Three-dimensional Spaces of Quasi-constant Curvature

In this paper some properties of three-dimensional spaces of quasi-constant curvature different from those of cases when dimension n≥4 are proved. In particular, two classes of non-conformally flat solutions of them are constructed. In physics,a three-dimensional space of quasi-constant curvature appears as the space-like hypersurface of the rotation-free cosmological model of type D for the fluids with heat flow in General Relativity.

Using"Three-dimensional Space Resources"for Fenlong Technology to Improve Grain Econoloy and Expand Human Living Spaces

Fenlong Technology has been applied to increase yield by 20%-50%,improve quality by 5%,and retain water by 100%in 40 kinds of crop cultivated land and saline-alkali land in 26 provinces of China.This paper clarified for the first time the scientific theory system of Fenlong Technology using three-dimensional space resources"Fenlong Agricultural Nature Theory"and the development of the relative"limits"of agricultural growth,which provides a huge power support and natural force for expanding human living spaces.Through inventing and creating a scientific and technological system of farming tools,farming machinery,farming modes,and magic weapons for cultivation,Fenlong Technology can increase grain,promote ecological development,and greatly expand the living spaces of the Chinese nation and achieve sustainable development.Using Fenlong Technology,China has expanded from the current single"cultivated land agriculture"to the"big pattern agriculture"of Fenlong"cultivated land+saline land+degraded grassland+marginal land+desertified land+river water",flexibly used 147 million ha of"three-dimensional space resources"of land,and the newly increased food,meat,and fish can feed 300 million to 400 million people,increased the water storage by 100 billion m^(3),and reduced the collection of groundwater by 20 million to 60 billion m^(3).

Permeability differences based on three-dimensional geometrical information of void spaces

In this study,the permeabilities of Berea and Otway sandstones were measured under different confining pressures,and porosity was investigated through mercury intrusion porosimetry(MIP).The total porosities of the Berea and Otway sandstones were approximately 17.4%and 25%,respectively.Pore size distributions of each sandstone were almost the same,but the pores in the Otway sandstone were slightly narrower.However,the permeability of the Otway sandstone was smaller than that of the Berea sandstone by one order of magnitude.Three-dimensional(3D)void geometry and geometrical properties of the void spaces relevant to flow were compared to obtain the relation between the permeability differences and porosities of the two sandstones.The 3D geometrical analysis using microfocus X-ray computed tomography(CT)was performed,and the pore geometries of both sandstones were compared using the 3D medial axis(3DMA)method.Pore and throat radii,pore coordination number,tortuosity,number of connecting paths,connecting path volume,and other factors were determined using 3DMA.The Otway sandstone was characterized by a small effective throat/pore radius ratio.Based on the fluid flow mechanism,the lower effective throat/pore radius ratio results in a lower permeability induced by the fluid energy loss,which means that the 3D geometrical shape of void spaces affects the permeability value.

L(Ω,μ) CANNOT ISOMETRICALLY CONTAIN SOME THREE-DIMENSIONAL SUBSPACES OF AM-SPACES

This article presents a novel method to prove that： let E be an AM-space and if dim E ≥ 3, then there does not exist any odd subtractive.isometric mapping from the unit sphere S（E） into S[L（Ω, μ）]. In particular, there does not exist any real linear isometry from E into L（Ω, μ）.

Head Pursuit Variable Structure Guidance Law for Three-dimensional Space Interception

This article aims to develop a head pursuit （HP） guidance law for three-dimensional hypervelocity interception, so that the effect of the perturbation induced by seeker detection can be reduced. On the basis of a novel HP three-dimensional guidance model, a nonlinear variable structure guidance law is presented by using Lyapunov stability theory. The guidance law positions the interceptor ahead of the target on its tlight trajectory, and the speed of the interceptor is required to be lower than that of the target, A numerical example of maneuvering ballistic target interception verifies the rightness of the guidance model and the effectiveness of the proposed method.

A theory for three-dimensional response of micropolar plates

Through combined applications of the transfer-matrix method and asymptotic expansion technique,we formulate a theory to predict the three-dimensional response of micropolar plates.No ad hoc assumptions regarding through-thickness assumptions of the field variables are made,and the governing equations are two-dimensional,with the displacements and microrotations of the mid-plane as the unknowns.Once the deformation of the mid-plane is solved,a three-dimensional micropolar elastic field within the plate is generated,which is exact up to the second order except in the boundary region close to the plate edge.As an illustrative example,the bending of a clamped infinitely long plate caused by a uniformly distributed transverse force is analyzed and discussed in detail.

Three-dimensional visualization technology for guiding one-step percutaneous transhepatic cholangioscopic lithotripsy for the treatment of complex hepatolithiasis

BACKGROUND Biliary stone disease is a highly prevalent condition and a leading cause of hospitalization worldwide.Hepatolithiasis with associated strictures has high residual and recurrence rates after traditional multisession percutaneous transhepatic cholangioscopic lithotripsy(PTCSL).AIM To study one-step PTCSL using the percutaneous transhepatic one-step biliary fistulation(PTOBF)technique guided by three-dimensional(3D)visualization.METHODS This was a retrospective,single-center study analyzing,140 patients who,between October 2016 and October 2023,underwent one-step PTCSL for hepatolithiasis.The patients were divided into two groups:The 3D-PTOBF group and the PTOBF group.Stone clearance on choledochoscopy,complications,and long-term clearance and recurrence rates were assessed.RESULTS Age,total bilirubin,direct bilirubin,Child-Pugh class,and stone location were similar between the 2 groups,but there was a significant difference in bile duct strictures,with biliary strictures more common in the 3D-PTOBF group(P=0.001).The median follow-up time was 55.0(55.0,512.0)days.The immediate stone clearance ratio(88.6%vs 27.1%,P=0.000)and stricture resolution ratio(97.1%vs 78.6%,P=0.001)in the 3D-PTOBF group were significantly greater than those in the PTOBF group.Postoperative complication(8.6%vs 41.4%,P=0.000)and stone recurrence rates(7.1%vs 38.6%,P=0.000)were significantly lower in the 3D-PTOBF group.CONCLUSION Three-dimensional visualization helps make one-step PTCSL a safe,effective,and promising treatment for patients with complicated primary hepatolithiasis.The perioperative and long-term outcomes are satisfactory for patients with complicated primary hepatolithiasis.This minimally invasive method has the potential to be used as a substitute for hepatobiliary surgery.

Oxygen tension modulates cell function in an in vitro three-dimensional glioblastoma tumor model

Hypoxia is a typical feature of the tumor microenvironment,one of the most critical factors affecting cell behavior and tumor progression.However,the lack of tumor models able to precisely emulate natural brain tumor tissue has impeded the study of the effects of hypoxia on the progression and growth of tumor cells.This study reports a three-dimensional(3D)brain tumor model obtained by encapsulating U87MG(U87)cells in a hydrogel containing type I collagen.It also documents the effect of various oxygen concentrations(1%,7%,and 21%)in the culture environment on U87 cell morphology,proliferation,viability,cell cycle,apoptosis rate,and migration.Finally,it compares two-dimensional(2D)and 3D cultures.For comparison purposes,cells cultured in flat culture dishes were used as the control(2D model).Cells cultured in the 3D model proliferated more slowly but had a higher apoptosis rate and proportion of cells in the resting phase(G0 phase)/gap I phase(G1 phase)than those cultured in the 2D model.Besides,the two models yielded significantly different cell morphologies.Finally,hypoxia(e.g.,1%O2)affected cell morphology,slowed cell growth,reduced cell viability,and increased the apoptosis rate in the 3D model.These results indicate that the constructed 3D model is effective for investigating the effects of biological and chemical factors on cell morphology and function,and can be more representative of the tumor microenvironment than 2D culture systems.The developed 3D glioblastoma tumor model is equally applicable to other studies in pharmacology and pathology.

Three-dimensional cell-based strategies for liver regeneration

Liver regeneration and the development of effective therapies for liver failure remain formidable challenges in modern medicine.In recent years,the utilization of 3D cell-based strategies has emerged as a promising approach for addressing these urgent clinical requirements.This review provides a thorough analysis of the application of 3D cell-based approaches to liver regeneration and their potential impact on patients with end-stage liver failure.Here,we discuss various 3D culture models that incorporate hepatocytes and stem cells to restore liver function and ameliorate the consequences of liver failure.Furthermore,we explored the challenges in transitioning these innovative strategies from preclinical studies to clinical applications.The collective insights presented herein highlight the significance of 3D cell-based strategies as a transformative paradigm for liver regeneration and improved patient care.

Three-dimensional stability calculation method for high and large composite slopes formed by mining stope and inner dump in adjacent open pits

The 2D limit equilibrium method is widely used for slope stability analysis.However,with the advancement of dump engineering,composite slopes often exhibit significant 3D mechanical effects.Consequently,it is of significant importance to develop an effective 3D stability calculation method for composite slopes to enhance the design and stability control of open-pit slope engineering.Using the composite slope formed by the mining stope and inner dump in Baiyinhua No.1 and No.2 open-pit coal mine as a case study,this research investigates the failure mode of composite slopes and establishes spatial shape equations for the sliding mass.By integrating the shear resistance and sliding force of each row of microstrip columns onto the bottom surface of the strip corresponding to the main sliding surface,a novel 2D equivalent physical and mechanical parameters analysis method for the strips on the main sliding surface of 3D sliding masses is proposed.Subsequently,a comprehensive 3D stability calculation method for composite slopes is developed,and the quantitative relationship between the coordinated development distance and its 3D stability coefficients is examined.The analysis reveals that the failure mode of the composite slope is characterized by cutting-bedding sliding,with the arc serving as the side interface and the weak layer as the bottom interface,while the destabilization mechanism primarily involves shear failure.The spatial form equation of the sliding mass comprises an ellipsoid and weak plane equation.The analysis revealed that when the coordinated development distance is 1500 m,the error rate between the 3D stability calculation result and the 2D stability calculation result of the composite slope is less than 8%,thereby verifying the proposed analytical method of equivalent physical and mechanical parameters and the 3D stability calculation method for composite slopes.Furthermore,the3D stability coefficient of the composite slope exhibits an exponential correlation with the coordinated development distance,with the coefficient gradually decreasing as the coordinated development distance increases.These findings provide a theoretical guideline for designing similar slope shape parameters and conducting stability analysis.

The combined application of stem cells and three-dimensional bioprinting scaffolds for the repair of spinal cord injury

Spinal cord injury is considered one of the most difficult injuries to repair and has one of the worst prognoses for injuries to the nervous system.Following surgery,the poor regenerative capacity of nerve cells and the generation of new scars can make it very difficult for the impaired nervous system to restore its neural functionality.Traditional treatments can only alleviate secondary injuries but cannot fundamentally repair the spinal cord.Consequently,there is a critical need to develop new treatments to promote functional repair after spinal cord injury.Over recent years,there have been seve ral developments in the use of stem cell therapy for the treatment of spinal cord injury.Alongside significant developments in the field of tissue engineering,three-dimensional bioprinting technology has become a hot research topic due to its ability to accurately print complex structures.This led to the loading of three-dimensional bioprinting scaffolds which provided precise cell localization.These three-dimensional bioprinting scaffolds co uld repair damaged neural circuits and had the potential to repair the damaged spinal cord.In this review,we discuss the mechanisms underlying simple stem cell therapy,the application of different types of stem cells for the treatment of spinal cord injury,and the different manufa cturing methods for three-dimensional bioprinting scaffolds.In particular,we focus on the development of three-dimensional bioprinting scaffolds for the treatment of spinal cord injury.

Application of three-dimensional speckle tracking technique in measuring left ventricular myocardial function in patients with diabetes

BACKGROUND Diabetic cardiomyopathy is considered as a chronic complication of diabetes mellitus(DM).Therefore,early detection of left ventricular systolic function(LVSF)damage in DM is essential.AIM To explore the use of the three-dimensional speckle tracking technique(3D-STI)for measuring LVSF in DM patients via meta-analysis.METHODS The electronic databases were retrieved from the initial accessible time to 29 April 2023.The current study involved 9 studies,including 970 subjects.We carried out this meta-analysis to estimate myocardial function in DM compared with controls according to myocardial strain attained by 3D-STI.RESULTS Night articles including 970 subjects were included.No significant difference was detected in the left ventricular ejection fraction between the control and the diabetic group(P>0.05),while differences in global longitudinal strain,global circumferential strain,global radial strain,and global area strain were markedly different between the controls and DM patients(all P<0.05).CONCLUSION The 3D-STI could be applied to accurately measure early LVSF damage in patients with DM.

Three-dimensional numerical modeling of gravity anomalies based on Poisson equation in spacewavenumber mixed domain

In gravity-anomaly-based prospecting, the computational and memory requirements for practical numerical modeling are potentially enormous. Achieving an efficient and precise inversion for gravity anomaly imaging over large-scale and complex terrain requires additional methods. To this end, we have proposed a new topography-capable By performing a two-dimensional Fourier transform in the horizontal directions, threedimensional partial differential equations in the spatial domain were transformed into a group of independent, one-dimensional differential equations engaged with different wave numbers. These independent differential equations are highly parallel across different wave numbers. differential equations with different wave numbers, and the efficiency of solving fixedbandwidth linear equations was further improved by a chasing method. In a synthetic test, a prism model was used to verify the accuracy and reliability of the proposed algorithm by comparing the numerical solution with the analytical solution. We studied the computational precision and efficiency with and without topography using different Fourier transform methods. The results showed that the Guass-FFT method has higher numerical precision, while the standard FFT method is superior, in terms of computation time, for inversion and quantitative interpretation under complicated terrain.

Risk Assessment of Coal Mine Water Hazard Based on Three-Dimensional Model of Geology and Underground Space

Mine safety have top-five disasters,which including the water,gas,fire,dust and geological dynamic disaster.The coal mine water disaster is one of the important factors which restricted the development of China’s coal production.It is showed by statistics that 60%of mine accidents are affected by groundwater,which not only result in the production losses,casualties and a variety of

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.

Three-dimensional simulation method of multipactor in microwave components for high-power space application

Based on the particle-in-cell technology and the secondary electron emission theory, a three-dimensional simulation method for multipactor is presented in this paper. By combining the finite difference time domain method and the panicle tracing method, such an algorithm is self-consistent and accurate since the interaction between electromagnetic fields and particles is properly modeled. In the time domain aspect, the generation of multipactor can be easily visualized, which makes it possible to gain a deeper insight into the physical mechanism of this effect. In addition to the classic secondary electron emission model, the measured practical secondary electron yield is used, which increases the accuracy of the algorithm. In order to validate the method, the impedance transformer and ridge waveguide filter are studied. By analyzing the evolution of the secondaries obtained by our method, multipactor thresholds of these components are estimated, which show good agreement with the experimental results. Furthermore, the most sensitive positions where multipactor occurs are determined from the phase focusing phenomenon, which is very meaningful for multipactor analysis and design.

Continuous imaging space in three-dimensional integral imaging

We report an integral imaging method with continuous imaging space. This method simultaneously reconstructs real and virtual images in the virtual mode, with a minimum gap that separates the entire imaging space into real and virtual space. Experimental results show that the gap is reduced to 45% of that in a conventional integral imaging system with the same parameters.

High-speed autopolarization synchronization modulation three-dimensional structured illumination microscopy

In recent years,notable progress has been achieved in both the hardware and algorithms of structured illumination microscopy(SIM).Nevertheless,the advancement of three-dimensional structured illumination microscopy(3DSIM)has been impeded by challenges arising from the speed and intricacy of polarization modulation.We introduce a high-speed modulation 3DSIM system,leveraging the polarizationmaintaining and modulation capabilities of a digital micromirror device(DMD)in conjunction with an electrooptic modulator.The DMD-3DSIM system yields a twofold enhancement in both lateral(133 nm)and axial(300 nm)resolution compared to wide-field imaging and can acquire a data set comprising 29 sections of 1024 pixels×1024 pixels,with 15 ms exposure time and 6.75 s per volume.The versatility of the DMD-3DSIM approach was exemplified through the imaging of various specimens,including fluorescent beads,nuclear pores,microtubules,actin filaments,and mitochondria within cells,as well as plant and animal tissues.Notably,polarized 3DSIM elucidated the orientation of actin filaments.Furthermore,the implementation of diverse deconvolution algorithms further enhances 3D resolution.The DMD-based 3DSIM system presents a rapid and reliable methodology for investigating biomedical phenomena,boasting capabilities encompassing 3D superresolution,fast temporal resolution,and polarization imaging.

THREE-DIMENSIONAL INTERACTIONS OF A HALF-PLANE CRACK IN A TRANSVERSELY ISOTROPIC PIEZOELECTRIC SPACE WITH RESULTANT SOURCES

Exact solutions in elementary functions are derived for the stress and electric displacement intensity factors of a half-plane crack in a transversely isotropic piezoelectric space interacting with various resultant sources, including force dipole, electric dipole, moment, force dilatation and rotation. Such force and charge sources may model defects like vacancies, foreign particles and dislocations. The locations and orientations of the stress and charge sources with respect to the crack are arbitrary.

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF C^(N)

In this paper,we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators T_(λ,τ,k),S_(λ,τ,k),Q_(λ,τ,k)and R_(λ,τ,k)are bounded between Lebesgue type spaces.In order to prove the main results,we first give some bidirectional estimates for several typical integrals.