17,302 research outputs found
Multivariate Polynomial Factorization by Interpolation Method
Factorization of polynomials arises in numerous areas in symbolic
computation. It is an important capability in many symbolic and algebraic
computation. There are two type of factorization of polynomials. One is
convention polynomial factorization, and the other approximate polynomial
factorization.
Conventional factorization algorithms use symbolic methods to get exact
factors of a polynomial while approximate factorization algorithms use
numerical methods to get approximate factors of a polynomial. Symbolic
computation often confront intermediate expression swell problem, which lower
the efficiency of factorization. The numerical computation is famous for its
high efficiency, but it only gives approximate results. In this paper, we
present an algorithm which use approximate method to get exact factors of a
multivariate polynomial. Compared with other methods, this method has the
numerical computation advantage of high efficiency for some class of
polynomials with factors of lower degree. The experimental results show that
the method is more efficient than {\it factor} in Maple 9.5 for polynomials
with more variables and higher degree
A Study on Artificial Intelligence IQ and Standard Intelligent Model
Currently, potential threats of artificial intelligence (AI) to human have
triggered a large controversy in society, behind which, the nature of the issue
is whether the artificial intelligence (AI) system can be evaluated
quantitatively. This article analyzes and evaluates the challenges that the AI
development level is facing, and proposes that the evaluation methods for the
human intelligence test and the AI system are not uniform; and the key reason
for which is that none of the models can uniformly describe the AI system and
the beings like human. Aiming at this problem, a standard intelligent system
model is established in this study to describe the AI system and the beings
like human uniformly. Based on the model, the article makes an abstract
mathematical description, and builds the standard intelligent machine
mathematical model; expands the Von Neumann architecture and proposes the
Liufeng - Shiyong architecture; gives the definition of the artificial
intelligence IQ, and establishes the artificial intelligence scale and the
evaluation method; conduct the test on 50 search engines and three human
subjects at different ages across the world, and finally obtains the ranking of
the absolute IQ and deviation IQ ranking for artificial intelligence IQ 2014.Comment: 16 pages, 8 figure
Coherent state path integral approach to correlated electron systems with deformed Hubbard operators: from Fermi liquid to Mott insulator
In strongly correlated electron systems the constraint which prohibits the
double electron occupation at local sites can be realized by either the
infinite Coulomb interaction or the correlated hopping interaction described by
the Hubbard operators, but they both render the conventional field theory
inapplicable. Relaxing such the constraint leads to a class of correlated
hopping models based on the deformed Hubbard operators which smoothly
interpolate the locally free and strong coupling limits by a tunable
interaction parameter . Here we propose a coherent state
path integral approach appropriate to the deformed Hubbard operators for {\it
arbitrary} . It is shown that this model system exhibits the
correlated Fermi liquid behavior characterized by the enhanced Wilson ratio for
all . It is further found that in the presence of on-site Coulomb
interaction a finite Mott gap appears between the upper and lower Hubbard
bands, with the upper band spectral weight being heavily reduced by .
Our approach stands in general spatial dimensions and reveals an unexpected
interplay between the correlated hopping and the Coulomb repulsion.Comment: 9 pages, 5 figures (including several appendices
Nonlinear Current Algebra in the SL(2,R)/U(1) Coset Model
Previously we have established that the second Hamiltonian structure of the
KP hierarchy is a nonlinear deformation, called , of the
linear, centerless algebra. In this letter we present a free-field
realization for all generators of in terms of two scalars as
well as an elegant generating function for the currents in
the classical conformal coset model. After quantization, a
quantum deformation of appears as the hidden current algebra
in this model. The current algebra results in an infinite
set of commuting conserved charges, which might give rise to -hair for the
2d black hole arising in the corresponding string theory at level .Comment: 11
On the KP Hierarchy, Algebra, and Conformal SL(2,R)/U(1) Model --- The Classical and Quantum Cases
We give a unified description of our recent results on the the
inter-relationship between the integrable infinite KP hierarchy, nonlinear
current algebra and conformal noncompact
coset model both at the classical and quantum levels. In particular, we present
the construction of a quantum version of the KP hierarchy by deforming the
second KP Hamiltonian structure through quantizing the model
and constructing an infinite set of commuting quantum
charges (at least at =1).Comment: (Invited talk given the second at the XXI International Conference on
Differential Geometric Methods in Theoretical Physics, Nankai Institute of
Mathematics, Tianjin, China; June 5-9, 1992; to appear in Proceedings.), 12p,
Latex fil
A Note on Gradually Varied Functions and Harmonic Functions
Any constructive continuous function must have a gradually varied
approximation in compact space. However, the refinement of domain for
-net might be very small. Keeping the original discretization (square
or triangulation), can we get some interesting properties related to gradual
variation? In this note, we try to prove that many harmonic functions are
gradually varied or near gradually varied; this means that the value of the
center point differs from that of its neighbor at most by 2. It is obvious that
most of the gradually varied functions are not harmonic.This note discusses
some of the basic harmonic functions in relation to gradually varied functions.Comment: 7 pages and 2 figure
Exact Bivariate Polynomial Factorization in Q by Approximation of Roots
Factorization of polynomials is one of the foundations of symbolic
computation. Its applications arise in numerous branches of mathematics and
other sciences. However, the present advanced programming languages such as C++
and J++, do not support symbolic computation directly. Hence, it leads to
difficulties in applying factorization in engineering fields. In this paper, we
present an algorithm which use numerical method to obtain exact factors of a
bivariate polynomial with rational coefficients. Our method can be directly
implemented in efficient programming language such C++ together with the GNU
Multiple-Precision Library. In addition, the numerical computation part often
only requires double precision and is easily parallelizable
A Short Note on Zero-error Computation for Algebraic Numbers by IPSLQ
The PSLQ algorithm is one of the most popular algorithm for finding
nontrivial integer relations for several real numbers. In the present work, we
present an incremental version of PSLQ. For some applications needing to call
PSLQ many times, such as finding the minimal polynomial of an algebraic number
without knowing the degree, the incremental PSLQ algorithm is more efficient
than PSLQ, both theoretically and practically.Comment: 4 page
p-norm-like Constraint Leaky LMS Algorithm for Sparse System Identification
In this paper, we propose a novel leaky least mean square (leaky LMS, LLMS)
algorithm which employs a p-norm-like constraint to force the solution to be
sparse in the application of system identification. As an extension of the LMS
algorithm which is the most widely-used adaptive filtering technique, the LLMS
algorithm has been proposed for decades, due to the deteriorated performance of
the standard LMS algorithm with highly correlated input. However, both ofthem
do not consider the sparsity information to have better behaviors. As a
sparse-aware modification of the LLMS, our proposed Lplike-LLMS algorithm,
incorporates a p-norm-like penalty into the cost function of the LLMS to obtain
a shrinkage in the weight update, which then enhances the performance in sparse
system identification settings. The simulation results show that the proposed
algorithm improves the performance of the filter in sparse system settings in
the presence of noisy input signals.Comment: 3 pages, 1 table, 4 figures, 10 equations, 10 references. arXiv admin
note: substantial text overlap with arXiv:1503.0133
Non-Fermi liquid behavior in Bose-Fermi mixtures at two dimensions
In this paper we study the low temperature behaviors of a system of
Bose-Fermi mixtures at two dimensions. Within a self-consistent ladder diagram
approximation, we show that at nonzero temperatures the
fermions exhibit non-fermi liquid behavior. We propose that this is a general
feature of Bose-Fermi mixtures at two dimensions. An experimental signature of
this new state is proposed.Comment: 4 pages, 2 figures. supplementary materia
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