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91.
《Mathematical Methods in the Applied Sciences》2018,41(5):1761-1773
In this paper, we construct a space of boundary values for minimal symmetric 1D Hamiltonian operator with defect index (1,1) (in limit‐point case at a(b) and limit‐circle case at b(a)) acting in the Hilbert space In terms of boundary conditions at a and b, all maximal dissipative, accumulative, and self‐adjoint extensions of the symmetric operator are given. Two classes of dissipative operators are studied. They are called “dissipative at a” and “dissipative at b.” For 2 cases, a self‐adjoint dilation of dissipative operator and its incoming and outgoing spectral representations are constructed. These constructions allow us to establish the scattering matrix of dilation and a functional model of the dissipative operator. Further, we define the characteristic function of the dissipative operators in terms of the Weyl‐Titchmarsh function of the corresponding self‐adjoint operator. Finally, we prove theorems on completeness of the system of root vectors of the dissipative operators. 相似文献
92.
Khai T. Nguyen 《Journal of Mathematical Analysis and Applications》2010,372(2):611-628
We prove that if the hypograph of a continuous function f admits at every boundary point a supporting ball then it has “essentially” positive reach, i.e. the hypograph of the restriction of f outside a closed set of zero measure has (locally) positive reach. Hence such a function enjoys some properties of a concave function, in particular a.e. twice differentiability. We apply this result to a minimum time problem in the case of a nonlinear smooth dynamics and a target satisfying internal sphere condition. 相似文献
93.
In this paper, we consider deviation inequalities for infinitely divisible random vectors in R
k and infinite-dimensional spaces l
p, 1 p We compare the results obtained using the covariance representation for infinitely divisible random vectors with the well-known Talagrand's result on measure concentration phenomenon. 相似文献
94.
Michael Falk 《Journal of multivariate analysis》1998,67(2):306-317
The comedianCOM(X, Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X, Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the correlation coefficientρwith range [−1, 1] and can therefore serve as a robust alternative toρ. We show that this result, which is not true in general, extends to elliptical distributions even in the case where moments ofX,Ydo not exist. 相似文献
95.
Fullerene polyhedra of icosahedral symmetry have the midpoints of their 12 pentagonal faces at the vertices of a macroicosahedron and can be characterized by the patterns of their hexagonal faces on the (triangular) macrofaces of this macroicosahedron. The numbers of the vertices in fullerene polyhedra of icosahedral symmetry satisfy the Goldberg equation v=20(h
2+hk+k
2), where h and k are two integers and 0 <h≥ k≥ 0 and define a two-dimensional Goldberg vector G = (h, k). The known tripling (leapfrog), quadrupling (chamfering), and septupling (capra) transformations correspond to the Goldberg vectors (1, 1), (2, 0), and (2, 1), respectively. The tripling and quadrupling transformations applied to the regular dodecahedron generate achiral fullerene polyhedra with the full I
h
point group. However, the septupling transformation destroys the reflection operations of the underlying icosahedron to generate chiral fullerene polyhedra having only the I icosahedral rotational point group. Generalization of the quadrupling transformation leads to the fundamental homologous series of achiral fullerene polyhedra having 20 n
2 vertices and Goldberg vectors (n, 0). A related homologous series of likewise achiral fullerene polyhedra having 60 n
2 vertices and Goldberg vectors (n, n) is obtained by applying the tripling transformation to regular dodecahedral C20 to give truncated icosahedral C60 followed by the generalized operations (as in the case of quadrupling) for obtaining homologous series of fullerenes. Generalization of the septupling (capra) transformation leads to a homologous series of chiral C20m
fullerenes with the I point group and Goldberg vectors G=(h, 1) where m=h
2+h+1. 相似文献
96.
Let S(n) = ξ(1)+?+ξ(n) be a sum of independent random vectors ξ(i) = ξ (n)(i) with general distribution depending on a parameter n. We find sufficient conditions for the uniform version of the integro-local Stone theorem to hold for the asymptotics of the probability P(S(n) ∈ Δ[x), where Δ[x) is a cube with edge Δ and vertex at a point x. 相似文献
97.
98.
Ian N. Deters 《Journal of Mathematical Analysis and Applications》2009,350(1):354-359
In this paper we extend the work done by Deters and Seubert in [I. Deters, S. Seubert, Cyclic vectors of diagonal operators on the space of functions analytic on a disk, J. Math. Anal. Appl. 334 (2007) 1209-1219]. In particular, we shall improve upon a theorem in the aforementioned paper and make connections between the strong operator topology on H(B(0,1)), polynomial behavior on a sequence of points, and the synthesis of diagonal operators on H(B(0,1)). 相似文献
99.
在感应型速调管调制器中使用了纳米晶磁性材料制作大尺寸磁环,使用伏安向量法对材料试样的磁性能进行测量,得到频率为20.03 kHz和50 kHz时的动态磁化曲线、磁导率、磁场损耗等参数。使用脉冲法对成型的大尺寸磁环动态磁性能进行测量,励磁方式和工作中完全一致,在测量脉冲脉宽3.5~4.0 μs,重复频率50 Hz,初次线圈均为1匝,外径220 mm,内径80 mm,高60 mm,截面积4 200 mm2时,得到磁环实际能够达到的伏秒数为0.007 V·s,此时所需的偏磁电流大小为8 A。 相似文献
100.
We consider quadratic forms of the type
where Xj are i.i.d. random variables with common distribution F and finite fourth moment,
denotes a symmetric matrix with eigenvalues λ1, ..., λN ordered to be non-increasing in absolute value. We prove explicit bounds in terms of sums of 4th powers of entries of the
matrix A and the size of the eigenvalue λ13 for the approximation of the distribution of Q(F,A) by the distribution of Q (φ, A) where φ is standard Gaussian distribution. In typical cases this error is of optimal order
Supported by the DFG-Forschergruppe FOR 399/1-1 at Bielefeld. Partially supported by INTAS N 03-51-5018.
Partially supported by RFBR and RFBR–DFG, grants NN 02-01-00233, 04-01-04000 相似文献