39,285 research outputs found
Periodic solutions of sublinear impulsive differential equations
In this paper, we consider sublinear second order differential equations with
impulsive effects. Basing on the Poincar\'{e}-Bohl fixed point theorem, we
first will prove the existence of harmonic solutions. The existence of
subharmonic solutions is also obtained by a new twist fixed point theorem
recently established by Qian etc in 2015 (\cite{Qian15})
Boundedness of solutions in impulsive Duffing equations with polynomial potentials and time dependent coefficients
In this paper, we are concerned with the impulsive Duffing equation with impulsive
effects ,
where the time dependent coefficients and with
. If impulsive times are 1-periodic and
for , basing on a so-called
large twist theorem recently established by X. Li, B. Liu and Y. Sun in
\cite{XLi}, we find large invariant curves diffeomorphism to circles
surrounding the origin and going to infinity, which confines the solutions in
its interior and therefore leads to the boundedness of these solutions.
Meanwhile, it turns out that the solutions starting at on the invariant
curves are quasiperiodic.Comment: 29 pages. arXiv admin note: text overlap with arXiv:1705.0272
Periodic solutions of semilinear Duffing equations with impulsive effects
In this paper we are concerned with the existence of periodic solutions for
semilinear Duffing equations with impulsive effects. Firstly for the autonomous
one, basing on Poincar\'{e}-Birkhoff twist theorem, we prove the existence of
infinitely many periodic solutions. Secondly, as for the nonautonomous case,
the impulse brings us great challenges for the study, and there are only
finitely many periodic solutions, which is quite different from the
corresponding equation without impulses. Here, taking the autonomous one as an
auxiliary equation, we find the relation between these two equations and then
obtain the result also by Poincar\'{e}-Birkhoff twist theorem
On some Liouville type Theorems for the stationary MHD and Hall-MHD equations
We prove several Liouville type results for the stationary MHD and Hall-MHD
equations. In particular, we show that the velocity and magnetic field,
belonging to some Lorentz spaces or satisfying a priori decay assumption, must
be zero.Comment: Our proof is incomplete. We need to check i
Dynamic Detection of False Data Injection Attack in Smart Grid using Deep Learning
Modern advances in sensor, computing, and communication technologies enable
various smart grid applications. The heavy dependence on communication
technology has highlighted the vulnerability of the electricity grid to false
data injection (FDI) attacks that can bypass bad data detection mechanisms.
Existing mitigation in the power system either focus on redundant measurements
or protect a set of basic measurements. These methods make specific assumptions
about FDI attacks, which are often restrictive and inadequate to deal with
modern cyber threats. In the proposed approach, a deep learning based framework
is used to detect injected data measurement. Our time-series anomaly detector
adopts a Convolutional Neural Network (CNN) and a Long Short Term Memory (LSTM)
network. To effectively estimate system variables, our approach observes both
data measurements and network level features to jointly learn system states.
The proposed system is tested on IEEE 39-bus system. Experimental analysis
shows that the deep learning algorithm can identify anomalies which cannot be
detected by traditional state estimation bad data detection
Optimal Puncturing of Polar Codes With a Fixed Information Set
For a given polar code construction, the existing literature on puncturing
for polar codes focuses in finding the optimal puncturing pattern, and then
re-selecting the information set. This paper devotes itself to find the optimal
puncturing pattern when the information set is fixed. Puncturing the coded bits
corresponding to the worst quality bit channels, called the worst quality
puncturing (WQP), is proposed, which is analyzed to minimize the bit channel
quality loss at the punctured positions. Simulation results show that WQP
outperforms the best existing puncturing schemes when the information set is
fixed.Comment: Polar codes, puncture, quasi-uniform puncturing,worst quality
puncturin
Estimates for L{\phi}-Lipschitz and L{\phi}-BMO Norms of Differential Forms
In this paper, we define the L{\phi}-Lipschitz norm and L{\phi}-BMO norm of
differential forms using Young functions, and prove the comparison theorems for
the homotopy operator T on differential forms with L{\phi}-Lipschitz and
L{\phi}-BMO norms. As applications, we give the L{\phi}-BMO norm estimate for
conjugate A-harmonic tensors and the weighted L{\phi}-Lipschitz norm estimate
for the homotopy operator T.Comment: 14 page
A Comparison Study of Credit Card Fraud Detection: Supervised versus Unsupervised
Credit card has become popular mode of payment for both online and offline
purchase, which leads to increasing daily fraud transactions. An Efficient
fraud detection methodology is therefore essential to maintain the reliability
of the payment system. In this study, we perform a comparison study of credit
card fraud detection by using various supervised and unsupervised approaches.
Specifically, 6 supervised classification models, i.e., Logistic Regression
(LR), K-Nearest Neighbors (KNN), Support Vector Machines (SVM), Decision Tree
(DT), Random Forest (RF), Extreme Gradient Boosting (XGB), as well as 4
unsupervised anomaly detection models, i.e., One-Class SVM (OCSVM),
Auto-Encoder (AE), Restricted Boltzmann Machine (RBM), and Generative
Adversarial Networks (GAN), are explored in this study. We train all these
models on a public credit card transaction dataset from Kaggle website, which
contains 492 frauds out of 284,807 transactions. The labels of the transactions
are used for supervised learning models only. The performance of each model is
evaluated through 5-fold cross validation in terms of Area Under the Receiver
Operating Curves (AUROC). Within supervised approaches, XGB and RF obtain the
best performance with AUROC = 0.989 and AUROC = 0.988, respectively. While for
unsupervised approaches, RBM achieves the best performance with AUROC = 0.961,
followed by GAN with AUROC = 0.954. The experimental results show that
supervised models perform slightly better than unsupervised models in this
study. Anyway, unsupervised approaches are still promising for credit card
fraud transaction detection due to the insufficient annotation and the data
imbalance issue in real-world applications
Symmetric properties for Choquard equations involving fully nonlinear nonlocal operator
In this paper, the positive solutions to Choquard equation involving fully
nonlinear nonlocal operator are shown to be symmetric and monotone by using the
moving plane method which has been introduced by Chen, Li and Li in 2015. The
key ingredients are to obtain the "narrow region principle" and "decay at
infinity" for the corresponding problems. Similar ideas can be easily applied
to various nonlocal problems with more general nonlinearities
Genus Two Stable Maps, Local Equations and Modular Resolutions
We geometrically describe a canonical sequence of modular blowups of the
relative Picard stack of the Artin stack of pre-stable genus two curves. The
final blowup stack locally diagonalizes certain tautological derived objects.
This implies a resolution of the primary component of the moduli space of genus
two stable maps to projective space and meanwhile makes the whole moduli space
admit only normal crossing singularities. Our approach should extend to higher
genera.Comment: 81 pages, 7 figure
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