bluuebunny/crossref_metadata_2025_split huggingface dataset:
Large-time behaviour of solutions of a reaction–diffusion equation
Authors: Pablo Arturo de 
Published: November 2011

We investigate the large-time behaviour of the solutions u = u(x, t) to the one-dimensional nonlinear heat equation with reactionwith exponents m > 1,p < 1. The initial function u(x, 0) is assumed to be measurable and nonnegative. In the case m + p ≧ 2 where the initial value does not uniquely determine the solution, we also fix the positivity set of the solution u(x, t) if the support of u(x, 0) is not the whole line ℝ, i.e. u(x, t) > 0 if and only if −s1(t) <x<s2(t), t ≧ 0, where 0≦si(t)≦∞ for t ≧ 0, i = 1, 2 are lower semicontinuous given functions. We prove that u converges to a self-similar function which depends only on the behaviour of u(x, 0) for |x| large or si(t) for t large. We classify the set of self-similar solutions and study the equation satisfied by their interfaces.
Anisotropic singular perturbations—the vectorial case
Authors: Barroso Ana Cristina , Fonseca Irene 
Published: November 2011

We obtain the Γ(L1(Ώ))-limit of the sequencewhere Eε is the family of anisotropic perturbationsof the nonconvex functional of vector-valued functionsThe proof relies on the blow-up argument introduced by Fonseca and Müller.
An integro-differential equation from population genetics and perturbations of differentiable semigroups in Fréchet spaces
Authors: Bürger Reinhard 
Published: November 2011

SynopsisExistence and uniqueness of solutions of an integro-differential equation that arises in population genetics are proved. This equation describes the evolution of type densities in a population that is subject to mutation and directional selection on a quantitative trait. It turns out that a certain Fréchet space is the natural framework to show existence and uniqueness. One of the main steps in the proof is the investigation of perturbations of generators of differentiable semigroups in Fréchet spaces.
Bifurcation of A-proper mappings without transversality considerations
Authors: Welsh Stewart C. 
Published: November 2011

SynopsisWe consider a nonlinear eigenvalue problem in the form F(x, λ) = Ax – T(λ)x – R(x, λ) = 0 with F:X × ℝ →Y where X, Y are Banach spaces. We assume that F(0, λ) = 0 for all λ ∈ ℝ and seek bifurcation points; that is, values λ0 ∈ ℝ for which there are solutions to F(x, λ) = 0 with x ≠ 0 in any neighbourhood of (0, λ0). Corresponding to these bifurcation points we obtain global properties of the maximal connected subset of solutions to F(x, λ) = 0 containing (0, λ0).Generalised topological degree techniques are employed in the proofs of our results without requiring a transversality condition. The operators involved belong to the general class of A-proper mappings which include compact and k-ball contractive perturbations of the identity operator, accretive mappings, and many more.
On the relation between distinct particular solutions of equation
Authors: Ke-ying Guan , Everitt W. N. 
Published: November 2011

SynopsisThere exists a relation (1.5) between any n + 2 distinct particular solutions of the differential equationIn this paper, we show that when and only when n = 0, 1 and 2, this relation can be represented by the following form:provided the form of this relation function Φn depends only on n and is independent of the coefficients of the equation. This result reveals interesting properties of these non-linear differential equations.
Solutions for the microsensor thermistor equations in the small bias case
Authors: Allegretto W. , Xie H. 
Published: November 2011

SynopsisThe behaviour of a microsensor thermistor is described by a system of nonlinear coupled elliptic equations subject to mixed Dirichlet-Neumann boundary conditions, to be solved on different domains. We employ the Implicit Function Theorem in Banach space to show that the system has a solution for small applied bias. It does not appear that earlier approaches for similar thermistor problems can be employed in this physically important situation. The fact that the problem is cast in a subset of R3 is significant in our presentation.
Spectral properties of a two parameter nonlinear Sturm-Liouville problem
Authors: Shibata Tetsutaro 
Published: November 2011

SynopsisWe consider the nonlinear Sturm–Liouville problem with two parameters on the general level setWe establish asymptotic formulae of the n-th variational eigenvalue λ = λn(μ, α) as α→∞ and α↓(nπ)2.
Steady states of the one-dimensional Cahn–Hilliard equation
Authors: Novick-Cohen A. , Peletier L. A. 
Published: November 2011

SynopsisThe steady states of the Cahn–Hilliard equation are studied as a function of interval length, L, and average mass, m. We count the number of nontrivial monotone increasing steady state solutions and demonstrate that if m lies within the spinodal region then for a.e. there is an even number of such solutions and for a.e. there is an odd number of such solutions. If m lies within the metastable region, then for a.e. L > 0 there is an even number of solutions. Furthermore, we prove that for all values of m, there are no secondary bifurcations.
Asymptotic expansions and Stokes multipliers of the confluent hypergeometric function Φ2, I
Authors: Shimomura Shun 
Published: November 2011

SynopsisThe confluent hypergeometric function Φ2(β,β′, γ, x, y) satisfies a system of partial differential equations which possesses the singular loci x = 0, y = 0, x − y = 0 of regular type and x = ∞, y = ∞ of irregular type. Near x = ∞ (|y| is bounded) and near y = ∞ (|x| is bounded), asymptotic expansions and Stokes multipliers of linearly independent solutions of the system are obtained. By a connection formula, the asymptotic behaviour of Φ2(β,β′, γ, x, y) itself is also clarified near these singular loci.
Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions
Authors: Grossi Massimo , Pacella Filomena 
Published: November 2011

SynopsisIn this paper we characterise the levels of the functional (0.3) at which the Palais-Smale condition fails in the Sobolev space V(Ω) defined below. From this result we deduce an existence theorem for positive solutions to the mixed boundary problem (0.1)–(0.2) under geometrical assumptions on the domain Ω and the part of the boundary of Ω where a Neumann condition is prescribed.
Invariant manifolds for metastable patterns in ut = ε2uxx—f(u)
Authors: Carr Jack , Pego Robert 
Published: November 2011

SynopsisWe consider the above equation on the interval 0 ≦ x ≦ 1 subject to Neumann boundary conditions with f(u) = F′(u) where F is a double well energy density function with equal minima. Our previous work [3] proved the existence and persistence of very slowly evolving patterns (metastable states) in solutions with two-phase initial data. Here we characterise these metastable states in terms of the global unstable manifolds of equilibria, as conjectured by Fusco and Hale [6].
A criterion for the complete continuity of the resolvent of a 2nth order differential operator with complex coefficients
Authors: Kamimura Yutaka 
Published: November 2011

SynopsisIn this paper, an ordinary differential operator of 2nth order, with complex-valued coefficients, is considered. A necessary and sufficient condition for the complete continuity of the resolvent operator of the differential operator is obtained. This is an extension of earlier work by Lidskii dealing with a second-order differential operator with a complex-valued potential.
Time harmonic electromagnetic waves in an inhomogeneous medium
Authors: Colton David , Kress Rainer 
Published: November 2011

SynopsisWe consider the scattering of time harmonic electromagnetic waves by an inhomogeneous medium of compact support, i.e. the permittivity ε = ε(x) and the conductivity σ = σ(x) are functions of x ∊ ℝ3. Existence, uniqueness and regularity results are established for the direct scattering problem. Then, based on existence and uniqueness results for the exterior and interior impedance boundary value problem, a method is presented for solving the inverse scattering problem.
Simple proofs of some results in perturbed bifurcation theory
Authors: Brown K. J. , Shivaji R. 
Published: November 2011

SynopsisIn this paper we discuss the existence and multiplicity of solutions to some perturbed bifurcation problems. By using sub and supersolution techniques along with an anti-maximum principle, simple proofs of some “well known” local results of perturbed bifurcation theory are obtained. The existence of global continua of solutions is proved by using degree theory arguments.
On the eigenvectors for a class of matrices arising from quasi-derivatives
Authors: Eastham M. S. P. 
Published: November 2011

SynopsisLet A be a product of symmetric matrices, A = RQ, with R non-singular, and let v be an eigenvector of A. For certain R and Q, a convenient formula for the expression (R−1v)tv is obtained. This expression occurs in the diagonalization of A and, in the particular case where A is associated with the quasi-derivative formulation of higher-order differential equations, the expression occurs in the asymptotic theory of solutions of the differential equation.
On positive differential operators (deficiency indices, factorization, perturbations)
Authors: Rofe-Beketov F. S. 
Published: November 2011

SynopsisA short survey is given of some recent results. The perturbations and stability of discrete spectrum and the problems of resolvent convergence of densely or non-densely defined elliptic differential operators are considered. The Courant theorem on variations of the domain is generalized. In connection with Berezanskiy's theorem on essential self-adjointness, the test for the finite velocity of propagation is extended. The Frobenius and the Krein-Heinz-Rellich factorization theorems and the Etgen Pawlowski oscillation criterion are generalized for equations of any order with operator-valued coefficients. Brusentsev's recent example of a two term fourth order differential operator with deficiency index 4 is discussed.
Periodic homogenisation of certain fully nonlinear partial differential equations
Authors: Evans Lawrence C. 
Published: November 2011

SynopsisWe demonstrate how a fairly simple “perturbed test function” method establishes periodic homogenisation for certain Hamilton-Jacobi and fully nonlinear elliptic partial differential equations. The idea, following Lions, Papanicolaou and Varadhan, is to introduce (possibly nonsmooth) correctors, and to modify appropriately the theory of viscosity solutions, so as to eliminate then the effects of high-frequency oscillations in the coefficients.
Moments of certain stochastic integrals occurring in mathematical physics
Authors: Smits Lieven 
Published: November 2011

SynopsisWe give an expression for the n-th moment of certain Itô integrals. The integrands considered are nonanticipating functionals of the form s↦a(s, Xs), where a is a measurable time-dependent vector field in space satisfying mild regularity conditions, and Xs is standard translated Brownian motion. The expressions are similar to the Dyson-Phillips terms for magnetic Schrödinger semigroups.We use these expressions to establish properties of the solutions of certain Cauchy problems and we relate our results to the framework of generalised Dyson expansions as set up by Johnson and Lapidus.
Multiple bifurcation in a predator–prey system with nonmonotonic predator response
Authors: Rothe Franz , Shafer Douglas S. 
Published: November 2011

SynopsisA model of a predator–prey system showing group defence on the part of the prey is formulated, and reduced to a three-parameter family of quartic polynomial systems of equations. Mathematically, this system contains the Volterra–Lotka system, and yields numerous kinds of bifurcation phenomena, including a codimension-two singularity of cusp type, in a neighbourhood of which the quartic system realises every phase portrait possible under small smooth perturbation. Biologically, the nonmonotonic behaviour of the predator response function allows existence of a second singularity in the first quadrant, so that the system exhibits an enrichment paradox, and, for certain choices of parameters, coexistence of stable oscillation and a stable equilibrium.
On inequalities for powers of linear operators and for quadratic forms
Authors: Phóng Vũ Qúôc 
Published: November 2011

SynopsisLetHbe a Hilbert space in which a symmetric operatorSwith a dense domainDsis given and letShave a finite deficiency index (r, s). This paper contains a necessary and sufficient condition for validity of the following inequalities of Kolmogorov typeand a method for calculating the best possible constantsCn,m(S).Moreover, let φ be a symmetric bilinear functional with a dense domainDφsuch thatDs⊂Dφand φ(f, g) = (Sf, g) for allf∈Ds,g∈Dφ. A necessary and sufficient condition for validity of the inequalityas well as a method for calculating the best possible constantKare obtained. Then an analogous approach is worked out in order to obtain the best possible additive inequalities of the formThe paper is concluded by establishing the best possible constants in the inequalitieswhereTis an arbitrary dissipative operator. The theorems are extensions of the results of Ju. I. Ljubič, W. N. Everitt, and T. Kato.
Analytic continuation and boundary continuity of functions of several complex variables
Authors: Lee Stout Edgar 
Published: November 2011

SynopsisThis note treats some questions about analytic continuation in several variables. The first theorem in effect determines the envelops of holomorphy of certain domains in ℂn. The second main result is a continuity theorem: If a bounded holomorphic function f on a convex domain ∆ in ℂn has boundary values that are continuous on the complement (in b∆) of a set of the form int∏ (b∆∩∏) where ∏ is a real hyperplane in ℂn that misses ∆, then f is continuous on . In addition, we obtain what may be regarded as a local version of the theorem in our earlier paper concerning the one-dimensional extension property. Our methods depend on Hartogs' theorem (n ≧ 3) and directly on the BochnerMartinelli formula (n = 2).
The orders of the Fibonacci groups
Authors: Seal D. J. 
Published: November 2011

SynopsisThe Fibonacci groups F(r, n) have been studied by various authors, chiefly in order to determine which ones are finite. This article contains a summary of the known results about this problem, followed by some further results obtained by the author. In particular, the orders of the groups F(r, 3) for r ≡ 2 (mod 3) and F(r, 4) for r ≡ 2 (mod 4) are determined, and various other Fibonacci groups are proved infinite by methods similar to those of Chalk and Johnson.
Effects of arbitrary Prandtl number on a forced convection flow near laminar separation
Authors: Akinrelere E. A. 
Published: November 2011

SynopsisFollowing an earlier paper by Akinrelere (1981), we consider a laminar boundary layer at low speeds in which density is sensibly constant and frictional heating is neglected. Also following the approach of Goldstein (1948) and Stewartson (1958), a singularity is established at separation for the thermal fields. The heat transfer is determined as a function of ξ = xs – x¼/l where xs is the separation point and l in a characteristic length.The results are for arbitrary Prandtl number σ. The results of Curle (1979) that the heat transfer near separation varies as σ¼ (at least for the first four terms) are confirmed.
Prevalence of hepatitis B virus infection in The Netherlands in 1996 and 2007
Authors: HAHNÉ S. J. M. , DE MELKER H. E. , KRETZSCHMAR M. , MOLLEMA L. , VAN DER KLIS F. R. , VAN DER SANDE M. A. B. , BOOT H. J. 
Published: November 2011

SUMMARYWe aimed to assess differences in the prevalence of hepatitis B virus (HBV) infection in The Netherlands between 1996 and 2007, and to identify risk factors for HBV infection in 2007. Representative samples of the Dutch population in 1996 and 2007 were tested for antibodies to hepatitis B core antigen (anti-HBc), hepatitis B surface antigen (HBsAg) and HBV-DNA. In 2007, the weighted anti-HBc prevalence was 3·5% (95% CI 2·2–5·5) and the HBsAg prevalence was 0·2% (95% CI 0·1–0·4). In indigenous Dutch participants, the anti-HBc prevalence was lower in 2007 than in 1996 (P=0·06). First-generation migrants (FGMs) had a 13-fold greater risk of being HBsAg- and/or HBV-DNA-positive than indigenous Dutch participants. In indigenous Dutch participants, risk factors for anti-HBc positivity were older age and having received a blood product before 1990. In FGMs, being of Asian origin was a risk factor. In second-generation migrants, having a foreign-born partner and injecting drug use were risk factors. FGMs are the main target group for secondary HBV prevention in The Netherlands.
Systematic review: the treatment of noncardiac chest pain
Authors: Hershcovici T. , Achem S. R. , Jha L. K. , Fass R. 
Published: November 2011

Aliment Pharmacol Ther 2012; 35: 5–14SummaryBackground  Treatment of noncardiac chest pain (NCCP) remains a challenge. This is in part due to the heterogenous nature of this disorder. Several conditions are associated with NCCP including gastro‐oesophageal reflux disease (GERD), oesophageal dysmotility, oesophageal hypersensitivity as well as others.Aim To determine the currently available therapeutic modalities for NCCP.Methods  We performed a systematic review of the literature that was published between January, 1980 and March, 2011. We identified 734 studies; 68 of them met entry criteria.Results  Patients with GERD‐related NCCP should receive proton pump inhibitors (PPI) twice daily for at least 8 weeks. Smooth muscle relaxants are only recommended for temporary relief of NCCP with motility disorders. Botulinum toxin injection of the distal oesophagus may be effective in the treatment of NCCP and spastic oesophageal motility disorders. Studies assessing the value of tricyclic antidepressants, trazodone and selective serotonine reuptake inhibitors in NCCP are relatively small, but suggest an oesophageal analgesic effect in NCCP patients that is limited by their side effects profile. The usage of theophylline to treat patients with non‐GERD‐related NCCP should be weighed against its potential toxicity. Use of complementary medicine has been scarcely studied in NCCP. Patients with coexisting psychological morbidity or those not responding to any medical therapy should be considered for psychological intervention. Cognitive behavioural therapy and hypnotherapy may be useful in the treatment of NCCP.Conclusions  Patients with GERD‐related noncardiac chest pain should be treated with at least double dose PPI. The primary treatment for non‐GERD‐related noncardiac chest pain, regardless if oesophageal dysmotility is present, is pain modulators.
Responses of immature permanent teeth with infected necrotic pulp tissue and apical periodontitis/abscess to revascularization procedures
Authors: Chen M. Y.‐H. , Chen K.‐L. , Chen C.‐A. , Tayebaty F. , Rosenberg P. A. , Lin L. M. 
Published: November 2011

Chen MY‐H, Chen K‐L, Chen C‐A, Tayebaty F, Rosenberg PA, Lin LM. Responses of immature permanent teeth with infected necrotic pulp tissue and apical periodontitis/abscess to revascularization procedures. International Endodontic Journal, 45, 294–305, 2012.AbstractAim  To report several types of response of immature permanent teeth with infected necrotic pulp tissue and either apical periodontitis or abscess to revascularization procedures.Methodology  Twenty immature permanent teeth with infected necrotic pulp tissue and either apical periodontitis or abscesses from 20 patients were included. The teeth were isolated with rubber dam, and pulp chambers was accessed through the crowns. The canals were gently irrigated with 5.25% sodium hypochlorite with minimal mechanical debridement. Calcium hydroxide was used as an inter‐appointment intracanal medicament and placed into the coronal half of the canal space. After resolution of clinical signs and symptoms, bleeding was induced into the canal space from the periapical tissues using K‐files. The coronal canal space was sealed with a mixture of mineral trioxide aggregate (MTA) and saline solution. The access cavity was filled with composite resin. These immature permanent teeth with infected necrotic pulp tissue and apical periodontitis/abscesses were followed up from 6 to 26 months.Results  Five types of responses of these immature permanent teeth with infected necrotic pulp tissue and apical periodontitis/abscess to revascularization procedures were observed: type 1, increased thickening of the canal walls and continued root maturation; type 2, no significant continuation of root development with the root apex becoming blunt and closed; type 3, continued root development with the apical foramen remaining open; type 4, severe calcification (obliteration) of the canal space; type 5, a hard tissue barrier formed in the canal between the coronal MTA plug and the root apex.Conclusions  Based on this case series, the outcome of continued root development was not as predictable as increased thickening of the canal walls in human immature permanent teeth with infected necrotic pulp tissue and apical periodontitis/abscess after revascularization procedures. Continued root development of revascularized immature permanent necrotic teeth depends on whether the Hertwig’s epithelial root sheath survives in case of apical periodontitis/abscess. Severe pulp canal calcification (obliteration) by hard tissue formation might be a complication of internal replacement resorption or union between the intracanal hard tissue and the apical bone (ankylosis) in revascularized immature permanent necrotic teeth.
Exploring leadership in community nursing teams
Authors: Cameron Shona , Harbison Jean , Lambert Vicky , Dickson Caroline 
Published: November 2011

cameron s., harbison j., lambert v. & dickson c. (2012) Exploring leadership in community nursing teams. Journal of Advanced Nursing68(7), 1469–1481.AbstractAims.  This article is a report on a study investigating how leadership is perceived in community nursing teams and how these perceptions are translated into working practices of team leaders.Background.  The consensus in community nursing literature is that leadership is important, and especially so in a time of change. However, little empirical evidence exists on how leadership works in practice.Method.  The study adopted an exploratory descriptive design, utilising individual semi‐structured interviews and focus groups in four case‐studies, with a total of 54 participants. Two case‐studies focussed on district nursing teams and two involved public health nursing teams, located in two geographical areas. Participants debated their understanding of the concept of leadership, its associated practices and behaviours in teams, if they saw themselves as leaders, and what preparation was required. The study was undertaken in 2009. Framework analysis techniques were employed to analyse the data.Findings.  A ‘quasi‐family’ model of leadership emerged, with significant emphasis on the importance of personal relationships and support. Nursing grade had a greater impact on perceptions of leadership than geographical context or professional and clinical focus.Conclusion.  No clear fit with any existing theoretical framework was identified. However, nurses in the highest grade banding, in particular, demonstrated practices associated with transformational leadership. Nurses expressed the very clear need to be acknowledged, respected and valued, and that those who provided this support were regarded as good leaders.