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81.
82.
Alberto Seeger 《Integral Equations and Operator Theory》2006,54(2):279-300
Let H be an infinite dimensional Hilbert space. Denote by Λ (E, F) the set of all
for which the multivalued system 0 ∈ (F − λ E) (x) admits a nonzero solution x ∈ H. One says that Λ (E, F) is the point spectrum of the pair (E, F). It is well known that Λ (E, F) does not behave in a stable manner with respect to perturbations in the argument (E, F). The purpose of this note is to study the outer-semicontinuous hull (or graph-closure) of the mapping Λ. 相似文献
83.
84.
《Mathematische Nachrichten》2018,291(2-3):518-538
The homology groups , , and of the Brauer complex for a triquadratic field extension are studied. In particular, given , we find equivalent conditions for the image of D in to be zero. We consider as well the second divided power operation , and show that there are nonstandard elements with respect to γ2. Further, a natural transformation , which turns out to be nondegenerate on the left, is defined. As an application we construct a field extension such that the cohomology group of the Brauer complex contains the images of prescribed elements of , provided these elements satisfy a certain cohomological condition. At the final part of the paper examples of triquadratic extensions with nontrivial are given. As a consequence we show that the homology group can be arbitrarily big. 相似文献
85.
86.
87.
In this paper, based on a multidimensional Riemann theta function, a lucid and straightforward generalization of the Hirota-Riemann method is presented to explicitly construct multiperiodic Riemann theta functions periodic wave solutions for nonlinear equations such as the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and (2+1)-dimensional breaking soliton equation. Among these periodic waves, the one-periodic waves are well-known cnoidal waves, their surface pattern is one-dimensional, and often they are used as one-dimensional models of periodic waves. The two-periodic waves are a direct generalization of one-periodic waves, their surface pattern is two-dimensional so that they have two independent spatial periods in two independent horizontal directions. A limiting procedure is presented to analyze in detail, asymptotic behavior of the multiperiodic waves and the relations between the periodic wave solutions and soliton solutions are rigorously established. This generalized Hirota-Riemann method can also be demonstrated on a class variety of nonlinear difference equations such as Toeplitz lattice equation. 相似文献
88.
Let Mm,n(B) be the semimodule of all m×n Boolean matrices where B is the Boolean algebra with two elements. Let k be a positive integer such that 2?k?min(m,n). Let B(m,n,k) denote the subsemimodule of Mm,n(B) spanned by the set of all rank k matrices. We show that if T is a bijective linear mapping on B(m,n,k), then there exist permutation matrices P and Q such that T(A)=PAQ for all A∈B(m,n,k) or m=n and T(A)=PAtQ for all A∈B(m,n,k). This result follows from a more general theorem we prove concerning the structure of linear mappings on B(m,n,k) that preserve both the weight of each matrix and rank one matrices of weight k2. Here the weight of a Boolean matrix is the number of its nonzero entries. 相似文献
89.
Characteristic parameter sets and limits of circulant Hermitian polygon transformations 总被引:1,自引:0,他引:1
Polygon transformations based on taking the apices of similar triangles constructed on the sides of an initial polygon are analyzed as well as the limit polygons obtained by iteratively applying such transformations. In contrast to other approaches, this is done with respect to two construction parameters representing a base angle and an apex perpendicular subdivision ratio. Furthermore, a combined transformation leading to circulant Hermitian matrices is proposed, which eliminates the rotational effect of the basic transformation. A finite set of characteristic parameter subdomains is derived for which the sequence converges to specific eigenpolygons. Otherwise, limit polygons turn out to be linear combinations of up to three eigenpolygons. This leads to a full classification of circulant Hermitian similar triangles based polygon transformations and their limit polygons. As a byproduct classical results as Napoleon’s theorem and the Petr-Douglas-Neumann theorem can be easily deduced. 相似文献
90.
Xijun Deng Jinlong Cao Xi Li 《Communications in Nonlinear Science & Numerical Simulation》2010,15(2):281-290
In this paper, travelling wave solutions for the nonlinear dispersion Drinfel’d–Sokolov system (called D(m,n) system) are studied by using the Weierstrass elliptic function method. As a result, more new exact travelling wave solutions to the D(m,n) system are obtained including not only all the known solutions found by Xie and Yan but also other more general solutions for different parameters m,n. Moreover, it is also shown that the D(m,1) system with linear dispersion possess compacton and solitary pattern solutions. Besides that, it should be pointed out that the approach is direct and easily carried out without the aid of mathematical software if compared with other traditional methods. We believe that the method can be widely applied to other similar types of nonlinear partial differential equations (PDEs) or systems in mathematical physics. 相似文献