Separation of variables in quasi-potential systems of bi-cofactor form

We perform variable separation in the quasi-potential systems of equations of the form $\ddot{q}=-A^{-1}\nabla k=-\tilde{A}^{-1}\nabla\tilde{k}${}, where $A$ and $\tilde{A}$ are Killing tensors, by embedding these systems into a bi-Hamiltonian chain and by calculating the corresponding Darboux-Nijenhuis coordinates on the symplectic leaves of one of the Hamiltonian structures of the system. We also present examples of the corresponding separation coordinates in two and three dimensions.Comment: LaTex, 30 pages, to appear in J. Phys. A: Math. Ge

Formation and Dynamics of Shock Waves in the Degasperis-Procesi Equation

Solutions of the Degasperis–Procesi nonlinear wave equation may develop discontinuities in finite time. As shown by Coclite and Karlsen, there is a uniquely determined entropy weak solution which provides a natural continuation of the solution past such a point. Here we study this phenomenon in detail for solutions involving interacting peakons and antipeakons. We show that a jump discontinuity forms when a peakon collides with an antipeakon, and that the entropy weak solution in this case is described by a "shockpeakon" ansatz reducing the PDE to a system of ODEs for positions, momenta, and shock strengths

Continuous and discontinuous piecewise linear solutions of the linearly forced inviscid Burgers equation

We study a class of piecewise linear solutions to the inviscid Burgers equation driven by a linear forcing term. Inspired by the analogy with peakons, we think of these solutions as being made up of solitons situated at the breakpoints. We derive and solve ODEs governing the soliton dynamics, first for continuous solutions, and then for more general shock wave solutions with discontinuities. We show that triple collisions of solitons cannot take place for continuous solutions, but give an example of a triple collision in the presence of a shock.Comment: To appear in Journal of Nonlinear Mathematical Physics (proceedings of NEEDS 2007). 16 pages, 3 figures, LaTeX + AMS packages + pstrick

The inverse spectral problem for the discrete cubic string

Given a measure $m$ on the real line or a finite interval, the "cubic string" is the third order ODE $-\phi'''=zm\phi$ where $z$ is a spectral parameter. If equipped with Dirichlet-like boundary conditions this is a nonselfadjoint boundary value problem which has recently been shown to have a connection to the Degasperis-Procesi nonlinear water wave equation. In this paper we study the spectral and inverse spectral problem for the case of Neumann-like boundary conditions which appear in a high-frequency limit of the Degasperis--Procesi equation. We solve the spectral and inverse spectral problem for the case of $m$ being a finite positive discrete measure. In particular, explicit determinantal formulas for the measure $m$ are given. These formulas generalize Stieltjes' formulas used by Krein in his study of the corresponding second order ODE $-\phi''=zm\phi$.Comment: 24 pages. LaTeX + iopart, xypic, amsthm. To appear in Inverse Problems (http://www.iop.org/EJ/journal/IP

The Cauchy two-matrix model

We introduce a new class of two(multi)-matrix models of positive Hermitean matrices coupled in a chain; the coupling is related to the Cauchy kernel and differs from the exponential coupling more commonly used in similar models. The correlation functions are expressed entirely in terms of certain biorthogonal polynomials and solutions of appropriate Riemann-Hilbert problems, thus paving the way to a steepest descent analysis and universality results. The interpretation of the formal expansion of the partition function in terms of multicolored ribbon-graphs is provided and a connection to the O(1) model. A steepest descent analysis of the partition function reveals that the model is related to a trigonal curve (three-sheeted covering of the plane) much in the same way as the Hermitean matrix model is related to a hyperelliptic curve.Comment: 34 pages, 2 figures. V2: changes only to metadat

No leader is an island : contextual antecedents to line managers’ constructive and destructive leadership during an organizational intervention

Purpose: Line managers can make or break organizational interventions, yet little is known about what makes them turn in either direction. As leadership does not occur in a vacuum it has been suggested that the organizational context plays an important role. Building on the intervention and leadership literature, we examine if span of control and employee readiness for change are related to line managers’ leadership during an organizational intervention. Design: Leadership is studied in terms of intervention-specific constructive, as well as passive and active forms of destructive, leadership behaviors. As a sample, we use employees (N = 172) from 37 groups working at a process industry plant. Multilevel analyses over two time points, with both survey and organizational register data were used to analyze the data. Findings: The results revealed that span of control was negatively related to constructive leadership and positively related to passive destructive leadership during the intervention. Employee readiness for change was positively related to constructive leadership, and negatively related to both passive and active destructive leadership. Practical implications: Our findings suggest that contextual factors need to be assessed and considered if we want line managers to engage in constructive rather than destructive leadership during interventions. Originality/value: The present study is the first to address line managers’ making or breaking of organizational interventions by examining the influence of context on both their destructive and constructive leadership

The Degasperis-Procesi equation with self-consistent sources

The Degasperis-Procesi equation with self-consistent sources(DPESCS) is derived. The Lax representation and the conservation laws for DPESCS are constructed. The peakon solution of DPESCS is obtained.Comment: 15 page

Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation

In this article, we construct loop soliton solutions and mixed soliton - loop soliton solution for the Degasperis-Procesi equation. To explore these solutions we adopt the procedure given by Matsuno. By appropriately modifying the $\tau$-function given in the above paper we derive these solutions. We present the explicit form of one and two loop soliton solutions and mixed soliton - loop soliton solutions and investigate the interaction between (i) two loop soliton solutions in different parametric regimes and (ii) a loop soliton with a conventional soliton in detail.Comment: Published in Physica Scripta (2012

Allelic expression mapping across cellular lineages to establish impact of non-coding SNPs

This is an open access article under the terms of the Creative Commons Attribution 4.0 License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited