480 research outputs found
Value appropriation in business exchange: literature review and future research opportunities
Purpose – Value appropriation is a central, yet neglected aspect in business exchange research. The purpose of the paper is to generate an overview of research on active value appropriation in business exchange and provide the foundation for further research into value appropriation, as well as some initial guidance for managers. Design/methodology/approach – Literatures investigating value appropriation were identified by the means of a systematic review of the overall management literature. Findings – The authors provide an overview and comparison of the literatures and find that they apply diverse understandings of the value appropriation process and emphasize different mechanisms and outcomes of value appropriation. Research limitations/implications – Based on the literature comparison and discussion, in combination with inspiration from alternative business exchange literature, the authors propose four areas with high potential for future research into value appropriation: network position effects, appropriation acts and behaviors, buyer-seller relationship effects, and appropriation over time. Practical implications – Boundary spanning managers acting in industrial markets must master the difficult balance between value creation and appropriation. This review has provided an overview of the many managerial options for value appropriation and created knowledge on the effects of the various appropriation mechanisms enabling managers to secure company rents while not jeopardizing value creation. Originality/value – To the authors’ knowledge, this paper represents the first attempt at reviewing the management literature on value appropriation in business exchange. The authors provide overview, details, comparisons, and frame a research agenda as a first step towards establishing value appropriation as a key phenomenon in business exchange research.Chris Ellegaard, Christopher J. Medlin, Jens Geersbr
Groupoid Extensions of Mapping Class Representations for Bordered Surfaces
The mapping class group of a surface with one boundary component admits
numerous interesting representations including as a group of automorphisms of a
free group and as a group of symplectic transformations. Insofar as the mapping
class group can be identified with the fundamental group of Riemann's moduli
space, it is furthermore identified with a subgroup of the fundamental path
groupoid upon choosing a basepoint. A combinatorial model for this, the mapping
class groupoid, arises from the invariant cell decomposition of Teichm\"uller
space, whose fundamental path groupoid is called the Ptolemy groupoid. It is
natural to try to extend representations of the mapping class group to the
mapping class groupoid, i.e., construct a homomorphism from the mapping class
groupoid to the same target that extends the given representations arising from
various choices of basepoint.
Among others, we extend both aforementioned representations to the groupoid
level in this sense, where the symplectic representation is lifted both
rationally and integrally. The techniques of proof include several algorithms
involving fatgraphs and chord diagrams. The former extension is given by
explicit formulae depending upon six essential cases, and the kernel and image
of the groupoid representation are computed. Furthermore, this provides
groupoid extensions of any representation of the mapping class group that
factors through its action on the fundamental group of the surface including,
for instance, the Magnus representation and representations on the moduli
spaces of flat connections.Comment: 24 pages, 4 figures Theorem 3.6 has been strengthened, and Theorems
8.1 and 8.2 have been adde
Counting function for a sphere of anisotropic quartz
We calculate the leading Weyl term of the counting function for a
mono-crystalline quartz sphere. In contrast to other studies of counting
functions, the anisotropy of quartz is a crucial element in our investigation.
Hence, we do not obtain a simple analytical form, but we carry out a numerical
evaluation. To this end we employ the Radon transform representation of the
Green's function. We compare our result to a previously measured unique data
set of several tens of thousands of resonances.Comment: 16 pages, 11 figure
Models of discretized moduli spaces, cohomological field theories, and Gaussian means
We prove combinatorially the explicit relation between genus filtrated
-loop means of the Gaussian matrix model and terms of the genus expansion of
the Kontsevich--Penner matrix model (KPMM). The latter is the generating
function for volumes of discretized (open) moduli spaces
given by for
. This generating function therefore enjoys
the topological recursion, and we prove that it is simultaneously the
generating function for ancestor invariants of a cohomological field theory
thus enjoying the Givental decomposition. We use another Givental-type
decomposition obtained for this model by the second authors in 1995 in terms of
special times related to the discretisation of moduli spaces thus representing
its asymptotic expansion terms (and therefore those of the Gaussian means) as
finite sums over graphs weighted by lower-order monomials in times thus giving
another proof of (quasi)polynomiality of the discrete volumes. As an
application, we find the coefficients in the first subleading order for
in two ways: using the refined Harer--Zagier recursion and
by exploiting the above Givental-type transformation. We put forward the
conjecture that the above graph expansions can be used for probing the
reduction structure of the Delgne--Mumford compactification of moduli spaces of punctured Riemann surfaces.Comment: 36 pages in LaTex, 6 LaTex figure
The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion
We introduce the boundary length and point spectrum, as a joint
generalization of the boundary length spectrum and boundary point spectrum in
arXiv:1307.0967. We establish by cut-and-join methods that the number of
partial chord diagrams filtered by the boundary length and point spectrum
satisfies a recursion relation, which combined with an initial condition
determines these numbers uniquely. This recursion relation is equivalent to a
second order, non-linear, algebraic partial differential equation for the
generating function of the numbers of partial chord diagrams filtered by the
boundary length and point spectrum.Comment: 16 pages, 6 figure
Partial chord diagrams and matrix models
In this article, the enumeration of partial chord diagrams is discussed via
matrix model techniques. In addition to the basic data such as the number of
backbones and chords, we also consider the Euler characteristic, the backbone
spectrum, the boundary point spectrum, and the boundary length spectrum.
Furthermore, we consider the boundary length and point spectrum that unifies
the last two types of spectra. We introduce matrix models that encode
generating functions of partial chord diagrams filtered by each of these
spectra. Using these matrix models, we derive partial differential equations -
obtained independently by cut-and-join arguments in an earlier work - for the
corresponding generating functions.Comment: 42 pages, 14 figure
Finite type invariants and fatgraphs
We define an invariant of pairs M,G, where M is a 3-manifold
obtained by surgery on some framed link in the cylinder , S is a
connected surface with at least one boundary component, and G is a fatgraph
spine of S. In effect, is the composition with the maps of
Le-Murakami-Ohtsuki of the link invariant of Andersen-Mattes-Reshetikhin
computed relative to choices determined by the fatgraph G; this provides a
basic connection between 2d geometry and 3d quantum topology. For each fixed G,
this invariant is shown to be universal for homology cylinders, i.e.,
establishes an isomorphism from an appropriate vector space
of homology cylinders to a certain algebra of Jacobi diagrams. Via
composition for any pair of fatgraph spines
G,G' of S, we derive a representation of the Ptolemy groupoid, i.e., the
combinatorial model for the fundamental path groupoid of Teichmuller space, as
a group of automorphisms of this algebra. The space comes equipped
with a geometrically natural product induced by stacking cylinders on top of
one another and furthermore supports related operations which arise by gluing a
homology handlebody to one end of a cylinder or to another homology handlebody.
We compute how interacts with all three operations explicitly in
terms of natural products on Jacobi diagrams and certain diagrammatic
constants. Our main result gives an explicit extension of the LMO invariant of
3-manifolds to the Ptolemy groupoid in terms of these operations, and this
groupoid extension nearly fits the paradigm of a TQFT. We finally re-derive the
Morita-Penner cocycle representing the first Johnson homomorphism using a
variant/generalization of .Comment: 39 page
Pattern Dynamics of Vortex Ripples in Sand: Nonlinear Modeling and Experimental Validation
Vortex ripples in sand are studied experimentally in a one-dimensional setup
with periodic boundary conditions. The nonlinear evolution, far from the onset
of instability, is analyzed in the framework of a simple model developed for
homogeneous patterns. The interaction function describing the mass transport
between neighboring ripples is extracted from experimental runs using a
recently proposed method for data analysis, and the predictions of the model
are compared to the experiment. An analytic explanation of the wavelength
selection mechanism in the model is provided, and the width of the stable band
of ripples is measured.Comment: 4 page
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