A Note on μ(Z)-homeomorphisms

This paper is a continuation work of the authors on (z)-homeomorphisms. We establish similar relationships between quasisymmetric function and dilatation function as in quasiconformal mappings under (z)-homeomorphisms. Furthermore, a weighted quasiisometric inequality is presented.AMS Subject Classification (1991) 30C62 30C65     

Estimates on μ(z)-homeomorphisms of the unit disk

In the theory ofK-quasiconformal mappings, Mori's theorem shows thatK-quasiconformal mappings on the unit disk satisfy the Hölder condition, where the coefficient 16 is best possible. In this paper, we prove that self-μ(z)-homeomorphisms on the unit disk have an analogical result to Mori's theorem when the integral mean dilatations are controlled by log function. An unimprovable inequality is obtained.     

One- and two-dimensional faces of the polyhedron μ(5)

Let (n) be the polyhedral surface [4] in the coefficient space corresponding to positive-definite quadratic forms with arithmetic minimum of 1. All one- and two-dimensional faces of the polyhedron (5) are determined. The results are applied to analyze quasiperfect forms (n=5) and forms that minimize Epstein zetafunctions in the sense of Fields [9].Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 151, pp. 95–103, 1986.We acknowledge the assistance of M. Kh. Umarov in the preparation of the paper for publication.     

Embedding an Edge-colored K(a (p); λ, μ) into a Hamiltonian Decomposition of K(a (p+r); λ, μ)

Let K(a ^(p); λ, μ) be a graph with p parts, each part having size a, in which the multiplicity of each pair of vertices in the same part (in different parts) is λ (μ, respectively). In this paper we consider the following embedding problem: When can a graph decomposition of K(a ^(p); λ, μ) be extended to a Hamiltonian decomposition of K(a ^(p+r); λ, μ) for r > 0? A general result is proved, which is then used to solve the embedding problem for all ${r \geq \frac{\lambda}{\mu a}+ \frac{p-1}{a-1}}$ . The problem is also solved when r is as small as possible in two different senses, namely when r = 1 and when ${r = \frac{\lambda}{\mu a} - p+1}$ .     

Small into-isomorphism from L∞ (A, μ) into L∞(B, υ)

In this paper we shall assert that if T is an isomorphism of L_∞(Ω₁, A, μ) into L_∞(Ω₂, B, υ) satisfying the condition ‖T‖·‖T ^?1‖?1+? for ?∈ $\left( {0,\frac{1}{5}} \right)$ , then $\frac{T}{{\parallel T\parallel }}$ is close to an isometry with an error less than 6ε in some conditions.     

关于u″ μ(u-u~k)=0(4≤k∈Z~ )分叉的注记

讨论了一类反应扩散方程 u″ μ(u -uk) =0 ,u(0 ) =u(π) =0 (4≤k∈Z ,μ为参数 )的分叉现象·　运用所谓基于李雅普诺夫_施密特约化的奇异理论方法 ,得到满意的结果     

Spectral functions of self-adjoint and symmetric multiplication operators inL 2(X, μ)-spaces

Explicit formulas are derived for the spectral function of double multiplication operator containing a multiplicative evolution inL ²(X, μ)-space and a convolution-type operator inL ²(ℝ ⁿ )-spaces. Symmetric convolution and multiplication operators are considered inL ²(X, μ) andL ²(ℝ ⁿ )-spaces. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 803–810, June, 2000.     

ALMOST PERIODIC SOLUTIONS OF THE EQUATIONx = x~3 + λg (t) x + μf (t) AND THEIR STABILITY

By using the Liapunov function and the contraction mapping principle, the authorinvestigates the existence and stability of almost periodic solutions of the first ordernonlinear equations dx/dt=-h_1(x)+h_2(x)g(t)+f(t)and dx/dt=r(t)x~n+λg(t)x+μf(t),where r(t), g(t), f(t) are given almost periodic functions, n(≥2) integer, and λ, μ realparameters.     

Some results on (k, μ)′-almost Kenmotsu manifolds

In this paper, we study the Weyl conformal curvature tensor 𝒲 and the concircular curvature tensor 𝒞 on a (k, μ)′-almost Kenmotsu manifold M²ⁿ⁺¹ of dimension greater than 3. We obtain that if M²ⁿ⁺¹ satisfies either R · 𝒲 = 0 or 𝒞 · 𝒞 = 0, then it is locally isometric to either the hyperbolic space ?²ⁿ⁺¹ (?1) or the Riemannian product ?ⁿ⁺¹(?4) × ?ⁿ.     

REMARKS ON BIFURCATIONS OF u" μu-u~κ=0(4≤k∈Z~ )

1. IntroductionOne class of reaction-diffusion equations in one-spatial dimension reads as [1,2],where p is a parameter, 1 < k E Z .Li has ever considered the static (or steady-stste) bifurcations of (4) for the simplercases with k = 2, 3 in [3]. In this paper, we focus on studying the static bifurcations of (4)for the complicated cases with 4 5 k E Z . That is, we consider the bifurcations of thefollowing equationwhere p is a parameter and 4 5 k E Z .Let X = {u E C'[0,7] I u(0) ~ u(x) = …     

Equivariant eilenberg maclane spaces K (G, μ, 1) for possibly non-connected or empty fixed point sets

Equivariant Eilenberg-MacLane spaces are constructed in [1, p. II.13], [3, p. 277], [8, p. 45], however, only for nonempty connected H-fixed point sets for all HG and in the pointed category. This is a reasonable assumption in equivariant homotopy theory (equivariant Posnikov-systems, homology, obstruction theory) but too restrictive for the study of equivariant manifolds. Therefore we develope a treatment of equivariant Eilenberg-MacLane spaces of type one in full generality. They are used, for example, in equivariant L-theory as reference spaces (see [5]) or in [4].     

Extended partial geometries with minimal μ

Recently Fisher and Hobart extended the original work of Buekenhout and Hubaut on extended generalized quadrangles with a certain minimal value (minimal ) for the nonempty residue intersections. We show that there is another minimal which is sometimes better than the earlier one, and we extend all this to the case of extended partial geometries. We examine especially the triangular case, and find only a few new possibilities, which we are unable to settle, although some of these look extremely interesting.     

Chemical collisions involving μ+ mesons

The phase shifts for the chemical reaction of μ⁺ mesons with Tritium molecular ions have been calculated using Hulthen–Kohen and Schwinger variational methods. Also the differential cross sections for different values of the wave number of the relative motion are computed. The obtained values are found to be comparable with the corresponding theoretical ones or that obtained by F. Ayoub and A. El-Shahawy [Journal de chimie physique (1986) 83]. They are, however, not far below the maximum values.     

EpGs with minimal μ: II

There are two known lower bounds for (P, Q) in an EpG, called ₁ and ₂, see for example [3]. In [4], =₁ was studied for the case of triangular EGQs and, in [3], =₂ was considered for EpGs in general. Here we extend this to the case =₁ for EpGs in general, including non-triangular EGQs, and we give a number of characterizations. For instance a triangular EpG with =₁ locally is an EGQ, an extended dual net or a semibiplane; if t>2–1, then an EpG(s, t) with =₁ locally is an EGQ. In general we have only partial results for t2–1.     

(二)作者索引(外文)

<正> This index lists all the mathematical works in Volumes Ⅰ and Ⅱ of Journal of Chinese Mathematical Society and from Volumes 1 through 29 of Acta Mathematica Sinica.Works are listed alphabetically by author's surnames. Those by joint authors are listed under the first-named author; cross-references are provided from secondary authors to the first.     

(高一)函数自测题(二)

一、选择题化简(。导b告)(一3·告b专)、(专·含b甘)的结果(A)6a(B)一a(C)一ga(D)(〕a匕2.设函数y一19(二之一5‘:)的定义域为M，函数y一馆(‘:一5) lgx的定义域为N，则(). (A)MUN~R(B)M卫N (C)M=N(I〕)M里N 3.下列函数中既是偶函数又在(一~，O)_上几是增函数的是(). (A)y一rZ     

μ-complete Souslin trees on μ+

Summary We prove thatµ=µ ^<µ , 2 ^µ =µ ⁺ and there is a non-reflecting stationary subset ofµ ⁺ composed of ordinals of cofinality < imply that there is a -complete Souslin tree onµ ⁺.The second author thanks the Binational Science Foundation for supporting this research. Publication no. 449