Russian text ignored Lp, 0 < p < 1

Certain weak forms of normality are discussed and are shown to coincide with normality in an appropriate setting by devising a strong form of semilocal connectedness. It is shown that every compact Hausdorff locally connected space is strongly semilocally connected. This improves a result of Mrówka and Pervin. Properties of s-continuous mappings are studied and in the process improvements of certain results of Pervin and Levine, Friedler, and Kohli are obtained.     

Представление функций классовL p [0, 1], 0<p<1, ортогональными рядами

u . uuu u     

A Note on the Embedding of Subspaces of Lp into ℓNr, 0 < r < 1, r ≦ p < 2

In this paper we extend a result by Bourgain-Lindenstrauss-Milman (see [1]). We prove: Let 0 < ? < 1/2, 0< r < 1, r< p < 2. There exists a constant C = C(r,p,?) such that if X is any n-dimensional subspace of L_p(0, l), then there exists Y ? ?^N_r with d(X, Y) ≦ 1 + ?, whenever N > Cn. As an application, we obtain the following partial result: Let 0 < r < 1. There exist constants C = C(r) and C' = C' (r) such that if X is any n-dimensional subspace of L_r(0,1), then there exists Y ? ^N_r with d(X, Y) ≦ C (logn)^l/^r, whenever N ≧ C'n.     

A simply connected surface of general type with <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">g</Emphasis></Subscript>=0 and <Emphasis Type="Italic">K</Emphasis><Superscript>2</Superscript>=2

In this paper we construct a simply connected, minimal, complex surface of general type with p _g =0 and K ²=2 using a rational blow-down surgery and a ℚ-Gorenstein smoothing theory. Mathematics Subject Classification (2000) Primary 14J29; Secondary 14J10, 14J17, 53D05     

A weak version of ◊ which follows from 2ℵ 0<2ℵ 1

We prove that if CH holds (or even if 2^ℵ ₀ < 2^ℵ ₁), then a weak version of ◊ holds. This weak version of ◊ is a ◊-like principle, and is strong enough to yield some of the known consequences of ◊. The second author wishes to thank the United States-Israel Binational Foundation for partially supporting his research by Grant 1110.     

Classification of amply regular graphs with <Emphasis Type="Italic">b</Emphasis><Subscript>1</Subscript> = 6

An undirected graph with v vertices in which the degrees of all vertices are equal to k, each edge is contained in exactly λ triangles, and the intersection of the neighborhoods of any two vertices at distance 2 contains exactly µ vertices is called amply regular with parameters (v, k, λ, µ). We complete the classification of amply regular graphs with b ₁ = 6, where b ₁ = k ? λ ? 1.     

Surfaces of general type with <Emphasis Type="Italic">p</Emphasis><Subscript><Emphasis Type="Italic">g</Emphasis></Subscript>=0, <Emphasis Type="Italic">K</Emphasis><Superscript>2</Superscript>=6 and non birational bicanonical map

Let S be a minimal surface of general type with p_g=0 and K²=6, such that its bicanonical map is not birational. The map is a morphism of degree 4 onto a surface. The case of deg = 4 is completely classified in [Topology, 40 (5) (2001), 977–991] and the present paper completes the characterization of these surfaces. It is proven that the degree of cannot be equal to 3, and the geometry of surfaces with deg = 2 is analysed in detail. The last section contains three examples of such surfaces, two of which appear to be new.Mathematics Subject Classification (2000): 14J29     

Interpolation of operators of weak type (ϕ<Subscript>0</Subscript>, ψ<Subscript>0</Subscript>, ϕ<Subscript>1</Subscript>, ψ<Subscript>1</Subscript>) in Lorentz spaces

We prove theorems on interpolation of quasilinear operators of weak type (ϕ₀, ψ₀, ϕ₀, ψ₁) in Lorentz spaces. The operators under study are analogs of the Calderón operator and the Benett operator for concave and convex functions ϕ₀(t), ψ₀(t), ϕ₁(t), and ψ₁(t). __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 11, pp. 1490–1507, November, 2005.     

A variety of exact travelling wave solutions for the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation

In this paper the (2 + 1)-dimensional Boiti-Leon-Pempinelli (BLP) equation will be studied. The tanh-coth method will be used to obtain exact travelling wave solutions for this equation. The Exp-function method will also be applied to the BLP equation to derive a new variety of travelling wave solutions with distinct physical structures.     

Projective normality of abelian surfaces of type (1, 2<Emphasis Type="Italic">d</Emphasis>)

We show that an abelian surface embedded in P^N by a very ample line bundle of type (1,2d) is projectively normal if and only if d4. This completes the study of the projective normality of abelian surfaces embedded by complete linear systems.Supported by EAGER.Mathematics Subject Classification (2000): Primary, 14K05; Secondary, 14N05, 14E20     

A classification of regular embeddings of hypercubes Q_(2m) with m odd

In this paper we give a classification of the orientable regular embeddings of Q_n for n=2m with m odd.Actually we prove that the known examples given by Kwon are the only regular maps of Q_n when n=2m (m odd).     

Existence of three HMOLS of type 2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript><Emphasis Type="Italic">u</Emphasis><Superscript>1</Superscript>

A Latin squares of order v with ni missing sub-Latin squares （holes） of order hi （1 〈= i 〈 k）, which are disjoint and spanning （i.e. ∑k i=l1 nihi = v）, is called a partitioned incomplete Latin squares and denoted by PILS. The type of PILS is defined by （h1n1 h2n2…hknk ）. If any two PILS inaset of t PILS of type T are orthogonal, then we denote the set by t-HMOLS（T）. It has been proved that 3-HMOLS（2n31） exist for n ≥6 with 11 possible exceptions. In this paper, we investigate the existence of 3-HMOLS（2nu1） with u ≥ 4, and prove that 3-HMOLS（2~u1） exist if n ≥ 54 and n ≥7/4u ＋ 7.     

A method of approximating functions in Hp, 0<p≤1

Translated from Matematicheskie Zametki, Vol. 57, No. 4, pp. 580–585, April, 1995.