In two previous papers we showed that any analytically integrable vector
field admits a local analytic Poincar\'e-Birkhoff normalization in the
neighborhood of a singular point. The aim of this paper is to extend this
analytic normalization...
Certificates in P and Subquadratic-Time Computation of Radius, Diameter,
and all Eccentricities in Graphs
March 13, 2018
| | |
Computer Science
Discrete Mathematics
Data Structures and Algorithms
Networking and Internet Architecture
In the context of fine-grained complexity, we investigate the notion of
certificate enabling faster polynomial-time algorithms. We specifically target
radius (minimum eccentricity), diameter (maximum eccentricity), and
all-eccentricity comp...
Counting of Shortest Paths in Cubic Grid
March 12, 2018
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Computer Science
Discrete Mathematics
Computational Geometry
The enumeration of shortest paths in cubic grid is presented herein, which
could have importance in image processing and also in the network sciences. The
cubic grid considers three neighborhoods - namely, 6-, 18- and 26-neighborhood
relate...
On some Hamiltonian properties of the isomonodromic tau functions
March 12, 2018
|
Physics
Mathematics
Mathematical Physics
Mathematical Physics
Exactly Solvable and Integrable Systems
We discuss some new aspects of the theory of the Jimbo-Miwa-Ueno tau function
which have come to light within the recent developments in the global
asymptotic analysis of the tau functions related to the Painlev\'e equations.
Specifically, ...
Enskog kinetic theory for a model of a confined quasi-two-dimensional
granular fluid
March 9, 2018
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Physics
Statistical Mechanics
The Navier-Stokes transport coefficients for a model of a confined
quasi-two-dimensional granular gas of smooth inelastic hard spheres are derived
from the Enskog kinetic equation. A normal solution to this kinetic equation is
obtained via ...
Inner Product in Highest-Weight Representation
March 7, 2018
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Physics
Mathematics
Mathematical Physics
Mathematical Physics
In this paper, we study the inner product of states corresponding to weights
of finite-dimensional highest-weight representations of classical groups.
We prove that the action of the raising operators would reduce a state of
hight-weight ...
Refining Fuchs' Theorem: Ensuring Uniqueness through No-Resummation
Constraints
March 5, 2018
|
Mathematics
Classical Analysis and ODEs
Classical Analysis and ODEs
This paper revisits Fuchs' theorem to address a critical limitation in its
framework: the implicit assumption that power series expansions remain
invariant under term rearrangement. We propose a \textit{No-Resummation
Constraint} that ensur...
On the index of minimal 2-tori in the 4-sphere
March 5, 2018
|
Mathematics
Differential Geometry
In this note we prove that any minimal 2-torus in S4 has Morse index at
least 6, with equality if and only if it is congruent to the Clifford torus
in some great S3⊂S4.For a minimal 2-torus in Sn with vanishing
Hopf d...
Perpertual Coupled Simulated Annealing for Continuous Optimization
March 2, 2018
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Mathematics
Optimization and Control
Optimization and Control
Global optimization heuristics are popular to optimize hard non-convex
problems. Despite their irrefutably large cost-to-solution, in the lack of
other working greedy or convex approaches, global optimization algorithms
remain the no-braine...
Rough Path Renormalization from Stratonovich to It\^o for Fractional
Brownian Motion
March 1, 2018
|
Mathematics
Probability
This paper develops an It\^o-type fractional pathwise integration theory for
fractional Brownian motion with Hurst parameters H∈(31,21], using the Lyons' rough path framework. This approach is
designed to fill g...