Estimation of the anisotropy of hydraulic conductivity through 3D fracture networks using the directional geological entropy

With an extension of the geological entropy concept in porous media,the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks.A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions.Compared with the traditional connectivity indexes based on the statistics of fracture geometry,the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks.According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks,the hydraulic conductivities and entropic scales in different directions both increase with spatial order(i.e.,trace length decreasing and spacing increasing)and are independent of the dip angle.As a result,the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function,which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors.

3D Road Network Modeling and Road Structure Recognition in Internet of Vehicles

Internet of Vehicles (IoV) is a new system that enables individual vehicles to connect with nearby vehicles,people, transportation infrastructure, and networks, thereby realizing amore intelligent and efficient transportationsystem. The movement of vehicles and the three-dimensional (3D) nature of the road network cause the topologicalstructure of IoV to have the high space and time complexity.Network modeling and structure recognition for 3Droads can benefit the description of topological changes for IoV. This paper proposes a 3Dgeneral roadmodel basedon discrete points of roads obtained from GIS. First, the constraints imposed by 3D roads on moving vehicles areanalyzed. Then the effects of road curvature radius (Ra), longitudinal slope (Slo), and length (Len) on speed andacceleration are studied. Finally, a general 3D road network model based on road section features is established.This paper also presents intersection and road section recognition methods based on the structural features ofthe 3D road network model and the road features. Real GIS data from a specific region of Beijing is adopted tocreate the simulation scenario, and the simulation results validate the general 3D road network model and therecognitionmethod. Therefore, thiswork makes contributions to the field of intelligent transportation by providinga comprehensive approach tomodeling the 3Droad network and its topological changes in achieving efficient trafficflowand improved road safety.

Numerical Study of the Biomechanical Behavior of a 3D Printed Polymer Esophageal Stent in the Esophagus by BP Neural Network Algorithm

Esophageal disease is a common disorder of the digestive system that can severely affect the quality of life andprognosis of patients. Esophageal stenting is an effective treatment that has been widely used in clinical practice.However, esophageal stents of different types and parameters have varying adaptability and effectiveness forpatients, and they need to be individually selected according to the patient’s specific situation. The purposeof this study was to provide a reference for clinical doctors to choose suitable esophageal stents. We used 3Dprinting technology to fabricate esophageal stents with different ratios of thermoplastic polyurethane (TPU)/(Poly-ε-caprolactone) PCL polymer, and established an artificial neural network model that could predict the radial forceof esophageal stents based on the content of TPU, PCL and print parameter. We selected three optimal ratios formechanical performance tests and evaluated the biomechanical effects of different ratios of stents on esophagealimplantation, swallowing, and stent migration processes through finite element numerical simulation and in vitrosimulation tests. The results showed that different ratios of polymer stents had different mechanical properties,affecting the effectiveness of stent expansion treatment and the possibility of postoperative complications of stentimplantation.

Luminescence regulation of Sb^(3+)in 0D hybrid metal halides by hydrogen bond network for optical anti-counterfeiting

The Sb^(3+) doping strategy has been proven to be an effective way to regulate the band gap and improve the photophysical properties of organic-inorganic hybrid metal halides(OIHMHs).However,the emission of Sb^(3+) ions in OIHMHs is primarily confined to the low energy region,resulting in yellow or red emissions.To date,there are few reports about green emission of Sb^(3+)-doped OIHMHs.Here,we present a novel approach for regulating the luminescence of Sb^(3+) ions in 0D C_(10)H_(2)_(2)N_(6)InCl_(7)·H_(2)O via hydrogen bond network,in which water molecules act as agents for hydrogen bonding.Sb^(3+)-doped C_(10)H_(2)2N_(6)InCl_(7)·H_(2)O shows a broadband green emission peaking at 540 nm and a high photoluminescence quantum yield(PLQY)of 80%.It is found that the intense green emission stems from the radiative recombination of the self-trapped excitons(STEs).Upon removal of water molecules with heat,C_(10)H_(2)_(2)N_(6)In_(1-x)Sb_(x)Cl_(7) generates yellow emis-sion,attributed to the breaking of the hydrogen bond network and large structural distortions of excited state.Once water molecules are adsorbed by C_(10)H_(2)_(2)N_(6)In_(1-x)Sb_(x)Cl_(7),it can subsequently emit green light.This water-induced reversible emission switching is successfully used for optical security and information encryption.Our findings expand the under-standing of how the local coordination structure influences the photophysical mechanism in Sb^(3+)-doped metal halides and provide a novel method to control the STEs emission.

SGT-Net: A Transformer-Based Stratified Graph Convolutional Network for 3D Point Cloud Semantic Segmentation

In recent years,semantic segmentation on 3D point cloud data has attracted much attention.Unlike 2D images where pixels distribute regularly in the image domain,3D point clouds in non-Euclidean space are irregular and inherently sparse.Therefore,it is very difficult to extract long-range contexts and effectively aggregate local features for semantic segmentation in 3D point cloud space.Most current methods either focus on local feature aggregation or long-range context dependency,but fail to directly establish a global-local feature extractor to complete the point cloud semantic segmentation tasks.In this paper,we propose a Transformer-based stratified graph convolutional network(SGT-Net),which enlarges the effective receptive field and builds direct long-range dependency.Specifically,we first propose a novel dense-sparse sampling strategy that provides dense local vertices and sparse long-distance vertices for subsequent graph convolutional network(GCN).Secondly,we propose a multi-key self-attention mechanism based on the Transformer to further weight augmentation for crucial neighboring relationships and enlarge the effective receptive field.In addition,to further improve the efficiency of the network,we propose a similarity measurement module to determine whether the neighborhood near the center point is effective.We demonstrate the validity and superiority of our method on the S3DIS and ShapeNet datasets.Through ablation experiments and segmentation visualization,we verify that the SGT model can improve the performance of the point cloud semantic segmentation.

Review of Artificial Intelligence for Oil and Gas Exploration: Convolutional Neural Network Approaches and the U-Net 3D Model

Deep learning, especially through convolutional neural networks (CNN) such as the U-Net 3D model, has revolutionized fault identification from seismic data, representing a significant leap over traditional methods. Our review traces the evolution of CNN, emphasizing the adaptation and capabilities of the U-Net 3D model in automating seismic fault delineation with unprecedented accuracy. We find: 1) The transition from basic neural networks to sophisticated CNN has enabled remarkable advancements in image recognition, which are directly applicable to analyzing seismic data. The U-Net 3D model, with its innovative architecture, exemplifies this progress by providing a method for detailed and accurate fault detection with reduced manual interpretation bias. 2) The U-Net 3D model has demonstrated its superiority over traditional fault identification methods in several key areas: it has enhanced interpretation accuracy, increased operational efficiency, and reduced the subjectivity of manual methods. 3) Despite these achievements, challenges such as the need for effective data preprocessing, acquisition of high-quality annotated datasets, and achieving model generalization across different geological conditions remain. Future research should therefore focus on developing more complex network architectures and innovative training strategies to refine fault identification performance further. Our findings confirm the transformative potential of deep learning, particularly CNN like the U-Net 3D model, in geosciences, advocating for its broader integration to revolutionize geological exploration and seismic analysis.

Lie symmetry analysis and invariant solutions for the(3+1)-dimensional Virasoro integrable model

Lie symmetry analysis is applied to a(3+1)-dimensional Virasoro integrable model and the corresponding similarity reduction equations are obtained with the different infinitesimal generators.Invariant solutions with arbitrary functions for the(3+1)-dimensional Virasoro integrable model,including the interaction solution between a kink and a soliton,the lump-type solution and periodic solutions,have been studied analytically and graphically.

Interaction solutions for the second extended(3+1)-dimensional Jimbo–Miwa equation

Based on the Hirota bilinear method,the second extended(3+1)-dimensional Jimbo–Miwa equation is established.By Maple symbolic calculation,lump and lump-kink soliton solutions are obtained.The interaction solutions between the lump and multi-kink soliton,and the interaction between the lump and triangular periodic soliton are derived by combining a multi-exponential function or trigonometric sine and cosine functions with quadratic functions.Furthermore,periodiclump wave solution is derived via the ansatz including hyperbolic and trigonometric functions.Finally,3D plots,2D curves,density plots,and contour plots with particular choices of the suitable parameters are depicted to illustrate the dynamical features of these solutions.

Development of an improved three-dimensional rough discrete fracture network model:Method and application

Structure plane is one of the important factors affecting the stability and failure mode of rock mass engineering.Rock mass structure characterization is the basic work of rock mechanics research and the important content of numerical simulation.A new 3-dimensional rough discrete fracture network(RDFN3D)model and its modeling method based on the Weierstrass-Mandelbrot(W-M)function were presented in this paper.The RDFN3D model,which improves and unifies the modelling methods for the complex structural planes,has been realized.The influence of fractal dimension,amplitude,and surface precision on the modeling parameters of RDFN3D was discussed.The reasonable W-M parameters suitable for the roughness coefficient of JRC were proposed,and the relationship between the mathematical model and the joint characterization was established.The RDFN3D together with the smooth 3-dimensional discrete fracture network(DFN3D)models were successfully exported to the drawing exchange format,which will provide a wide application in numerous numerical simulation codes including both the continuous and discontinuous methods.The numerical models were discussed using the COMSOL Multiphysics code and the 3-dimensional particle flow code,respectively.The reliability of the RDFN3D model was preliminarily discussed and analyzed.The roughness and spatial connectivity of the fracture networks have a dominant effect on the fluid flow patterns.The research results can provide a new geological model and analysis model for numerical simulation and engineering analysis of jointed rock mass.

Nonlinear fluid flow through three-dimensional rough fracture networks:Insights from 3D-printing,CT-scanning,and high-resolution numerical simulations

Nonlinear flow behavior of fluids through three-dimensional(3D)discrete fracture networks(DFNs)considering effects of fracture number,surface roughness and fracture aperture was experimentally and numerically investigated.Three physical models of DFNs were 3D-printed and then computed tomography(CT)-scanned to obtain the specific geometry of fractures.The validity of numerically simulating the fluid flow through DFNs was verified via comparison with flow tests on the 3D-printed models.A parametric study was then implemented to establish quantitative relations between the coefficients/parameters in Forchheimer’s law and geometrical parameters.The results showed that the 3D-printing technique can well reproduce the geometry of single fractures with less precision when preparing complex fracture networks,numerical modeling precision of which can be improved via CT-scanning as evidenced by the well fitted results between fluid flow tests and numerical simulations using CT-scanned digital models.Streamlines in DFNs become increasingly tortuous as the fracture number and roughness increase,resulting in stronger inertial effects and greater curvatures of hydraulic pressure-low rate relations,which can be well characterized by the Forchheimer’s law.The critical hydraulic gradient for the onset of nonlinear flow decreases with the increasing aperture,fracture number and roughness,following a power function.The increases in fracture aperture and number provide more paths for fluid flow,increasing both the viscous and inertial permeabilities.The value of the inertial permeability is approximately four orders of magnitude greater than the viscous permeability,following a power function with an exponent a of 3,and a proportional coefficient b mathematically correlated with the geometrical parameters.

Probabilistic analysis on fault tolerance of 3-Dimensional mesh networks

The probability model is used to analyze the fault tolerance of mesh. To simplify its analysis, it is as-sumed that the failure probability of each node is independent. A 3-D mesh is partitioned into smaller submeshes,and then the probability with which each submesh satisfies the defined condition is computed. If each submesh satis-fies the condition, then the whole mesh is connected. Consequently, the probability that a 3-D mesh is connected iscomputed assuming each node has a failure probability. Mathematical methods are used to derive a relationship be-tween network node failure probability and network connectivity probability. The calculated results show that the 3-D mesh networks can remain connected with very high probability in practice. It is formally proved that when thenetwork node failure probability is boutded by 0.45 %, the 3-D mesh networks of more than three hundred thousandnodes remain connected with probability larger than 99 %. The theoretical results show that the method is a power-ful technique to calculate the lower bound of the connectivity probability of mesh networks.

Fang-Xia-Dihuang decoction inhibits breast cancer progression induced by psychological stress via down-regulation of PI3K/AKT and JAK2/STAT3 pathways:An in vivo and a network pharmacology assessment

Background:The development and prognosis of breast cancer are intricately linked to psychological stress.In addition,depression is the most common psychological comorbidity among breast cancer survivors,and reportedly,Fang-Xia-Dihuang decoction(FXDH)can effectively manage depression in such patients.However,its pharmacological and molecular mechanisms remain obscure.Methods:Public databases were used for obtaining active components and related targets.Main active components were further verified by ultra-high-performance liquid chromatography-high-resolution mass spectrometry(UPLC-HRMS).Protein–protein interaction and enrichment analyses were taken to predict potential hub targets and related pathways.Molecule docking was used to understand the interactions between main compounds and hub targets.In addition,an animal model of breast cancer combined with depression was established to evaluate the intervention effect of FXDH and verify the pathways screened by network pharmacology.Results:174 active components of FXDH and 163 intersection targets of FXDH,breast cancer,and depression were identified.Quercetin,methyl ferulate,luteolin,ferulaldehyde,wogonin,and diincarvilone were identified as the principal active components of FXDH.Protein–protein interaction and KEGG enrichment analyses revealed that the phosphoinositide-3-kinase–protein kinase B(PI3K/AKT)and Janus kinase/signal transducer and activator of transcription(JAK2/STAT3)signaling pathways played a crucial role in mediating the efficacy of FXDH for inhibiting breast cancer progression induced by depression.In addition,in vivo experiments revealed that FXDH ameliorated depression-like behavior in mice and inhibited excessive tumor growth in mice with breast cancer and depression.FXDH treatment downregulated the expression of epinephrine,PI3K,AKT,STAT3,and JAK2 compared with the control treatment(p<0.05).Molecular docking verified the relationship between the six primary components of FXDH and the three most important targets,including phosphatidylinositol-4,5-bisphosphate 3-kinase catalytic subunit alpha(PIK3CA),AKT,and STAT3.Conclusion:This study provides a scientific basis to support the clinical application of FXDH for improving depression-like behavior and inhibiting breast cancer progression promoted by chronic stress.The therapeutic effects FXDH may be closely related to the PI3K/AKT and JAK2/STAT3 pathways.This finding helps better understand the regulatory mechanisms underlying the efficacy of FXDH.

Zuo Gui Wan Promotes Osteogenesis via PI3K/AKT Signaling Pathway:Network Pharmacology Analysis and Experimental Validation

Objective Osteogenesis is vitally important for bone defect repair,and Zuo Gui Wan(ZGW)is a classic prescription in traditional Chinese medicine(TCM)for strengthening bones.However,the specific mechanism by which ZGW regulates osteogenesis is still unclear.The current study is based on a network pharmacology analysis to explore the potential mechanism of ZGW in promoting osteogenesis.Methods A network pharmacology analysis followed by experimental validation was applied to explore the potential mechanisms of ZGW in promoting the osteogenesis of bone marrow mesenchymal stem cells(BMSCs).Results In total,487 no-repeat targets corresponding to the bioactive components of ZGW were screened,and 175 target genes in the intersection of ZGW and osteogenesis were obtained.And 28 core target genes were then obtained from a PPI network analysis.A GO functional enrichment analysis showed that the relevant biological processes mainly involve the cellular response to chemical stress,metal ions,and lipopolysaccharide.Additionally,KEGG pathway enrichment analysis revealed that multiple signaling pathways,including the phosphatidylinositol-3-kinase/protein kinase B(PI3K/AKT)signaling pathway,were associated with ZGW-promoted osteogensis.Further experimental validation showed that ZGW could increase alkaline phosphatase(ALP)activity as well as the mRNA and protein levels of ALP,osteocalcin(OCN),and runt related transcription factor 2(Runx 2).What’s more,Western blot analysis results showed that ZGW significantly increased the protein levels of p-PI3K and p-AKT,and the increases of these protein levels significantly receded after the addition of the PI3K inhibitor LY294002.Finally,the upregulated osteogenic-related indicators were also suppressed by the addition of LY294002.Conclusion ZGW promotes the osteogenesis of BMSCs via PI3K/AKT signaling pathway.

A 3-DIMENSIONAL DATA MODEL FOR VISUALIZING CLOVERLEAF JUNCTION IN A CITY MODEL

The research work has been seldom done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its main body is bestraddle in air,and has aerial intersections between its parts. This complex feature made cloverleaf junction quite different from buildings and terrain, therefore, it is difficult to express this kind of spatial objects in the same way as for buildings and terrain. In this paper,authors analyze spatial characteristics of cloverleaf junction, propose an all-constraint points TIN algorithm to partition cloverleaf junction road surface, and develop a method to visualize cloverleaf junction road surface using TIN. In order to manage cloverleaf junction data efficiently, the authors also analyzed the mechanism of 3DCM data management, extended BLOB type in relational database, and combined R-tree index to manage 3D spatial data. Based on this extension, an appropriate data

Evaluation of Airway Obstruction at Soft Palate Level in Male Patients with Obstructive Sleep Apnea/Hypopnea Syndrome:Dynamic 3-Dimensional CT Imaging of Upper Airway

This study examined the dynamic characteristics of upper airway collapse at soft palate level in patients with obstructive sleep apnea/hypopnea syndrome（OSAHS） by using dynamic 3-Dimensional（3-D） CT imaging.A total of 41 male patients who presented with 2 of the following symptoms,i.e.,daytime sleepiness and fatigue,frequent snoring,and apnea with witness,were diagnosed as having OSAHS.They underwent full-night polysomnography and then dynamic 3-D CT imaging of the upper airway during quiet breathing and in Muller＇s maneuver.The soft palate length（SPL）,the minimal cross-sectional area of the retropalatal region（mXSA-RP）,and the vertical distance from the hard palate to the upper posterior part of the hyoid（hhL） were compared between the two breathing states.These parameters,together with hard palate length（HPL）,were also compared between mild/moderate and severe OSAHS groups.Association of these parameters with the severity of OSAHS [as reflected by apnea hypopnea index（AHI） and the lowest saturation of blood oxygen（LSaO2）] was examined.The results showed that 31 patients had severe OSAHS,and 10 mild/moderate OSAHS.All the patients had airway obstruction at soft palate level.mXSA-RP was significantly decreased and SPL remarkably increased during Muller＇s maneuver as compared with the quiet breathing state.There were no significant differences in these airway parameters（except the position of the hyoid bone） between severe and mild/moderate OSAHS groups.And no significant correlation between these airway parameters and the severity of OSAHS was found.The position of hyoid was lower in the severe OSAHS group than in the mild/moderate OSAHS group.The patients in group with body mass index（BMI）≥26 had higher collapse ratio of mXSA-RP,greater neck circumference and smaller mXSA-RP in the Muller＇s maneuver than those in group with BMI26（P0.05 for all）.It was concluded that dynamic 3-D CT imaging could dynamically show the upper airway changes at soft palate level in OSAHS patients.All the OSAHS patients had airway obstruction of various degrees at soft palate level.But no correlation was observed between the airway change at soft palate level and the severity of OSAHS.The patients in group with BMI≥26 were more likely to develop airway obstruction at soft palate level than those with BMI26.

Three-dimensional Fusion of Spaceborne and Ground Radar Reflectivity Data Using a Neural Network–Based Approach

The spaceborne precipitation radar onboard the Tropical Rainfall Measuring Mission satellite （TRMM PR） can provide good measurement of the vertical structure of reflectivity, while ground radar （GR） has a relatively high horizontal resolution and greater sensitivity. Fusion of TRMM PR and GR reflectivity data may maximize the advantages from both instruments. In this paper, TRMM PR and GR reflectivity data are fused using a neural network （NN）-based approach. The main steps included are： quality control of TRMM PR and GR reflectivity data; spatiotemporal matchup; GR calibration bias correction; conversion of TRMM PR data from Ku to S band; fusion of TRMM PR and GR reflectivity data with an NN method： interpolation of reflectivity data that are below PR＇s sensitivity; blind areas compensation with a distance weighting-based merging approach; combination of three types of data： data with the NN method, data below PR＇s sensitivity and data within compensated blind areas. During the NN fusion step, the TRMM PR data are taken as targets of the training NNs, and gridded GR data after horizontal downsampling at different heights are used as the input. The trained NNs are then used to obtain 3D high-resolution reflectivity from the original GR gridded data. After 3D fusion of the TRMM PR and GR reflectivity data, a more complete and finer-scale 3D radar reflectivity dataset incorporating characteristics from both the TRMM PR and GR observations can be obtained. The fused reflectivity data are evaluated based on a convective precipitation event through comparison with the high resolution TRMM PR and GR data with an interpolation algorithm.

NOVEL 6-SPS PARALLEL 3-DIMENSIONAL PLATFORM MANIPULATOR AND ITS FORCE/MOTION TRANSMISSION ANALYSIS

The unique design for a novel 6-SPS parallel 3-dimensional platformmanipulator with an orthogonal configuration is investigated. The layout feature of the parallelmanipulator is described. Its force/motion transmission capability, evaluation criteria arepresented. At the orthogonal configuration, the criteria and the relationships between the criteriaand the link lengths are analyzed, which is important since it can provide designer a piece ofvaluable information about how to choose the linear actuators. From the analysis of the results itis shown that the force/motion transmission capabilities of the parallel manipulator arecharacterized by isotropy at the orthogonal configuration. The manipulator is particularly suitablefor certain applications in 6-DOF micromanipulators and 6-axis force/moment transducers.

Segmentation of retinal fluid based on deep learning:application of three-dimensional fully convolutional neural networks in optical coherence tomography images

AIM: To explore a segmentation algorithm based on deep learning to achieve accurate diagnosis and treatment of patients with retinal fluid.METHODS: A two-dimensional(2D) fully convolutional network for retinal segmentation was employed. In order to solve the category imbalance in retinal optical coherence tomography(OCT) images, the network parameters and loss function based on the 2D fully convolutional network were modified. For this network, the correlations of corresponding positions among adjacent images in space are ignored. Thus, we proposed a three-dimensional(3D) fully convolutional network for segmentation in the retinal OCT images.RESULTS: The algorithm was evaluated according to segmentation accuracy, Kappa coefficient, and F1 score. For the 3D fully convolutional network proposed in this paper, the overall segmentation accuracy rate is 99.56%, Kappa coefficient is 98.47%, and F1 score of retinal fluid is 95.50%. CONCLUSION: The OCT image segmentation algorithm based on deep learning is primarily founded on the 2D convolutional network. The 3D network architecture proposed in this paper reduces the influence of category imbalance, realizes end-to-end segmentation of volume images, and achieves optimal segmentation results. The segmentation maps are practically the same as the manual annotations of doctors, and can provide doctors with more accurate diagnostic data.

Short‐term and long‐term memory self‐attention network for segmentation of tumours in 3D medical images

Tumour segmentation in medical images(especially 3D tumour segmentation)is highly challenging due to the possible similarity between tumours and adjacent tissues,occurrence of multiple tumours and variable tumour shapes and sizes.The popular deep learning‐based segmentation algorithms generally rely on the convolutional neural network(CNN)and Transformer.The former cannot extract the global image features effectively while the latter lacks the inductive bias and involves the complicated computation for 3D volume data.The existing hybrid CNN‐Transformer network can only provide the limited performance improvement or even poorer segmentation performance than the pure CNN.To address these issues,a short‐term and long‐term memory self‐attention network is proposed.Firstly,a distinctive self‐attention block uses the Transformer to explore the correlation among the region features at different levels extracted by the CNN.Then,the memory structure filters and combines the above information to exclude the similar regions and detect the multiple tumours.Finally,the multi‐layer reconstruction blocks will predict the tumour boundaries.Experimental results demonstrate that our method outperforms other methods in terms of subjective visual and quantitative evaluation.Compared with the most competitive method,the proposed method provides Dice(82.4%vs.76.6%)and Hausdorff distance 95%(HD95)(10.66 vs.11.54 mm)on the KiTS19 as well as Dice(80.2%vs.78.4%)and HD95(9.632 vs.12.17 mm)on the LiTS.

Residual symmetry, CRE integrability and interaction solutions of two higher-dimensional shallow water wave equations

Two(3+1)-dimensional shallow water wave equations are studied by using residual symmetry and the consistent Riccati expansion(CRE) method. Through localization of residual symmetries, symmetry reduction solutions of the two equations are obtained. The CRE method is applied to the two equations to obtain new B?cklund transformations from which a type of interesting interaction solution between solitons and periodic waves is generated.