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Your search keyword '"Department of Mathematics (HIT Harbin Institute of Technology)"' showing total 7 results
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7 results on '"Department of Mathematics (HIT Harbin Institute of Technology)"'

1. On the polynomiality and asymptotics of moments of sizes for random $(n, dn\pm 1)$-core partitions with distinct parts

Author

Wenston J.T. Zang, Huan Xiong, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics (HIT Harbin Institute of Technology), and Harbin Institute of Technology (HIT)

Subjects
Coprime integers, General Mathematics, 0102 computer and information sciences, 01 natural sciences, 05A17, 11P81, 010101 applied mathematics, Combinatorics, Average size, 010201 computation theory & mathematics, [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], FOS: Mathematics, Mathematics - Combinatorics, Partition (number theory), Combinatorics (math.CO), 0101 mathematics, Mathematics
Abstract

Amdeberhan's conjectures on the enumeration, the average size, and the largest size of $(n,n+1)$-core partitions with distinct parts have motivated many research on this topic. Recently, Straub and Nath-Sellers obtained formulas for the numbers of $(n, dn-1)$ and $(n, dn+1)$-core partitions with distinct parts, respectively. Let $X_{s,t}$ be the size of a uniform random $(s,t)$-core partition with distinct parts when $s$ and $t$ are coprime to each other. Some explicit formulas for the $k$-th moments $\mathbb{E} [X_{n,n+1}^k]$ and $\mathbb{E} [X_{2n+1,2n+3}^k]$ were given by Zaleski and Zeilberger when $k$ is small. Zaleski also studied the expectation and higher moments of $X_{n,dn-1}$ and conjectured some polynomiality properties concerning them in arXiv:1702.05634. Motivated by the above works, we derive several polynomiality results and asymptotic formulas for the $k$-th moments of $X_{n,dn+1}$ and $X_{n,dn-1}$ in this paper, by studying the beta sets of core partitions. In particular, we show that these $k$-th moments are asymptotically some polynomials of n with degrees at most $2k$, when $d$ is given and $n$ tends to infinity. Moreover, when $d=1$, we derive that the $k$-th moment $\mathbb{E} [X_{n,n+1}^k]$ of $X_{n,n+1}$ is asymptotically equal to $\left(n^2/10\right)^k$ when $n$ tends to infinity. The explicit formulas for the expectations $\mathbb{E} [X_{n,dn+1}]$ and $\mathbb{E} [X_{n,dn-1}]$ are also given. The $(n,dn-1)$-core case in our results proves several conjectures of Zaleski on the polynomiality of the expectation and higher moments of $X_{n,dn-1}$., Comment: This paper has been accepted for publication in SCIENCE CHINA Mathematics

Published
2020

2. Adaptive Image Assimilation for 2D Velocity Reconstruction

Author

Li, Long, Vidard, Arthur, Le Dimet, François-Xavier, Ma, Jianwei, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS), and LI, LONG

Subjects
[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC], [INFO]Computer Science [cs], [MATH] Mathematics [math], [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [INFO] Computer Science [cs], [MATH]Mathematics [math], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2019

3. A level-set based image assimilation method: Potential applications for predicting the movement of oil spills

Author

Arthur Vidard, Jianwei Ma, François-Xavier Le Dimet, Long Li, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Mathematics and computing applied to oceanic and atmospheric flows (AIRSEA), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Laboratoire Jean Kuntzmann (LJK ), and Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Centre National de la Recherche Scientifique (CNRS)

Subjects
Pollution, Level set method, Computer science, media_common.quotation_subject, ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION, 010103 numerical & computational mathematics, 01 natural sciences, Image (mathematics), Level set, 0101 mathematics, Electrical and Electronic Engineering, Diffusion (business), Structural information, media_common, Remote sensing, Pollutant, Image assimilation, Movement (music), Oil spills, 010101 applied mathematics, 13. Climate action, Oil spill, General Earth and Planetary Sciences, State (computer science), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Algorithm
Abstract

In this paper, we present a novel method for assimilating geometric information from observed images. Image assimilation technology fully utilizes structural information from the dynamics of the images to retrieve the state of a system and thus to better predict its evolution. Level-set method describing the evolution of the geometry shapes of a given system is taken into account to include the dynamics of the images. This method takes advantage of Lagrangian information in an Eulerian numerical framework. In our numerical experiments, we apply this state-of-the-art technique to a pollutant transport problem, to calibrate the initial contours of pollutants and to identify diffusion coefficients of the model. It can be shown a potential approach for oil spills, because topological merging and breaking of oil slicks are well defined and easily performed by this proposed approach. Numerical results show that the proposed method is visibly efficient compared with the classical method based on the concentration map when the concentration measurements and the background fields are not well available.

Published
2017

4. Stability of planar traveling fronts in bistable reaction–diffusion systems

Author

Wei-Jie Sheng, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), and China Scholarship Council.NSF of China 11401134.

Subjects
Bistability, Semigroup, Applied Mathematics, 010102 general mathematics, Mathematical analysis, 01 natural sciences, 010101 applied mathematics, Planar traveling fronts, Planar, Reaction-diffusion systems, Rate of convergence, 35K45 (35B10 35B35 35B65 35C07 35K57), Stability theory, Bounded function, Reaction–diffusion system, Initial value problem, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Analysis, Mathematics, Multidimensional stability
Abstract

This paper is concerned with the multidimensional stability of planar traveling fronts in bistable reaction–diffusion systems. It is first shown that planar traveling fronts are asymptotically stable under spatially decaying initial perturbations by appealing to the comparison principle and super-subsolution method. In particular, if the perturbations belong to L 1 ( R n − 1 ) in a certain sense, we obtain a convergence rate like t − n − 1 2 . Then we show that the solution of the Cauchy problem converges to the planar traveling front with rate t − n + 1 4 for a spatially non-decaying perturbation with the help of semigroup theory. Finally, we prove that there exists a solution oscillating permanently between two planar traveling fronts, which indicates that planar traveling fronts are not always asymptotically stable in multidimensional space under general bounded perturbations.

Published
2017

5. Time periodic traveling curved fronts of bistable reaction–diffusion equations in R-3

Author

Wei-Jie Sheng, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Institut de Mathématiques de Marseille (I2M), Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU), NSF of China 11401134. China Postdoctoral Science Foundation 2012M520716. China Scholarship Council., and Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
35K57 (35B10 35C07), Applied Mathematics, 010102 general mathematics, Mathematical analysis, Regular polygon, Boundary (topology), Curvature, 01 natural sciences, Domain (mathematical analysis), 010101 applied mathematics, Nonlinear system, Polyhedron, Bistable, Traveling fronts, Reaction-diffusion equations, Bounded function, Reaction–diffusion system, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], 0101 mathematics, Time periodic, Mathematics
Abstract

This paper is concerned with the existence and stability of time periodic traveling curved fronts for reaction–diffusion equations with bistable nonlinearity in \({\mathbb {R}}^3\). We first study the existence and other qualitative properties of time periodic traveling fronts of polyhedral shape. Furthermore, for any given \(g\in C^{\infty }(S^1)\) with \(\min \nolimits _{0\le \theta \le 2\pi }g(\theta )=0\) that gives a convex bounded domain with smooth boundary of positive curvature everywhere, which is included in a sequence of convex polygons, we show that there exists a three-dimensional time periodic traveling front by taking the limit of the solutions corresponding to the convex polyhedrons as the number of the lateral surfaces goes to infinity.

Published
2017

6. A Hybrid Finite Volume Method for Advection Equations and Its Applications in Population Dynamics

Author

Yang, Chang, Tine, Léon Matar, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Multi-scale modelling of cell dynamics : application to hematopoiesis (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Centre de génétique et de physiologie moléculaire et cellulaire (CGPhiMC), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS)-Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Camille Jordan (ICJ), and Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL)

Subjects
Discontinuity detector, WENO scheme, population dynamics, [MATH]Mathematics [math], anti-diffusive method
Abstract

International audience; We present in this article a very adapted finite volume numerical scheme for transport type-equation. Thescheme is an hybrid one combining an anti-dissipative method with down-winding approach for the flux(Després and Lagoutière, C R Acad Sci Paris Sér I Math 328(10) (1999), 939–944; Goudon, Lagoutière,and Tine, Math Method Appl Sci 23(7) (2013), 1177–1215) and an high accurate method as the WENO5one (Jiang and Shu, J Comput Phys 126 (1996), 202–228). The main goal is to construct a scheme ableto capture in exact way the numerical solution of transport type-equation without artifact like numericaldiffusion or without “stairs” like oscillations and this for any regular or discontinuous initial distribution.This kind of numerical hybrid scheme is very suitable when properties on the long term asymptotic behaviorof the solution are of central importance in the modeling what is often the case in context of populationdynamics where the final distribution of the considered population and its mass preservation relation arerequired for prediction.

Published
2017

7. Monotone traveling waves for delayed neural field equations

Author

Jian Fang, Grégory Faye, Department of Mathematics (HIT Harbin Institute of Technology), Harbin Institute of Technology (HIT), Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), and Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS)

Subjects
Applied Mathematics, 010102 general mathematics, Mathematical analysis, Function (mathematics), Type (model theory), 01 natural sciences, Exponential function, 010101 applied mathematics, Monotone polygon, Exponential growth, Modeling and Simulation, Kernel (statistics), Bounded function, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Uniqueness, 0101 mathematics, [MATH]Mathematics [math], Mathematics
Abstract

International audience; We study the existence of traveling wave solutions and spreading properties for single-layer delayed neural field equations. We focus on the case where the kinetic dynamics are of monos-table type and characterize the invasion speeds as a function of the asymptotic decay of the connectivity kernel. More precisely, we show that for exponentially bounded kernels the minimal speed of traveling waves exists and coincides with the spreading speed, which further can be explicitly characterized under a KPP type condition. We also investigate the case of algebraically decaying kernels where we prove the non-existence of traveling wave solutions and show the level sets of the solutions eventually locate in between two exponential functions of time. The uniqueness of traveling waves modulo translation is also obtained.

Published
2016

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