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81.
In this paper, we study the problem of existence of zero points for set-valued operators in Banach spaces. We present a simple
condition which can be used to verify that under some conditions, set-valued operators have zero points. Furthermore, we derive
the surjectivity result and the Kakutani fixed point theorem by using this condition.
相似文献
82.
设D是C中的单位圆盘及为[0,1)上的正规函数。对于0<P<∞,这样的函数用于定义一个带权为 ̄p(|z|)/(1-|z| ̄2)的Bergman空间A ̄p.本文刻画了A ̄p中函数之零点集的结构.作为应用,又给出了A ̄p中函数序列插值的条件。 相似文献
83.
CHEN ZONGXUAN 《高校应用数学学报(英文版)》1994,9(4):365-374
THEZEROANDORDEROFSOMESECONDORDERLINEARDIFFERENTIALEQUATIONSWITHTRANSCENDENTALMEROMORPHICCOEFFICIENTSCHENZONGXUANAbstract:Inth... 相似文献
84.
O. I. Mokhov 《Theoretical and Mathematical Physics》2007,152(2):1183-1190
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions
of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of
flat torsionless potential submanifolds. We show that all flat torsionless potential submanifolds in pseudo-Euclidean spaces bear natural structures
of Frobenius algebras on their tangent spaces. These Frobenius structures are generated by the corresponding flat first fundamental
form and the set of the second fundamental forms of the submanifolds (in fact, the structural constants are given by the set
of the Weingarten operators of the submanifolds). We prove that each N-dimensional Frobenius manifold can be locally represented
as a flat torsionless potential submanifold in a 2N-dimensional pseudo-Euclidean space. By our construction, this submanifold
is uniquely determined up to motions. Moreover, we consider a nonlinear system that is a natural generalization of the associativity
equations, namely, the system describing all flat torsionless submanifolds in pseudo-Euclidean spaces, and prove that this
system is integrable by the inverse scattering method.
To the memory of my wonderful mother Maya Nikolayevna Mokhova (4 May 1926–12 September 2006)
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 2, pp. 368–376, August, 2007. 相似文献
85.
Fuyi Li Zhanping Liang Qi Zhang Yuhua Li 《Journal of Mathematical Analysis and Applications》2007,327(2):1010-1028
In this paper, the existence of sign-changing solutions for nonlinear operator equations is discussed by using the topological degree and fixed point index theory. The main theorems are some new three-solution theorems which are different from the famous Amann's and Leggett-Williams' three-solution theorems as well as the results in [F. Li, G. Han, Generalization for Amann's and Leggett-Williams' three-solution theorems and applications, J. Math. Anal. Appl. 298 (2004) 638-654]. These three solutions are all nonzero. One of them is positive, another is negative, and the third one is a sign-changing solution. Furthermore, the theoretical results are successfully applied to both integral and differential equations. 相似文献
86.
We extend integrable systems on quad-graphs, such as the Hirota equation and the cross-ratio equation, to the noncommutative context, when the fields take values in an arbitrary associative algebra. We demonstrate that the three-dimensional consistency property remains valid in this case. We derive the noncommutative zero curvature representations for these systems, based on the latter property. Quantum systems with their quantum zero curvature representations are particular cases of the general noncommutative ones. 相似文献
87.
Pavol Brunovský 《Journal of Dynamics and Differential Equations》1990,2(3):293-323
For the scalar reaction diffusion equation with Dirichlet boundary conditions, it is proved that its maximal compact attractor is the graph of a C1 function from a subset with nonempty interior of a subspace of the state space the dimension of which is equal to the maximal Morse index of the equilibria of the equation. 相似文献
88.
Dong-Yang Jing 《中国物理 B》2023,32(1):17401-017401
One-dimensional s-wave superconductor with spin-orbit coupling is a platform for the realization of Majorana zero modes. The spin-exchange with the magnetic skyrmion lattice can induce spin-orbit coupling in a s-wave superconductor system and the effects are different from the constant spin-orbit coupling. The strength of the effective spin-orbit coupling as well as the rich topoloigcal phase diagram are directly connected to the radius of the skyrmion lattice R. We obtain the rich topological phase diagram of this system with different skyrmion lattice radii by numerically evaluating the spectrum of the system under the periodic boundary condition, and we also find the Majorana zero modes under the open boundary condition to verify the bulk-edge correspondence. 相似文献
89.
90.
微机电陀螺零点漂移数据滤波方法的研究 总被引:9,自引:2,他引:9
微机电石英音叉陀螺虽然有突出的优点,但也存在噪声比较大的缺点。普通的数字滤波方法通常会造成比较大的滞后,减小了系统的相位裕度,而且对截止频率以内的噪声不起作用。作者在对石英音叉陀螺零点漂移数据建立时间序列模型(AR模型)的基础上,采用卡尔曼滤波算法对石英音叉陀螺的漂移数据进行了处理。仿真实验表明,所采用的滤波方法合理有效。 相似文献