共查询到20条相似文献,搜索用时 31 毫秒
1.
Let 𝔄 denote the C*-algebra of bounded operators on L
2 ℝ generated by: (i) all multiplications a(M) by functions a∈C[ − ∞, + ∞], (ii) all multiplications by 2π-periodic continuous functions, and (iii) all operator of the form F
−1
b(M)F, where F denotes the Fourier transform and b∈C[ − ∞, + ∞]. A given A ∈ 𝔄 is a Fredholm operator if and only if σ(A) and γ(A) are invertible, where σ denotes the continuous extension of the usual principal symbol, while γ denotes an operator-valued “boundary principal symbol” (the “boundary” here consists of two copies of the circle, one at
each end of the real line). We give two proofs of the fact that K
0(𝔄) is isomorphic to ℤ and that K
1(𝔄) is isomorphic to ℤ ⊕ ℤ . We do it first by computing the connecting mappings in the six-term exact sequence associated
to σ. For the second proof, we show that the image of γ is isomorphic to the direct sum of two copies of the crossed product
, where α denotes the translation-by-one automorphism. Its K-theory can be computed using the Pimsner–Voiculescu exact sequence,
and that information suffices for the analysis of the standard cyclic exact sequence associated to γ.
Received: February 2006 相似文献
2.
In this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functionsF(a,b;c;x), c ≤a + b, near the singularityx = 1. Further, we obtain monotonous properties of the quotient of two hypergeometric functions and inequalities for certain
combinations of them. Finally, we also solve an open problem of finding conditions ona, b > 0 such that 2F(−a,b;a +b;r
2) < (2−r
2)F(a,b;a +b;r
2) holds for all r∈(0,1). 相似文献
3.
For a Lie algebra L, a bilinear map is called a commutative cocycle if ψ(a, b) = ψ(b, a) and ψ([a, b], c) + ψ([b, a], c) + ψ([c, a], b) = 0 for any a, b, c ∈ L. We prove that any commutative cocycle of a simple Lie algebra of characteristic p ≠ 2, 3 is trivial if the rank of L is at least 2. In particular, any two-sided Alia algebra connected with a simple, finite-dimensional Lie algebra L is isomorphic to L, except for the case where L = sl
2
.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 60, Algebra,
2008. 相似文献
4.
Branko Sarić 《Czechoslovak Mathematical Journal》2010,60(4):1043-1048
Let [a, b] be an interval in ℝ Rand let F be a real valued function defined at the endpoints of [a, b] and with a certain number of discontinuities within [a, b]. Assuming F to be differentiable on a set [a, b] | E to the derivative f, where E is a subset of [a, b] at whose points F can take values ±∞ or not be defined at all, we adopt the convention that F and f are equal to 0 at all points of E and show that KH-vt ∝
a
b
f = F(b) − F(a), where KH-vt denotes the total value of the Kurzweil-Henstock integral. The paper ends with a few examples that illustrate the theory. 相似文献
5.
G. Kuba 《Acta Mathematica Hungarica》2000,87(1-2):173-178
For fixed c > 1 and for arbitrary and independent a,b ≧ 1 let Z
2|b( cosh(x/a)−c) ≦ y < 0}. We investigate the asymptotic behaviour of R(a,b) for a,b → ∞. In the special case b = o(a
5/6) the lattice rest has true order of magnitude
.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
M. Ivette Gomes 《Annals of the Institute of Statistical Mathematics》1984,36(1):71-85
Summary Let {X
n}n≧1 be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) ofM
n=max (X
1,…,X
n), suitably normalized with attraction coefficients {αn}n≧1(αn>0) and {b
n}n≧1, converges to a non-degenerate d.f.G(x), asn→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s
which better approximate the d.f. of(M
n−bn)/an thanG(x), for moderaten. We thus consider differences of the formF
n(anx+bn)−G(x), whereG(x) is a type I d.f. of largest values, i.e.,G(x)≡Λ(x)=exp (-exp(−x)), and show that for a broad class of d.f.'sF in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [Ф
α(x)=exp (−x−α), x>0] or a type III [Ψ
α(x)= exp (−(−x)α), x<0] d.f. of largest values, much closer toF
n(anx+bn) than the ultimate itself. 相似文献
7.
N. M. Timofeev 《Mathematical Notes》1999,66(4):474-488
Suppose thatg(n) is equal to the number of divisors ofn, counting multiplicity, or the number of divisors ofn, a≠0 is an integer, andN(x,b)=|{n∶n≤x, g(n+a)−g(n)=b orb+1}|. In the paper we prove that sup
b
N(x,b)≤C(a)x)(log log 10
x
)−1/2 and that there exists a constantC(a,μ)>0 such that, given an integerb |b|≤μ(log logx)1/2,x≥x
o, the inequalityN(x,b)≥C(a,μ)x(log logx(−1/2) is valid.
Translated fromMatematicheskie Zametki, Vol. 66, No. 4, pp. 579–595, October, 1999. 相似文献
8.
E. Preissmann 《Aequationes Mathematicae》1987,32(1):195-212
We solve independently the equations 1/θ(x)θ(y)=ψ(x)−ψ(y)+φ(x−y)/θ(x−y) and 1/θ(x)θ(y)=σ(x)−σ(y)/θ(x−y)+τ(x)τ(y), τ(0)=0. In both cases we find θ2=aθ4+bθ2+c. We deduce estimates for the spectral radius of a matrix of type(1/θ(x
r
−x
s
)) (the accent meaning that the coefficients of the main diagonal are zero) and we study the case where thex
r
are equidistant.
Dédié to à Monsieur le Professeur Otto Haupt à l'occasion de son cententiare avec les meilleurs voeux 相似文献
9.
Ahmet Tekcan 《Applications of Mathematics》2007,52(5):407-415
In this paper we consider proper cycles of indefinite integral quadratic forms F = (a, b, c) with discriminant Δ. We prove that the proper cycles of F can be obtained using their consecutive right neighbors R
i(F) for i ⩾ 0. We also derive explicit relations in the cycle and proper cycle of F when the length l of the cycle of F is odd, using the transformations τ(F) = (−a, b, −c) and ϰ(F) = (−c, b, −a). 相似文献
10.
In this paper, we will prove the existence of infinitely many harmonic and subharmonic solutions for the second order differential
equation ẍ + g(x) = f(t, x) using the phase plane analysis methods and Poincaré–Birkhoff Theorem, where the nonlinear restoring field g exhibits superlinear conditions near the infinity and strong singularity at the origin, and f(t, x) = a(t)x
γ + b(t, x) where 0 ≤ γ ≤ 1 and b(t, x) is bounded. 相似文献
11.
Do Yong Kwon 《Acta Mathematica Hungarica》2011,131(3):285-294
Let f(x)=a
d
x
d
+a
d−1
x
d−1+⋅⋅⋅+a
0∈ℝ[x] be a reciprocal polynomial of degree d. We prove that if the coefficient vector (a
d
,a
d−1,…,a
0) or (a
d−1,a
d−2,…,a
1) is close enough, in the l
1-distance, to the constant vector (b,b,…,b)∈ℝ
d+1 or ℝ
d−1, then all of its zeros have moduli 1. 相似文献
12.
In this paper, we will prove the existence of infinitely many harmonic and subharmonic solutions for the second order differential
equation ẍ + g(x) = f(t, x) using the phase plane analysis methods and Poincaré–Birkhoff Theorem, where the nonlinear restoring field g exhibits superlinear conditions near the infinity and strong singularity at the origin, and f(t, x) = a(t)x
γ + b(t, x) where 0 ≤ γ ≤ 1 and b(t, x) is bounded.
This project was supported by the Program for New Century Excellent Talents of Ministry of Education of China and the National
Natural Science Foundation of China (Grant No. 10671020 and 10301006). 相似文献
13.
We present a fully polynomial time approximation scheme (FPTAS) for minimizing an objective (a
T
x + γ)(b
T
x + δ) under linear constraints A
x ≤ d. Examples of such problems are combinatorial minimum weight product problems such as the following: given a graph G = (V,E) and two edge weights find an s − t path P that minimizes a(P)b(P), the product of its edge weights relative to a and b.
相似文献
14.
Let X be a closed smooth 4-manifold which is homotopy equivalent to S
2 × S
2. In this paper we use Seiberg-Witten theory to prove that if X admits a spin symmetric group S
4 action of even type with b
2
+ (X/S
4) = b
2
+ (X), then as an element of R (S
4), Ind
S4
D
X
= k
1 (1 − θ) + k
2(ψ1 − ψ2) for some integers k
1 and k
2, where 1, θ, ψ1, ψ2 are irreducible characters of S
4 of degree 1, 1, 3, and 3 respectively.
Authors’ address: Ximin Liu and Hongxia Li, Department of Applied Mathematics, Dalian University of Technology, Dalian 116024,
P.R. China 相似文献
15.
16.
Analgebra (A, ∘) with the identity [a, b]∘c + [b, c]∘a + [c, a]∘b = 0, where [a, b] = a∘b−b∘a, is called 0-Alia. We prove that the algebra (ℂ[x], ∘) with multiplication a ∘ b = ∂2(2a∂(b)+∂(a)b) is a simple, exceptional 0-Alia algebra.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 60, Algebra,
2008. 相似文献
17.
For the equation K(t)u
xx
+ u
tt
− b
2
K(t)u = 0 in the rectangular domain D = “(x, t)‖ 0 < x < 1, −α < t < β”, where K(t) = (sgnt)|t|
m
, m > 0, and b > 0, α > 0, and β > 0 are given real numbers, we use the spectral method to obtain necessary and sufficient conditions for the unique solvability
of the boundary value problem u(0, t) = u(1, t), u
x
(0, t) = u
x
(1, t), −α ≤ t ≤ β, u(x, β) = φ(x), u(x,−α) = ψ(x), 0 ≤ x ≤ 1. 相似文献
18.
The hypergeometric function type I distribution with the pdf proportional to x
ν−1(1−x)
γ−1
2
F
1(α,β;γ;1−x), 0<x<1 occurs as the distribution of the product of two independent beta variables. In this article, a multivariate generalization
of this distribution is defined and its properties are derived.
相似文献
19.
We consider the differential operators Ψ
k
, defined by Ψ1(y) =y and Ψ
k+1(y)=yΨ
k
y+d/dz(Ψ
k
(y)) fork ∈ ℕ fork∈ ℕ. We show that ifF is meromorphic in ℂ and Ψ
k
F has no zeros for somek≥3, and if the residues at the simple poles ofF are not positive integers, thenF has the formF(z)=((k-1)z+a)/(z
2+β
z+γ) orF(z)=1/(az+β) where α, β, γ ∈ ℂ. If the residues at the simple poles ofF are bounded away from zero, then this also holds fork=2. We further show that, under suitable additional conditions, a family of meromorphic functionsF is normal if each Ψ
k
(F) has no zeros. These conditions are satisfied, in particular, if there exists δ>0 such that Re (Res(F, a)) <−δ for all polea of eachF in the family. Using the fact that Ψ
k
(f
′/f) =f
(k)/f, we deduce in particular that iff andf
(k) have no zeros for allf in some familyF of meromorphic functions, wherek≥2, then {f
′/f :f ∈F} is normal.
The first author is supported by the German-Israeli Foundation for Scientific Research and Development G.I.F., G-643-117.6/1999,
and INTAS-99-00089. The second author thanks the DAAD for supporting a visit to Kiel in June–July 2002. Both authors thank
Günter Frank for helpful discussions. 相似文献
20.
Edith Adan-Bante 《Israel Journal of Mathematics》2008,168(1):93-100
Let G be a supersolvable group and A be a conjugacy class of G. Observe that for some integer η(AA
−1) > 0, AA
−1 = {ab
−1: a, b ∈ A} is the union of η(AA
−1) distinct conjugacy classes of G. Set C
G
(A) = {g ∈ G: a
g
= a for all a ∈ A. Then the derived length of G/C
G
(A) is less or equal than 2η(AA
−1) − 1. 相似文献