共查询到20条相似文献,搜索用时 15 毫秒
1.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 相似文献
2.
Let A be a central simple algebra with involution σ of the first or second kind. Let v be a valuation on the σ-fixed part F of Z(A). A σ-special v-gauge g on A is a kind of value function on A extending v on F, such that g(σ(x)x) = 2g(x) for all x in A. It is shown (under certain restrictions if the residue characteristic is 2) that if v is Henselian, then there is a σ-special v-gauge g if and only if σ is anisotropic, and g is unique. If v is not Henselian, it is shown that there is a σ-special v-gauge g if and only if σ remains anisotropic after scalar extension from F to the Henselization of F with respect to v; when this occurs, g is the unique σ-invariant v-gauge on A. 相似文献
3.
Joginder S Dhiman 《Proceedings Mathematical Sciences》2000,110(3):335-345
Recently discovered hydrodynamic instability [1], in a simple Bénard configuration in the parameter regime
under the action of a nonadverse temperature gradient, is shown to be suppressed by the simultaneous action of a uniform
rotation and a uniform magnetic field both acting parallel to gravity for oscillatory perturbations whenever (Qσ
1/π2 + J/π4) > 1 and the effective Rayleigh numberR(1 -T
0α2) is dominated by either 27π4(1 + l/σ1/4 or 27π4/2 according as σ1 ≥1 or σ1
≤ 1 respectively. HereT
0is the temperature of the lower boundary while α2 is the coefficient of specific heat at constant volume due to temperature variation and σ1,R,Q andJ respectively denote the magnetic Prandtl number, the Rayleigh number, the Chandrasekhar number and the Taylor number. 相似文献
4.
Jumela F. Sarmiento 《Graphs and Combinatorics》2002,18(3):621-632
A t(v,k,λ) design is a set of v points together with a collection of its k-subsets called blocks so that t points are contained in exactly λ blocks. PG(n,q), the n-dimensional projective geometry over GF(q) is a 2(q
n
+q
n−1
+⋯+q+1,q
2+q+1, q
n−2
+ q
n−3
+⋯+q+1) design when we take its points as the points of the design and its planes as the blocks of the design. A 2(v,k,λ) design is said to be resolvable if the blocks can be partitioned as ℱ={R
1,R
2,…,R
s
}, where s=λ(v−1)/(k−1) and each R
i
consists of v/k disjoint blocks. If a resolvable design has an automorphism σ which acts as a cycle of length v on the points and ℱσ=ℱ, then the design is said to be point-cyclically resolvable. The design consisting of points and planes of PG(5,2) is shown to be point-cyclically resolvable by enumerating all inequivalent
resolutions which are invariant under a cyclic automorphism group G=〈σ〉 where σ is a cycle of length v. These resolutions are shown to be the only resolutions which admit point-transitive automorphism group.
Received: November 10, 1999 Final version received: September 18, 2000
Acknowledgments. The author would like to thank A. Munemasa for his assistance in writing computer programs on constructing projective spaces
and searching for partial spreads. Moreover, she's thankful to T. Hishida and M.␣Jimbo for helpful discussions and for verifying
the results of this paper.
Present address: Mathematics Department, Ateneo de Manila University, Loyola Heights, Quezon City 1108, Philippines. e-mail: jumela@mathsci.math.admu.edu.ph 相似文献
5.
V. A. Moskalenko M. E. Palistrant V. A. Ursu 《Theoretical and Mathematical Physics》2008,154(1):94-107
We calculate the upper critical magnetic field H
c2 in the framework of a microscopic superconductivity theory with two energy bands of different dimensions on the Fermi surface
with the cavity topology typical of the compound MgB2 taken into account (an anisotropic system). We assume an external magnetic field parallel to the crystallographic z axis. We obtain analytic formulas in the low-temperature range (T/Tc ≪ 1) and also near the critical temperature ((T-Tc)/Tc ≪ 1). We compare the temperature dependence of Hc2 for a two-band anisotropic system with that of H
c2
0
corresponding to a two-band isotropic system (with Fermi-surface cavities of the same topology). We determine the role of
the band-structure anisotropy, the positive curvature of the upper critical field near the critical temperature, and the important
role of the ratio v1/v2 of the velocities on the Fermi surface in determining Hc2. We also obtain the values of the parameters Δ1 and Δ2 along the line of the critical magnetic field.
This paper is dedicated to the 90th birthday of Professor D. N. Zubarev
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 113–128, January, 2008. 相似文献
6.
For a graph G, we define σ2(G) := min{d(u) + d(v)|u, v ≠ ∈ E(G), u ≠ v}. Let k ≥ 1 be an integer and G be a graph of order n ≥ 3k. We prove if σ2(G) ≥ n + k − 1, then for any set of k independent vertices v
1,...,v
k
, G has k vertex-disjoint cycles C
1,..., C
k
of length at most four such that v
i
∈ V(C
i
) for all 1 ≤ i ≤ k. And show if σ2(G) ≥ n + k − 1, then for any set of k independent vertices v
1,...,v
k
, G has k vertex-disjoint cycles C
1,..., C
k
such that v
i
∈ V(C
i
) for all 1 ≤ i ≤ k, V(C
1) ∪...∪ V(C
k
) = V(G), and |C
i
| ≤ 4 for all 1 ≤ i ≤ k − 1.
The condition of degree sum σ2(G) ≥ n + k − 1 is sharp.
Received: December 20, 2006. Final version received: December 12, 2007. 相似文献
7.
Yuval Z. Flicker 《Israel Journal of Mathematics》2001,122(1):61-77
The torsorP
δ=Hom⊗ (H
DR,H
σ) under the motivic Galois groupG
σ=Aut⊗
H
δ of the Tannakian category
generated by one-motives related by absolute Hodge cycles over a field κ with an embedding σ:k↪ℂ is shown to be determined by its projectionP
σ→P
σ/G
σ
0
to a Gal(
)-torsor, and by its localizationsP
σ⊕k
k
ξ at a dense subset of orderings ϕ of the field κ, provided κ has virtual cohomological dimension (vcd) one. This result is
an application of a recent local-global principle for connected linear algebraic groups over a field κ of vcd ≤1. 相似文献
8.
The paper deals with the structure of intermediate subgroups of the general linear group GL(n, k) of degree n over a field k of odd characteristic that contain a nonsplit maximal torus related to a radical extension of degree n of the ground field k. The structure of ideal nets over a ring that determine the structure of intermediate subgroups containinga transvection
is given. Let K = k( n?{d} ) K = k\left( {\sqrt[n]{d}} \right) be a radical degree-n extension of a field k of odd characteristic, and let T =(d) be a nonsplit maximal torus, which is the image of the multiplicative group of the field K under the regular embedding in G =GL(n, k). In the paper, the structure of intermediate subgroups H, T ≤ H ≤ G, that contain a transvection is studied. The elements of the matrices in the torus T = T (d) generate a subring R(d) in the field k.Let R be an intermediate subring, R(d) ⊆ R ⊆ k, d ∈ R. Let σR denote the net in which the ideal dR stands on the principal diagonal and above it and all entries of which beneath the principal diagonal are equal to R. Let σR denote the net in which all positions on the principal diagonal and beneath it are occupied by R and all entries above the principal diagonal are equal to dR. Let E(σR) be the subgroup generated by all transvections from the net group G(σR). In the paper it is proved that the product TE(σR) is a group (and thus an intermediate subgroup). If the net σ associated with an intermediate subgroup H coincides with σR,then TE(σR) ≤ H ≤ N(σR),where N(σR) is the normalizer of the elementary net group E(σR) in G. For the normalizer N(σR),the formula N(σR)= TG(σR) holds. In particular, this result enables one to describe the maximal intermediate subgroups. Bibliography: 13 titles. 相似文献
9.
Let R be a Noetherian domain and let (σ,δ) be a quasi-derivation of R such that σ is an automorphism. There is an induced quasi-derivation on the classical quotient ring Q of R. Suppose F=t
2−v is normal in the Ore extension R[t;σ,δ] where v∈R. We show F is prime in R[t;σ,δ] if and only if F is irreducible in Q[t;σ,δ] if and only if there does not exist w∈Q such that v=σ(w)w−δ(w). We apply this result to classify prime quadratic forms in quantum planes and quantized Weyl algebras. 相似文献
10.
María del Mar González 《Calculus of Variations and Partial Differential Equations》2006,27(4):439-466
In this paper we address the problem of understanding the singularities of the fully non-linear elliptic equation σ
k
(v) = 1. These σ
k
curvature are defined as the symmetric functions of the eigenvalues of the Schouten tensor of a Riemannian metric and appear naturally in conformal geometry, in fact, σ1 is just the scalar curvature.Here we deal with the local behavior of isolated singularities. We give a sufficient condition for the solution to be bounded near the singularity. The same result follows for a more general singular set Λ as soon as we impose some capacity conditions. The main ingredient is an estimate of the L
∞ norm in terms of a suitable L
p
norm.
Mathematics Subject Classification (2000) 35J60, 53A30 相似文献
11.
For a nontrivial connected graph G, let ${c: V(G)\to {{\mathbb N}}}For a nontrivial connected graph G, let
c: V(G)? \mathbb N{c: V(G)\to {{\mathbb N}}} be a vertex coloring of G, where adjacent vertices may be colored the same. For a vertex v of G, let N(v) denote the set of vertices adjacent to v. The color sum σ(v) of v is the sum of the colors of the vertices in N(v). If σ(u) ≠ σ(v) for every two adjacent vertices u and v of G, then c is called a sigma coloring of G. The minimum number of colors required in a sigma coloring of a graph G is called its sigma chromatic number σ(G). The sigma chromatic number of a graph G never exceeds its chromatic number χ(G) and for every pair a, b of positive integers with a ≤ b, there exists a connected graph G with σ(G) = a and χ(G) = b. There is a connected graph G of order n with σ(G) = k for every pair k, n of positive integers with k ≤n if and only if k ≠ n − 1. Several other results concerning sigma chromatic numbers are presented. 相似文献
12.
We prove that the bicrossed product of two groups is a quotient of the pushout of two semidirect products. A matched pair
of groups (H;G; α; β) is deformed using a combinatorial datum (σ; v; r) consisting of an automorphism σ of H, a permutation v of the set G and a transition map r: G → H in order to obtain a new matched pair (H; (G; *); α′, β′) such that there exists a σ-invariant isomorphism of groups H
α⋈β
G ≅H
α′⋈β′
(G, *). Moreover, if we fix the group H and the automorphism σ ∈ Aut H then any σ-invariant isomorphism H
α⋈β
G ≅ H
α′⋈β′
G′ between two arbitrary bicrossed product of groups is obtained in a unique way by the above deformation method. As applications
two Schreier type classification theorems for bicrossed products of groups are given. 相似文献
13.
Kazem Ghanbari 《Positivity》2006,10(4):721-729
We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σi(A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ1 and σ2. The pairs σ, σ1 and σ1, σ2 must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ1 in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ1 and σ2 in common. 相似文献
14.
Piotr Kalemba Szymon Plewik Anna Wojciechowska 《Central European Journal of Mathematics》2008,6(2):218-227
The σ-ideal (v
0) is associated with the Silver forcing, see [5]. Also, it constitutes the family of all completely doughnut null sets, see
[9]. We introduce segment topologies to state some resemblances of (v
0) to the family of Ramsey null sets. To describe add(v
0) we adopt a proof of Base Matrix Lemma. Consistent results are stated, too. Halbeisen’s conjecture cov(v
0) = add(v
0) is confirmed under the hypothesis t = min{cf(c), r}. The hypothesis cov(v
0) = ω
1 implies that (v
0) has the ideal type (c, ω
1, c).
相似文献
15.
Douglas W. Larmour 《Mathematische Zeitschrift》2006,252(3):459-472
Throughout this paper, we let (D,σ) be a central F -division algebra with involution σ such that Fσ={d ∈ F|σ(d)=d} is a Henselian valued field. By [11], the valuation on Fσ extends uniquely to a valuation on D. We denote this valuation by v. Moreover, we assume that the characteristic of the residue field, , is not 2. If the valuation on F is discrete, then any quadratic form q can be written as q= q1⊥πq2, where π is a uniformizer and qi are unit forms. Springer's Theorem states that q is isotropic if and only if at least one of the residue forms and is isotropic. In this paper we generalize this result to ɛ -Hermitian forms. In Section 4, we use the connection between involutions on algebras and ɛ-Hermitian forms to prove an analog of the Springer Theorem for involutions.
This paper was part of the author's doctoral dissertation at New Mexico State University. The author wishes to thank his advisor
Pat Morandi for his tireless help. 相似文献
16.
S. R. Kulkarni 《Annals of the Institute of Statistical Mathematics》1973,25(1):187-203
Summary Suppose we have two independent experiments conducted with a set of ‘t’ treatments each, at different places. This paper deals with two interesting problems of testing of hypotheses associated
with these experiments. The first problem deals with the test of the equality of the respective treatment effects in the two
experiments. The second problem is concerned with the testing of the equality of treatment into places interactions. Though
we assume normality, the variance σ
1
2
in one experiment is assumed different from the variance σ
2
2
in the other experiment. When no information is available aboutR=σ
1
2
/(σ
1
2
+σ
2
2
) except that 0≦R≦1, tests known as ‘bilateral tests’ are proposed in the literature, to test the hypotheses mentioned above. This paper studies
some important small sample properties of these bilateral tests. More specifically we study the probability of the first and
second kind of error of these bilateral tests as a function ofR. When the two experiments have the same number of observations on each treatment, the bilateral test is shown to control
the first kind of error. Fort=1,2, the level of these tests is a strictly convex function ofR and hence these tests can be very conservative. Some power properties of these tests are also obtained. Two tests which are
equivalent to the bilateral tests for large sample sizes, and which are superior to the bilateral tests for small sample sizes,
are obtained. 相似文献
17.
Masahiro Iwano 《Annali di Matematica Pura ed Applicata》1959,47(1):91-149
Résumé Nous avons formé dans le premier mémoire une solution formelle de(28.1) ordonnée suivant les puissances entière des solutions de(E). En annulant les Zj qui correspondent aux polynomes
de degrés différents de σv*(<σi*), nous obtenons une solution formelle (F
v). Dans le chapitre III, nous cherchons la condition suffisante pour la convergence uniforme de la série formelle (F
v). Dans le chapi tre IV, ce résultat est étendu au cas où la solution formelle dépend essentiellement des polynomes λj(x) de divers degrés. Le dernier chapitre est consacré à l'extension du théorème d'existence deM. M. Hukuhara qui joue un r?le important dans notre Mémoire. 相似文献
18.
Jorge García-Melián José C. Sabina De Lis Julio D. Rossi 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(5-6):499-525
We deal with positive solutions of Δu = a(x)u
p
in a bounded smooth domain subject to the boundary condition ∂u/∂v = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if |∂Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile
of the solution as λ → σ1.
Supported by DGES and FEDER under grant BFM2001-3894 (J. García-Melián and J. Sabina) and ANPCyT PICT No. 03-05009 (J. D.
Rossi). J.D. Rossi is a member of CONICET. 相似文献
19.
E. V. Abakumov 《Journal of Mathematical Sciences》1997,85(2):1759-1766
The following theorem is proved. Let Λ be a divisor of n points of the unit disk and let σ1, σ2,...σ
n
be a finite sequence of nonzero complex numbers. Then there exists a Hankel operator Γ of rank n such that the divisor of
the poles of its symbol is Λ and the eigenvalues of Γ (counted with the multiplicities) are σ1, σ2,...σ
n
Bibliography: 11 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 217, 1994, pp. 5–15 相似文献
20.
We characterize the surjective additive maps compressing the spectral function Δ(·) between standard operator algebras acting on complex Banach spaces, where Δ(·) stands for any one of nine spectral functions σ(·), σl(·), σr(·),σl(·) ∩ σr(·), δσ(·), ησ(·), σap(·), σs(·), and σap(·) ∩ σs(·). 相似文献