and remote myocardial regions were significantly decreased in the MI group within 1 week after the operation （P〈0.05） and the low levels lasted 8 weeks; （2） Compared with those at baseline, LVIDd, LVIDs, FS, EF and LVM in the MI group showed no significant dif-ference 1 week after the operation （P〉0.05）. However, LVIDd, LVIDs and LVM were increased sig-nificantly 4 and 8 weeks after the operation （P〈0.05）, and FS and EF were decreased substantially （P〈0.05）. Van Gieson staining showed that fibrosis developed in all the three myocardial regions to varying degrees. It is concluded that 2D-STI is non-invasive and can be used to assess regional func-tion of myocardium with different blood supply in rats following acute occlusion of the LAD, and can be used as a sensitive and reliable means to follow up the process of left ventricular remodeling.

Constructions of <i>n</i>-Dimensional Overlap Functions Based on Bivariate Overlap Functions

In this paper, we firstly introduce some new results on overlap functions and n-dimensional overlap functions. On the other hand, in a previous study, Gómez et al. presented some open problems. One of these open problems is “to search the construction of n-dimensional overlapping functions based on bi-dimensional overlapping functions”. To answer this open problem, in this paper, we mainly introduce one construction method of n-dimensional overlap functions based on bivariate overlap functions. We mainly use the conjunction operator ∧ to construct n-dimensional overlap functions based on bivariate overlap functions and study their basic properties.

The Additive Generators of <i>n</i>-Dimensional Overlap Functions

In this paper, we introduce the concepts of additive generators and additive generator pair of n-dimensional overlap functions, in order to extend the dimensionality of overlap functions from 2 to n. We mainly discuss the conditions under which an n-dimensional overlap function can be expressed in terms of its generator pair.

Assessment of Myocardial Perfusion and Systolic Function in Patients with Coronary Artery Disease after Coronary Artery Bypass Surgery by Myocardial Contrast Echocardiography and Two-dimensional Strain Echocardiography

The clinically applied value of myocardial perfusion and systolic function in patients with coronary artery disease after coronary artery bypass surgery using real-time myocardial contrast echocardiography （RT-MCE） combined with two-dimensional strain echocardiography was assessed. Twenty patients underwent intravenous RT-MCE by intravenous injections of SonoVue before and after coronary artery bypass surgery. Two-dimensional images were recorded from the left ventricular four-chamber view, two-chamber view and the apical view before, and two weeks and three months after coronary artery bypass surgery, and the peak systolic longitudinal strain was measured. The results showed that myocardial perfusion was significantly increased after coronary artery bypass surgery in about 71.6% segments. In the group that myocardial perfusion was improved, the peak systolic longitu- dinal strain three months after bypass surgery was significantly higher than that before operation [（-15.78±5.91）% vs （-10.45±8.31）%, P〈0.05]. However, the parameters did not change in the group without myocardial perfusion improvement [（-10.33±6.53）% vs （-9.41±6.09）%, P〉0.05]. It was concluded that whether or not the improvement of myocardial perfusion can mirror the recovery trend of regional systolic function, two-dimensional strain echocardiography can observe dynamic change of regional systolic function. The combination of myocardial perfusion with two-dimensional strain echocardiography can more accurately assess the curative effectiveness of coronary artery bypass surgery.

THREE-DIMENSIONAL ANALYSIS OF FUNCTIONALLY GRADED PLATE BASED ON THE HAAR WAVELET METHOD

A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied.

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.

Evaluation of the Effect of Sigmoid-Shaped Interventricular Septum on Left Ventricular Systolic Function in Patients with Essential Hypertension by Two-Dimensional Speckle Tracking Echocardiography

Objective: To evaluate left ventricular regional and global systolic function by measuring left ventricular longitudinal strain (LS) in hypertensive patients with sigmoid-shaped interventricular septum (SIS) by two-dimensional speckle tracking (2D-STE);in order to explore whether the sigmoid-shaped interventricular septum affects the left ventricular systolic function in patients with hypertension. Methods: Routine echocardiographic parameters were measured in 30 hypertensive patients with SIS (SIS group) and 30 hypertensive patients without SIS (non-SIS group). The left ventricular segments and global LS were measured by 2D-STE, and the two sets of parameters were compared. Results: The value of the thickness of the basal segment of the interventricular septum (IVSBT), the thickness of the middle segment of the interventricular septum (IVSMT) and the ratio of the basal segment of the ventricular septum to the middle segment of the interventricular septum (IVSBT/IVSMT) in SIS group was higher than that in non-SIS group. However, the value of left ventricular outflow tract diameter (LVOTD) in SIS group was lower than that in non-SIS group. There was a significant difference between the two groups (all P Conclusion: SIS affects left ventricular regional systolic function of patients with hypertension. 2D-STE can early evaluate left ventricular longitudinal systolic function in hypertensive patients with SIS.