bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic Expansions for Second‐Order Linear Difference Equations, II
Authors: Wong R. , Li H.
Published: September 2015

Infinite asymptotic expansions are derived for the solutions to the second‐order linear difference equation
urn:x-wiley:00222526:media:sapm1992874289:sapm1992874289-math-0001
where p and q are integers, a(n) and b(n) have power series expansions of the form urn:x-wiley:00222526:media:sapm1992874289:sapm1992874289-math-0002 for large values of n, and a0 ≠ 0, b0 ≠ 0. Recurrence relations are also given for the coefficients in the asymptotic solutions. Our proof is based on the method of successive approximations. This paper is a continuation of an earlier one, in which only the special case p ≤ 0 and q = 0 is considered.
Resonant Generation of Finite‐Amplitude Waves by Flow Past Topography on aβ‐Plane
Authors: Grimshaw R. , Yi Z.
Published: September 2015

The forced Korteweg‐de Vries (fKdV) equation is the generic equation for resonant flow past an obstacle. However, for flow past topography on aβ‐plane, the case when the upstream flow is uniform is anomalous in that there is no quadratic nonlinear term in the fKdV equation. Here we show that in this important case an alternative theory is required and obtain a new evolution equation, which has some similarities to the fKdV equation with two significant differences. These are that a small‐amplitude topography now produces finite‐amplitude waves and the flow response is limited by a wave breakdown characterized by an incipient flow reversal. Various numerical solutions are described.
Painlevé Classification of All Semilinear Partial Differential Equations of the Second Order. II. Parabolic and Higher Dimensional Equations
Authors: Cosgrove Christopher M.
Published: September 2015

This paper extends the work of the previous paper (I) on the Painlevé classification of second‐order semilinear partial differential equations to the case of parabolic equations in two independent variables, uxx = F(x, y, u, ux, uy), and irreducible equations in three or more independent variables of the form, ΣijRij (x1,…, xn)u,ij = F(x1,…, xn; u,1,…, u,n). In each case, F is assumed to be rational in u and its first derivatives and no other simplifying assumptions are made. In addition to the 22 hyperbolic equations found in paper I, we find 10 equivalence classes of parabolic equations with the Painlevé property, denoted PS‐I, PS‐I1,…, PS‐X, equation PS‐II being a generalization of Burgers' equation denoted the Forsyth‐Burgers equation, and 13 higher‐dimensional Painlevé equations, denoted GS‐I, GS‐II,…, GS‐XIII. The lists are complete up to the equivalence relation of Möbius transformations in u and arbitrary changes of the independent variables. In order to avoid repetition, the proofs are sketched very briefly in cases where they closely resemble those for the corresponding hyperbolic problem. Every equation is solved by transforming to a linear partial differential equation, from which it follows that there are no non trivial soliton equations among the two classes of Painlevé equations treated in this paper.
On the Simultaneous Approximation of Functions and Their Derivatives by the Szász‐Mirakyan Operator (II)
Authors: Sun Xie‐Hua
Published: September 2015

The paper solves the problem of finding a unified estimate of the rate by the Szász‐Mirakyan operator that remained open in [1].
Shock Wave Tracking for Hyperbolic Systems Exhibiting Local Linear Degeneracy
Authors: He Yuanping , Moodie T. Bryant
Published: September 2015

Extending the results of our previous study [2], we now investigate the propagation of interior shocks corresponding to the signaling problem of small‐amplitude, high‐frequency type. We derive a formula for the shock front and show that the previously constructed asymptotic solution is valid on both sides of this front. This solution is further distinguished to a higher order in which the effects of material inhomogeneity are accounted for. Moreover, if λ = λ(u, x) represents the eigenvalue under consideration, we show that the single‐wave‐mode boundary disturbance of [2] can lead only to a λ‐shock. We also derive an entropy condition for the shock wave. As an application of our theory, the fluid‐filled hyperelastic tube problem of [7] is further examined and an example calculation made in which we show that a compressive shock wave is generated at the shock‐initiation point. This demonstration is effected as a particular example of the solution to a general bifurcation problem.
Oscillating Tails in the Perturbed Korteweg‐de Vries Equation
Authors: Milewski Paul
Published: September 2015

A simple method is used to derive the exponentially small oscillatory tails of solitons when the Korteweg‐de Vries equation is perturbed with a higher‐order dispersive term. A physical interpretation of the results is given, and several possible extensions to the problem are proposed.
Asymptotic Analysis of a Hyperbolic Mixed Problem in One‐Dimensional Viscoelasticity
Authors: Sabri Öncü T. , Bryant Moodie T.
Published: September 2015

We present an asymptotic analysis of the boundary‐generated, small‐amplitude, high‐frequency waves in a one‐dimensional, semi‐infinite, viscoelastic solid characterized by a single‐integral constitutive functional. The equations governing the wave motion constitute a 2×2 system of hyperbolic Volterra integrodifferential equations. The method of analysis is based on a single‐wave expansion of nonlinear geometric optics.
A Dimensional Integrable Generalization of the Sine‐Gordon Equation I. ‐∂‐Dressing and the Initial Value Problem
Authors: Konopelchenko B. G. , Dubrovsky V. G.
Published: September 2015

The 2+1 dimensional integrable generalization of the sine‐Gordon equation symmetric in the spatial variables is studied by the inverse spectral transform method. The solutions with functional parameters, plane solitons (kinks) and plane breathers are constructed by the dressing method based on the mixed nonlocal ‐∂‐problem. The initial value problem for this equation with the constant boundaries is solved in both cases σ2 = ± 1.
The Use of an lnvariance Condition in the Solution of Multiple‐Scale Singular Perturbation Problems: Ordinary Differential Equations
Authors: Woodruff S. L.
Published: September 2015

A new method is proposed for the solution of multiple‐scale perturbation problems. The straightforward perturbation solution, with secular terms, is used to construct a uniformly‐valid solution by enforcing an invariance property implicit in the expansion procedure. It is suggested that this method is more systematic than many methods currently in use and requires fewer a priori assumptions about the nature of the solution. A proof of the asymptotic validity of the method is given and some examples are presented.
On The Parametric Model of Western Boundary Outflow
Authors: Mallier Roland
Published: September 2015

A simple model equation for western boundary outflow in the Stommel model of the large scale ocean circulation is obtained by evaluating the potential vorticity equation at the western boundary. A series solution to this model equation demonstrates similar behavior to the boundary layer solution of the potential vorticity equation, in particular that “resonances” are present at a discrete series of parameter values which necessitate the addition of logarithms to the series; these resonances occur because the model equation has a logarithmic branch point at these values.
Geometric Aspects of Degenerate Modulation Equations
Authors: Bridges Thomas J.
Published: September 2015

Geometric aspects of degenerate modulation equations associated with spatially reversible systems are considered. Our primary observation is that stationary solutions of such equations always have a Poisson structure that is reminiscent of the equations governing the rigid body in mechanics. The Poisson structure is used to study the geometry of “spatial” phase space: A nontrivial Casimir of the Poisson structure provides a foliation of the phase space, spatially periodic states are given by critical points on level sets of the Casimir and stability type is given by the rate of change of the Casimir function. The bifurcation of spatially periodic states is then studied using singularity theory. The case where branches intersect transversely is treated in detail.
Connection across a Separatrix with Dissipation
Authors: Bourland F. Jay , Haberman Richard
Published: September 2015

Dissipative perturbations of strongly nonlinear oscillators that correspond to slowly varying double‐well potentials are considered. The method of averaging, which describes the solution as nearly periodic, fails as the trajectory approaches the unperturbed separatrix, a homoclinic orbit of the saddle point, significantly before it is captured in either well. Nevertheless, perturbed initial conditions corresponding to the boundary of the basin of attraction for each well, which are the perturbed stable manifolds of the saddle point, are accurately determined using only the method of averaging modified by Melnikov energy ideas near the separatrix. To determine the amplitude and phase of the captured oscillations after crossing the separatrix, a transition region is constructed consisting of a large sequence of nearly solitary pulses along the separatrix. The amplitude and phases of the slowly varying nonlinear oscillations away from the separatrix, both before and after capture, are matched to this transition region. In this way, analytic connection formulas across the separatrix are obtained and are shown to depend on the perturbed initial conditions.
A Class of Solutions for the Equations Governing the Steady Two‐Dimensional Motion of a Viscous Incompressible Liquid
Authors: Ranger K. B.
Published: September 2015

A general viscosity dependent solution for the stream function is found satisfying the simplest nondegenerate form of the steady flow Navier‐Stokes equations for a viscous incompressible liquid. The solution is two‐dimensional and is expressed in terms of arbitrary analytic functions in the fluid domain. This class of flows is generated by complex stream functions, and the region of definition is restricted by an inequality containing these analytic functions. A general potential flow, and degenerate Stokes or creeping flows are recovered as particular solutions in limiting cases.
The Inverse Scattering Method and Systems of Equations qxy = F(q, qy)
Authors: Beals Richard , Nouikou Roman G.
Published: September 2015

Consider equations of the form
urn:x-wiley:00222526:media:sapm1994923201:sapm1994923201-math-0001
where q is in general a complex vector and the function F depends nontrivially both on q and on qy. We show that a family S of such equations can be investigated by the inverse scattering method. If an equation (*) belongs to S, the function F depends linearly on q and algebraically on qy. We show that the family S contains a subfamily in which each equation can be obtained from the two dimensional Toda lattice equations by a Bäcklund transformation.
Geometric Aspects of Spatially Periodic Interfacial Waves
Authors: Dias Frédéric , Bridges Thomas J.
Published: September 2015

Periodic waves at the interface between two inviscid fluids of differing densities are considered from a geometric point of view. A new Hamiltonian formulation is used in the analysis and restriction of the Hamiltonian structure to space‐periodic functions leads to an O‐invariant Hamiltonian system. Motivated by the simplest O‐invariant Hamiltonian system, the spherical pendulum, we analyze the properties of traveling waves, standing waves, interactions between standing and traveling waves (mixed waves) and time‐modulated spatially periodic waves. A singularity in the bifurcation of traveling waves leads to a nonlinear resonance and this is investigated numerically.
A Direct Proof that Solutions of the Six Painlevé Equations Have No Movable Singularities Except Poles
Authors: Joshi Nalini , Kruskal Martin D.
Published: September 2015

The Painlevé property of an nth‐order differential equation is that no solution has any movable singularities other than poles. This property is strongly indicative of complete integrability (the existence of n − 1 integrals). However, the usual technique employed to test for the Painlevé property seeks only movable algebraic (or logarithmic) singularities. More general singularities are ignored. But, the six standard Painlevé equations are known to have no such singularities. Painlevé's proof of this is long and laborious; we give here a direct proof.
Rotational Effects on Surface Waves
Authors: Lu Qingyuan , Benney D. J.
Published: September 2015

In the classical theory of water waves only irrotational motions are considered. In the present paper a class of wave problems associated with inviscid rotational motions is examined and the consequences explored.
Resonant Interactions between Vortical Flows and Water Waves. Part I: Deep Water
Authors: Milewski P. A. , Benney D. J.
Published: September 2015

Any weak, steady vortical flow is a solution to leading order of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic, resonant interactions can occur between the various components of the flow. The periodic vortical component of the flow is proposed as a model for more complicated vortical flows that would affect surface waves in the ocean, such as the turbulence in the wake of a ship. These resonant interactions are studied in two dimensions, both in the limit of deep water (Part I) and shallow water (Part II). For deep water, the resonant set of surface waves is governed by “triad‐like” ordinary differential equations for the wave amplitudes, whose coefficients depend on the underlying rotational flow. These coefficients are calculated explicitly and the stability of various configurations of waves is discussed. The effect of three dimensionality is also briefly mentioned.
Explicit Solutions of the Steady Two‐Dimensional Navier‐Stokes Equations
Authors: Ranger K. B.
Published: September 2015

A method is described to determine exact general solutions of the steady two‐dimensional Navier‐Stokes equations. The solutions can also be utilized to construct the stream function for a class of unsteady flows, which in turn contain two arbitrary analytic functions of a complex variable defined in the fluid region.
Resonant Interactions between Vortical Flows and Water Waves. Part II: Shallow Water
Authors: Milewski P. A.
Published: September 2015

Any weak, steady vortical flow is a solution, to leading order, of the inviscid fluid equations with a free surface, so long as this flow has horizontal streamlines coinciding with the undisturbed free surface. This work considers the propagation of long irrotational surface gravity waves when such a vortical flow is present. In particular, when the vortical flow and the irrotational surface waves are both periodic and have comparable length scales, resonant interactions can occur between the various components of the flow. The interaction is described by two coupled Korteweg‐de Vries equations and a two‐dimensional streamfunction equation.
On the Asymptotic and Numerical Analyses of Exponentially III‐Conditioned Singularly Perturbed Boundary Value Problems
Authors: Lee June‐Yub , Ward Michael J.
Published: September 2015

Asymptotic and numerical methods are used to study several classes of singularly perturbed boundary value problems for which the underlying homogeneous operators have exponentially small eigenvalues. Examples considered include the familiar boundary layer resonance problems and some extensions and certain linearized equations associated with metastable internal layer motion. For the boundary layer resonance problems, a systematic projection method, motivated by the work of De Groen [1], is used to analytically calculate high‐order asymptotic solutions. This method justifies and extends some previous results obtained from the variational method of Grasman and Matkowsky [2]. A numerical approach, based on an integral equation formulation, is used to accurately compute boundary layer resonance solutions and their associated exponentially small eigenvalues. For various examples, the numerical results are shown to compare very favorably with two‐term asymptotic results. Finally, some Sturm‐Liouville operators with exponentially small spectral gap widths are studied. One such problem is applied to analyzing metastable internal layer motion for a certain forced Burgers equation.
Rossby Waves
Authors: Knessl Charles , Keller Joseph B.
Published: September 2015

An asymptotic solution of the linear shallow water equations for small Rossby number is constructed to describe Ross by waves. It leads to a dispersion or eiconal equation for the phase of the waves and a transport equation for their amplitude. It is shown how these equations can be solved by means of rays for both planetary and topographic Rossby waves. The method is illustrated by constructing the wave field produced by a time harmonic point source in fluid of uniform depth. This solution is a Green's function for the equations.
Duality Theory in Nonlinear Buckling Analysis for von Kármán Equations
Authors: Yang Gao David
Published: September 2015

The nonlinear eigenvalue problem in buckling analysis is studied for von Kármán plates. By using the general duality theory developed by Gao‐Strang [1, 2] it is proved that the stability criterion for the bifurcated state depends on a reduced complementary gap function. The duality theory is established for nonlinear bifurcation problems. This theory shows that the nonlinear eigenvalue problem is eventually equivalent to a coupled quadratic dual optimization problem. A series of equivalent variational principles are constructed and a lower bound theorem for the first eigenvalue of the buckling factor is proved.
Nonclassical Symmetries and the Singular Manifold Method: Theory and Six Examples
Authors: Estévez P. G. , Gordoa P. R.
Published: September 2015

In this paper we discuss a new approach to the relationship between integrability and symmetries of a nonlinear partial differential equation. The method is based heavily on ideas using both the Painlevé property and the singular manifold analysis, which is of outstanding importance in understanding the concept of integrability of a given partial differential equation. In our examples we show that the solutions of the singular manifold possess Lie point symmetries that correspond precisely to the so‐called nonclassical symmetries. We also point out the connection between the singular manifold method and the direct method of Clarkson and Kruskal. Here the singular manifold is a function of its reduced variable. Although the Painlevé property plays an essential role in our approach, our method also holds for equations exhibiting only the conditional Painlevé property. We offer six full examples of how our method works for the six equations, which we believe cover all possible cases.
Viscous Shock Motion for Advection‐Diffusion Equations
Authors: Laforgue Jacques G. L. , O'Malley Robert E.
Published: September 2015

This paper studies the asymptotic solution of the initial‐boundary value problem for scalar convection‐dominated evolution equations on a bounded spatial domain when initial and boundary conditions are such that the solution develops a single thin shock layer of steep change. The exponentially slow motion of the shock is determined for exponentially long times using an ansatz based on the solution for the special case of Burgers' equation, obtained through the Cole‐Hopf transformation. Results obtained analytically are confirmed by numerical experiments.
A Hybrid Asymptotic‐Numerical Study of a Model for Intracranial Pressure Dynamics
Authors: Yu J. , Lakin D. , Penar P.
Published: September 2015

Lumped parameter, compartmental models of the human intracranial system are studied through development of a hybrid asymptotic‐numerical technique. Dimensionless variables are introduced so that disparate time scales can be identified, and analysis shows that the system of model equations varies over both a fast and a slow time scale. On the fast time scale, the 5 × 5 system of equations may be decoupled to give a reduced 3 × 3 system combined with two conservation laws for the cerebrospinal fluid and brain compartmental volumes, respectively. The stiffness condition of the reduced system is shown to be considerably improved over that of the original system. For the general nonlinear problem, a uniformly valid asymptotic approximation for large time is derived by a hybrid asymptotic‐numerical technique. In the special case of the linear problem, where compliances and resistances are assumed to be constants, the uniform approximation for large time is obtained analytically. To verify accuracy, both asymptotic and hybrid asymptotic‐numerical results are compared with direct numerical integration of the full system. Physiological interpretations of the results are also given.
Biorthogonal Polynomial Bases and Vandermonde‐like Matrices
Authors: Verde‐Star Luis
Published: September 2015

This article considers a family of Gram matrices of pairs of bases of a finite dimensional vector space of polynomials with respect to certain indefinite inner products. Such a family includes all the generalized confluent Vandermonde matrices relative to any polynomial basis, like the Chebyshev‐Vandermonde matrices, for example. Using the biorthogonality of pairs of bases with respect to a divided difference functional, properties of matrices and functionals, as well as interpolation formulas are obtained. I show that the computation of the inverse of a Vandermonde‐like matrix is essentially equivalent to the computation of the partial fractions decompositions of a set of rational functions with a common denominator. I also explain why the various Chebyshev‐Vandermonde matrices are the simplest generalizations of the classic Vandermonde matrices and describe a simple algorithm for the computation of their inverses, which requires a number of multiplications of the order of 3N2.
Forbidden Regions for Shock Formation in Diffusive Systems
Authors: Witelski Thomas P. , Cohen Donald S.
Published: September 2015

We consider an initial‐boundary value problem for a nonlinear parabolic system. Using perturbation methods, this problem is reduced to one of considering an evolution equation for the long‐time asymptotics of the system. This model can be related to the leading order approximation for a spatially inhomogeneous reaction‐diffusion system with time‐dependent forcing. The evolution equation yields solutions with steady state shocks. We study some of the subtle effects introduced by time‐dependent forcing. Most significant among these effects is the creation of “forbidden regions” where stationary shocks cannot form. Results are presented for bi‐ and tri‐stable one‐dimensional models as well as multidimensional systems.
On Wave Interactions, I: Explosive Resonant Triads
Authors: Mahoney Daniel J.
Published: September 2015

This paper considers the phenomenon of explosive resonant triads in weakly nonlinear, dispersive wave systems. These nearly linear waves with slowly varying amplitudes become unbounded in finite time. It is shown that such interactions are much stronger than previously thought. These waves can be thought of as a nonlinear instability in the sense that a weakly nonlinear perturbation to some system grows to such a magnitude that the behavior of the system is governed by strongly nonlinear effects. This may occur for systems that are linearly or neutrally stable. This resolution is contrasted with previous resolutions of the problem, which assumed such perturbations remained large amplitude, nearly linear waves. Analytical and numerical evidence is presented to support these claims.
A Remarkable Endofunction Involving Compositions
Authors: Yeh Yeong‐Nan
Published: September 2015

We define a state as an arbitrary composition of a non‐negative integer n on m circularly labeled positions around a disk. A move is defined as the following endofunction: for each i, 1 ≤ i ≤ m; the value at position i (a non‐negative integer si) is distributed clockwise, one unit at a time, to itself and the following (si − 1) positions. The structures of states keep changing in irregular ways as we perform a series of moves. Definitions and necessary and sufficient conditions for cyclic states, root states, and leaf states are given in this paper. We provide the sharp upper bounds for the length of a path from a given nontrivial state to its nearest leaf state and for the length of a path from a given nontrivial state to its farthest leaf state in T(n, m). Surprisingly, it turns out that regardless of the initial state, one is sure to reach a cyclic state, which has only the values [n/m] and [(n + m − 1)/m] at all positions, in at most m − 1 moves.
Some Properties of Nonlinear Wave Systems
Authors: Yang J. , Benney D. J.
Published: September 2015

The results of a preliminary study of a particular nonlinear system of partial differential equations are presented. While much of this work pertains to two coupled nonlinear Schrödinger equations, it is believed that the properties found are representative of many other dispersive wave systems.
Asymptotics beyond All Orders for a Certain Type of Nonlinear Oscillators
Authors: Hu Jishan
Published: September 2015

This paper shows that a special class of smooth nonlinear oscillators, called bisuperlinear,
urn:x-wiley:00222526:media:sapm199696185:sapm199696185-math-0001
has a family of adiabatically symmetric solutions. This was motivated by a problem studied in sloshing water waves. A potential application of the work is to compute the nontrivial leading order term of the adiabatic invariants for a certain type of nonlinear nearly periodic Hamiltonian systems.
A Family of Wave‐Mean Shear Interactions and Their Instability to Longitudinal Vortex Form
Authors: Phillips W. R. C. , Shen Q.
Published: September 2015

The inviscid instability of O(ε) two‐dimensional periodic flows to spanwiseperiodic longitudinal vortex modes in parallel O(1) shear flows of the form ū = ± |z|q is considered. Here the mean velocity ū is relative to the wave and q is a constant. Such shear flows admit neutral Rayleigh waves with amplitudes that either diminish or diverge with |αz|; both are considered. Of particular interest are streamwise α and spanwise l wavenumbers in the range l2 ≫ α2, α = O(1), as it is here that the most analytical progress can be made. A generalized Lagrangian‐mean formulation is used to describe the effect of fluctuations upon the mean state and, because the developing mean flow acts to distort the waves, a further equation, the Rayleigh‐Craik equation, is employed to complete the specification. It is shown that instability to longitudinal vortex form is likely for both classes of waves in many physically interesting situations, from simple mixing layers to atmospheric boundary layers over undulating surfaces.
Nonlinear Stability of Baroclinic Fronts in a Channel with Variable Topography
Authors: Karsten Richard H. , Swaters Gordon E.
Published: September 2015

The governing equations describing baroclinic bottom‐trapped fronts in a channel with variable bottom topography are shown to be a noncanonical Hamiltonian system. The Hamiltonian formalism is exploited to derive a variational principle for arbitrary steady solutions based on an appropriately constrained energy functional. The variational principle is exploited to obtain formal and nonlinear stability conditions. In the infinitesimal amplitude limit, these stability conditions reduce to previously obtained normal mode results for the transverse gradient of the mean frontal potential vorticity.
The Existence of Görtler Vortices in Separated Boundary Layers
Authors: Denier James P. , Bassom Andrew P.
Published: September 2015

The linear stability properties of Görtler vortices within a general separated boundary layer flow are addressed. There has been little previous theoretical work directed toward this problem and here we are able to characterize the important features of vortices over the complete wavenumber spectrum. This investigation complements earlier studies of vortices within an attached flow which demonstrated that there are three distinctive wavenumber régimes which together describe the most relevant possibilities for vortex behavior. In the first of these, at relatively small wavenumbers, the mode is inviscid in character; as the vortex wavenumber increases so the spatial amplification rate of the vortices increases until viscous effects become significant and the growth rate begins to diminish. As the wavenumber increases yet further so the vortex is completely stabilized. Here we discuss the corresponding structures which may exist within a separated flow and the most significant result we find is that the maximum growth rate of a mode in this type of flow is actually greater than that which occurs when the flow has not separated. In addition, the inviscid modes are shown to have a far more complicated configuration than within an attached boundary layer and, indeed, their structure can only be completely determined by implementation of numerical procedures.
Gravity Currents Produced by Sudden Release of a Fixed Volume of Heavy Fluid
Authors: D'Alessio S. J. D. , Moodie T. Bryant , Pascal J. P. , Swaters G. E.
Published: September 2015

In this paper we study various aspects of gravity (or density) currents arising from instantaneous releases of heavy fluids in a rectangular channel with a horizontal bottom. It is shown, by means of a scaling argument, that these plane currents can be successfully modeled by a two‐by‐two system in conservation form together with a pair of algebraic relations. A number of numerical experiments are carried out using this “weak stratification” model to elicit information concerning the behavior of gravity currents. A weakly nonlinear analysis is employed to clarify some aspects that were uncovered by the numerical experimentation.
The Coalescence Limit of the Second Painlevé Equation
Authors: Halburd Rod , Joshi Nalini
Published: September 2015

In this paper, we study a well‐known asymptotic limit in which the second Painlevé equation (PII) becomes the first Painlevé equation (PI). The limit preserves the Painlevé property (i.e., that all movable singularities of all solutions are poles). Indeed it has been commonly accepted that the movable simple poles of opposite residue of the generic solution of PII must coalesce in the limit to become movable double poles of the solutions of PI, even though the limit naively carried out on the Laurent expansion of any solution of PII makes no sense. Here we show rigorously that a coalescence of poles occurs. Moreover we show that locally all analytic solutions of PI arise as limits of solutions of PII.
The Reconstruction of the Attracting Potential in the Sturm‐Liouville Equation through Characteristics of Negative Discrete Spectrum
Authors: Henkin G. M. , Novikova N. N.
Published: September 2015

Let us consider the Sturm‐Liouville equationurn:x-wiley:00222526:media:sapm199697119:sapm199697119-math-0001
on the positive half‐axis with negative potential of the form q(x) = ω2Q(x)+Q0(x), where functions Q and Q0 are integrable together with derivatives of the order m + 1 and have polynomial decreasing at infinity. In the development of the Lax‐Levermore result we show that the function Q(x) + ω−2Q0(x) can be reconstructed with accuracy O(ω−m)( only through characteristics of discrete negative spectrum of the Dirichlet problem for(*). As an application we prove that it is possible to reconstruct with prescribed accuracy a density and a compressibility of the horizontal homogeneous liquid half‐space through wavenumbers and amplitudes of surface waves excited by monochromatic source with sufficiently large but fixed frequencies ω1 and ω2.
Interaction of a Solitary Wave with an External Force Moving with Variable Speed
Authors: Grimshaw Roger , Pelinovsky Efim , Sakov Pavel
Published: September 2015

The interaction of a solitary wave with an external force moving with constant acceleration is studied within the forced Korteweg‐de Vries equation. For the case of a weak isolated force an asymptotic model based on equations for the amplitude and position of the solitary wave is developed. Phase portraits for this asymptotic system are obtained analytically and numerically. Analysis has shown that an accelerated force of either sign can capture a solitary wave if the acceleration is less than a certain critical value, depending on the forcing amplitude (for the case of a constant force speed only a positive force can capture a solitary wave). Direct numerical simulation of the forced Korteweg‐de Vries equation has confirmed the predictions of the asymptotic model. Also, it is shown numerically that the accelerated force can capture more than one solitary wave.
Exact N‐Wave Solutions of Generalized Burgers Equations
Authors: Sachdev P. L. , Joseph K. T. , vaganan B. Mayil
Published: September 2015

Exact N‐Wave solutions for the generalized Burgers equation
urn:x-wiley:00222526:media:sapm1996974349:sapm1996974349-math-0001
where j, α, β, and γ are nonnegative constants and n is a positive integer, are obtained. These solutions are asymptotic to the (linear) old‐age solution for large time and extend the validity of the latter so as to cover the entire time regime starting where the originally sharp shock has become sufficiently thick and the viscous effects are felt in the entire N wave.
Mobility of membrane-trapped particles
Authors: Stone Howard A. , Masoud Hassan
Published: September 2015

Rheological and transport studies of model thin films and membranes, often inspired by biological systems, make use of translational or rotational motion or diffusion of particles trapped in the surface film. Here, we consider the translational mobility of spherical and oblate spheroidal particles protruding into the surrounding subphase liquid. Both the subphase and surface film contribute to the resistance experienced by the particle, which is calculated as a function of the degree of protrusion as well as the viscosity contrast between the surface film and the surrounding fluid. The calculations are based on a combination of a perturbation expansion involving the particle shape and the Lorentz reciprocal theorem.
Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution
Authors: Serero D. , Gunkelmann N. , Pöschel T.
Published: September 2015

A hydrodynamic description of dilute binary gas mixtures comprising smooth inelastic spheres interacting by binary collisions with a random coefficient of restitution is presented. Constitutive relations are derived using the Chapman–Enskog perturbative method, associated with a computer-aided method to allow high-order Sonine polynomial expansions. The transport coefficients obtained are checked against DSMC simulations. The resulting equations are applied to the analysis of a vertically vibrated system. It is shown that differences in the shape of the distributions of the coefficient of restitution are sufficient to produce partial segregation.
Intake of total and added sugars and nutrient dilution in Australian children and adolescents
Authors: Louie Jimmy Chun Yu , Tapsell Linda C.
Published: September 2015

This analysis aimed to examine the association between intake of sugars (total or added) and nutrient intake with data from a recent Australian national nutrition survey, the 2007 Australian National Children’s Nutrition and Physical Activity Survey (2007ANCNPAS). Data from participants (n4140; 51 % male) who provided 2×plausible 24-h recalls were included in the analysis. The values on added sugars for foods were estimated using a previously published ten-step systematic methodology. Reported intakes of nutrients and foods defined in the 2007ANCNPAS were analysed by age- and sex-specific quintiles of %energy from added sugars (%EAS) or %energy from total sugars (%ETS) using ANCOVA. Linear trends across the quintiles were examined using multiple linear regression. Logistic regression analysis was used to calculate the OR of not meeting a specified nutrient reference values for Australia and New Zealand per unit in %EAS or %ETS. Analyses were adjusted for age, sex, BMIz-score and total energy intake. Small but significant negative associations were seen between %EAS and the intakes of most nutrient intakes (allP<0·001). For %ETS the associations with nutrient intakes were inconsistent; even then they were smaller than that for %EAS. In general, higher intakes of added sugars were associated with lower intakes of most nutrient-rich, ‘core’ food groups and higher intakes of energy-dense, nutrient-poor ‘extra’ foods. In conclusion, assessing intakes of added sugars may be a better approach for addressing issues of diet quality compared with intakes of total sugars.
Hall of Mirrors: The Great Depression, the Great Recession, and the Uses—and Misuses—of History
Authors: Hansen Per H.
Published: September 2015

Barry Eichengreen's new bookHall of Mirrorsis a detailed, excellent, and somewhat pessimistic comparison of the two most serious financial crises ever—their causes, development, and consequences. Readers well versed in the comprehensive literature on the Great Depression and the Great Recession in the United States and Europe will not find much information inHall of Mirrorsthat is completely new, but most others will. Whatisnew is the comparative approach: the detailed and analytically successful search for similarities and differences between the Great Depression and the Great Recession.
ARCHEDEMUS
Authors: Hooper Thomas
Published: September 2015

Ἀϱχέδημος ὁ τοῦ δήμου τότε πϱοεστηκὼς ἐν Ἀθήναις καὶ τῆς διωβελίας ἐπιμελόμενος Ἐϱασινίδῃ ἐπιβολὴν ἐπιβαλὼν κατηγόϱει ἐν δικαστηϱίῳ, ϕάσκων ἐξ Ἑλλησπόντου αὐτὸν ἔχειν χϱήματα ὄντα τοῦ δήμου· κατηγόϱει δὲ καὶ πεϱὶ τῆς στϱατηγίας. καὶ ἔδοξε τῷ δικαστηϱίῳ δῆσαι τὸν Ἐϱασινίδην.

Archedemus, who at that time was leader of the dēmos in Athens and overseer of the diōbelia, brought an accusation before a jury-court that a fine should be imposed on Erasinides, claiming that he had in his possession money from the Hellespont which belonged to the dēmos; he also brought an accusation against him concerning his generalship. It was decided by the jury-court to fetter Erasinides.

(Xenophon, Hellenica 1.7.2)

Moses Finley once remarked, apropos of Cleon, that ‘this man led Athens for several years after the death of Pericles, but Thucydides gives him four appearances only, one of them restricted to a single sentence and one a speech. The picture that emerges is complete and dramatic—but is it right? We do not know’. To penetrate beyond the Thucydidean portrait—and the Aristophanic caricature that buttresses it—is a complex and challenging exercise, but that has not stopped numerous scholars from attempting the task.
Beyond Legislation: Genuine Change in the Interaction between Victims of Sexual Crimes and the Criminal Law System
Authors: Paz-Wolk Tzili
Published: September 2015

This article examines the changes in the encounter between sexual assault victims and representatives of the law enforcement and judicial systems in Israel as perceived by workers and volunteers in the sexual assault crisis centres. After more than four decades of action in legal contexts – from spurring changes in legislation, through the training of professionals within the legal system, up to escorting victims – it is still hard to find studies that describe any change beyond legislation and procedures in the forms that this encounter assumes in Israel and in the world.

For the purpose of the study, this interaction was separated from the other aspects of the procedure, observed in depth and, with the interviewees' help, broken down into its relevant components. Data gathered and processed using quantitative and qualitative methods show that, according to the impression of the critical and experienced interviewees, representatives of the legal system truly endeavoured during the first decade of the second millennium to provide victims with better conditions than in the past, encouraging them to speak out in criminal proceedings.

As a possible background for the changes in the interpersonal encounter, the article suggests focusing on two mutually related processes, historical but also ongoing. The first is a change in the modes of thought and action in the crisis centres that dealt with this matter and promoted specific changes in the interpersonal encounter. The second process is reflected in the way in which legislators chose to intervene in the interpersonal encounters through four sections in the Rights of Victims of Crime Law. These processes influenced one another and still largely accompany the developments in this sphere, teaching important lessons about change in systems that are not easily amenable to change.
Endoscopic transpterygoidal repair of a large cranial defect with cerebrospinal fluid leak in a patient with extensive osteoradionecrosis of the skull base: case report and technical note
Authors: Brand Y , Lim E , Waran V , Prepageran N
Published: September 2015

Background:

Endoscopic endonasal techniques have recently become the method of choice in dealing with cerebrospinal fluid leak involving the anterior cranial fossa. However, most surgeons prefer an intracranial approach when leaks involve the middle cranial fossa. This case report illustrates the possibilities of using endoscopic techniques for cerebrospinal fluid leaks involving the middle fossa.

Case report:

A 37-year-old male patient presented with multiple areas of cranial defect with cerebrospinal fluid leak due to osteoradionecrosis following radiation for nasopharyngeal carcinoma 4 years earlier. Clinical examination showed involvement of all cranial nerves except the IInd and XIth nerves on the left side. A prior attempt to repair the cerebrospinal fluid leak with craniotomy was not successful.

Conclusion:

This case demonstrates the successful endoscopic repair of a large cranial defect with cerebrospinal fluid leak.
Stomach contents of by-caught striped dolphins (Stenella coeruleoalba) in the eastern Mediterranean Sea
Authors: Dede Ayhan , Salman Alp , Tonay Arda M.
Published: September 2015

Stomach contents of six striped dolphins taken as by-catch in the swordfish fishery in the eastern Mediterranean Sea off the Turkish coast were examined. In total, 29 taxa were identified to species or family and 1777 individual food items (1394 bony fishes, 289 cephalopods, 94 crustaceans) were counted.Diaphusspp. andCeratoscopelus maderensiswere the most remarkable ones, as they accounted for 70.45% of the total number of fishes.Onychoteuthis banksii, on the other hand, was the only cephalopod species found in all stomach content analyses and represented 38.06% of the total number of cephalopods. Bony fish species:Myctophum punctatum, Notoscopelus elongatus, Electrona risso, Sudis hyalina,Moridae sp., Phycidae sp., Sternoptychidae sp. and cephalopods:Pterygioteuthis giardiandChtenopteryx siculawere reported the first time in the stomach contents of striped dolphin in the Mediterranean Sea.
Picturing the liturgy: Notes on the iconography of the Holy Women at the Tomb in fourteenth- and early fifteenth-century Ethiopian manuscript illumination
Authors: Gnisci Jacopo
Published: September 2015

Almost five decades ago the late Stanislaw Chojnacki, one of the founding fathers of Ethiopian art history, began the task of describing the themes in Christian Ethiopian painting. Since then, others have contributed to the study of different subjects in Ethiopian art. Yet there are still gaps in our understanding of Ethiopian iconography. The aim of this study is to help fill these gaps by offering some remarks on the iconography of the Holy Women at the Tomb in fourteenth-century Ethiopian manuscript illumination.
Have Antarctic toothfish returned to McMurdo Sound?
Authors: Parker Steven J. , Mormede Sophie , Devries Arthur L. , Hanchet Stuart M. , Eisert Regina
Published: September 2015

A dramatic reduction in catch rates of Antarctic toothfish in McMurdo Sound, Antarctica, has led to conclusions that the commercial bottom longline fishery for toothfish in the Ross Sea has drastically altered the toothfish population with cascading effects on the McMurdo Sound ecosystem. However, results from a new monitoring programme for Antarctic toothfish and other top predators carried out in McMurdo Sound in 2014 have shown toothfish catch rate, fish size and fish age similar to those observed prior to 2002. These results suggest that either large and old fish have returned to McMurdo Sound following a temporary environmentally driven absence or that they remained locally present but were not detected in the areas sampled. These findings highlight the importance of continued standardized monitoring for detecting the potential effects of fishing on the Ross Sea ecosystem.
Blakiston’s Fish-owl Bubo blakistoni and logging: Applying resource selection information to endangered species conservation in Russia
Authors: SLAGHT JONATHAN C. , SURMACH SERGEI G.
Published: September 2015

Blakiston's Fish-owl Bubo blakistoni is classified as ‘Endangered’ by IUCN; this species is associated with riparian old-growth forests in north-east Asia, a landscape threatened by a variety of impacts (e.g. logging, agricultural development, human settlement). We examined a 20,213 km2 study area in Primorye, Russia, and assessed the ability of the protected area network to conserve Blakiston's Fish-owls by analysing resource selection of radio-marked individuals. Based on resource selection functions, we predicted that 60–65 Blakiston's fish-owl home ranges could occur within the study area. We found that the protected area network within our study area contained only 19% of optimal Blakiston's fish-owl habitat and contained only eight potential home ranges (five of these within a single protected area—Sikhote-Alin Biosphere Reserve). We also found that 43% of optimal Blakiston's Fish-owl habitat was within current logging leases; lands capable of supporting habitat equivalent to 24 home ranges. The remaining optimal habitat (38%) was on federal land and potentially contained 28–33 Blakiston's Fish-owl home ranges. The current protected area network, by itself, is not sufficient to conserve the species because relatively few home ranges are actually protected. Therefore, outside of protected areas, we recommend protecting specific locations within potential home ranges that likely contain suitable nest and foraging sites, maintaining integrity of riparian areas, modifying road construction methods, and closing old and unused logging roads to reduce anthropogenic disturbance to the owls and the landscape.
THE INTENSIVE MARGIN PUZZLE AND LABOR MARKET ADJUSTMENT COSTS
Authors: Wesselbaum Dennis
Published: September 2015

This paper documents a puzzling fact, namely that there is a significant negative relation between employment protection legislation and the usage of the intensive margin of labor market adjustments. I make use of a real business cycle model and introduce search and matching frictions as well as adjustment costs along the extensive and the intensive labor market margins. I show that the model is able to replicate the observed patterns of cyclicality, volatility, and especially the behavior of extensive and intensive margins if we assume low firing costs and relatively high hours adjustment costs.