75,105 research outputs found
New error bounds for linear complementarity problems of Nekrasov matrices and B-Nekrasov matrices
New error bounds for the linear complementarity problems are given
respectively when the involved matrices are Nekrasov matrices and B-Nekrasov
matrices. Numerical examples are given to show that new bounds are better
respectively than those provided by Garcia-Esnaola and Pena in [15,16] in some
cases
Integral almost square-free modular categories
We study integral almost square-free modular categories; i.e., integral
modular categories of Frobenius-Perron dimension , where is a prime
number, is a square-free natural number and . We prove
that if or is prime with then they are group-theoretical.
This generalizes several results in the literature and gives a partial answer
to the question posed by the first author and H. Tucker. As an application, we
prove that an integral modular category whose Frobenius-Perron dimensions is
odd and less than is group-theoretical.Comment: Some typos are corrected. Section 4 in previous version is moved. The
current version is revised by Libin Li and Li Da
Non-uniform continuous dependence on initial data of solutions to the Euler-Poincar\'{e} system
In this paper, we investigate the continuous dependence on initial data of
solutions to the Euler-Poincar\'{e} system. By constructing a sequence
approximate solutions and calculating the error terms, we show that the
data-to-solution map is not uniformly continuous in Sobolev space
for .Comment: 10 pages. arXiv admin note: text overlap with arXiv:1505.00086 by
other author
Existence of Tannakian subcategories and its applications
We study several classes of braided fusion categories, and prove that they
all contain nontrivial Tannakian subcategories. As applications, we classify
some fusion categories in terms of solvability and group-theoreticality.Comment: Title is changed; Section 5 is new; one result is correcte
On semisimple quasitriangular Hopf algebras of dimension
Let be a prime number, be an odd square-free natural number, and
be a non-negative integer. We prove that a semisimple quasitriangular Hopf
algebra of dimension is solvable in the sense of Etingof, Nikshych and
Ostrik. In particular, if then it is either isomorphic to for
some abelian group , or twist equivalent to a Hopf algebra which fits into a
cocentral abelian exact sequence.Comment: 9 pages, first version, comments are welcom
New implementation of hybridization expansion quantum impurity solver based on Newton-Leja interpolation polynomial
We introduce a new implementation of hybridization expansion continuous time
quantum impurity solver which is relevant to dynamical mean-field theory. It
employs Newton interpolation at a sequence of real Leja points to compute the
time evolution of the local Hamiltonian efficiently. Since the new algorithm
avoids not only computationally expansive matrix-matrix multiplications in
conventional implementations but also huge memory consumptions required by
Lanczos/Arnoldi iterations in recently developed Krylov subspace approach, it
becomes advantageous over the previous algorithms for quantum impurity models
with five or more bands. In order to illustrate the great superiority and
usefulness of our algorithm, we present realistic dynamical mean-field results
for the electronic structures of representative correlated metal SrVO.Comment: 10 pages, 6 figure
On Kaplansky's sixth conjecture
About years ago, Kaplansky conjectured that the dimension of a
semisimple Hopf algebra over an algebraically closed field of characteristic
zero is divisible by the dimensions of its simple modules. Although it still
remains open, some partial answers to this conjecture play an important role in
classifying semisimple Hopf algebras. This paper focuses on the recent
development of Kaplansky's sixth conjecture and its applications in classifying
semisimple Hopf algebras.Comment: 17 pages, final version was accepted for publication in Rendiconti
del Seminario Matematico della Universita di Padova (European Mathematical
Society). arXiv admin note: text overlap with arXiv:0809.3031 by other
author
Mass under the Ricci flow
In this paper, we study the change of the ADM mass of an ALE space along the
Ricci flow. Thus we first show that the ALE property is preserved under the
Ricci flow. Then, we show that the mass is invariant under the flow in
dimension three (similar results hold in higher dimension with more
assumptions). A consequence of this result is the following. Let be an
ALE manifold of dimension . If , then the Ricci flow starting
at can not have Euclidean space as its (uniform) limit
Special Relativity for the Full Speed Range -- speed slower than also equal to and faster than
In this paper, we establish a theory of Special Relativity valid for the
entire speed range without the assumption of constant speed of light. Two
particles species are defined, one species of particles have rest frames with
rest mass, and another species of particles do not have rest frame and can not
define rest mass. We prove that for the particles which have rest frames, the
Galilean transformation is the only linear transformation of space-time that
allows infinite speed of particle motion. Hence without any assumption, an
upper bound of speed is required for all non-Galilean linear transformations.
We then present a novel derivation of the mass-velocity and the mass-energy
relations in the framework of relativistic dynamics, which is solely based on
the principle of relativity and basic definitions of relativistic momentum and
energy. The generalized Lorentz transformation is then determined. The new
relativistic formulas are not related directly to the speed of light , but
are replaced by a Relativity Constant which is an universal speed
constant of the Nature introduced in relativistic dynamics. Particles having
rest mass are called tardyons moving slower than . Particles having
neither rest frames nor rest mass are called moving faster than
, and with the real mass-velocity relation where is the finite momentum of tachyon
at infinite speed. Moreover, the particles with constant-speed , also
having neither rest frames nor rest mass, are called . For all
particles, remains invariant under
transformation between inertia frames. The invariant reads
for tardyons, for constons and for
tachyons, respectively.Comment: 22 pages, 10 figure
On cyclic Higgs bundles
In this paper, we derive a maximum principle for a type of elliptic systems
and apply it to analyze the Hitchin equation for cyclic Higgs bundles. We show
several domination results on the pullback metric of the (possibly branched)
minimal immersion associated to cyclic Higgs bundles. Also, we obtain a
lower and upper bound of the extrinsic curvature of the image of . As an
application, we give a complete picture for maximal
-representations in the Gothen components and the
Hitchin components.Comment: 27 pages, comments are welcom
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