bluuebunny/crossref_metadata_2025_split huggingface dataset:
EXISTENCE OF POSITIVE EVANESCENT SOLUTIONS TO SOME QUASILINEAR ELLIPTIC EQUATIONS
Authors: MUSTAFA OCTAVIAN G. 
Published: September 2008

AbstractWe establish that the elliptic equationdefined in an exterior domain of ℝn,n≥3, has a positive solution which decays to 0 as$\vert x\vert \rightarrow +\infty $under quite general assumptions uponfandg.
POSITIVE PERIODIC SOLUTIONS OF SECOND-ORDER DIFFERENTIAL EQUATIONS WITH SINGULARITIES
Authors: LI HONG-XU 
Published: September 2008

AbstractIn this work, we consider the periodic boundary value problem where a,c∈L1(0,T) and f is a Carathéodory function. An existence theorem for positive periodic solutions is proved in the case where the associated Green function is nonnegative. Our result is valid for systems with strong singularities, and answers partially the open problem raised in Torres [‘Weak singularities may help periodic solutions to exist’, J. Differential Equations232 (2007), 277–284].
Reciprocating procedure device for thyroid cyst aspiration and ablative sclerotherapy
Authors: Sibbitt R R , Palmer D J , Sibbitt W L 
Published: September 2008

AbstractMost thyroid cysts are benign; however, they require aspiration if symptomatic or atypical on ultrasound scanning, and ablation with ethanol injection if recurrent. We have systematically studied the use of new safety technologies for surgical procedures, which protect both the surgeon and the patient. Here, we describe the use of one such technology, the reciprocating procedure device, which enables simpler, safer, more efficient and less painful thyroid cyst aspiration and therapeutic ablation.
Bilateral profound sudden sensorineural hearing loss presenting a diagnostic conundrum in a child with sickle cell anaemia
Authors: Mace A D , Ferguson M S , Offer M , Ghufoor K , Wareing M J 
Published: September 2008

AbstractObjective:To present the first published case of a child with bilateral profound sudden sensorineural hearing loss found in association with sickle cell anaemia, and to demonstrate the importance of early recognition, investigation and empirical treatment of sudden sensorineural hearing loss.Method:Case report and review of world literature.Case report:The authors present the case of a seven-year-old child with known sickle cell anaemia, who presented with bilateral profound sensorineural hearing loss developing over a period of five days. There was a history of ophthalmological disease in the preceding weeks, and inflammatory markers were raised. The differential diagnosis included a vaso-occlusive or inflammatory aetiology such as Cogan's syndrome, and treatment for both was instigated. Hearing thresholds did not recover, and the patient underwent cochlear implantation 12 weeks later.Conclusion:Sudden sensorineural hearing loss has a variable aetiology and is rare in children. Immediate treatment for all possible aetiologies is essential, along with targeted investigations and early referral for cochlear implantation if no recovery is demonstrated.
Quality of life after free-flap tongue reconstruction
Authors: Hartl D M , Dauchy S , Escande C , Bretagne E , Janot F , Kolb F 
Published: September 2008

AbstractObjective:To analyse correlations between quality of life measures, aspiration and extent of surgical resection in patients who have undergone free-flap tongue reconstruction.Patients and methods:Nine consecutive patients (seven men and two women; average age 51 years) who had been diagnosed with T4a carcinoma of the mobile tongue and/or tongue base and treated by glossectomy, free-flap reconstruction, and either radiation therapy or chemoradiation responded to the European Organization for Research and Treatment of Cancer Head and Neck-35 questionnaire, the performance status scale questionnaire and the hospital anxiety–depression scale questionnaire, an average of 43 months after treatment (range 18–83 months). Aspiration was evaluated by fibre-optic laryngoscopy. Correlations between quality of life domain scores, extent of surgery and the presence of aspiration were evaluated using non-parametric statistical analysis.Results:Scores for the swallowing and aspiration domains of the European Organization for Research and Treatment of Cancer Head and Neck-35 questionnaire were significantly correlated with the extent of tongue base resection (Spearman's correlation, p = 0.037 and 0.042, respectively). Despite a strong correlation between the European Organization for Research and Treatment of Cancer Head and Neck-35 questionnaire results and the performance status scale global scores (correlation coefficient = 0.89, p = 0.048), the performance status scale domain scores were not correlated with the extent of tongue resection. Clinically apparent aspiration was not correlated with the extent of tongue resection, nor were the anxiety or depression scores. However, clinically apparent aspiration was significantly related to the swallowing and aspiration domain scores of the European Organization for Research and Treatment of Cancer Head and Neck-35 questionnaire (p = 0.017 in both cases).Conclusions:Our results imply that the volume of tongue base resection is a major factor in swallowing- and aspiration-related quality of life following tongue resection and free-flap reconstruction. Free-flap reconstruction does not seem to palliate the effect of the loss of functional tongue base volume, as regards swallowing-related quality of life.
Reproductive biology of Neohelice granulata (Decapoda: Varunidae) in two salt marshes of the estuarine region of the Lagoa dos Patos Lagoon, southern Brazil
Authors: Barutot Roberta A. , D'Incao Fernando , Fonseca Duane B. 
Published: September 2008

Neohelice granulata is a crab found in salt marshes and mangroves of the south and south-eastern Atlantic coast of South America. Reproductive biology was studied by taking samples for two years at two salt marshes—‘Prainha’ and ‘Ilha’—in the estuarine region of Patos Lagoon (southern Brazil). Ovigerous females were found most of the year in both salt marshes with average CW ranging from 18.5 (Prainha) to 22.8 mm (Ilha). A significant linear relationship was found between log(CW) and log(number of eggs). Average size at the onset of maturation was 14.9 and 14 mm at Prainha, for males and females, respectively, while at Ilha it was 18.2 and 16.8 mm, for males and females, respectively. Results provided evidence of significant differences in reproductive traits between populations of the two salt marshes. Differences are likely related to the higher organic matter content found in the sediment from Ilha.
Cohomology of groups and almost periodic extensions of minimal sets
Authors: Ellis Robert 
Published: September 2008

AbstractLet ℬ and be minimal flows which are disjoint over their intersection. A dynamical interpretation is given of the groups H1(B/S, C/S) and H2(B/S, C/S), where B and C are the groups of ℬ and respectively, and S is the group of the flow ℬ ⋁ .
Checking ergodicity of some geodesic flows with infinite Gibbs measure
Authors: Rees Mary 
Published: September 2008

AbstractThis paper concerns a problem which arose from a paper of Sullivan. Let Γ be a discrete group of isometries of hyperbolic space Hd+1. We study the question of when the geodesic flow on the unit tangent bundle UT (Hd+1/Γ) of Hd+1/Γ is ergodic with respect to certain natural measures. As a consequence, we study the question of when Γ is of divergence type. Ergodicity when the non-wandering set of UT (Hd+1/Γ) is compact is already known from the theory of symbolic dynamics, due to Bowen, or from Sullivan's work. For such a Γ, we consider a subgroup Γ1 of Γ with Γ/Γ1 ≅ℤυ and prove the geodesic flow on UT (Hd+1/Γ1) is ergodic (with respect to one of these natural measures) if and only if υ ≤ 2.
A C∞ Denjoy counterexample
Authors: Hall Glen Richard 
Published: September 2008

AbstractIn this paper we construct an example of a homeomorphism of the circle onto itself which is C∞, has no periodic points and no dense orbits. Moreover, the homeomorphism will have no more than two points of zero derivative. We alter this example to form a C∞ map of an interval to itself which has homtervals.
Periodic orbits of continuous mappings of the circle without fixed points
Authors: Bernhardt Chris 
Published: September 2008

AbstractLet f be a continuous map of the circle to itself. Let P(f) denote the set of periods of the periodic points. In this paper the set P(f) is studied for functions without fixed points, so 1∉P(f). In particular, it is shown that if s, t are the two smallest integers in P(f) and s and t are relatively prime then αs+βt∈P(f) for any positive integers α and β.
On lattices acting on boundaries of semi-simple groups
Authors: Spatzier R. J. 
Published: September 2008

AbstractIt is shown that for a lattice Γ in a semi-simple group of real rank 1 the action on the boundary always admits an equivariant topological Γ-factor. We also show that there are no such factors for SL (n, ℤ) acting on ℙn−1,n≥3.
On the ergodicity of geodesic flows
Authors: Ballmann W. , Brin M. 
Published: September 2008

AbstractIn this paper we study the ergodic properties of the geodesic flows on compact manifolds of non-positive curvature. We prove that the geodesic flow is ergodic and Bernoulli if there exists a geodesic γ such that there is no parallel Jacobi field along γ orthogonal to γ. In particular, this is true if there exists a tangent vector v such that the sectional curvature is strictly negative for all two-planes containing v, or if there exists a tangent vector v such that the second fundamental form of the horosphere determined by v is definite at the support of v.
Perturbations of random matrix products in a reducible case
Authors: Kifer Yuri , Slud Eric 
Published: September 2008

AbstractIt is known that for any sequence X1, X2…, of identically distributed independent random matrices with a common distribution μ. the limitexists with probability 1. We study some conditions under which Λ(μk)→Λ(μ) provided μk → μ in the weak sense.
Hyperbolic behaviour of geodesic flows on manifolds with no focal points
Authors: Burns Keith 
Published: September 2008

AbstractIt is shown that the unit tangent bundle of a compact uniform visibility manifold with no focal points contains a subset of positive Liouville measure on which all the characteristic exponents of the geodesic flow (except in the flow direction) are non-zero. This completes Pesin's proof that the geodesic flow of such a manifold is Bernoulli.
Positive Liapunov exponents and absolute continuity for maps of the interval
Authors: Collet P. , Eckmann J.-P. 
Published: September 2008

AbstractWe give a sufficient condition for a unimodal map of the interval to have an invariant measure absolutely continuous with respect to the Lebesgue measure. Apart from some weak regularity assumptions, the condition requires positivity of the forward and backward Liapunov exponent of the critical point.
Rigidity of lattices of non-positive curvature
Authors: Eberlein P. 
Published: September 2008

AbstractLet M, M* denote compact, connected manifolds of non-positive sectional curvature whose fundamental groups are isomorphic and whose Euclidean de Rham factors are trivial. We prove that: if M is a compact irreducible quotient of a reducible symmetric space H, then M and M* are isometric up to a constant multiple of the metric; and that the number and dimensions of the local de Rham factors are the same for M and M*. Gromov has independently proved the first result in the more general case that M is locally symmetric and globally irreducible with rank at least two.
Dynamical semigroups commuting with compact abelian actions
Authors: Bratteli Ola , Evans David E. 
Published: September 2008

AbstractLet be a C*-algebra and τ:G → Aut a compact abelian action such that the fixed point algebra τ is simple. Denote by F the *-subalgebra of G-finite elements. Let H: F → be a *-operator commuting with τ such that and the matrix inequalityholds for all finite sequences X1, …, Xn in F. Then H is closable, and the closure is the generator of a strongly continuous semigroup {exp (−t): t ≥ 0} of completely positive contractions. Furthermore, there exists a convolution semigroup {μt: t ≥ 0} of probability measures on G such that.This result has various extensions and refinements.
Periodic points of surface homeomorphisms with zero entropy
Authors: Smillie John 
Published: September 2008

AbstractThis paper deals with the question of which periods can occur as periods of periodic points of zero entropy surface homeomorphisms in a given isotopy class. We give new examples of isotopy classes for which there are non-trivial restrictions and describe how the possible periods can be computed. Certain phenomena occur only for surfaces of large genus. These results have applications to the periodic data question for Morse–Smale maps.
Geometry, electrostatic measure and orthogonal polynomials on Julia sets for polynomials
Authors: Barnsley M. F. , Geronimo J. S. , Harrington A. N. 
Published: September 2008

AbstractThe Julia set B for an N'th degree polynomial T and its equilibrium electrostatic measure μ are considered. The unique balanced measure on B is shown to be μ. Integral properties of μ and of the monic polynomials orthogonal with respect to μ, Pn, n = 0, 1, 2, …, are derived. Formulae relating orthogonal polynomials of the second kind of different degrees are displayed. The measure μ is recovered both in the limit from the zeros and from the poles of the [Nn − 1/Nn] Padé approximant to the moment generating function to μ. For infinitely many polynomials of each degree N the zeros and poles all lie on an increasing sequence of trees of analytic arcs contained in B. The properties of these Padé approximant sequences support conjectures of George Baker which have not previously been tested on measures supported on sets nearly as complicated as Julia sets spread out in the complex plane.
Homoclinic and non-wandering points for maps of the circle
Authors: Block Louis , Coven Ethan , Mulvey Irene , Nitecki Zbigniew 
Published: September 2008

AbstractFor continuous maps ƒ of the circle to itself, we show: (A) the set of nonwandering points of ƒ coincides with that of ƒn for every odd n; (B) ƒ has a horseshoe if and only if it has a non-wandering homoclinic point; (C) if the set of periodic points is closed and non-empty, then every non-wandering point is periodic.
Structure de certains produits semi directs
Authors: Lamotte A. 
Published: September 2008

AbstractWe consider the skew product of a dynamical system with a Bernoulli flow and we prove that under additional conditions this skew product is isomorphic to a direct product. We use this result to show that the minimal diffeomorphism with strictly positive entropy (constructed by M. R. Herman) is isomorphic to a direct product of a 0-entropy dynamical system with a Bernoulli shift.
Flots d'Anosov sur les 3-variétés fibrées en cercles
Authors: Ghys Etienne 
Published: September 2008

AbstractWe consider Anosov flows on closed 3-manifolds which are circle bundles. Our main result is that, up to a finite covering, these flows are topologically equivalent to the geodesic flow of a suface of constant negative curvature. The same method shows that, if M is a closed hyperbolic manifold of any dimension, all the geodesic flows which correspond to different metrics on M and which are of Anosov type are topologically equivalent.
Kakutani equivalence of ergodic ℤn actions
Authors: Junco Andres Del , Rudolph Daniel J. 
Published: September 2008

AbstractWe define two families of relations between ergodic ℤn actions, both indexed equivariantly by non-singular n × n matrices. The first is to be Katok cross-sections of the same flow, indexed in a natural way by the matrices. The second is determined by the existence of an orbit preserving injection with an extra asymptotic linearity condition. We demonstrate that these two families are identical. In one dimension this is the classical theory of Kakutani equivalence.
Bowen's equidistribution theory and the Dirichlet density theorem
Authors: Parry William 
Published: September 2008

AbstractLet φ be an Axiom A flow restricted to a basic set, let g be a C∞ function and let , where λg(τ) is the g length of the closest orbit τ, λ(τ) is the period of τ and h is the topological entropy of φ. We obtain an asymptotic formula for πg which includes the ‘prime number’ theorem for closed orbits. This result generalizes Bowen's theorem on the equidistribution of closed orbits. After establishing an analytic extension result for certain zeta functions the proofs proceed by orthodox number theoretical techniques.
A complex Ruelle-Perron-Frobenius theorem and two counterexamples
Authors: Pollicott Mark 
Published: September 2008

AbstractIn this paper a new proof of a theorem of Ruelle about real Perron-Frobenius type operators is given. This theorem is then extended to complex Perron-Frobenius type operators in analogy with Wielandt's theorem for matrices. Finally two questions raised by Ruelle and Bowen concerning analyticity properties of zeta functions for flows are answered.
A return time invariant for finitary isomorphisms
Authors: Fiebig U. R. 
Published: September 2008

AbstractPoincare's recurrence theorem says that, given a measurable subset of a space on which a finite measure-preserving transformation acts, almost every point of the subset returns to the subset after a finite number of applications of the transformation. Moreover, Kac's recurrence theorem refines this result by showing that the average of the first return times to the subset over the subset is at most one, with equality in the ergodic case. In particular, the first return time function to any measurable set is integrable. By considering the supremum over all p ≥ 1 for which the first return time function is p-integrable for all open sets, we obtain a number for each almost-topological dynamical system, which we call the return time invariant. It is easy to show that this invariant is non-decreasing under finitary homomorphism. We use the invariant to construct a continuum number of countable state Markov shifts with a given entropy (and hence measure-theoretically isomorphic) which are pairwise non-finitarily isomorphic.
Non-existence of invariant circles
Authors: Mather John N. 
Published: September 2008

AbstractThe dynamical system associated to the difference equationhas been studied numerically by several authors. On the basis of numerical evidence, they conclude that there exists a numberk0≈ 0.97 such that there are homotopically non-trivial invariant circles for |k|≤k0and there are none for |k|>k0. In this note, we give a simple rigorous proof that there are none for |k|>.
Ergodic and mixing sequences of transformations
Authors: Berend Daniel , Bergelson Vitaly 
Published: September 2008

AbstractThe notions of ergodicity, strong mixing and weak mixing are defined and studied for arbitrary sequences of measure-preserving transformations of a probability space. Several results, notably ones connected with mean ergodic theorems, are generalized from the case of the sequence of all powers of a single transformation to this case. The conditions for ergodicity, strong mixing and weak mixing of sequences of affine transformations of compact groups are investigated.
Stability of the weak Pinsker property for flows
Authors: Fieldsteel Adam 
Published: September 2008

AbstractAn ergodic flow is said to have the weak Pinsker property if it admits a decreasing sequence of factors whose entropies tend to zero and each of which has a Bernoulli complement. We show that this property is preserved under taking factors and d-limits. In addition, we show that a flow has the weak Pinsker property whenever one ergodic transformation in the flow has this property.
Unfoldings of discrete dynamical systems
Authors: Robbin Joel W. 
Published: September 2008

AbstractA universal unfolding of a discrete dynamical system f0 is a manifold F of dynamical systems such that each system g sufficiently near f0 is topologically conjugate to an element f of F with the conjugacy φ and the element f depending continuously on f0. An infinitesimally universal unfolding of f0 is (roughly speaking) a manifold F transversal to the topological conjugacy class of f0. Using Nash-Moser iteration we show infinitesimally universal unfoldings are universal and (in part II) give a class of examples relating to moduli of stability introduced by Palis and De Melo.
Rotation intervals of endomorphisms of the circle
Authors: Bamon R. , Malta I. P. , Pacifico M. J. , Takens F. 
Published: September 2008

AbstractThe rotation number of a diffeomorphism f: S1 → S1 with lift is defined as . We investigate the case where f is an endomorphism. Then this limit may not exist and may depend on x. We investigate the set of limit points of , as a function of x.
Non-integrability of the 1:1:2–resonance
Authors: Duistermaat J. J. 
Published: September 2008

AbstractA Hamiltonian system of n degrees of freedom, defined by the function F, with an equilibrium point at the origin, is called formally integrable if there exist A A formal power series , functionally independent, in involution, and such that the Taylor expansion of F is a formal power series in the .Take n = 3, , F(k) homogeneous of degree k, F(2) > 0 and the eigenfrequencies in ratio 1:1:2. If F(3) avoids a certain hypersurface of ‘symmetric’ third order terms, then the F system is not formally integrable. If F(3) is symmetric but F(4) is in a non-void open subset, then homoclinic intersection with Devaney spiralling occurs; the angle decays of order 1 when approaching the origin.
Billiards on almost integrable polyhedral surfaces
Authors: Gutkin E. 
Published: September 2008

AbstractThe phase space of the geodesic flow on an almost integrable polyhedral surface is foliated into a one-parameter family of invariant surfaces. The flow on a typical invariant surface is minimal. We associate with an almost integrable polyhedral surface its holonomy group which is a subgroup of the group of motions of the Euclidean plane. We show that if the holonomy group is discrete then the flow on an invariant surface is ergodic if and only if it is minimal.
A topological version of a theorem of Mather on twist maps
Authors: Richard Hall Glen 
Published: September 2008

AbstractIn this report we show that a twist map of an annulus with a periodic point of rotation number p/q must have a Birkhoff periodic point of rotation number p/q. We use topological techniques so no assumption of area-preservation or circle intersection property is needed. If the map is area-preserving then this theorem andthe fixed point theorem of Birkhoff imply a recent theorem of Aubry and Mather. We also show that periodic orbits of (significantly) smallest period for a twist map must be Birkhoff.
Finite group actions on shifts of finite type
Authors: Adler R. L. , Kitchens B. , Marcus B. H. 
Published: September 2008

AbstractA continuous ℤ⊗TG action on a subshift of finite type consists of a subshift of finite type with its shift transformation, together with a group, G, of homeomorphisms of the subshift and a group automorphism T, so that the commutation relation σ ° g = Tg ° ∑A is any positive entropy subshift of finite type, G is any finite group and T is any automorphism of G then there is a non-trivial ℤ⊗TG action on ∑A. We then classify all such actions up to ‘almost topological‘ conjugacy.
An invariant for bounded-to-one factor maps between transitive sofic subshifts
Authors: Nasu Masakazu 
Published: September 2008

AbstractWe define a ‘core-matrix’ of a transitive sofic subshift, which is unique up to similarity for each transitive sofic subshift. We prove that if there exists a bounded-to-one factor map from one transitive sofic subshift to another, the block of the Jordan form of a core-matrix of this second subshift with non-zero eigenvalues is a principal submatrix of the Jordan form of a core-matrix of the first. We also prove that the subshifts that are almost of finite type are ‘spectrally of finite type’.