40,304 research outputs found
On the possible exceptions for the transcendence of the log-gamma function at rational entries
In a recent work [JNT \textbf{129}, 2154 (2009)], Gun and co-workers have
claimed that the number , being a
rational number between and , is transcendental with at most \emph{one}
possible exception, but the proof presented there in that work is
\emph{incorrect}. Here in this paper, I point out the mistake they committed
and I present a theorem that establishes the transcendence of those numbers
with at most \emph{two} possible exceptions. As a consequence, I make use of
the reflection property of this function to establish a criteria for the
transcendence of , a number whose irrationality is not proved yet.
This has an interesting consequence for the transcendence of the product , another number whose irrationality remains unproven.Comment: 7 pages, 1 figure. Fully revised and shortened (02/05/2014
Assigning Grammatical Relations with a Back-off Model
This paper presents a corpus-based method to assign grammatical
subject/object relations to ambiguous German constructs. It makes use of an
unsupervised learning procedure to collect training and test data, and the
back-off model to make assignment decisions.Comment: To appear in Proceedings of the Second Conference on Empirical
Methods in Natural Language Processing, 7 pages, LaTe
Majority-vote model on Opinion-Dependent Networks
We study a nonequilibrium model with up-down symmetry and a noise parameter
known as majority-vote model of M.J. Oliveira on opinion-dependent
network or Stauffer-Hohnisch-Pittnauer networks. By Monte Carlo simulations and
finite-size scaling relations the critical exponents , ,
and and points and are obtained. After extensive
simulations, we obtain , , and
. The calculated values of the critical noise parameter and
Binder cumulant are and . Within the error bars,
the exponents obey the relation and the results
presented here demonstrate that the majority-vote model belongs to a different
universality class than the equilibrium Ising model on
Stauffer-Hohnisch-Pittnauer networks, but to the same class as majority-vote
models on some other networks.Comment: 9 figures, accepted for publication in IJMP
A shortcut for evaluating some log integrals from products and limits
In this short paper, I introduce an elementary method for exactly evaluating
the definite integrals ,
,
, and
in finite terms. The method
consists in to manipulate the sums obtained from the logarithm of certain
products of trigonometric functions at rational multiples of , putting
them in the form of Riemann sums. As this method does not involve any search
for primitives, it represents a good alternative to more involved integration
techniques. As a bonus, I show how to apply the method for easily evaluating
.Comment: 6 pages, no figures. Revised form. Some small corrections. Submitted
to: IJMEST (06/26/2012
Majority-vote model with heterogeneous agents on square lattice
We study a nonequilibrium model with up-down symmetry and a noise parameter
known as majority-vote model of M.J. Oliveira 1992 with heterogeneous
agents on square lattice. By Monte Carlo simulations and finite-size scaling
relations the critical exponents , , and and
points and are obtained. After extensive simulations, we obtain
, , and . The calculated
values of the critical noise parameter and Binder cumulant are
and . Within the error bars, the exponents obey
the relation and the results presented here
demonstrate that the majority-vote model heterogeneous agents belongs to a
different universality class than the nonequilibrium majority-vote models with
homogeneous agents on square lattice.Comment: 9 pages e 8 figures. arXiv admin note: substantial text overlap with
arXiv:1306.034
Electronic structure of a graphene superlattice with massive Dirac fermions
We study the electronic and transport properties of a graphene-based
superlattice theoretically by using an effective Dirac equation. The
superlattice consists of a periodic potential applied on a single-layer
graphene deposited on a substrate that opens an energy gap of in its
electronic structure. We find that extra Dirac points appear in the electronic
band structure under certain conditions, so it is possible to close the gap
between the conduction and valence minibands. We show that the energy gap
can be tuned in the range by changing the periodic
potential. We analyze the low energy electronic structure around the contact
points and find that the effective Fermi velocity in very anisotropic and
depends on the energy gap. We show that the extra Dirac points obtained here
behave differently compared to previously studied systems
Some transcendence results from a harmless irrationality theorem
The arithmetic nature of values of some functions of a single variable,
particularly, , , , , , and
, is a relevant topic in number theory. For instance, all those
functions return transcendental values for all non-zero algebraic values of
( in the case of ). On the other hand, not even an
irrationality proof is known for some numbers like , ,
, , and , though it is
well-known that at least one of the last two numbers is irrational. In this
note, I first derive a more general form of this last result, showing that at
least one of the sum and product of any two transcendental numbers is
transcendental. I then use this to show that, given any complex number , at least two of the numbers , and
are transcendental. I also show that , and
return transcendental values for all , , . Finally, I use a recent algebraic independence
result by Nesterenko to show that, for all integer ,
and are linearly independent over .Comment: 12 pages, no figures. Inclusion of a new theorem (Theor.3). Submitted
to Expos. Math. (Feb/07/2014
A rapidly converging Ramanujan-type series for Catalan's constant
In this note, by making use of a known hypergeometric series identity, I
prove two Ramanujan-type series for the Catalan's constant. The convergence
rate of these central binomial series surpasses those of all known similar
series, including a classical formula by Ramanujan and a recent formula by
Lupas. Interestingly, this suggests that an Ap\'{e}ry-like irrationality proof
could be found for this constant.Comment: Improved version of the previous manuscript, with revised text and
small corrections. 11 pages, 1 table. Submitted (06/03/2017
A shortened recurrence relation for the Bernoulli numbers
In this note, starting with a little-known result of Kuo, I derive a
recurrence relation for the Bernoulli numbers , being any positive
integer. This new recurrence seems advantageous in comparison to other known
formulae since it allows the computation of both and
from only .Comment: 7 pages, no figures. Submitted to "J. Number Theory" (09/22/2011
Potts model with q states on directed Barabasi-Albert networks
On directed Barabasi-Albert networks with two and seven neighbours selected
by each added site, the Ising model with spin S=1/2 was seen not to show a
spontaneous magnetisation. Instead, the decay time for flipping of the
magnetisation followed an Arrhenius law for Metropolis and Glauber algorithms,
but for Wolff cluster flipping the magnetisation decayed exponentially with
time. However, on these networks the Ising model spin S=1 was seen to show a
spontaneous magnetisation.
In this model with spin S=1 a first-order phase transition for values of
connectivity z=2 and z=7 is well defined. On these same networks the Potts
model with q=3 and 8 states is now studied through Monte Carlo simulations.
We have obtained also for q=3 and 8 states a first-order phase transition for
values of connectivity z=2 and z=7 of the directed Barabasi-Albert network.
Theses results are different from the results obtained for same model on
two-dimensional lattices, where for q=3 the phase transition is of second
order, while for q=8 the phase transition is first-order.Comment: 14 pages including many firgures, for Communications in Computational
Physic
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