Arc-transitive cubic cayley graphs on PSL(2, <Emphasis Type="Italic">p</Emphasis>)

For a prime p at least 5, let T = PSL(2, p). This paper gives a classification of the connected arc-transitive cubic Cayley graphs on T and a determination of the generated pairs (ā,−) of T such that o(ā) = 2 and o(−)= 3.     

Varieties with quadratic entry locus, <Emphasis Type="Italic">I</Emphasis>

We introduce and study (L)QEL-manifolds of type δ, a class of projective varieties whose extrinsic and intrinsic geometry is very rich, especially when δ >  0. We prove a strong Divisibility Property for LQEL-manifolds of type δ ≥  3, allowing the classification of those of type . In particular we obtain a new and very short proof that Severi varieties have dimension 2,4, 8 or 16 and also an almost self-contained proof of their classification due to Zak. We also provide the classification of special Cremona transformations of type (2,3) and (2,5). Partially supported by CNPq (Centro Nacional de Pesquisa), grant 308745/2006-0, and by PRONEX/FAPERJ–Algebra Comutativa e Geometria Algebrica.     

Finite 2-generator equilibrated p-groups

Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of metacyclic p-groups given by Newman and Xu, we give a complete classification of 2-generator equilibrated p-groups in this note.     

Complex<Emphasis Type="BoldItalic">n</Emphasis>-dimensional manifolds with a real<Emphasis Type="BoldItalic">n</Emphasis><Superscript>2</Superscript>-dimensional automorphism group

The main theorem of this article is a characterization of non compact simply connected complete Kobayashi hyperbolic complex manifold of dimension n≽ 2 with real n ²-dimensional holomorphic automorphism group. Together with the earlier work [11, 12] and [13] of Isaev and Krantz, this yields a complete classification of the simply-connected, complete Kobayashi hyperbolic manifolds with dim_ℝ Aut (M) ≽ (dim_ℂ M)².     

Hyperbolic <Emphasis Type="Italic">n</Emphasis>-dimensional manifolds with automorphism group of dimension <Emphasis Type="Italic">n</Emphasis><Superscript>2</Superscript>

We obtain a complete classification of complex Kobayashihyperbolic manifolds of dimension n ≥ 2, for which the dimension of the group of holomorphic automorphisms is equal to n². Received: May 2005 Accepted: November 2005     

Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection

A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.     

The Fine Spectra of the Difference Operator △ Over the Sequence Space bvp, （1 ≤ p 〈 ∞）^＊

The sequence space bvp consisting of all sequences （xk） such that （xk -xk-1） belongs to the space gp has recently been introduced by Basar and Altay [Ukrainian Math. J., 55（1）, 136-147（2003）]; where 1 ≤ p ≤ ∞. In the present paper, some results concerning with the continuous dual and f-dual, and the AD-property of the sequence space bvp have been given and the norm of the difference operator A acting on the sequence space bvp has been found. The fine spectrum with respect to the Goldberg＇s classification of the difference operator △ over the sequence space bvp has been determined, where 1≤p〈∞.     

The classification of filiform Leibniz superalgebras of nilindex <Emphasis Type="Italic">n</Emphasis> + <Emphasis Type="Italic">m</Emphasis>

In this work the classification of filiform Leibniz superalgebras of nilindex n ＋ m, where n and m （m≠0） are dimensions of even and odd parts, respectively, is obtained.     

Maps from a Simply Connected Space to Flag Manifold G／T

In this paper the classification of maps from a simply connected space X to a flag manifold G/T is studied. As an application, the structure of the homotopy set for self-maps of flag manifolds is determined.     

A characterization of L p(ℝ) by local trigonometric bases with 1<p<∞

We show that the local trigonometric bases introduced by Malvar, Coifman and Meyer constitute bases, but not unconditional bases, for L^p(ℝ) with 1<p<∞, p≠2. In addition, we characterize the functions in L^p(ℝ) for 1<p<∞ in terms of their local trigonometric basis coefficients. Dedicated to Dr. Charles A. Micchelli for his 60th birthday Mathematics subject classification (2000) 42C15. Supported by Prof. Y. Xu under his grant in program of “One Hundred Distinguished Chinese Scientists” of the Chinese Academy of Sciences, the National Natural Science Foundation of China (No. 10371122), and the second author is supported by Tianyuan Fund for Mathematics (No. A0324648).     

Classification of compatible Lie-Poisson brackets on the manifold <Emphasis Type="Italic">e</Emphasis>*(3)

A classification of compatible Lie-Poisson brackets on e*(3) is constructed. The corresponding bi-Hamiltonian systems are the classical integrable cases of the Euler-Poisson and Kirchhoff equations which describe the motion of a solid body. Bibliography: 12 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 335, 2006, pp. 231–245.     

A conic and an <Emphasis Type="Italic">M</Emphasis>-quintic with a point at infinity

Topological classification of plane projective real algebraic curves of degree seven that split into a product of two M-factors of degrees two and five is considered. A list of 153 possible topological models is presented, 53 of which are realized. Proofs are outlined. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 14–27.     

<Emphasis Type="Italic">r</Emphasis>-Tuple almost product structures

A generalization of an almost product structure and an almost complex structure on smooth manifolds is constructed. The set of tensor differential invariants of type (2, 1) and the set of differential 2-forms for such structures are constructed. We show how these tensor invariants can be used to solve the classification problem for Monge–Ampère equations and Jacobi equations.     

An example of a rightq-ring

We show that Ivanov’s classification of indecomposable non-local rightq-rings is incomplete and provide a complete classification. Next, we correct and sharpen Byrd’s classification of rightq-rings. Partially supported by a grant from the National Science Council of Taiwan.     

Singular Probability Distributions and Fractal Properties of Sets of Real Numbers Defined by the Asymptotic Frequencies of Their <Emphasis Type="Italic">s</Emphasis>-Adic Digits

Properties of the set T _s of “particularly nonnormal numbers” of the unit interval are studied in detail (T _s consists of real numbers x some of whose s-adic digits have the asymptotic frequencies in the nonterminating s-adic expansion of x, and some do not). It is proved that the set T _s is residual in the topological sense (i.e., it is of the first Baire category) and is generic in the sense of fractal geometry (T _s is a superfractal set, i.e., its Hausdorff-Besicovitch dimension is equal to 1). A topological and fractal classification of sets of real numbers via analysis of asymptotic frequencies of digits in their s-adic expansions is presented. Dedicated to V. S. Korolyuk on occasion of his 80th birthday __________ Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 9, pp. 1163–1170, September, 2005.     

A <Emphasis Type="Italic">p</Emphasis>-adic RANSAC algorithm for stereo vision using Hensel lifting

A p-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developed. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised p-adic hierarchical classification algorithm imitiating the known LBG quantization method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the “true” solution of the problem.