4,401 research outputs found
Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation
We construct solutions of an infinite Toda system and an analogue of the
Painlev'e II equation over noncommutative differential division rings in terms
of quasideterminants of Hankel matrices.Comment: 16 pp; final revised version, will appear in J.Phys. A, minor changes
(typos corrected following the Referee's List, aknowledgements and a new
reference added
Darboux dressing and undressing for the ultradiscrete KdV equation
We solve the direct scattering problem for the ultradiscrete Korteweg de
Vries (udKdV) equation, over for any potential with compact
(finite) support, by explicitly constructing bound state and non-bound state
eigenfunctions. We then show how to reconstruct the potential in the scattering
problem at any time, using an ultradiscrete analogue of a Darboux
transformation. This is achieved by obtaining data uniquely characterising the
soliton content and the `background' from the initial potential by Darboux
transformation.Comment: 41 pages, 5 figures // Full, unabridged version, including two
appendice
Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
A non-Abelian version of the Hirota-Miwa equation is considered. In an
earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it
was shown how solutions expressed as quasideterminants could be constructed for
this system by means of Darboux transformations. In this paper we discuss these
solutions from a different perspective and show that the solutions are
quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may
be written as a quasi-Pl\"{u}cker relation. The special case of the matrix
Hirota-Miwa equation is also considered using a more traditional, bilinear
approach and the techniques are compared
Bäcklund transformations for noncommutative anti-self-dual Yang-Mills equations
We present Bäcklund transformations for the non-commutative anti-self-dual Yang–Mills equations where the gauge group is G = GL(2) and use it to generate a series of exact solutions from a simple seed solution. The solutions generated by this approach are represented in terms of quasi-determinants and belong to a non-commutative version of the Atiyah–Ward ansatz. In the commutative limit, our results coincide with those by Corrigan, Fairlie, Yates and Goddard
Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation
Matrix solutions of a noncommutative KP and a noncommutative mKP equation
which can be expressed as quasideterminants are discussed. In particular, we
investigate interaction properties of two-soliton solutions.Comment: 2 figure
The azimuthal component of Poynting's vector and the angular momentum of light
The usual description in basic electromagnetic theory of the linear and angular momenta of light is centred upon the identification of Poynting's vector as the linear momentum density and its cross product with position, or azimuthal component, as the angular momentum density. This seemingly reasonable approach brings with it peculiarities, however, in particular with regards to the separation of angular momentum into orbital and spin contributions, which has sometimes been regarded as contrived. In the present paper, we observe that densities are not unique, which leads us to ask whether the usual description is, in fact, the most natural choice. To answer this, we adopt a fundamental rather than heuristic approach by first identifying appropriate symmetries of Maxwell's equations and subsequently applying Noether's theorem to obtain associated conservation laws. We do not arrive at the usual description. Rather, an equally acceptable one in which the relationship between linear and angular momenta is nevertheless more subtle and in which orbital and spin contributions emerge separately and with transparent forms
Creditor Control in Financially Distressed Firms: Empirical Evidence
In this Article we present the results of empirical research that examines how creditor control is manifested in financially troubled firms that have to renegotiate their debt contracts
On a direct approach to quasideterminant solutions of a noncommutative KP equation
A noncommutative version of the KP equation and two families of its solutions
expressed as quasideterminants are discussed. The origin of these solutions is
explained by means of Darboux and binary Darboux transformations. Additionally,
it is shown that these solutions may also be verified directly. This approach
is reminiscent of the wronskian technique used for the Hirota bilinear form of
the regular, commutative KP equation but, in the noncommutative case, no
bilinearising transformation is available.Comment: 11 page
Do Analysts Add Value When They Most Can? Evidence From Corporate Spin-Offs
This article investigates how securities analysts help investors understand the value of diversification. By studying the research that analysts produce about companies that have announced corporate spin-offs, we gain unique insights into how analysts portray diversified firms to the investment community. We find that while analysts\u27 research about these companies is associated with improved forecast accuracy, the value of their research about the spun-off subsidiaries is more limited. For both diversified firms and their spun-off subsidiaries, analysts\u27 research is more valuable when information asymmetry between the management of these entities and investors is higher. These findings contribute to the corporate strategy literature by shedding light on the roots of the diversification discount and by showing how analysts\u27 research enables investors to overcome asymmetric information
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