bluuebunny/crossref_metadata_2025_split huggingface dataset:
Symmetry sets of piecewise-circular curves
Authors: Giblin P. J. , Banchoff T. F. 
Published: November 2011

SynopsisPiecewise-circular (PC) curves are made up of circular arcs and segments of straight lines, joined so that the (undirected) tangent line turns continuously. PC curves have arisen in various applications where they are used to approximate smooth curves. In a previous paper, the authors introduced some of their geometrical properties. In this paper they investigate the ‘symmetry sets’ of PC curves and one-parameter families of such curves. The symmetry set has also arisen in applications (this time to shape recognition) and its mathematical properties for smooth curves have been investigated by Bruce, Giblin and Gibson. It turns out that the symmetry sets of general one-parameter families of plane curves are mirrored remarkably faithfully by the symmetry sets arising from the much simpler class of PC curves.
Schrödinger-Poisson systems in dimension d ≦ 3: The whole-space case
Authors: Nier F. 
Published: November 2011

SynopsisAfter a study made for bounded domains and in the periodic case, we investigate the variational formulation of Schrödinger-Poisson systems set on the whole space ℝd,d≦ 3. This variational formulation leads to a uniqueness result, while the existence of a solution is proved only for ‘small data’ because of the lack of coerciveness. The end of this paper briefly presents the extension of this formalism to a physically relevant problem where the potential is periodic in one direction.
Focusing blow-up for quasilinear parabolic equations
Authors: Budd C. J. , Galaktionov V. A. , Chen Jianping 
Published: November 2011

We study the behaviour of the non-negative blowing up solutions to the quasilinear parabolic equation with a typical reaction–diffusion right-hand side and with a singularity in the space variable which takes the formwhere m ≧ 1,p> 1 are arbitrary constants, in the critical exponent caseq= (p–1)/m> 0. We impose zero Dirichlet boundary conditions at the singular pointx= 0 and atx= 1, and take large initial data. For a class of ‘concave’ initial functions, we prove focusing at the origin of the solutions astapproaches the blow-up timeTin the sense thatx= 0 belongs to the blow-up set. The proof is based on an application of the intersection comparison method with an explicit ‘separable’ solution which has the same blow-up time asu. The method has a natural generalisation to the case of more general nonlinearities in the equation. A description of different fine structures of blow-up patterns in the semilinear casem= 1 and in the quasilinear onem> 1 is also presented. A numerical study of the semilinear equation is also made using an adaptive collocation method. This is shown to give very close agreement with the fine structure predicted and allows us to make some conjectures about the general behaviour.
Multiple solutions for nonhomogeneous elliptic equations involving critical Sobolev exponent
Authors: Cao Dao-Min , Li Gong-Bao , Zhou Huan-Song 
Published: November 2011

We consider the following problem:where is continuous on RN and h(x)≢0. By using Ekeland's variational principle and the Mountain Pass Theorem without (PS) conditions, through a careful inspection of the energy balance for the approximated solutions, we show that the probelm (*) has at least two solutions for some λ* > 0 and λ ∈ (0, λ*). In particular, if p = 2, in a different way we prove that problem (*) with λ ≡ 1 and h(x) ≧ 0 has at least two positive solutions as
Approximation of attractors for nongradient systems
Authors: Kostin I. N. 
Published: November 2011

The problem of approximation of attractors for semidynamical systems (SDSs) in a metric space is studied. Let some (exact) SDS possessing an attractor M be inaccurately defined, i.e. let another (approximate) SDS, which is close in some sense to the exact one, be given. The problem is to construct a set , which is close to M in the Hausdorff metric.The suggested procedure for constructing is finite, which makes it possible to use it in computations. The results obtained are suitable for numerical approximation of attractors for a rather large class of semidynamical systems, including ones generated by the Lorenz equations and the Navier–Stokes equations.
Sturmian comparison theorem for half-linear second-order differential equations
Authors: Li Horng Jaan , Yeh Cheh Chih 
Published: November 2011

Let φ:ℝ→ℝ be defined by φ(s) = |s|p−2s, with p > 1 a fixed number. We extend Sturm Comparison Theorem of the linear differential equationto the nonlinear differential equationby using the Wirtinger inequality. A Lyapunov inequality and some oscillation criteria of (E) are also given.
Semilinear elliptic problems with singular potentials in ℝN
Authors: Badiale Marino , Tchou Nicoletta A. 
Published: November 2011

SynopsisWe study a semilinear elliptic problem on ℝN where a potential is not a bounded function but can also be an infinite measure. We analyse the lack of compactness of the problem, obtaining a structure theorem for Palais-Smale sequences. This result allows us to obtain different kinds of existence theorems by a variational approach.
A reduction principle for topological classification of nonautonomous differential equations
Authors: Minh Nguyen Van 
Published: November 2011

SynopsisThe paper is concerned with equations of the form x' = A(t)x +f(t, x), where A is a continuous matrix function defined on ℝ, f is a continuous vector-valued function of (t, x) with f(t, 0) = 0. It is proved that if x' = A(t)x has an exponential trichotomy, A is bounded and f satisfies the Lipschitz condition with coefficient sufficiently small, then these equations are topologically equivalent to the systems of equations of the form , where B, g satisfy the same conditions as A, f.
Hyperasymptotics and the Stokes' phenomenon
Authors: Daalhuis A. B. Olde 
Published: November 2011

SynopsisHyperasymptotic expansions were recently introduced by Berry and Howls, and yield refined information by expanding remainders in asymptotic expansions. In a recent paper of Olde Daalhuis, a method was given for obtaining hyperasymptotic expansions of integrals that represent the confluent hypergeometric U-function. This paper gives an extension of that method to neighbourhoods of the so-called Stokes lines. At each level, the remainder is exponentially small compared with the previous remainders. Two numerical illustrations confirm these exponential improvements.
Solutions in Lebesgue spaces of the Navier-Stokes equations with dynamic boundary conditions
Authors: Dalsen Marié Grobbelaar-Van , Sauer Niko 
Published: November 2011

SynopsisThis paper, although self-contained, is a continuation of the work done in [8], where the motion of a viscous, incompressible fluid is considered in conjunction with the rotation of a rigid body which is immersed in the fluid. The resulting mathematical model is a Navier-Stokes problem with dynamic boundary conditions. In [8] a uniqueL2,3solution is constructed under certain regularity assumptions on the initial states. In this paper we consider the Navier-Stokes problem with dynamic boundary conditions in the Lebesgue spacesLr,3(3<r<∞) and prove the existence of a unique solution, local in time, without imposing any regularity conditions on the initial states.
On inhomogeneous biharmonic equations involving critical exponents
Authors: Deng Yinbin , Wang Gengsheng 
Published: November 2011

In this paper, we consider the existence of multiple solutions of biharmonic equations boundary value problemwhere Ω is a bounded smooth domain in ℝN, N ≥ 5; λ ∈ ℝ1 is a given constant; p = 2N/(N − 4) is the critical Sobolev exponent for the embedding ; Δ2 = ΔΔ denotes iterated N-dimensional Laplacian; f(x) is a given function. Some results on the existence and non-existence of multiple solutions for the above problem have been obtained by Ekeland's variational principle and the mountain-pass lemma under some assumptions on f(x) and N.
Semilinear elliptic equations with near critical growth rates
Authors: Budd C. 
Published: November 2011

SynopsisWe discuss the symmetric solutions of the semilinear elliptic equation Δu + λ(u+ u|u|p−1) = 0, u|∂B = 0 (*), where B is the unit ball in ℝ3. The value of p is taken close to 5, the critical Sobolev exponent for ℝ3. An asymptotic description of the solutions of (*) with large norm is obtained. This predicts a fold bifurcation if p > 5 and the structure of this bifurcation is studied in the limit p – 5→ 0. We find good agreement between the asymptotic description and some numerical calculations. These results are illuminated by recasting the problem (*) in the form of a dynamical system by means of a suitable change of variables. When |p – 5|≪1 and ∥u ≫1, the transformed solutions of (*) are also solutions of a perturbed Hamiltonian system and we study the behaviour of these solutions by using Melnikov methods.
Extremals in Landau's inequality for the difference operator
Authors: Kwong Man Kam , Zettl A. 
Published: November 2011

SynopsisThe best constants in Landau's inequality for the difference operator in the classical sequence spaces lp are known explicitly only for p = 1, 2, ∞. This is true in both the infinite N = (0, 1, 2, …) and biinfinite Z= (… − 1, 0, 1, …) cases. It is known that there are no extremals when p = 2 in both the infinite and biinfinite cases. Also, it is known that there are extremals when p = ∞ in the biinfinite case. Here we prove that there are no extremals in the other three cases where the best constants are known explicitly. The proofs for these three cases are quite different from each other.
Adjoints and self-adjointness for a differential operator with a varying structure
Authors: Das P. C. , Prasad Uma Shanker 
Published: November 2011

SynopsisIn this paper the adjoint operator is derived for a multi-point differential operator with a varying structure in a suitably chosen Hilbert space. The formal differential operator is given by different differential expressions in the adjoining intervals. This form of adjoint operator is used to characterize self-adjointness.
Semiprimitivity of inverse semigroup algebras
Authors: Munn W. D. 
Published: November 2011

SynopsisLet S be an inverse semigroup and F a field. It is shown that if F has characteristic 0 and is not algebraic over its prime subfield then the algebra of S over F is semiprimitive (i.e. Jacobson semisimple). This generalises a well-known theorem on group algebras due to Amitsur. Similar results for the case in which F has prime characteristic are obtained under the additional hypotheses that S is completely semisimple or that S is E-unitary with a totally ordered semilattice.
On bounds for Titchmarsh–Weyl m-coefficients and for spectral functions for second-order differential operators
Authors: Atkinson F. V. 
Published: November 2011

SynopsisOrder-of-magnitude results are extended to the case of general second-order term, with coefficient not necessarily of fixed sign, with general positive weight-function. The bounds are used to establish the expression for the Titchmarsh–Weyl function m(λ) as a Nevanlinna function in terms of the spectral function.
A general version of the Hardy–Littlewood–Polya–Everitt (HELP) inequality
Authors: Bennewitz Christer 
Published: November 2011

SynopsisThe inequality (0·1) below is naturally associated with the equation −(pu′)′ + qu = λu. By assuming that one end-point of the interval (a, b) is regular and the other limit-point for this equation, Everitt characterized the best constant K in tems of spectral properties of the equation. This paper sketches a theory for more general inequalities (0·2), (0·3) similarly related to the equation Su = λTu. Here S and T are ordinary, symmetric differential expressions. A characterization of the best constants in (0·2), (0·3) is given which generalises that of Everitt.For the case when S is of order 1 and T is multiplication by a positive function, all possible inequalities are given together with the best constants and cases of equality. Furthermore, an example is given of a valid inequality (0·1) on an interval with both end-points regular for the corresponding differential equation. This contradicts a conjecture by Everitt and Evans. Finally, the general theory for the left-definite inequality (0·3) is specialised to the case when S is a Sturm-Liouville expression. A family of examples is given for which the best constants can be explicitly calculated.
Spiral motion for components of a Dirac system of limit circle type
Authors: Halvorsen S. G. , Shaw J. K. 
Published: November 2011

SynopsisThe components of a two (complex) dimensional Dirac system are studied as trajectories in the complex plane. The system, defined on an interval [a, b) of regular points, is assumed to be of limit circle type at t = b, and to be non-oscillatory there. By introducing moduli ρ1(t) = |y1(t)|, ρ2(t) = |y2(t)| and continuous complex arguments θ1(t) = arg y1(t), θ2(t) = arg y2(t) for the components, the principal result proved is that θ1(t) and θ2(t) are bounded as t → b. Examples show that monotonicity of the argument function θ1(t), which is a feature of the corresponding problem for Sturm–Liouville equations, fails for Dirac systems.
On the Spectrum of a one-dimensional Schrödinger operator whose potential is a limit of finite-zone potentials
Authors: Levitan B. M. 
Published: November 2011

SynopsisDenote by (αj, βj), j = 1, 2, … an infinite set of disjoint open intervals on the half-line (0, ∞). Suppose that the following conditions are fulfilled:With the aid of the first two trace formula presented earlier by the author, we prove in this paper that there exists a function q, defined on the whole real line, such that for the Schrödinger equation −y″ + q(x)y = λy (−∞<x<∞), the intervals (αj, βj) are spectrum lacunae. As an example, we consider the case when the intervals (αj, βj) are adjacent intervals of the Cantor trinary perfect set.
On the essential self-adjointness of powers of Schrödinger operators
Authors: Read Thomas T. 
Published: November 2011

SynopsisSufficient conditions are given for the minimal operator T0 generated by the elliptic differential expression τ = ρ−1 (−Σ DjajkDk + q) to be essentially self-adjoint in the weighted Hilbert space , and for all powers of T0 to be essentially self-adjoint.
A note on primeness of semigroup rings
Authors: Silva Pedro V. 
Published: November 2011

SynopsisThis note discusses primeness for semigroup rings of semigroups satisfying a certain condition, weaker than the u.p. property. These semigroups include free products of semigroups, semigroups presented by a single relator and at least three generators, and free inverse semigroups of infinite rank.
The compact weak topology on a Banach space
Authors: González Manuel , Gutiérrez Joaquín M. 
Published: November 2011

SynopsisThe compact weak topology (kw) on a Banach space is defined as the finest topology that agrees with the weak topology on weakly compact subsets. It appears in a natural manner in the study of certain classes of continuous and holomorphic maps between Banach spaces. In this paper we treat the kw topology and the finest locally convex topology contained in kw, which we call the ckw topology. We prove that kw = ckw if and only if the space is reflexive or Schur, and we derive characterisations of Banach spaces not containing l1, and of other classes of Banach spaces, in terms of these topologies. We also show that ckw is the topology of uniform convergence on (L)-subsets of the dual space. As a consequence, Banach spaces with the reciprocal Dunford–Pettis property are characterised.
Hankel operators with PC symbols and the space H∞ + PC
Authors: Bonsall F. F. , Gillespie T. A. 
Published: November 2011

SynopsisWe obtain an explicit formula for the essential norm of a Hankel operator with its symbol in the space PC, which is the closure in L∞ of the space of piecewise continuous functions on the unit circle . It follows from this formula that functions in PC can be approximated as closely by functions in C, the continuous functions on the circle, as by functions in the much larger space H∞ + C. This is an example of the way in which properties of the Hardy spaces can be derived from properties of Hankel operators.
Semi-discrete Galerkin approximation method applied to initial boundary value problems for Maxwell's equations in anisotropic, inhomogeneous media
Authors: Neittaanmäki Pekka , Saranen Jukka 
Published: November 2011

SynopsisIn this paper the semi-discrete Galerkin approximation of initial boundary value problems for Maxwell's equations is analysed. For the electric field a hyperbolic system of equations is first derived. The standard Galerkin method is applied to this system and a priori error estimates are established for the approximation.
Spectral properties of two-parameter eigenvalue problems
Authors: Binding Paul , Browne Patrick J. 
Published: November 2011

SynopsisWe study the self-adjoint eigenvalue problem W(λ)x = 0, (*), in Hilbert space for one equation in two parameters. Hereis bounded below with compact resolvent for each λ = (λ1, λ2). We give necessary and sufficient conditions for the existence of λ so that (*) holds with W(λ)= ≧0 and we investigate the geometry of the set Z0 of such λ. We also discuss higher order solution sets Zi where the ith eigenvalue of W(λ) vanishes, deriving various asymptotic results in a unified fashion.
Direct products of finite monogenic inverse semigroups
Authors: Trueman D. C. 
Published: November 2011

SynopsisWe characterize direct products of finite monogenic inverse semigroups; we show that a finite monogenic inverse semigroup which is not a group is directly indecomposable and that a finite semigroup which is decomposable into a direct product of monogenic inverse semigroups which are not groups is uniquely so decomposable. We determine when a finite semigroup can be decomposed into a direct product of non-group monogenic inverse semigroups and show how the direct factors, if they exist, can be found.
Novel Techniques for Microspectroscopy and Chemical Imaging Analysis of Soybean Seeds and Embryos
Authors: Baianu I. , You Tiefeng , Costescu Doina 
Published: November 2011

AbstractNovel methodologies are currently being evaluated for the Chemical Analysis of soybean seeds as well as developing mature soybean embryos by FT-IR/NIR Microspectroscopy. This is the first report of FT-NIR Chemical Images obtained with 1 micron resolution. NIR spectra of Proteins, Oil and DNA fibers are obtained for regions as small as 1μ^2^.
Anti‐tumour activity of 4‐(4‐fluorophenyl)amino‐5,6,7‐trimethoxyquinazoline against tumour cells in vitro
Authors: Huang Yinjiu , Liu Fang , Zhao Li , Wu Huazhang , Liu Hui 
Published: November 2011

AbstractIn order to create novel, potent and selective anti‐cancer agents, the action of 4‐(4‐fluorophenyl)amino‐5,6,7‐trimethoxyquinazoline (compound 1018) on 10 different kinds of tumour cells were assayed by MTT [3‐(4,5‐dimethylthiazol‐2‐yl)‐2,5‐diphenyl‐2H‐tetrazolium bromide]. It possesses a broad spectrum of anti‐cancer activity. The mechanism of action of 4‐(4‐fluorophenyl)amino‐5,6,7‐trimethoxyquinazoline (hereafter referred to as compound 1018) against tumour cells was studied in androgen‐independent prostate cancer PC‐3 cells by microscopic observation, LDH (lactate dehydrogenase) release assay and Western blotting. Its activity was dose‐dependent, with an IC50 of 13.0±1.4 μM after 72 h treatment. Microscopy and LDH release assay indicated that the effect was through anti‐proliferation rather than cytotoxicity. Western blot analysis also showed that treatment of cells with 50 μM compound 1018 for 30 min almost completely inhibited EGF (epidermal growth factor)‐induced phosphorylation of ERK1/2 (extracellular‐signal‐regulated kinase 1/2), which suggests that its anti‐proliferative effect is largely associated due to ERK1/2 activation being inhibited. Thus compound 1018 is a potential anti‐cancer agent.
Effects of hydrocortisone on acute β‐adrenoceptor blocker and histamine induced bronchoconstriction
Authors: Short Philip M. , Williamson Peter A. , Lipworth Brian J. 
Published: November 2011

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT• β‐adrenoceptor blockers are avoided in asthma due to concerns of the potential for β‐adrenoceptor blocker induced bronchoconstriction with the greatest risk after first dose.WHAT THIS STUDY ADDS• Nebulized salbutamol and ipratropium produced a full recovery of lung function in the presence of acute β‐adrenoceptor blocker and histamine induced bronchoconstriction. Salbutamol reversibility was not potentiated by intravenous hydrocortisone.AIMSβ‐adrenoceptor blockers are avoided in asthma due to concerns of bronchoconstriction. We investigated the safety of acute exposure to propranolol in asthmatics, sequentially challenged with histamine to mimic an asthma exacerbation and evaluated the role of intravenous hydrocortisone in potentiating salbutamol reversibility.METHODSPersistent atopic asthmatics, requiring ≤1000 µg day−1 budesonide, performed a randomized double‐blind placebo‐controlled crossover study. Following 10 mg or 20 mg of oral propranolol, patients received 400 mg intravenous hydrocortisone or placebo, followed by histamine challenge with nebulized salbutamol 5 mg and ipratropium 500 µg recovery.RESULTSThirteen patients completed per protocol. Hydrocortisone did not potentiate salbutamol recovery post propranolol and histamine challenge vs. placebo (mean difference in FEV1 0.04 ml, 95% CI −0.07, 0.15, P= 0.417). β‐adrenoceptor blocker induced bronchoconstriction was demonstrated by spirometry and impulse oscillometry. For the placebo visit, FEV1 fell 4.7% 2 hours post propranolol (95% CI 1.8, 7.5, P= 0.008) whilst total airway resistance (R5%) increased 31.3% (95% CI 15.6, 47.0, P= 0.04). On both visits FEV1% and R5% returned to baseline after salbutamol post histamine.CONCLUSIONNebulized salbutamol and ipratropium produced a full recovery after propranolol and histamine induced bronchoconstriction, independent of hydrocortisone use. Since the greatest risk of β‐adrenoceptor blockade is after first dose, our findings offer reassurance to those undertaking further evaluation of chronic β‐adrenoceptor blockade as a potential treatment for mild‐to‐moderate asthma.
Investigation of six selected bacterial species in endo‐periodontal lesions
Authors: Didilescu A. C. , Rusu D. , Anghel A. , Nica L. , Iliescu A. , Greabu M. , Bancescu G. , Stratul S. I. 
Published: November 2011

Didilescu AC, Rusu D, Anghel A, Nica L, Iliescu A, Greabu M, Bancescu G, Stratul SI. Investigation of six selected bacterial species in endo‐periodontal lesions. International Endodontic Journal, 45, 282–293, 2012.AbstractAim  To investigate and determine possible associations of six tested bacteria belonging to ‘orange’ and ‘green’ complexes, in endo‐periodontal lesions: Parvimonas micra, Fusobacterium nucleatum, Campylobacter rectus, Eubacterium nodatum, Eikenella corrodens and Capnocytophaga sputigena.Methodology  Forty‐six patients presenting with different types of endo‐periodontal lesions were investigated. Clinical examinations, periapical radiographs and microbiological sampling from the canal system (endo) and periodontal pockets (perio) were performed. Qualitative and semiquantitative evaluation of bacteria was performed by polymerase chain reaction (PCR) and DNA–DNA hybridization (micro‐IDent plus; Hain Lifescience, Germany).Results  Extremely high bacterial loads in endodontic samples were recorded for P. micra, F. nucleatum and C. sputigena, while periodontal samples were often colonized by the same species, plus C. rectus. Significant association was recorded between F. nucleatum‐endo and P. micra‐endo (P = 0.03, Fisher’s exact test). There was marginal evidence of associations between: (i) C. sputigena‐endo and C. sputigena‐perio (P = 0.06, Fisher’s exact test); (ii) P. micra‐endo and P. micra‐perio (P = 0.05, Fisher’s exact test). Sensitivity to percussion was associated with an increased chance of cases with P. micra‐endo (P = 0.03, Pearson chi‐square test).Conclusion  The findings suggest that F. nucleatum, P. micra and C. sputigena may play a role in the pathogenesis of endo‐periodontal lesions.