In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum...In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.展开更多
This article is concerned with the 3 D nonhomogeneous incompressible magnetohydrodynamics equations with a slip boundary conditions in bounded domain.We obtain weighted estimates of the velocity and magnetic field,and...This article is concerned with the 3 D nonhomogeneous incompressible magnetohydrodynamics equations with a slip boundary conditions in bounded domain.We obtain weighted estimates of the velocity and magnetic field,and address the issue of local existence and uniqueness of strong solutions with the weaker initial data which contains vacuum states.展开更多
Applications of Wireless Sensor devices are widely used byvarious monitoring sections such as environmental monitoring, industrialsensing, habitat modeling, healthcare and enemy movement detection systems.Researchers ...Applications of Wireless Sensor devices are widely used byvarious monitoring sections such as environmental monitoring, industrialsensing, habitat modeling, healthcare and enemy movement detection systems.Researchers were found that 16 bytes packet size (payload) requires MediaAccess Control (MAC) and globally unique network addresses overheads asmore as the payload itself which is not reasonable in most situations. Theapproach of using a unique address isn’t preferable for most Wireless SensorNetworks (WSNs) applications as well. Based on the mentioned drawbacks,the current work aims to fill the existing gap in the field area by providingtwo strategies. First, name/address solutions that assign unique addresseslocally to clustered topology-based sensor devices, reutilized in a spatialmanner, and reduce name/address size by a noticeable amount of 2.9 basedon conducted simulation test. Second, name/address solutions that assignreutilizing of names/addresses to location-unaware spanning-tree topologyin an event-driven WSNs case (that is providing minimal low latenciesand delivering addressing packet in an efficient manner). Also, to declinethe approach of needing both addresses (MAC and network) separately, itdiscloses how in a spatial manner to reutilize locally unique sensor devicename approach and could be utilized in both contexts and providing anenergy-efficient protocol for location unawareness clustered based WSNs.In comparison, an experimental simulation test performed and given theaddresses solution with less overhead in the header and 62 percent fairpayload efficiency that outperforms 34 percent less effective globally uniqueaddresses. Furthermore, the proposed work provides addresses uniquenessfor network-level without using network-wide Duplicate Address Detection(DAD) algorithm. Consequently, the current study provides a roadmap foraddressing/naming scheme to help researchers in this field of study. In general,some assumptions were taken during the work phases of this study such asnumber of Cluster Head (CH) nodes is 6% of entire sensor nodes, locationunawareness for entire sensor network and 4 bits per node address space whichconsidered as the limitation of the study.展开更多
An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of...An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.展开更多
Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applicat...Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applications in physics lead to mathematical models where boundary data is inhomogeneous, e.g. in radio frequency wave experiments. In this paper, we investigate the mixed initial-boundary condition problem for the nonlinear Schrödinger equation iu<sub>t</sub> = u<sub>xx</sub> – g|u|<sup>p-1</sup>u, g ∈R, p > 3 on a semi-infinite strip. The equation satisfies an initial condition and Dirichlet boundary conditions. We utilize semi-group theory to prove existence and uniqueness theorem of a strong local solution.展开更多
In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. Wit...In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.展开更多
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
基金partially supported by the National Natural Science Foundation of China (11671273 and 11931010)key research project of the Academy for Multidisciplinary Studies of CNU and Beijing Natural Science Foundation (1192001).
文摘In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong solutions.The initial vacuum is allowed.
基金This work was supported by Natural Science Foundation of China(11871412).
文摘This article is concerned with the 3 D nonhomogeneous incompressible magnetohydrodynamics equations with a slip boundary conditions in bounded domain.We obtain weighted estimates of the velocity and magnetic field,and address the issue of local existence and uniqueness of strong solutions with the weaker initial data which contains vacuum states.
文摘Applications of Wireless Sensor devices are widely used byvarious monitoring sections such as environmental monitoring, industrialsensing, habitat modeling, healthcare and enemy movement detection systems.Researchers were found that 16 bytes packet size (payload) requires MediaAccess Control (MAC) and globally unique network addresses overheads asmore as the payload itself which is not reasonable in most situations. Theapproach of using a unique address isn’t preferable for most Wireless SensorNetworks (WSNs) applications as well. Based on the mentioned drawbacks,the current work aims to fill the existing gap in the field area by providingtwo strategies. First, name/address solutions that assign unique addresseslocally to clustered topology-based sensor devices, reutilized in a spatialmanner, and reduce name/address size by a noticeable amount of 2.9 basedon conducted simulation test. Second, name/address solutions that assignreutilizing of names/addresses to location-unaware spanning-tree topologyin an event-driven WSNs case (that is providing minimal low latenciesand delivering addressing packet in an efficient manner). Also, to declinethe approach of needing both addresses (MAC and network) separately, itdiscloses how in a spatial manner to reutilize locally unique sensor devicename approach and could be utilized in both contexts and providing anenergy-efficient protocol for location unawareness clustered based WSNs.In comparison, an experimental simulation test performed and given theaddresses solution with less overhead in the header and 62 percent fairpayload efficiency that outperforms 34 percent less effective globally uniqueaddresses. Furthermore, the proposed work provides addresses uniquenessfor network-level without using network-wide Duplicate Address Detection(DAD) algorithm. Consequently, the current study provides a roadmap foraddressing/naming scheme to help researchers in this field of study. In general,some assumptions were taken during the work phases of this study such asnumber of Cluster Head (CH) nodes is 6% of entire sensor nodes, locationunawareness for entire sensor network and 4 bits per node address space whichconsidered as the limitation of the study.
基金The National Natural Science Foundation of China(No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education(No.200802860024)the Natural Science Foundation of Jiangsu Province(No.BK2010393)
文摘An element a of a ring R is called uniquely strongly clean if it is the sum of an idempotent and a unit that commute, and in addition, this expression is unique. R is called uniquely strongly clean if every element of R is uniquely strongly clean. The uniquely strong cleanness of the triangular matrix ring is studied. Let R be a local ring. It is shown that any n × n upper triangular matrix ring over R is uniquely strongly clean if and only if R is uniquely bleached and R/J（R） ≈Z2.
文摘Pure initial value problems for important nonlinear evolution equations such as nonlinear Schrödinger equation (NLS) and the Ginzburg-Landau equation (GL) have been extensively studied. However, many applications in physics lead to mathematical models where boundary data is inhomogeneous, e.g. in radio frequency wave experiments. In this paper, we investigate the mixed initial-boundary condition problem for the nonlinear Schrödinger equation iu<sub>t</sub> = u<sub>xx</sub> – g|u|<sup>p-1</sup>u, g ∈R, p > 3 on a semi-infinite strip. The equation satisfies an initial condition and Dirichlet boundary conditions. We utilize semi-group theory to prove existence and uniqueness theorem of a strong local solution.
基金supported by National Natural Sciences Foundation of China(No.11171229,11231006 and 11228102)project of Beijing Chang Chen Xue Zhe
文摘In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/4.Moreover,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization technique.Our results extend ones on the 3D Navier-Stokes equations with fractional diffusion.
