Recursos de colección
Ishiwata, Tetsuya
The behavior of solution polygons to generalized
crystalline curvature flow is discussed.
The conditions to guarantee that
the solution polygon keeps its admissibility
as long as enclosed area of solution polygon is positive
are clarified.
We also show that the solution polygon becomes ``almost convex''
before the extinction time.
Ken'ichiro, Tanaka; Sugihara, Masaaki; Kazuo, Murota
This paper is concerned with theoretical error estimates
for a sampling formula with the sinc-Gaussian kernel.
Qian et al. have recently given
an error estimate for the class of band-limited functions
by Fourier-analytic approach.
In contrast,
we adopt in this paper a complex-analytic approach
to derive an error estimate for a wider class of functions
including unbounded functions on $\mathbf{R}$.
Part of the result of Qian et al. can be derived from ours
as an immediate corollary.
Computational results show a fairly good agreement
with our theoretical analysis.
Ito, Tokushi; Hayami, Ken
For least squares problems of minimizing
$\|\boldsymbol{b}-A\boldsymbol{x}\|_2$ where $A$ is a large sparse
$m\times n$ ($m\ge n$) matrix, the common method is to apply the
conjugate gradient method to the normal equation
$A^{\mathrm{T}} A\boldsymbol{x}=A^{\mathrm{T}} \boldsymbol{b}$.
However, the condition number of $A^{\mathrm{T}} A$ is square of that of $A$,
and convergence becomes problematic for severely ill-conditioned
problems even with preconditioning.
In this paper, we propose two methods for applying the GMRES method to
the least squares problem by using an $n\times m$ matrix $B$.
We give the necessary and sufficient condition that $B$ should satisfy
in order that the proposed methods give a least squares solution.
Then, for implementations for $B$, we propose...
Mori, Masatake; Nurmuhammad, Ahniyaz; Murai, Takefumi
A method for numerical solution of Volterra integral equations
of the second kind with a weakly singular kernel
based on the double exponential (DE) transformation is proposed.
In this method we first express the approximate solution in the form
of a Sinc expansion based on the double exponential transformation
by Takahasi and Mori in 1974
followed by collocation at the Sinc points.
We also apply the DE formula to the kernel integration.
In every sample equation a numerical solution
with very high accuracy is obtained
and a nearly exponential convergence rate $\exp(-cM/{\log M})$, $c>0$
in the error is observed where $M$ is a parameter representing the
number of terms in the Sinc...
Asano, Tetsuo; Katoh, Naoki; Tamaki, Hisao; Tokuyama, Takeshi
Voronoi diagrams for a set of geometric objects is a partition of the plane
(or space in higher dimensions) into disjoint regions each dominated by
some given object under a predetermined criterion.
In this paper we are interested in various measures associated with
criteria on goodness of an input line segment with respect to each
point in the plane as the ``point of view.''
These measures basically show how well a segment or information displayed
on the segment can be seen from the point.
Mathematically, the measures are defined in terms of the shapes of the
triangle determined by the point and the line segment.
We study the combinatorial and...
Ei, Shin-Ichiro; Ikeda, Hideo; Kawana, Takeyuki
In this paper, two component reaction-diffusion systems with
a specific bistable nonlinearity are concerned. The systems have the
bifurcation structure of pitch-fork type of traveling front
solutions with opposite velocities, which is
rigorously proved and the ordinary differential equations
describing the dynamics of such traveling front solutions
are also derived explicitly. It enables us to know
rigorously precise information on the dynamics of
traveling front solutions. As an application of this result,
the imperfection structure under small perturbations and
the dynamics of traveling front solutions on heterogeneous media
are discussed.
Yanagi, Shigenori
We consider the asymptotic behavior of the complete
system of equations governing a heat-conductive, reactive, compressible
viscous gas bounded by two infinite parallel plates. The motion is proved to
tend towards the corresponding constant state, as time tends to
infinity. Moreover, the decay rate is investigated.
Farooq, Rashid
We study an extension of the Gale--Shapley marriage model and the
Shapley--Shubik assignment model by considering linear valuations and
bounded side payments. Our model includes the Eriksson--Karlander hybrid
model as a special case. We propose a polynomial-time
algorithm which finds a pairwise-stable outcome.
Aishima, Kensuke; Matsuo, Takayasu; Murota, Kazuo
Fernando and Parlett observed that
the dqds algorithm for singular values
can be made extremely efficient with Rutishauser's choice of shift;
in particular it enjoys ``local'' (or one-step) cubic convergence
at the final stage of iteration, where a certain condition is to be
satisfied.
Their analysis is, however, rather heuristic and
what has been shown is not sufficient to ensure
asymptotic cubic convergence in the strict sense of the word.
The objective of this paper is to specify a concrete procedure
for the shift strategy and to prove with mathematical rigor that
the algorithm with this shift strategy always reaches
the ``final stage'' and enjoys asymptotic cubic convergence.
Glowinski, R.; Dean, E.J.; Guidoboni, G.; Juárez, L.H.; Pan, T.-W.
The main goal of this article is to review some recent
applications of operator-splitting methods.
We will show that these methods are well-suited to the numerical
solution of outstanding problems from various areas in Mechanics,
Physics and Differential Geometry, such as the direct numerical
simulation of particulate flow, free boundary problems with surface
tension for incompressible viscous fluids, and the elliptic real
Monge--Ampère equation. The results of numerical experiments
will illustrate the capabilities of these methods.
Yamauchi, Takuya
Let $A$ be a principally
polarized Abelian surface defined over $\mathbb{Q}$ with
$\End(A)=\mathbb{Z}$ and $\widetilde{A}$
be the reduction at a good prime $p$.
In this paper, we study the density of prime numbers $p$ for which
$\widetilde{A}(\mathbb{F}_p)$ is a cyclic group and establish a conjecture
which relates this density.
Nagao, Koh-ichi
This paper introduces a fast algorithm for solving the DLP of Jacobian of
hyperelliptic curve of small genus. To solve the DLP, Gaudry first shows that
the idea of index calculus is effective,
if a subset of the points of the hyperelliptic
curve of the base field is taken by the smooth elements of index calculus.
In an index calculus theory, a special element
(in our case it is the point of hyperelliptic curve),
which is not a smooth element, is called a large prime.
A divisor, written by the sum of
several smooth elements and one large prime, is called an almost smooth divisor.
By the use of the...
Goto, Takeshi; Okeya, Katsuyuki
A positive integer $n$ is said to be \textit{harmonic}
if the harmonic mean $H(n)$ of its positive divisors is an integer.
Ore proved that every perfect number is harmonic and
conjectured that there exist no odd harmonic numbers greater than $1$.
In this article, we give the list of all harmonic numbers
up to $10^{14}$. In particular, we find that there exist
no nontrivial odd harmonic numbers less than $10^{14}$.
Harasawa, Ryuichi; Sueyoshi, Yutaka; Kudo, Aichi
In this paper,
we consider the Tate and Ate pairings for the genus-$2$
supersingular hyperelliptic curves $y^{2}=x^{5} -\alpha x$ ($\alpha = \pm2$)
defined over finite fields of characteristic five.
More precisely,
we construct a distortion map explicitly, and show that the map indeed
gives an input for which the value of the Tate pairing is not trivial.
We next
describe a computation of the Tate pairing by using the proposed
distortion map.
We also see that this type of curve is equipped with a simple
quintuple operation on the Jacobian group,
which leads to an improvement for computing the Tate pairing.
We further show the Ate pairing,
a variant of the Tate pairing for...
Brown, Gavin; Suzuki, Kaori
We use the computer algebra system Magma to study graded rings
of Fano 3-folds of index $\ge 3$ in terms of their Hilbert series.
Bach, Eric; Ryan, Nathan C.
An integer $n$ is congruent if there is a triangle with rational
sides whose area is $n$. In the 1980s Tunnell gave an algorithm to
test congruence which relied on counting integral points on the
ellipsoids $2x^2+y^2+8z^2 = n$ and $2x^2+y^2+32z^2=n$. The
correctness of this algorithm is conditional on the conjecture of
Birch and Swinnerton-Dyer. The known methods for testing Tunnell's
criterion use $O(n)$ operations. In this paper we give several
methods with smaller exponents, including a randomized algorithm
using time $n^{1/2 + o(1)}$ and space $n^{o(1)}$, and a
deterministic algorithm using space and time $n^{1/2 + o(1)}$.
Sugihara, Kokichi; Nakamula, Ken
Sasaki, Tateaki
Let $P(z)$ be a monic univariate polynomial over $\mathbf{C}$,
of degree $n$ and having roots $\zeta_1,\ldots,\zeta_n$.
Given approximate roots $z_1,\ldots,z_n$,
with $\zeta_i \simeq z_i$ ($i=1,\ldots,n$), we derive a very tight
upper bound of $|\zeta_i - z_i|$, by assuming that $\zeta_i$ has
no close root. The bound formula has a similarity with Smale's
and Smith's formulas.
We also derive a lower bound of $|\zeta_i - z_i|$ and
a lower bound of $\min\{|\zeta_j - z_i|\mid j \neq i\}$.
Yamamoto, Hiroshi; Ohtsuki, Toshiya; Fujihara, Akihiro; Tanimoto, Satoshi; Yamamoto, Keizo; Miyazima, Sasuke
The z-transform technique is used to investigate the model for
distribution of high-tax payers,
which is proposed by two of the authors (K. Y and S. M)
and others [12]--[14].
Our analysis shows an asymptotic power-law of this model with the
exponent $-5/2$ when a total ``mass'' has a certain critical value. Below
the critical value, the system exhibits an ordinary critical behavior,
and scaling relations hold.
Above the threshold, numerical simulations show that a power-law
distribution coexists with a huge ``monopolized'' member.
It is argued that these behaviors are observed universally
in conserved aggregation processes, by analizing an extended model.
Wu, Berlin; Chang, Shu-Kwang
In many expositions of fuzzy methods, fuzzy techniques are described as
an alternative to a more traditional statistical approach. In this
paper, we present a class of fuzzy statistical decision process in
which testing hypothesis can be naturally reformulated in terms of
interval-valued statistics. We provide the definitions of fuzzy mean,
fuzzy distance as well as investigation of their related properties. We
also give some empirical examples to illustrate the techniques and to
analyze fuzzy data. Empirical studies show that fuzzy hypothesis
testing with soft computing for interval data are more realistic and
reasonable in the social science research. Finally certain comments are
suggested for the further studies. We hope...