Damped vibration problems with nonlinearities being sublinear at both zero and infinity

In this paper, we study a class of damped vibration problems with nonlinearities being sublinear at both zero and infinity, and we obtain infinitely many nontrivial periodic solutions by using a variant fountain theorem. To the best of our knowledge, there is no published result concerning this case by this method. Copyright © 2015 John Wiley & Sons, Ltd.     

An oscillatory integral estimate associated to rational phases

Let R(t)=P(t)/Q(t) be a quotient of real polynomials. We show that ∫exp(iR(t)) dt/t has a uniform bound with a bound depending only on the degrees of P and Q and not on their coefficients. Also L^P estimates are obtained for certain associated singular integral operators.     

Besicovitch Covering Lemma,Hadamard manifolds,and zero entropy

It is proved that if the Besicovitch Covering Lemma is true on either a Hadamard manifold or a simply connected surface without focal points that covers a compact quotient, then the manifold is the Euclidean space. As a corollary, the vanishing of the topological entropy of a compact manifold of nonpositive curvature or of a compact surface without focal points is equivalent to the validity of the Besicovitch Covering Lemma on the universal covering space of the manifold. The author was partially supported by an NSF grant.     

Lyapunov exponents,bifurcation currents and laminations in bifurcation loci

Bifurcation loci in the moduli space of degree d rational maps are shaped by the hypersurfaces defined by the existence of a cycle of period n and multiplier 0 or e ^iθ. Using potential-theoretic arguments, we establish two equidistribution properties for these hypersurfaces with respect to the bifurcation current. To this purpose we first establish approximation formulas for the Lyapunov function. In degree d = 2, this allows us to build holomorphic motions and show that the bifurcation locus has a lamination structure in the regions where an attracting basin exists.     

Collapsing monoids consisting of permutations and constants

In this paper we determine all collapsing transformation monoids that contain at least one unary constant operation and whose nonconstant operations are permutations. Furthermore, we find an infinite family of transformation monoids that consist of at least three unary constant operations and some permutations for which the corresponding monoidal intervals are 2-element chains. This research is supported by Hungarian National Foundation for Scientific Research grant nos. T 37877 and K 60148.     

Axiomatizing the Harsanyi solution,the symmetric egalitarian solution and the consistent solution for NTU-games

The validity of the axiomatization of the Harsanyi solution for NTU-games by Hart (1985) is shown to depend on the regularity conditions imposed on games. Following this observation, we propose two related axiomatic characterizations, one of the symmetric egalitarian solution (Kalai and Samet, 1985) and one of the consistent solution (Maschler and Owen, 1992). The three axiomatic results are studied, evaluated and compared in detail.Revised October 2004We thank an anonymous referee and an associate editor for their helpful comments. Geoffroy de Clippel also thanks Professors Sergiu Hart, Jean-François Mertens and Enrico Minelli. Horst Zank thanks the Dutch Science Foundation NWO and the British Council for support under the UK-Netherlands Partnership Programme in Science (PPS 706). The usual disclaimer applies.     

Existence and uniqueness of complete constant mean curvature surfaces at infinity ofH 3

A set of conditions are given, each equivalent to the constancy of mean curvature of a surface in H ³.It is shown that analogs of these equivalences exist for surfaces in S _∞ ² ,the bounding ideal sphere of H ³,leading to a notion of constant mean curvature at infinity of H ³.A parametrization of all complete constant mean curvature surfaces at infinity of H ³ is given by holomorphic quadratic differentials on Ĉ,C, and D.     

Norm behavior and zero distribution for orthogonal polynomials with nonsymmetric weights

The asymptotic behavior of thenth root of the leading coefficient of orthogonal polynomials on (–,) and the distribution of their zeros is studied for nonsymmetric weights that behave like exp(–2B|x|) whenx>0 and exp(–2Ax ) whenx<0,>AB. These results generalize previous investigations of Rakhmanov and Mhaskar and Saff who handle the symmetric caseA=B.Communicated by Paul Nevai.     

Coboundaries, Flows, and Tutte Polynomials of Matrices

Using matroid duality and the critical problem, we show that certain evaluations of the Tutte polynomial of a matroid represented as a matrix over a finite field GF(q) can be interpreted as weighted sums over pairs f , g of functions defined from the ground set to GF(q) whose difference f – g is the restriction of a linear functional on the column space of the matrix. Similar interpretations are given for the characteristic polynomial evaluated at q. These interpretations extend and elaborate interpretations for Tutte and chromatic polynomials of graphs due to Goodall and Matiyasevich. Received July 14, 2006     

Length Bounds on Curves Arising from Tight Geodesics

Let M be a complete hyperbolic 3-manifold admitting a homotopy equivalence to a compact surface ∑, such that the cusps of M are in bijective correspondence with the boundary components of ∑. Suppose we realise a tight geodesic in the curve complex as a sequence of closed geodesics M. There is an upper bound on the lengths of such curves in terms of the lengths of the terminal curves and the topologicial type of ∑. We give proofs of these and related bounds. Similar bounds have been proven by Minsky using the sophisticated machinery of hierarchies. Such bounds feature in the work of Brock, Canary and Minsky towards the ending lamination conjecture, and can also be used to study the action of the mapping class group on the curve complex. Received: January 2006, Revision: March 2007, Accepted: July 2007     

An application of index forms in cryptography

We investigate the possibility of using index forms as basic ingredients of cryptographically important functions. We suggest the use of a hash function based on index forms and we prove some important properties of the suggested function. The research was supported in part by the Hungarian Academy of Sciences, by grants T048791 and K67580 of the Hungarian NFSR, by the National Office for Research and Technology and by the grant JP-26/2006.     

Avoidable structures, I: Finite ordered sets, semilattices and lattices

We find all finite unavoidable ordered sets, finite unavoidable semilattices and finite unavoidable lattices. While working on this paper, the second and third authors were supported by US NSF grant DMS-0604065. The second author was also supported by the Grant Agency of the Czech Republic, grant #201/05/0002 and by the institutional grant MSM0021620839 financed by MSMT.     

Einstein Metrics with Prescribed Conformal Infinity on 4-Manifolds

This paper considers the existence of conformally compact Einstein metrics on 4-manifolds. A reasonably complete understanding is obtained for the existence of such metrics with prescribed conformal infinity, when the conformal infinity is of positive scalar curvature. We find in particular that general solvability depends on the topology of the filling manifold. The obstruction to extending these results to arbitrary boundary values is also identified. While most of the paper concerns dimension 4, some general results on the structure of the space of such metrics hold in all dimensions. Received: April 2006, Revision: November 2006, Accepted: February 2008     

The product of two von Neumann n-frames, its characteristic, and modular fractal lattices

Let L be a bounded lattice. If for each a₁ < b₁ ∈ L and a₂ < b₂ ∈ L there is a lattice embedding ψ: [a₁, b₁] → [a₂, b₂] with ψ(a₁) = a₂ and ψ(b₁) = b₂, then we say that L is a quasifractal. If ψ can always be chosen to be an isomorphism or, equivalently, if L is isomorphic to each of its nontrivial intervals, then L will be called a fractal lattice. For a ring R with 1 let denote the lattice variety generated by the submodule lattices of R-modules. Varieties of this kind are completely described in [16]. The prime field of characteristic p will be denoted by F_p. Let be a lattice variety generated by a nondistributive modular quasifractal. The main theorem says that is neither too small nor too large in the following sense: there is a unique , a prime number or zero, such that and for any n ≥ 3 and any nontrivial (normalized von Neumann) n-frame of any lattice in , is of characteristic p. We do not know if in general; however we point out that, for any ring R with 1, implies . It will not be hard to show that is Arguesian. The main theorem does have a content, for it has been shown in [2] that each of the is generated by a single fractal lattice L_p; moreover we can stipulate either that L_p is a continuous geometry or that L_p is countable. The proof of the main theorem is based on the following result of the present paper: if is a nontrivial m-frame and is an n-frame of a modular lattice L with m, n ≥ 3 such that and , then these two frames have the same characteristic and, in addition, they determine a nontrivial mn-frame of the same characteristic in a canonical way, which we call the product frame. Presented by E. T. Schmidt.     

Amalgamation,interpolation and epimorphisms in algebraic logic

In his landmark paper on amalgamation published in Algebra Universalis in 1971, Don Pigozzi posed some open questions in connection with amalgamation of subclasses of cylindric algebras. Some of these questions were originally raised by Comer, Daigneault, Johnson, McKenzie and others. In this paper we give answers to all these as well as a number of other related questions. Most of the solutions were found by the authors of this paper. However, a few were contributed by others who will of course be given due credit at the appropriate points. This paper is dedicated to Don Pigozzi on his retirement. Presented by R. W. Quackenbush. The first author’s research was supported by the Hungarian National Foundation for Scientific Research grants no T30314 and T23234. The second author’s research was supported by the Hungarian National Foundation for Scientific Reserach OKTA grant no T30314. All the new results in this article were announced by Judit Madarász in the Workshop on Abstract Algebraic Logic, held in Centre de Recerca Matematica Bellaterra, Spain July 1–5, 1997. Received December 15, 2002; accepted in final form January 3, 2006.     

Stable bundles on 3-fold hypersurfaces

Using monads, we construct a large class of stable bundles of rank 2 and 3 on 3-fold hypersurfaces, and study the set of all possible Chern classes of stable vector bundles.     

An improvement of the Ivanov bound

Let be a distance-regular graph of diameterd, valencyk andr=max{i|(c _i ,b _i )=(c ₁,b ₁)}. In this paper, we prove that

Remez-, Nikolskii-, and Markov-type inequalities for generalized nonnegative polynomials with restricted zeros

Sharp Remez-, Nikolskii-, and Markov-type inequalities are proved for functions of the form

An exotic sphere with positive curvature almost everywhere

In this article we show that there is an exotic sphere with positive sectional curvature almost everywhere. In 1974 Gromoll and Meyer found a metric of nonnegative sectional on an exotic 7-sphere. They showed that the metric has positive curvature at a point and asserted, without proof, that the metric has positive sectional curvature almost everywhere [4]. We will show here that this assertion is wrong. In fact, the Gromoll-Meyer sphere has zero curvatures on an open set of points. Never the less, its metric can be perturbed to one that has positive curvature almost everywhere.     

A generalization of an integral of Ramanujan

This paper considers a generalization of an integral introduced by S. Ramanujan in his third notebook. Ramanujan’s integral is itself a version of the dilogarithm,