2,122 research outputs found
Archaeological evidence for historical navigation on the Mureş (Maros) river. Enquiries based on a medieval boat imprint from Bizere abbey (Romania)
The boat imprint unearthed at the site of the Benedictine abbey from Bizere (Frumuşeni, Romania) is a unique discovery for two reasons: its preservation as a negative imprint, due to its reuse for preparing mortar, and its dating back to the 12th century, based on the context of its discovery. It has been identified as a logboat, due to the absence of any technical details specific for plank boats, and now stands as the only vessel of this type with known dating for the territory of Romania. The article also enquires into the wider historical context of the discovery, thus bringing forth the archival data available with regard to medieval inland navigation
Gopakumar-Vafa invariants via vanishing cycles
In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of
Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal
is a modification of a recent approach of Kiem-Li, which is itself based on
earlier ideas of Hosono-Saito-Takahashi. We conjecture that these invariants
are equivalent to other curve-counting theories such as Gromov-Witten theory
and Pandharipande-Thomas theory. Our main theorem is that, for local surfaces,
our invariants agree with PT invariants for irreducible one-cycles. We also
give a counter-example to the Kiem-Li conjectures, where our invariants match
the predicted answer. Finally, we give examples where our invariant matches the
expected answer in cases where the cycle is non-reduced, non-planar, or
non-primitive.Comment: 63 pages, many improvements of the exposition following referee
comments, final version to appear in Inventione
Phase Transition and Strong Predictability
The statistical mechanical interpretation of algorithmic information theory
(AIT, for short) was introduced and developed in our former work [K. Tadaki,
Local Proceedings of CiE 2008, pp.425-434, 2008], where we introduced the
notion of thermodynamic quantities into AIT. These quantities are real
functions of temperature T>0. The values of all the thermodynamic quantities
diverge when T exceeds 1. This phenomenon corresponds to phase transition in
statistical mechanics. In this paper we introduce the notion of strong
predictability for an infinite binary sequence and then apply it to the
partition function Z(T), which is one of the thermodynamic quantities in AIT.
We then reveal a new computational aspect of the phase transition in AIT by
showing the critical difference of the behavior of Z(T) between T=1 and T<1 in
terms of the strong predictability for the base-two expansion of Z(T).Comment: 5 pages, LaTeX2e, no figure
A Class of Parameter Dependent Commuting Matrices
We present a novel class of real symmetric matrices in arbitrary dimension
, linearly dependent on a parameter . The matrix elements satisfy a set
of nontrivial constraints that arise from asking for commutation of pairs of
such matrices for all , and an intuitive sufficiency condition for the
solvability of certain linear equations that arise therefrom. This class of
matrices generically violate the Wigner von Neumann non crossing rule, and is
argued to be intimately connected with finite dimensional Hamiltonians of
quantum integrable systems.Comment: Latex, Added References, Typos correcte
A class of integrable lattices and KP hierarchy
We introduce a class of integrable -field first-order lattices together
with corresponding Lax equations. These lattices may be represented as
consistency condition for auxiliary linear systems defined on sequences of
formal dressing operators. This construction provides simple way to build
lattice Miura transformations between one-field lattice and -field () ones. We show that the lattices pertained to above class is in some sense
compatible with KP flows and define the chains of constrained KP Lax operators.Comment: LaTeX, 13 pages, accepted for publication in J. Phys. A: Math. Ge
Noncommutative Burgers Equation
We present a noncommutative version of the Burgers equation which possesses
the Lax representation and discuss the integrability in detail. We find a
noncommutative version of the Cole-Hopf transformation and succeed in the
linearization of it. The linearized equation is the (noncommutative) diffusion
equation and exactly solved. We also discuss the properties of some exact
solutions. The result shows that the noncommutative Burgers equation is
completely integrable even though it contains infinite number of time
derivatives. Furthermore, we derive the noncommutative Burgers equation from
the noncommutative (anti-)self-dual Yang-Mills equation by reduction, which is
an evidence for the noncommutative Ward conjecture. Finally, we present a
noncommutative version of the Burgers hierarchy by both the Lax-pair generating
technique and the Sato's approach.Comment: 24 pages, LaTeX, 1 figure; v2: discussions on Ward conjecture, Sato
theory and the integrability added, references added, version to appear in J.
Phys.
N-Soliton Solutions to a New (2 + 1) Dimensional Integrable Equation
We give explicitly N-soliton solutions of a new (2 + 1) dimensional equation,
. This equation is obtained by unifying two
directional generalization of the KdV equation, composing the closed ring with
the KP equation and Bogoyavlenskii-Schiff equation. We also find the Miura
transformation which yields the same ring in the corresponding modified
equations.Comment: 7 pages, uses ioplppt.st
Fulvous Whistling Ducks and Man
This is where the abstract of this record would appear. This is only demonstration data
Point Symmetries of Generalized Toda Field Theories II Applications of the Symmetries
The Lie symmetries of a large class of generalized Toda field theories are
studied and used to perform symmetry reduction. Reductions lead to generalized
Toda lattices on one hand, to periodic systems on the other. Boundary
conditions are introduced to reduce theories on an infinite lattice to those on
semi-infinite, or finite ones.Comment: 26 pages, no figure
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