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81.
Linear systems whose associated block Jacobi iteration matrixB is weakly cyclic generated by the cyclic permutation = (1,2,...,
p
) in the spirit of Li and Varga are considered. Regions of convergence for the corresponding blockp-cyclic SOR method are derived and the exact convergence domains for real spectra, (B
p
), of the same sign are obtained. Moreover, analytical expressions for two special cases forp = 5 are given and numerical results are presented confirming the theory developed. The tools used for this work are mainly from complex analysis and extensive use of (asteroidal) hypocycloids in the complex plane is made to produce our results.This work was supported in part by AFOSR grant F49620-92-J-0069 and NSF grant 9202536-CCR. 相似文献
82.
Shaul K. Bar-Lev Daoud Bshouty Peter Enis Gérard Letac I-Li Lu Donald Richards 《Journal of Theoretical Probability》1994,7(4):883-929
A natural exponential family (NEF)F in ? n ,n>1, is said to be diagonal if there existn functions,a 1,...,a n , on some intervals of ?, such that the covariance matrixV F (m) ofF has diagonal (a 1(m 1),...,a n (m n )), for allm=(m 1,...,m n ) in the mean domain ofF. The familyF is also said to be irreducible if it is not the product of two independent NEFs in ? k and ? n-k , for somek=1,...,n?1. This paper shows that there are only six types of irreducible diagonal NEFs in ? n , that we call normal, Poisson, multinomial, negative multinomial, gamma, and hybrid. These types, with the exception of the latter two, correspond to distributions well established in the literature. This study is motivated by the following question: IfF is an NEF in ? n , under what conditions is its projectionp(F) in ? k , underp(x 1,...,x n )∶=(x 1,...,x k ),k=1,...,n?1, still an NEF in ? k ? The answer turns out to be rather predictable. It is the case if, and only if, the principalk×k submatrix ofV F (m 1,...,m n ) does not depend on (m k+1,...,m n ). 相似文献
83.
In order to study the density of the set of positive integers for which the negative Pell equation is solvable in integers, we compute the norm of the fundamental unit in certain well-chosen families of real quadratic orders. A fast algorithm that computes 2-class groups rather than units is used. It is random polynomial-time in as the factorization of is a natural part of the input for the values of we encounter. The data obtained provide convincing numerical evidence for the density heuristics for the negative Pell equation proposed by the second author. In particular, an irrational proportion of the real quadratic fields without discriminantal prime divisors congruent to 3 mod 4 should have a fundamental unit of norm .
84.
Stefano Serra 《BIT Numerical Mathematics》1996,36(1):135-142
In this paper we are concerned with the asymptotic behavior of the smallest eigenvalue
1
(n)
of symmetric (Hermitian)n ×n Toeplitz matricesT
n
(f) generated by an integrable functionf defined in [–, ]. In [7, 8, 11] it is shown that
1
(n)
tends to essinff =m
f
in the following way:
1
(n)
–m
f
1/n
2k
. These authors use three assumptions:A1)f –m
f
has a zero inx =x
0 of order 2k.A2)f is continuous and at leastC
2k
in a neighborhood ofx
0.A3)x =x
0 is the unique global minimum off in [–, ]. In [10] we have proved that the hypothesis of smoothnessA2 is not necessary and that the same result holds under the weaker assumption thatf L
1[–, ]. In this paper we further extend this theory to the case of a functionf L
1[–, ] having several global minima by suppressing the hypothesisA3 and by showing that the maximal order 2k of the zeros off –m
f
is the only parameter which characterizes the rate of convergence of
1
(n)
tom
f
. 相似文献
85.
Richard C. Bradley 《Journal of Theoretical Probability》1996,9(3):659-678
Schmidt(10) showed that if the family of distributions of the partial sums of a strictly stationary random sequence is tight, then that random sequence is a coboundary. Here an analog of that result is proved for some sequences of random matrices, with partial sums replaced by matrix products. 相似文献
86.
Ron M. Roth 《Designs, Codes and Cryptography》1996,9(2):177-191
Codes
of length 2
m
over {1, -1} are defined as null spaces of certain submatrices of Hadamard matrices. It is shown that the codewords of
all have an rth order spectral null at zero frequency. Establishing the connection between
and the parity-check matrix of Reed-Muller codes, the minimum distance of
is obtained along with upper bounds on the redundancy of
. An efficient algorithm is presented for encoding unconstrained binary sequences into
. 相似文献
87.
It is shown that new parametersX can be defined such that the heat capacity CxT(S/T)x is negative, even when the canonical ensemble [i.e., at fixed T=(U/S)Y and YX] is stable. This implies an extension of the classical theory of polytropes from ideal gases to general fluids. As examples of negative heat capacity systems we treat blackbody radiation and general gas systems with nonsingular T. For the case of a simple ideal gas we even exhibit an apparatus which enforces a constraint X(p, V)=const that makes Cx<0. We then show that it is possible to infer the statistical mechanics of canonicallyunstable systems-for which even the traditional heat capacities are negative-by imposing constraints that stabilize the associated noncanonical ensembles. Two explicit models are discussed. 相似文献
88.
本文比较了在标准石墨管,热解涂层和全热解石墨管中钒的吸收信号形状。用全热解石墨管和EDTA铵盐作基体改进剂,直接测定水系沉积物中痕量钒。方法的特征量为61pg/0.0044A。 相似文献
89.
双电层相互重叠时蒙脱胶体表面阴离子的负吸附 总被引:2,自引:0,他引:2
本文用Ag-AgCl电极判断平衡,测定双电层处于不同重叠程度下肢体表面阴离子的负吸附量Γ.结果表明,胶体表面双电层相互重叠程度可由两胶体表面间的中点电位φd与外Helmhotz面处的电位φd之比表征;阴离子负吸附随双电层重叠程度和电解质浓度的增加而显著减小. 相似文献
90.
R. De
Lisi G. Lazzara S. Milioto N. Muratore 《Journal of Thermal Analysis and Calorimetry》2007,87(1):61-67
Macromolecule/laponite nanomaterials were
studied by DSC and X-ray diffraction techniques. The matrices are poly(ethylene)
glycols at various molecular masses and poly(ethylene oxides)-poly(propylene
oxides)-poly(ethylene oxides) tri-block copolymers. The latter were tuned
by modulating the molecular masses, at constant hydrophilic/hydrophobic ratio,
and the hydrophilicity. For all the investigated systems, the enthalpy of
melting (ΔH
m)
is nearly constant up to a given composition thereafter it increases monotonically
reaching the value of the pure macromolecule. We proposed a model to interpret
the DSC data.
Briefly, it was invoked a mechanism of interaction
following which some segments of the adsorbed macromolecule are anchored to
the laponite (RD) particles and the remaining segments are radiating away
from the surface. The portion of the macromolecule in contact with RD does
not contribute to ΔH
m
whereas that radiating away from the clay does. Once that the RD surface is
saturated, the excess of the macromolecule behaves like the pure one. The
proposed model allowed to compute successfully the ΔH
m
values. The X-ray diffraction experiments ruled out the polymer intercalation
between the silicate sheets. 相似文献