524 research outputs found
On the computation of the term of the series defining the center manifold for a scalar delay differential equation
In computing the third order terms of the series of powers of the center
manifold at an equilibrium point of a scalar delay differential equation, with
a single constant delay some problems occur at the term
More precisely, in order to determine the values at 0,
respectively of the function an algebraic system of
equations must be solved. We show that the two equations are dependent, hence
the system has an infinity of solutions. Then we show how we can overcome this
lack of uniqueness and provide a formula for Comment: Presented at the Conference on Applied and Industrial Mathematics-
CAIM 2011, Iasi, Romania, 22-25 September, 2011. Preprin
Structural results on convexity relative to cost functions
Mass transportation problems appear in various areas of mathematics, their
solutions involving cost convex potentials. Fenchel duality also represents an
important concept for a wide variety of optimization problems, both from the
theoretical and the computational viewpoints. We drew a parallel to the
classical theory of convex functions by investigating the cost convexity and
its connections with the usual convexity. We give a generalization of Jensen's
inequality for cost convex functions.Comment: 10 page
Generating random density matrices
We study various methods to generate ensembles of random density matrices of
a fixed size N, obtained by partial trace of pure states on composite systems.
Structured ensembles of random pure states, invariant with respect to local
unitary transformations are introduced. To analyze statistical properties of
quantum entanglement in bi-partite systems we analyze the distribution of
Schmidt coefficients of random pure states. Such a distribution is derived in
the case of a superposition of k random maximally entangled states. For another
ensemble, obtained by performing selective measurements in a maximally
entangled basis on a multi--partite system, we show that this distribution is
given by the Fuss-Catalan law and find the average entanglement entropy. A more
general class of structured ensembles proposed, containing also the case of
Bures, forms an extension of the standard ensemble of structureless random pure
states, described asymptotically, as N \to \infty, by the Marchenko-Pastur
distribution.Comment: 13 pages in latex with 8 figures include
Interesting magnetic properties of FeCoSi alloys
Solid solution between nonmagnetic narrow gap semiconductor FeSi and
diamagnetic semi-metal CoSi gives rise to interesting metallic alloys with
long-range helical magnetic ordering, for a wide range of intermediate
concentration. We report various interesting magnetic properties of these
alloys, including low temperature re-entrant spin-glass like behaviour and a
novel inverted magnetic hysteresis loop. Role of Dzyaloshinski-Moriya
interaction in the magnetic response of these non-centrosymmetric alloys is
discussed.Comment: 11 pages and 3 figure
Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space
The Dirac theory in the Euclidean Taub-NUT space gives rise to a large
collection of conserved operators associated to genuine or hidden symmetries.
They are involved in interesting algebraic structures as dynamical algebras or
even infinite-dimensional algebras or superalgebras. One presents here the
infinite-dimensional superalgebra specific to the Dirac theory in manifolds
carrying the Gross-Perry-Sorkin monopole. It is shown that there exists an
infinite-dimensional superalgebra that can be seen as a twisted loop
superalgebra.Comment: 16 pages, LaTeX, references adde
Supersymmetry and discrete transformations of the Dirac operators in Taub-NUT geometry
It is shown that the N=4 superalgebra of the Dirac theory in Taub-NUT space
has different unitary representations related among themselves through unitary
U(2) transformations. In particular the SU(2) transformations are generated by
the spin-like operators constructed with the help of the same covariantly
constant Killing-Yano tensors which generate Dirac-type operators. A parity
operator is defined and some explicit transformations which connect the
Dirac-type operators among themselves are given. These transformations form a
discrete group which is a realization of the quaternion discrete group. The
fifth Dirac operator constructed using the non-covariant Killing-Yano tensor of
the Taub-NUT space is quite special. This non-standard Dirac operator is
connected with the hidden symmetry and is not equivalent to the Dirac-type
operators of the standard N=4 supersymmetry.Comment: 14 pages, latex, no figure
A Study of Information & Knowledge Generated During Engineering Design Meetings
During the design process, there is a wealth of information generated, and although it may not be obvious at the time, this information can be extremely useful at a later instance when it may be no longer available. Many information capture solutions utilise tools such as video and media capture, incorporating the idea that if you capture all information then you will not miss anything. However, this creates another problem. Not all the information captured will be useful, therefore how can you distinguish the information that is useful from information that is not? The challenge many organisations face is how to capture and store valuable informal information in a way that is both simple and efficient, whilst remaining unobtrusive to the designers involved and without inhibiting the design activities. Through the undertaking of a series of case studies and test scenarios, it is possible to observe, identify and evaluate the various degrees of information and knowledge being generated and passed amongst design engineering teams whilst performing design activities in meeting situations. Using multi-media recording equipment and observation techniques, insight can be gained into the decision making process design engineering teams encounter during the course of a design project, and thus it is possible to evaluate where improved techniques can be applied to enhance the recording of information for re-use
Hierarchy of Dirac, Pauli and Klein-Gordon conserved operators in Taub-NUT background
The algebra of conserved observables of the SO(4,1) gauge-invariant theory of
the Dirac fermions in the external field of the Kaluza-Klein monopole is
investigated. It is shown that the Dirac conserved operators have physical
parts associated with Pauli operators that are also conserved in the sense of
the Klein-Gordon theory. In this way one gets simpler methods of analyzing the
properties of the conserved Dirac operators and their main algebraic structures
including the representations of dynamical algebras governing the Dirac quantum
modes.Comment: 16 pages, latex, no figure
Evolutionary Events in a Mathematical Sciences Research Collaboration Network
This study examines long-term trends and shifting behavior in the
collaboration network of mathematics literature, using a subset of data from
Mathematical Reviews spanning 1985-2009. Rather than modeling the network
cumulatively, this study traces the evolution of the "here and now" using
fixed-duration sliding windows. The analysis uses a suite of common network
diagnostics, including the distributions of degrees, distances, and clustering,
to track network structure. Several random models that call these diagnostics
as parameters help tease them apart as factors from the values of others. Some
behaviors are consistent over the entire interval, but most diagnostics
indicate that the network's structural evolution is dominated by occasional
dramatic shifts in otherwise steady trends. These behaviors are not distributed
evenly across the network; stark differences in evolution can be observed
between two major subnetworks, loosely thought of as "pure" and "applied",
which approximately partition the aggregate. The paper characterizes two major
events along the mathematics network trajectory and discusses possible
explanatory factors.Comment: 30 pages, 14 figures, 1 table; supporting information: 5 pages, 5
figures; published in Scientometric
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