Unique global strong solutions of a Cauchy problem arising in electrophoretic separation are constructed with arbitrary initial data in L1, thus generalizing an earlier global existence result. For small diffusion coefficients, the solutions can be viewed as approximate solutions for the corresponding zero-diffusion Riemann problem.

The class of primary abelian groups whose subsocles are purifiable is not yet completely characterized and it contains the class of direct sums of cyclic groups and torsion complete groups. In sharp constrast with this, the class of groups whose p2-bounded subgroups are purifiable consist only of those groups which are the direct sum of a bounded and a divisible group. Various tools are developed and a short application to the pure envelopes of cyclic subgroups is given in the last section.

A characterization is given of those families ℱ of subsets of the positive integers for which σ(ℓ1, ) is sequentially complete, where denotes the linear span of the characteristic functions of ℱ. Consequences include some known matrix results, such as Hahn's Theorem and conditions required for a matrix to "sum" the characteristic functions of the lacunary sets.

In this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.

W. Deeb, R. Khalil and M. Marzuq have studied some properties of H(ϕ), the Hardy-Orlicz spaces. They introduced the functions class Np (0 < p ≦ 1 ) and discussed some properties of Np. In the present short note we prove that Np = N+ for 0 < p ≦ 1. We also give a condition of H(ϕ) = H(ψ).

Let G be a locally compact Abelian group, with character group X. Suppose that X contains a measurable order P. For the conjugate function of f is the function whose Fourier transform satisfies the identity for almost all χ in X where sgnp(χ) = - 1 , 0, 1, according as We prove that, when f is bounded with compact support, the conjugate function satisfies some weak type inequalities similar to those of the Hilbert transform of a bounded function with compact support in ℝ. As a consequence of these inequalities, we prove that possesses strong integrability properties, whenever f is bounded and G is compact. In particular, we show that, when G is compact and f is continuous on G, the function is integrable for all p > 0.

A nonstandard proof of the fact that a Banach space in which a ball is contained in the range of a countably additive measure is superreflexive is given. The proof is an application of a general method in which we first transfer certain standard objects to the nonstandard hull of a Banach space and then, using the quite well developed theory of nonstandard hulls, derive results about the objects in the original Banach space. It also provides us with an example of the applications of the theory of nonstandard hull valued measures.

The paper is motivated by a result of Ankeny [1] above Dirichlet L functions in 1952. We generalize this from Dirichlet L functions to Artin L functions of relative abelian extensions, by complementing the ingenious proof of Ankeny's theorem given by Iwasaki [4]. Moreover, we characterize Dirichlet L functions in the class of all Artin L functions in terms of coefficients as Dirichlet series.

Through successive radial perturbations of a certain planar Hamiltonian polynomial vector field of degree 2K + 1, we obtain a least K limit cycles containing (2K + 1)2 singularities.

We study a class of matrices (introduced by T. Kato) with principal homogeneous part, and use Mellin transform of the homogeneous kernel to determine spectral density of the positive infinite matrices.

It is proved that a pseudoumbilical 2-type surface in a sphere has constant mean curvature. Moreover, the dimension of the sphere is greater than four.

In this paper we show that a ring derivation on a function algebra is trivial provided that the Choquet boundary of the algebra contains a dense sequentially non-isolated set.

Some equationally defined classes of loops are identified and characterized among a class of loops which are isomorphic to all of their loop isotopes.

Let L be a finitely generated extension of a field k. L is a k-rational factor if there is a field extension K of k such that the total quotient ring of L ꕕk K is a rational (pure transcendental) extension of K. We present examples of non-rational rational factors and explicitly determine both factors.

We show that the Bogdanov-Takens system has at most one limit cycle. Similarly we show that the maximum number of limit cycles in the universal unfolding of the symmetric cusp of order 2 (resp. 3) is one (resp. 2). The proof uses the elementary technique of Liénard's equation, yielding a global result for all values of the parameters.

Let 0 → N → E → F → 0 be a short exact sequence of torsion-free Kronecker modules. Suppose that N and F have rank one. The module F is classified by a height function h defined on the projective line. If N is finite-dimensional, h is supported on a set of cardinality less than that of its domain and h takes on the value ∞, then E embeds into F. The converse holds if all such E embed into F. This embeddability is in contrast to the situation with other rings such as commutative domains, where it never occurs.

Analytic multivalued functions are a powerful tool in spectral theory. In this paper we study analytic multivalued functions λ → K(λ) whose values are segments. Under the additional assumption that K is continuous, we prove that the endpoints of K vary locally holomorphically.

We give a simple construction of non-Noetherian Hilbert domains whose maximal ideals are all finitely generated. Such domains we call unruly Hilbert domains.

Consider a covering p : X → B of connected topological spaces. If B is a compact polyhedron, a classical result of H. Hopf [4] says that the end space E(X) of X is an invariant of the group G of covering transformations. Thus it becomes meaningful to define the end space of the finitely generated group G as E(G) := E(X).

We propose the following problem. Given an array of vertical mirrors that simultaneously transmit and reflect, and a single incoming ray of light, describe the configuration of all light rays that are generated. We solve the problem here for a certain infinite configuration of mirrors; the solution involves the winning positions (a(n), b(n)) of Wythoff's game.