The existence of positive solutions of some semilinear elliptic equations of the form −Δu = λf(u) is studied. The major results are a nonexistence theorem which gives a λ* = λ*(f,Ω) > 0 below which no positive solutions exist and a lower bound theorem for umax for Ω a ball. As a corollary of the nonexistence theorem that describes the dependence of the number of solutions on λ, two other nonexistence theorems, and an existence theorem are also proved.

The aim of this paper is to prove some embedding theorems for groups with Černikov conjugacy classes. Moreover a characterization of periodic central-by-Černikov groups is given.

Sets of independence are studied for compact abelian hypergroups and they are used, along with Riesz products, to investigate lacunarity questions on the dual object. It is shown that bounded Stechkin sets are always Sidon and that every bounded infinite subset of the dual contains an infinite Sidon set which is also a Λ set. Independent sets are shown to always be Sidon and a necessary condition for Sidonicity is provided. A result of Pisier is used to show that for compact non-abelian groups Sidon and central Λ are equivalent. Several applications are provided, primarily to questions regarding lacunarity on compact groups.

We investigate the effect on the Jones polynomial of a ribbon knot when two of its bands are twisted together. We use our results to prove that each of the three S-equivalence classes of genus 2 fibered doubly slice knots in S3 can be represented by infinitely many distinct prime fibered doubly slice ribbon knots.

In the first paper of this series we studied on a compact regular contact manifold the integral of the Ricci curvature in the direction of the characteristic vector field considered as a functional on the set of all associated metrics. We showed that the critical points of this functional are the metrics for which the characteristic vector field generates a 1-parameter group of isometries and conjectured that the result might be true without the regularity of the contact structure. In the present paper we show that this conjecture is false by studying this problem on the tangent sphere bundle of a Riemannian manifold. In particular the standard associated metric is a critical point if and only if the base manifold is of constant curvature +1 or −1; in the latter case the characteristic vector field does not generate a 1-parameter group of isometries.

This paper is concerned with the three-parameter generalized gamma distribution (g.g.d.) which is widely employed as a model in life testing. The structural probability distributions of the parameters and a number of structural prediction densities for specific future measurements have been derived based on type-Il progressively censored sample.

It is well-known that quasi-Frobenius rings are characterized by the property that all propective right modules are injective, as well as by the property that all injective right modules are projective. Similarly, either the property that every quasi-injective or that every quasi-injective is quasi-projective characterizes uniserial rings. Oshiro has given similar characterizations for generalized uniserial rings. The purpose of this paper is to characterize rings for which continuous right modules are discrete. We show that these rings are precisely the uniserial rings. The property that every discrete module is continuous is also investigated.

The best lattice quantizers seem to be duals of extreme lattices. The quantizing constant associated with the dual lattice of Barnes's senary form φ6 is found, together with a new type of quantizing technique. The quantizing constant is better than expected in the sense that it is better than D*6 even though D6 provides a denser packing. This is the smallest dimension for which this occurs.

Let 1 ≤ p < ∞, p ≠ 2 and let K be any complex Hilbert space. We prove that every isometry T of Hp(K) onto itself is of the form , where U ia a unitary operator on K and φ is a conformal map of the unit disc onto itself.

Takai duality for full C*-crossed products holds for twisted actions in the sense of Green and fails for coactions.

It is well-known that if G is a multigraph (that is, a graph with multiple edges), the maximum number of pairwise disjoint edges in G is ν(G) and its maximum degree is D(G), then |E(G)| ≤ ν [3D/2’. We extend this theorem for r-graphs (that is, families of r-element sets) and for r-multihypergraphs (that is, r-graphs with repeated edges). Several problems remain open.

In this paper we present a minimax theorem of infinite dimension. The result contains several earlier duality results for various trigonometrical extremal problems including a problem of Fejér. Also the present duality theorem plays a crucial role in the determination of the exact number of zeros of certain Beurling zeta functions, and hence leads to a considerable generalization of the classical Beurling's Prime Number Theorem. The proof used functional analysis.

Let Q denote the Banach space (under the sup norm) of quasi-continuous functions on the unit interval [0, 1]. Let ℳ denote the closed convex cone comprised of monotone nondecreasing functions on [0, 1]. For f and g in Q and 1 < p < ∞, let hp denote the best Lp-simultaneous approximant of f and g by elements of ℳ. It is shown that hp converges uniformly as p → ∞ to a best L∞-simultaneous approximant of f and g by elements of ℳ. However, this convergence is not true in general for any pair of bounded Lebesgue measurable functions. If f and g are continuous, then each hp is continuous; so is limp→∞ hp = h∞.

We prove that the split integral group ring of a finite p-solvable group of finite representation type has a structure analogous to that of the p-modular semisimple deformation. The split integral deformation can be put in the same form as the p-modular deformation by an appropriate substitution for the parameter T. As an application we derive a simple formula for the matrix units in the semisimple group algebra over a nonmodular prime.

A ring R is called right pseudo-semisimple if every right ideal not isomorphic to R is semisimpie. Rings of this type in which the right socle S splits off additively were characterized; such a ring has S2 = 0. The existence of right pseudo-semisimple rings with zero right singular ideal Z remained open, except for the trivial examples of semisimple rings and principal right ideal domains. In this work we give a complete characterization of right pseudo-semisimple rings with S2 = 0. We also give examples of non-trivial right pseudo-semisimple rings with Z = 0; in fact it is shown that such rings exist as subrings in every infinite-dimensional full linear ring. A structure theorem for non-singular right pseudo-semisimple rings, with homogeneous maximal socle, is given. The general case is still open.

In this article we continue the study of weighted inductive limits of spaces of Fréchet-valued continuous functions, concentrating on the problem of projective descriptions and the barrelledness of the corresponding “projective hull”. Our study is related to the work of Vogt on the study of pairs (E, F) of Fréchet spaces such that every continuous linear mapping from E into F is bounded and on the study of the functor Ext1 (E, F) for pairs (E, F) of Fréchet spaces.

Let 0 = λ0 < λ1 ≤ λ2 ≤ λ3 ≤ … denote the sequence of eigenvalues of the Laplacian of a compact minimal submanifold in a unit sphere. Yang and Yau obtained an upper bound on λn+1 in terms of λn and the sum λ1 + … + λn. In this note we shall prove an improved version of this upper bound by using the method of Hile and Protter.

A pair of symmetric dual multiobjective fractional programming problems is formulated and appropriate duality theorems are established.

Generalizing known results for special examples, we derive a Khintchine type decomposition of probability measures on symmetric hypergroups. This result is based on a triangular central limit theorem and a discussion of conditions ensuring that the set of all factors of a probability measure is weakly compact. By our main result, a probability measure satisfying certain restrictions can be written as a product of indecomposable factors and a factor in I0(K), the set of all measures having decomposable factors only. Some contributions to the classification of I0(K) are given for general symmetric hypergroups and applied to several families of examples like finite symmetric hypergroups and hypergroup joins. Furthermore, all results are discussed in detail for a class of discrete symmetric hypergroups which are generated by infinitely many joins, for a class of countable compact hypergroups, for Sturm-Liouville hypergroups on [0, ∞[ and, finally, for polynomial hypergroups.

We present a symmetric version of a normed algebra of quotients for each ultraprime normed algebra. In addition, a C*-a1gebra of quotients of an arbitrary C*-a1gebra is introduced.