The KP-II equation was derived by Kadmotsev and Petviashvili to explain stability of line solitary waves of shallow water. Recently, Mizumachi proved nonlinear stability of 1-line solitons for exponentially localized perturbations. In this paper, we prove stability of 1-line solitons for perturbations in (1 + x 2)−1/2−0 H 1(ℝ2) and perturbations in H 1(ℝ2) ∩ ∂xL 2(ℝ2).

The action of any group on itself by conjugation and the corresponding conjugacy relation play an important role in group theory. There have been many attempts to find notions of conjugacy in semigroups that would be useful in special classes of semigroups occurring in various areas of mathematics, such as semigroups of matrices, operator and topological semigroups, free semigroups, transition monoids for automata, semigroups given by presentations with prescribed properties, monoids of graph endomorphisms, etc. In this paper we study four notions of conjugacy for semigroups, their interconnections, similarities and dissimilarities. They appeared originally in various different settings (automata, representation theory, presentations, and transformation semigroups). Here we study them in full generality. The paper ends with a large list of open problems.

We study inversion of the spherical Radon transform with centres on a sphere (the data acquisition set). Such inversions are essential in various image reconstruction problems arising in medical, radar and sonar imaging. In the case of radially incomplete data, we show that the spherical Radon transform can be uniquely inverted recovering the image function in spherical shells. Our result is valid when the support of the image function is inside the data acquisition sphere, outside that sphere, as well as on both sides of the sphere. Furthermore, in addition to the uniqueness result, our method of proof provides reconstruction formulas for all those cases. We present a robust computational algorithm and demonstrate its accuracy and efficiency on several numerical examples.

In this paper, we study the bounded approximation property for the weighted space $\mathcal{HV}$(U) of holomorphic mappings defined on a balanced open subset U of a Banach space E and its predual $\mathcal{GV}$(U), where $\mathcal{V}$ is a countable family of weights. After obtaining an $\mathcal{S}$-absolute decomposition for the space $\mathcal{GV}$(U), we show that E has the bounded approximation property if and only if $\mathcal{GV}$(U) has. In case $\mathcal{V}$ consists of a single weight v, an analogous characterization for the metric approximation property for a Banach space E has been obtained in terms of the metric approximation property for the space $\mathcal{G}_v$(U).

Over the two days 2–3 March 2017, about 80 mathematicians and friends gathered in Cambridge to celebrate the life and work of Joseph Bishop Keller (1923–2016), one of the pre-eminent applied mathematicians of the 20th century. Joe, as he was known throughout the world, made pioneering contributions to a wide range of natural phenomena and developed fundamental mathematical techniques with which to understand them. Twenty-four talks were presented at the meeting, given by mathematicians who have either worked with Joe or have been influenced by his work. Rather than summarise each presentation, we have collated all the contributions under the headings of waves, fluids, solids, chemistry and biology, and finally some history.

The special lead article in this issue of EJAM, by Profs. John Ockendon and Brian Sleeman, is dedicated to Prof. Joseph B. Keller (referred to as Joe by his friends), Emeritus professor of Stanford University, who was one of the greatest applied mathematicians of our time. Joe died in September 2016. A workshop in honour of Joe was held at the Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, in March 2017, focussing on some of the astonishingly wide range of topics in the mathematical sciences and continuum mechanics that Joe made substantial contributions to over his long career. This article discusses some of these pioneering contributions, describes some modern developments as discussed by the workshop speakers, and provides a more personal tribute to Joe, his history, and to his large influence on the international applied mathematics community. May the spirit of Joe, and his flavour of applied mathematics, continue to be reflected in EJAM.

We determine the lower rank of the direct product of finitely many hereditarily just infinite profinite groups of finite lower rank.

We compute the involutive Heegaard Floer homology of the family of three-manifolds obtained by plumbings along almost-rational graphs. (This includes all Seifert fibered homology spheres.) We also study the involutive Heegaard Floer homology of connected sums of such three-manifolds, and explicitly determine the involutive correction terms in the case that all of the summands have the same orientation. Using these calculations, we give a new proof of the existence of an infinite-rank subgroup in the three-dimensional homology cobordism group.

In this note, we establish a Schwarz–Pick type inequality for holomorphic mappings between unit balls B n and B m in corresponding complex spaces. We also prove a Schwarz-Pick type inequality for pluri-harmonic functions.

Uniformization transforms a pseudo-Poisson process with unequal intensities (leaving rates) into one with uniform intensity. Self-transitions is the price to pay. Two intensities arise when one considers an absorbing barrier of a Markov process as a body in its own right: a pair of Markov processes intertwined by an extended Chapman–Kolmogorov equation naturally arises. We show that Sauer's two-state space empathy theory handles such intertwined processes. The price of self-transitions is also avoided.

The article concerns the existence and uniqueness of quantisations of cluster algebras. We prove that cluster algebras with an initial exchange matrix of full rank admit a quantisation in the sense of Berenstein-Zelevinsky and give an explicit generating set to construct all quantisations.

The main purpose of this paper is to investigate some natural problems regarding the order structure of representable functionals on *-algebras. We describe the extreme points of order intervals, and give a non-trivial sufficient condition to decide whether or not the infimum of two representable functionals exists. To this aim, we offer a suitable approach to the Lebesgue decomposition theory, which is in complete analogy with the one developed by Ando in the context of positive operators. This tight analogy allows to invoke Ando's results to characterize uniqueness of the decomposition, and solve the infimum problem over certain operator algebras.

We show that an action of a group on a set X is locally finite if and only if X is not equidecomposable with a proper subset of itself. As a consequence, a group is locally finite if and only if its uniform Roe algebra is finite.

In this paper, we mainly provide a categorical view on the braided structures appearing in the Hom-quantum groups. Let $\mathcal{C}$ be a monoidal category on which F is a bimonad, G is a bicomonad, and ϕ is a distributive law, we discuss the necessary and sufficient conditions for $\mathcal{C}^G_F(\varphi)$ , the category of mixed bimodules to be monoidal and braided. As applications, we discuss the Hom-type (co)quasitriangular structures, the Hom–Yetter–Drinfeld modules, and the Hom–Long dimodules.

We present a detailed derivation and analysis of a model consisting of seven coupled delay differential equations for louse-borne relapsing fever (LBRF), a disease transmitted from human to human by the body louse Pediculus humanus humanus. Delays model the latency stages of LBRF in humans and lice, which vary in duration from individual to individual, and are therefore modelled using distributed delays with relatively general kernels. A particular feature of the transmission of LBRF to a human is that it involves the death of the louse, usually by crushing which has the effect of releasing the infected body fluids of the dead louse onto the hosts skin. Careful attention is paid to this aspect. We obtain results on existence, positivity, boundedness, linear and nonlinear stability, and persistence. We also derive a basic reproduction number R0 for the model and discuss its dependence on the model parameters. Our analysis of the model suggests that effective louse control without crushing should be the best strategy for LBRF eradication. We conclude that simple measures and precautions should, in general, be sufficient to facilitate disease eradication.

We investigate the following nonlinear Neumann boundary-value problem with associated p(x)-Laplace-type operator

where the function φ(x, v) is of type |v|p(x)−2v with continuous function p: → (1,∞) and both f : Ω × ℝ → ℝ and g : ∂Ω × ℝ → ℝ satisfy a Carathéodory condition. We first show the existence of infinitely many weak solutions for the Neumann problems using the Fountain theorem with the Cerami condition but without the Ambrosetti and Rabinowitz condition. Next, we give a result on the existence of a sequence of weak solutions for problem (P) converging to 0 in L ∞ -norm by employing De Giorgi's iteration and the localization method under suitable conditions.

This paper proposes the use of a generalized finite difference method for the numerical simulation of free surface single phase flows during mould filling process which are common in some industrial processes particularly in the area of metal casting. A novel and efficient idea for the computation of the normal vectors for free surface flows is introduced and presented for the first time. The incompressible Navier–Stokes equations are numerically solved by the well-known Chorin's projection method. After we showed the main ideas behind the meshless approach, some numerical results in two and three dimensions are presented corresponding to mould filling process simulation.

In this paper, inverse spectral problems for Sturm–Liouville operators on a tree (a graph without cycles) are studied. We show that if the potential on an edge is known a priori, then b – 1 spectral sets uniquely determine the potential functions on a tree with b external edges. Constructive solutions, based on the method of spectral mappings, are provided for the considered inverse problems.

Due to a calculation error, the constant in the main theorem is not $80 \sqrt{k\log k}$ but $80\sqrt{k} \log k$ . The error was discovered by Xizhi Liu.

For a new discussion on the limit of the method used in this paper see the revised arXiv version of the paper.

A cutset is a non-empty finite subset of ℤd which is both connected and co-connected. A cutset is odd if its vertex boundary lies in the odd bipartition class of ℤd . Peled [18] suggested that the number of odd cutsets which contain the origin and have n boundary edges may be of order e Θ(n/d) as d → ∞, much smaller than the number of general cutsets, which was shown by Lebowitz and Mazel [15] to be of order d Θ(n/d). In this paper, we verify this by showing that the number of such odd cutsets is (2+o(1))n/2d .