Mathematics and Computers in Simulation最新文献

{"title":"Multi-material topology optimization using isogeometric method based reaction–diffusion level set techniques","authors":"Harsh Kumar,&nbsp;Sourav Rakshit","doi":"10.1016/j.matcom.2025.02.010","DOIUrl":"10.1016/j.matcom.2025.02.010","url":null,"abstract":"<div><div>This work presents a new approach to multi-material topology optimization (MMTO) using Isogeometric Analysis (IGA) based reaction–diffusion equation (RDE) level set method. Level set based topology optimization, frequently used for achieving clear material boundaries and avoiding checkerboard patterns in topology optimization problems is further augmented by RDEs which enhance numerical stability of the solver. The multi-material formulation uses a blended combination of different level-set functions to ensure that each point in the domain corresponds to a single material. In this work, isogeometric analysis (IGA) is used for the first time in RDE-based level set for solving MMTO problems. The same Non-Uniform Rational B-Splines (NURBS) basis function is used for approximating state variables, geometry modeling and level set function, thus facilitating seamless coupling between analysis and product design. Using the IGAFEM toolbox (Nguyen et al., 2015), MMTO is performed for a few benchmark problems for varying material composition and mesh sizes. Results indicate that satisfactory distribution of material is achieved in all the MMTO examples and bi-quadratic element based IGA is a competent tool to be applied in RDE-based level set method for topology optimization. Future work will focus on using the same IGA framework for further shape optimization of the designed structures to produce fabrication ready CAD models.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 530-552"},"PeriodicalIF":4.4,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143471319","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new MATLAB software for numerical computation of biological observables for metastatic tumor growth","authors":"Iulia Martina Bulai ,&nbsp;Maria Carmela De Bonis ,&nbsp;Concetta Laurita","doi":"10.1016/j.matcom.2025.02.014","DOIUrl":"10.1016/j.matcom.2025.02.014","url":null,"abstract":"<div><div>In this paper a new MATLAB Toolbox is introduced, Metastatic Tumor Growth Modeling (MTGM). MTGM Toolbox is freely available on a GitHub repository <span><span>https://github.com/IuliaMartinaBulai/MTGM_Toolbox</span><svg><path></path></svg></span> and equips the researchers with five different functionalities. The first one refers to the numerical resolution of a general Volterra Integral Equation (VIE) of the second kind on the positive semiaxis while the last four ones to the computation of biological observables related to metastatic tumor growth models. In particular, the computed observables are the cumulative number of metastases (CNM) and the total metastatic mass (TMM) derived from: (i) a 1D metastatic tumor growth (t.g.) model where the analytical solution of the ODE describing the t.g. law is known, (ii) a 1D model where this solution has to be numerically computed, (iii) a 2D non-autonomous metastatic t.g. model where also the treatment is considered, (iv) a 2D autonomous model, i.e., in the absence of therapies. Moreover, the Toolbox implementation was designed in order to give the users the possibility to extend its functionalities.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"234 ","pages":"Pages 31-49"},"PeriodicalIF":4.4,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143519889","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pattern formation of Cucker–Smale system with nonlinear velocity couplings","authors":"Jianlong Ren,&nbsp;Qiming Liu,&nbsp;Ping Li","doi":"10.1016/j.matcom.2025.02.002","DOIUrl":"10.1016/j.matcom.2025.02.002","url":null,"abstract":"<div><div>In this paper, we propose a novel Cucker–Smale system with nonlinear velocity couplings and a targeted driving force. Firstly, by imposing assumptions on the initial state, the system can achieve flocking behavior. Secondly, the collision avoidance results under various velocity coupling degrees are deduced by applying the triangle inequality. Thirdly, by applying the Barb<span><math><mover><mrow><mi>a</mi></mrow><mrow><mo>̆</mo></mrow></mover></math></span>lat’s lemma, all agents eventually reach the prescribed line-shaped formation with a targeted driving force. In particular, for <span><math><mrow><mn>1</mn><mo>/</mo><mn>2</mn><mo>&lt;</mo><mi>α</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span> and <span><math><mrow><mn>1</mn><mo>&lt;</mo><mi>β</mi><mo>&lt;</mo><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math></span>, the finite-time and fixed-time line-shaped formation can be successfully achieved without the symbolic function, and an upper bound on the settling time is obtained. Finally, the results of the theoretical analysis are verified by numerical simulations, and the final formation’s trajectory equation is derived by using the least squares method.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 413-432"},"PeriodicalIF":4.4,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446018","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A digital twin approach based method in civil engineering for classification of salt damage in building evaluation","authors":"J.A. Guzmán-Torres ,&nbsp;F.J. Domínguez-Mota ,&nbsp;E.M. Alonso Guzmán ,&nbsp;G. Tinoco-Guerrero ,&nbsp;J.G. Tinoco-Ruíz","doi":"10.1016/j.matcom.2025.02.003","DOIUrl":"10.1016/j.matcom.2025.02.003","url":null,"abstract":"<div><div>The integration of digital twins and machine learning models in civil engineering has revolutionized the inspection and maintenance of buildings and structures. Digital twins, as precise virtual replicas of physical assets, enable continuous monitoring and predictive maintenance, enhancing the reliability and efficiency of structural assessments.</div><div>This research aims to develop a convolutional neural network (CNN)-based approach for classifying salt damage in concrete structures, integrating digital twin technologies to enhance structural health monitoring and damage detection. This study leverages transfer learning techniques, utilizing six state-of-the-art pre-trained architectures, including VGG-16, InceptionV3, ResNet50, VGG-19, DenseNet121, and MobileNet. After extensive evaluation, VGG-16, was chosen as the final model for fine-tuning, achieving high <em>accuracy</em> in the classification of salt damage. The digital twin approach provides a virtual representation of structures to enable predictive maintenance and reduce subjectivity in inspections.</div><div>The fine-tuned CNN models demonstrated state-of-the-art accuracy in detecting salt damage, significantly outperforming traditional visual inspection methods. The use of digital twins enabled continuous monitoring and effective prediction of structural damage. The developed models offer a robust and efficient alternative to manual inspections, supporting the transformation of structural health monitoring in civil engineering. The results underline the potential of combining digital twins and deep learning to achieve precise and reliable structural assessments.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 433-447"},"PeriodicalIF":4.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Discrete gradient-zeroing neural network algorithm for solving future Sylvester equation aided with left–right four-step rule as well as robot arm inverse kinematics","authors":"Pengfei Guo ,&nbsp;Yunong Zhang ,&nbsp;Zheng-an Yao","doi":"10.1016/j.matcom.2025.02.009","DOIUrl":"10.1016/j.matcom.2025.02.009","url":null,"abstract":"<div><div>The temporal-variant Sylvester equation (TVSE) occupies a significant position in applied mathematics, particularly in the realms of optimal control theory and matrix optimization engineering applications. Within the framework of prediction modeling systems, the future Sylvester equation (FSE) emerges as the discrete manifestation of TVSE, characterized by unknown future information. Leveraging a novel left and right four-step (LRFS) rule, we propose a novel discrete gradient-zeroing neural network (DGZNN) algorithm with order-5 precision, which is developed from the continuous gradient-zeroing neural network (GZNN) model, for solving the FSE problem. The proposed algorithm is named as LRFS-DGZNN algorithm, which stands out as an inverse-less neurodynamic algorithm. Additionally, the convergence properties of the GZNN model in solving the TVSE problem are elucidated through Lyapunov stability theory and matrix spectral theory. Furthermore, the LRFS-DGZNN algorithm’s error pattern property in solving the FSE problem is established and proven using stability theory of linear multi-step methods and ordinary differential equation numerical approximation theory. Three numerical experiments are conducted to evaluate the performance of the proposed GZNN model for solving the TVSE problem and the LRFS-DGZNN algorithm for solving the FSE problem. Moreover, the study showcases the inverse-kinematics solutions and simulations involving planar robot arm with 2 degrees of freedom (DOFs), the Kinova Jaco2 robot arm with 6 DOFs, and the Franka Emika Panda robot arm with 7 DOFs, illustrating the high efficiency of the LRFS-DGZNN algorithm.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 475-501"},"PeriodicalIF":4.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy-preserving exponential wave integrator method and the long-time dynamics for the two-dimensional space fractional coupled Klein–Gordon–Dirac equation","authors":"Pingrui Zhang,&nbsp;Xiaoyun Jiang,&nbsp;Junqing Jia","doi":"10.1016/j.matcom.2025.02.008","DOIUrl":"10.1016/j.matcom.2025.02.008","url":null,"abstract":"<div><div>In this article, uniform error bounds of an exponential wave integrator Fourier pseudo-spectral (EWIFP) method are established for the long-time dynamics of two-dimensional nonlinear space fractional Klein–Gordon–Dirac equation (NSFKGDE) with a small coupling parameter <span><math><mrow><mi>ɛ</mi><mo>∈</mo><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> and small potentials. By using the Fourier spectral discretization in space, followed with a second-order exponential wave integrator based on certain efficient quadrature rule in phase field, we construct a time-symmetric and energy-preserving numerical scheme. Rigorous analysis of uniform error bounds at <span><math><mrow><mi>O</mi><mfenced><mrow><msup><mrow><mi>h</mi></mrow><mrow><msub><mrow><mi>m</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msup><mo>+</mo><msup><mrow><mi>ɛ</mi></mrow><mrow><mn>1</mn><mo>−</mo><mi>γ</mi></mrow></msup><msup><mrow><mi>τ</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></mfenced></mrow></math></span> for <span><math><mrow><mi>γ</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow></math></span> is carried out with the tool of cut-off technique as well as the energy method. Extensive numerical experiments demonstrate that the proposed discretization performs identically with our theoretical results. For applications, we profile the dynamical evolution of NSFKGDE in two dimensions (2D) with a honeycomb lattice potential, which correlates greatly with coupling, amplitude of potentials and fractional orders.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 448-474"},"PeriodicalIF":4.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143446019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stabilization of nonlinear stochastic systems via event-triggered impulsive control","authors":"Daipeng Kuang ,&nbsp;Dongdong Gao ,&nbsp;Jianli Li","doi":"10.1016/j.matcom.2025.01.025","DOIUrl":"10.1016/j.matcom.2025.01.025","url":null,"abstract":"<div><div>This paper addresses the problem of stabilizing nonlinear stochastic systems using an event-triggered impulse mechanism (ETIM) and control theory. Sufficient criteria for achieving asymptotic stability (AS), finite-time stability (FTS), and finite-time contraction stability (FTCS) are obtained. In the ETIM, respectively, the timer threshold and free-control indexes are introduced to effectively prevent Zeno behavior and unnecessary impulses, thus conserving control resources. Furthermore, the impulse policy is formulated by considering both the current state and past information of the system, resulting in the generation of impulses that encompass both common and delay-dependent characteristics. The research findings reveal that the stability of the system is influenced by the stochastic system, impulse strength, time delay, and the ETIM. It is demonstrated that the impulse strength and the impulse sequence are the primary factors contributing to system stability, while time delay in impulse has a negative impact. The obtained criteria are applied to a stochastic network system, and the validity of the results is supported through illustrative examples and numerical simulations.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 389-399"},"PeriodicalIF":4.4,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437019","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical study of mixed convection and thermal enhancement in Williamson ternary nanofluid flow over a non-isothermal wedge using the keller box method","authors":"Sushmitha Kannan,&nbsp;Vallampati Ramachandra Prasad","doi":"10.1016/j.matcom.2025.02.016","DOIUrl":"10.1016/j.matcom.2025.02.016","url":null,"abstract":"<div><div>The aim of the present analysis is to examine the mixed convection flow of Williamson ternary <span><math><mrow><mo>(</mo><mi>Ag</mi><mo>,</mo><mi>MgO</mi><mo>,</mo><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>/</mo><mi>water</mi><mo>)</mo><mspace></mspace></mrow></math></span>nanofluid over a non-isothermal wedge. During the study, the dimensional continuity, momentum, energy, and concentration equations are transformed into non-dimensional equations using a non-similarity transformation. Keller box (KBM) numerical solution methods are then applied to analyse the impacts of various dimensionless parameters on velocity, temperature, and concentration. The focus of this research is on two primary instances: the behaviour of Newtonian fluids and the unique properties of Williamson fluids, which are categorized as non-Newtonian. Various factors are analysed in both cases, including the buoyancy ratio<span><math><mrow><mspace></mspace><mrow><mfenced><mrow><mi>N</mi></mrow></mfenced></mrow></mrow></math></span>, mixed convection<span><math><mrow><mspace></mspace><mrow><mfenced><mrow><mi>λ</mi></mrow></mfenced></mrow></mrow></math></span>, Brownian motion<span><math><mrow><mspace></mspace><mrow><mfenced><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>T</mi></mrow></msub></mrow></mfenced></mrow></mrow></math></span>, thermophoresis<span><math><mrow><mspace></mspace><mrow><mfenced><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>B</mi></mrow></msub></mrow></mfenced></mrow></mrow></math></span>, and heat source and sink<span><math><mrow><mspace></mspace><mrow><mfenced><mrow><mi>Q</mi></mrow></mfenced></mrow></mrow></math></span> parameters. The Williamson fluid model describes non-Newtonian fluids where viscosity changes with shear rate. The results indicate that variations in the Williamson fluid, buoyancy, and mixed convection parameter result in alterations in the fluid viscosity, subsequently influencing the thermal mass-transfer properties of the fluid. Fluid flow over a wedge surface is utilized in various fields such as aerodynamics, heat transfer, chemical engineering, geophysics, and material processing. The application of the Williamson ternary fluid model, incorporating <span><math><mrow><mi>Ag</mi><mo>,</mo><mi>MgO</mi><mo>,</mo></mrow></math></span> and <span><math><mrow><mi>F</mi><msub><mrow><mi>e</mi></mrow><mrow><mn>3</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math></span> nanoparticles dispersed in water flowing over a wedge surface, has the potential to transform heat dissipation in advanced electronic cooling systems. This innovation could significantly boost performance and reliability, particularly in demanding high-power applications, representing a significant advancement in thermal management technology. Finally, the main findings of this article are highlighted in the last section.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 502-529"},"PeriodicalIF":4.4,"publicationDate":"2025-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143465051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Vertical modeling of carbon sequestration in coastal wetlands using fractional-order derivatives and moisture dynamics","authors":"Vsevolod Bohaienko ,&nbsp;Fasma Diele ,&nbsp;Fabio V. Difonzo ,&nbsp;Carmela Marangi ,&nbsp;Angela Martiradonna ,&nbsp;Antonello Provenzale","doi":"10.1016/j.matcom.2025.02.005","DOIUrl":"10.1016/j.matcom.2025.02.005","url":null,"abstract":"<div><div>Wetlands are essential for global biogeochemical cycles and ecosystem services, with the dynamics of soil organic carbon (SOC) serving as the critical regulatory mechanism for these processes. However, accurately modeling carbon dynamics in wetlands presents challenges due to their complexity. Traditional approaches often fail to capture spatial variations, long-range transport, and periodical flooding dynamics, leading to uncertainties in carbon flux predictions. To tackle these challenges, we introduce a novel extension of the fractional RothC model, integrating temporal fractional-order derivatives into spatial dimensions. This enhancement allows for the creation of a more adaptive tool for analyzing SOC dynamics. Our differential model incorporates Richardson–Richard’s equation for moisture fluxes, a diffusion–advection–reaction equation for fractional-order dynamics of SOC compounds, and a temperature transport equation. We examine the influence of diffusive movement and sediment moisture content on model solutions, as well as the impact of including advection terms. Finally, we validated the model on a restored wetland scenario at the Ebro Delta site, aiming to evaluate the effectiveness of flooding strategies in enhancing carbon sequestration and ecosystem resilience.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 369-388"},"PeriodicalIF":4.4,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143427935","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multi-period mean–variance portfolio optimization with capital injections","authors":"Longyu Shi ,&nbsp;Yunyun Wang ,&nbsp;Wenyue Li ,&nbsp;Zhimin Zhang","doi":"10.1016/j.matcom.2025.02.006","DOIUrl":"10.1016/j.matcom.2025.02.006","url":null,"abstract":"<div><div>In this study, we explore the portfolio optimization problem where the investors initially allocate portions of their capital across a large asset pool, followed by gradual capital injections over the subsequent periods. We introduce a multi-period mean–variance model with capital injections to develop a sparse long-term investment strategy within this framework. This model adopts the fused Lasso technique, integrating two <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> penalty terms designed to lower both holding and trading costs. We utilize a two-block alternating direction method of multipliers algorithm to solve this complex, non-smooth optimization problem involving multiple variables. A thorough analysis of the convergence of the algorithm is provided. In addition, we empirically validate the efficacy of our model using two real datasets, demonstrating its practical applicability and effectiveness in real-world scenarios.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"233 ","pages":"Pages 400-412"},"PeriodicalIF":4.4,"publicationDate":"2025-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}