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1.
Shmuel Friedland 《Israel Journal of Mathematics》1980,35(1-2):89-108
LetA(ε) andB(ε) be complex valued matrices analytic in ε at the origin.A(ε)≈
p
B(ε) ifA(ε) is similar toB(ε) for any |ε|<r,A(ε)≈a
B(ε) ifB(ε)=T(ε)A(ε)T
−1(ε) andT(ε) is analytic and |T(ε)|≠0 for |ε|<r! In this paper we find a necessary and sufficient conditions onA(ε) andB(ε) such thatA(ε)≈
a
B(ε) provided thatA(ε)≈
p
B(ε). This problem arises in study of certain ordinary differential equations singular with respect to a parameter ε in the
origin and was first stated by Wasow.
Sponsored by the United States Army under Contract No. DAAG29-75-C-0024 相似文献
2.
We study the minimal and maximal closed extension of a differential operator A on a manifold B with conical singularities, when A acts as an unbounded operator on weighted L
p
-spaces over B, 1<p<∞. Under suitable ellipticity assumptions we can define a family of complex powers A
z
, zℂ. We also obtain sufficient information on the resolvent of A to show the boundedness of the purely imaginary powers. Examples concern unique solvability and maximal regularity for the
solution of the Cauchy problem for the Laplacian on conical manifolds as well as certain quasilinear diffusion equations.
Received: 12 June 2001; in final form: 3 June 2002 /
Published online: 1 April 2003
Mathematics Subject Classification (2000): 35J70, 47A10, 35K57 相似文献
3.
F. S. de Blasi 《Set-Valued Analysis》2006,14(3):263-272
For maps φ on hyperspaces the existence of semifixed sets, i.e., of sets A satisfying one of the relations A ⊂ φ(A), A ⊃ φ(A), A ∩ φ(A) ≠ ∅, is considered. An application to set differential equations is also presented. 相似文献
4.
An Abelian group A is called correct if for any Abelian group B isomorphisms A ≅ B′ and B ≅ A′, where A′ and B′ are subgroups of the groups A and B, respectively, imply the isomorphism A ≅ B. We say that a group A is determined by its subgroups (its proper subgroups) if for any group B the existence of a bijection between the sets of all subgroups (all proper subgroups) of groups A and B such that corresponding subgroups are isomorphic implies A ≅ B. In this paper, connections between the correctness of Abelian groups and their determinability by their subgroups (their
proper subgroups) are established. Certain criteria of determinability of direct sums of cyclic groups by their subgroups
and their proper subgroups, as well as a criterion of correctness of such groups, are obtained.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 21–36, 2003. 相似文献
5.
L. Delvaux 《Algebras and Representation Theory》2007,10(6):533-554
Let B be a regular multiplier Hopf algebra. Let A be an algebra with a non-degenerate multiplication such that A is a left B-module algebra and a left B-comodule algebra. By the use of the left action and the left coaction of B on A, we determine when a comultiplication on A makes A into a “B-admissible regular multiplier Hopf algebra.” If A is a B-admissible regular multiplier Hopf algebra, we prove that the smash product A # B is again a regular multiplier Hopf algebra. The comultiplication on A # B is a cotwisting (induced by the left coaction of B on A) of the given comultiplications on A and B. When we restrict to the framework of ordinary Hopf algebra theory, we recover Majid’s braided interpretation of Radford’s
biproduct.
Presented by K. Goodearl. 相似文献
6.
We prove that affine straight lineϕ
A,B(t)=(1−t)A+tB going through bounded closed convex setsA andB is not injective if and only ifA−B is symmetric andA−A,B−B are homotetic. 相似文献
7.
We investigate the problem of approximation of a bounded solution of a difference analog of the differential equation
by solutions of the corresponding boundary-value problems. Here, A is an unbounded operator in a Banach space B, {A
1,...,A
m-1} ⊂L(B) and f:ℝ→B is a fixed function. 相似文献
8.
Vanessa Miemietz 《Algebras and Representation Theory》2008,11(4):369-405
Ariki’s and Grojnowski’s approach to the representation theory of affine Hecke algebras of type A is applied to type B with unequal parameters to obtain – under certain restrictions on the eigenvalues of the lattice operators – analogous multiplicity-one
results and a classification of irreducibles with partial branching rules as in type A.
Research supported by the Studienstiftung des deutschen Volkes. 相似文献
9.
In this paper, we study the solvability of the operator equations A*X + X*A = C and A*XB + B*X*A = C for general adjointable operators on Hilbert C*-modules whose ranges may not be closed. Based on these results we discuss the solution to the operator equation AXB = C, and obtain some necessary and sufficient conditions for the existence of a real positive solution, of a solution X with B*(X* + X)B ≥ 0, and of a solution X with B*XB ≥ 0. Furthermore in the special case that R(B) í [`(R(A*))]{R(B)\subseteq\overline{R(A*)}} we obtain a necessary and sufficient condition for the existence of a positive solution to the equation AXB = C. The above results generalize some recent results concerning the equations for operators with closed ranges. 相似文献
10.
Gerald Beer 《Israel Journal of Mathematics》1987,58(2):205-212
IfA andB are closed nonempty sets in a locally convex space, the straight line path fromA toB is defined by the formulaφ(α)=cl (αA+(1−α)B), 0≦α≦1. IfA andB are convex, then continuity of the path with respect to the Hausdorff uniform topology is necessary for both connectedness
and path connectedness ofA toB within the convex sets so topologized. We also produce internal necessary and sufficient conditions for continuity of the
path between pairs of convex sets. 相似文献
11.
Let H be an infinite dimensional complex Hilbert space. Denote by B(H) the algebra of all bounded linear operators on H, and by I(H) the set of all idempotents in B(H). Suppose that Φ is a surjective map from B(H) onto itself. If for every λ ∈ -1,1,2,3, and A, B ∈ B(H),A-λB ∈I(H) ⇔ Φ(A) -λΦ(B) ∈I(H, then Φ is a Jordan ring automorphism, i.e. there exists a continuous invertible linear or conjugate linear operator T on H such that Φ(A) = TAT
-1 for all A ∈ B(H), or Φ(A) = TA*T
-1 for all A ∈ B(H); if, in addition, A-iB ∈I(H)⇔ Φ(A)-iΦ(B) ∈I(H), here i is the imaginary unit, then Φ is either an automorphism or an anti-automorphism. 相似文献
12.
Yu. O. Vorontsov Kh. D. Ikramov 《Computational Mathematics and Mathematical Physics》2011,51(5):691-698
An algorithm of the Bartels-Stewart type for solving the matrix equation AX + X
T
B = C is proposed. By applying the QZ algorithm, the original equation is reduced to an equation of the same type having triangular
matrix coefficients A and B. The resulting matrix equation is equivalent to a sequence of low-order systems of linear equations for the entries of the
desired solution. Through numerical experiments, the situation where the conditions for unique solvability are “nearly” violated
is simulated. The loss of the quality of the computed solution in this situation is analyzed. 相似文献
13.
Anthony Joseph 《Transformation Groups》2009,14(3):557-612
A Lie theoretic interpretation is given to a pattern with five-fold symmetry occurring in aperiodic Penrose tiling based on
isosceles triangles with length ratios equal to the Golden Section. Specifically a B(∞) crystal based on that of Kashiwara is constructed exhibiting this five-fold symmetry. It is shown that it can be represented
as a Kashiwara B(∞) crystal in type A4. Similar crystals with (2n + 1)-fold symmetry are represented as Kashiwara crystals in type A2n
. The weight diagrams of the latter inspire higher aperiodic tiling. In another approach alcove packing is seen to give aperiodic
tiling in type A4. Finally 2m-fold symmetry is related to type B
m
.
Work supported in part by Minerva grant, no. 8596/1. 相似文献
14.
Christine Lescop 《Inventiones Mathematicae》1998,133(3):613-681
We study the following question: How does the Casson-Walker invariant λ of a rational homology 3-sphere obtained by gluing
two pieces along a surface depend on the two pieces? Our partial answer may be stated as follows. For a compact oriented 3-manifold
A with boundary ∂A, the kernel L
A
of the map from H
1(∂A;Q) to H
1(A;Q) induced by the inclusion is called the Lagrangian of A. Let Σ be a closed oriented surface, and let A, A′, B and B′ be four rational homology handlebodies such that ∂A, ∂A′, −∂B and −∂B′ are identified via orientation-preserving homeomorphisms with Σ. Assume that L
A
= L
A
′ and L
B
= L
B
′ inside H
1(Σ;Q) and also assume that L
A
and L
B
are transverse. Then we express
in terms of the form induced on ∧3 L
A
by the algebraic intersection on H
2(A∪Σ−A′) paired to the analogous form on ∧3 L
B
via the intersection form of Σ. The simple formula that we obtain naturally extends to the extension of the Casson-Walker
invariant of the author. It also extends to gluings along non-connected surfaces.
Oblatum 6-III-1995 & 31-X-1997 相似文献
15.
Harry Lakser 《Algebra Universalis》1981,13(1):78-81
Grant A. Fraser defined the semilattice tensor productA ⊗B of distributive latticesA, B and showed that it is a distributive lattice. He proved that ifA ⊗B is projective then so areA andB, that ifA andB are finite and projective thenA ⊗B is projective, and he gave two infinite projective distributive lattices whose semilattice tensor product is not projective.
We extend these results by proving that ifA andB are distributive lattices with more than one element thenA ⊗B is projective if and only if bothA andB are projective and both have a greatest element.
Presented by W. Taylor. 相似文献
16.
Mohamed Ali Toumi 《Czechoslovak Mathematical Journal》2010,60(1):85-94
Let A and B be two Archimedean vector lattices and let (A′)′
n
and (B′)′
n
be their order continuous order biduals. If Ψ: A × A → B is a positive orthosymmetric bimorphism, then the triadjoint Ψ***: (A′)′
n
× (A′)′
n
→ (B′)′
n
of Ψ is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost f-algebras. 相似文献
17.
A new method of constructing quasitriangular group-cograded multiplier Hopf algebras is provided. For a multiplier Hopf dual
pairing σ between regular multiplier Hopf algebras A and B, we introduce the concept of a σ-compatible pairing (Φ, Ψ, σ ), where Φ and Ψ are actions of the twisted semi-direct group of a group G on A and B, respectively. We construct a twisted double group-cograded multiplier Hopf algbera D(A, B; σ, Φ, Ψ). Furthermore, if there is a canonical multiplier in M(B ⊗ A) we show existence of quasitriangular structure on D(A, B; σ, Φ, Ψ). As an application, special cases and examples are given. 相似文献
18.
19.
Let A, B be two archimedean ℓ-algebras and let U,V be two positive linear maps from A to B. We call that the couple (U,V) is separating with respect to A and B if |a||b| = 0 in A implies |U (a)||V (b)| = 0 in B. In this paper, we prove that if A is an f-algebra with unit elment e, if B is an ℓ-algebra and if (U,V) is a separating couple with respect to A and B then (U
∼∼,V
∼∼), where U
∼∼ (resp V
∼∼) is the bi-adjoint of U (resp of V), is again a separating couple with respect to the order continuous order biduals (A′)′
n
and (B′)′
n
of A and B respectively furnished with their Arens products respectively. Moreover, in the case where B′ separates the points of B, we give a characterization of any separating couple with respect to A and B.
相似文献
20.
E. M. Kolenova 《Journal of Mathematical Sciences》2008,154(2):208-213
Let A be a class of Abelian groups, A ∈ A, and End(A) be the additive endomorphism group of the group A. The group A is said to be defined by its endomorphism group in the class {ie208-01} if for every group B ∈ B such that End(B) ≅ End(A) the isomorphism B ≅ A holds. The paper considers the problem of definability of a periodic Abelian group A such that End-End(A) ≅ End(A). The classes of periodical Abelian groups, of divisible Abelian groups, of reduced Abelian groups, of nonreduced Abelian
groups, and of all Abelian groups are investigated in this paper.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 2, pp. 123–131, 2007. 相似文献