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California Bar Association, the California State Bar Association, and the California
Bar Association's Board of Directors.
online review research
online review analysis (CMA) showed that the number of cases in our series was higher
compared with other series, and our patients had a higher risk of developing
cardiovascular events (11% vs. 0%, *P* = 0.01) \[[@B17]\]. Thus, our findings suggested
that these patients were more likely to develop vascular events.
There are some
limitations in the study. First, this was an observational study, and our cohort
consisted of patients at the time of revascularization. Moreover, the use of
nonselective stents would have been associated with other adverse outcomes including
increased risks of amputation, death, myocardial infarction, stroke, myocardial
infarction, congestive heart failure, and myocardial infarction. Second, the patients
were aged less than 35 years, which is less common than other younger patients. Third,
as a retrospective study, the number of patients with revascularized patients was low
(\< 3% of the total study cohort), and this could affect the final results. Fourth,
because this study included only patients aged ≥ 45 years, our results might not be
generalizable to older patients. Fifth, because the study is a case series, a
comparison of patients with different revascularization techniques was not possible.
Because some of the patients who were revascularized during this period may have been
lost to follow-up (e.g., those with previous heart surgery in the past may have had a
higher risk of revascularization in the future), it is necessary to further explore the
role of a different revascularization technique. However, our findings suggested that
most patients had very high cardiovascular events. Future studies are needed to address
this aspect of this issue in a larger number of patients to be able to determine the
real risk of cardiovascular events.
In conclusion, our findings suggested that
patients who underwent a total revascularization were more likely to have a high event
risk, but were less likely to have a high event rate, due to the difference in the
timing of revascularization. Thus, this result may be useful for patient counseling
when revascularization is suspected during the initial assessment.
Financial support
and sponsorship {sec2-2}
---------------------------------
Nil.
Conflicts of interest
{sec2-3}
---------------------
There are no conflicts of interest.
Conflicts of
interest: {sec2-4}
----------------------
There are no conflicts of interest.
The
authors have no conflicts of interest to declare.
online review analysis for the 2018
National Science Foundation Research Computing Workshop at the National Technical
University of Singapore, the work entitled 'Dice and Nonlinear Dynamical Systems: An
Examination of Their Eigenvectors', published by Springer Proceedings Press (WPI),
Singapore, in March 2017, was published online at arXiv:1807.08698. This article shows
that the general solution of the coupled nonlinear system with equation $\lambda u +
uv=0$ does not satisfy a simple linear algebra analysis.
The following table
summarises the general solution of a coupled nonlinear system that the authors refer to
as the (N-D-D-O) system, $$\label{N-D-O}
u=\alpha_1(\lambda^2)e^{-\lambda^2}\,,
\quad
\alpha_2(\lambda)=\alpha_0\,.$$
*Acknowledgements*: This research was partially
supported by NSF grant DMS-0500335.
This article is distributed under the terms of the
Creative Commons Attribution Noncommercial License which permits any noncommercial use,
distribution, and reproduction in any medium, provided the original author(s) and
source are credited.
1. It is a result of my research interests to study the linear
stability of solutions of the coupled nonlinear system.
2. This research is inspired
by [@Hou], which gives a complete analysis of the Eigenvalues.
3. This is because of
its results about the stability of the coupled nonlinear system, which were originally
proposed by [@WZR], [@MS].
4. This is due to my research interests to study the
nonlinear stability of the nonlocal systems, which are coupled nonlinear systems.
5.
This is due to the fact that the numerical stability of coupled nonlinear systems is
based on the following formula of the nonlocal solution $\psi(x,y)$ of the coupled
nonlinear system: $$\begin{aligned}
\psi^\prime(x,y)=\psi(x,\lambda y) + (\alpha_1
\psi)^2 + \psi^\prime(x,\lambda y) \quad\mbox{for}\quad x,y\geq \lambda\in
(0,\infty)\,.\end{aligned}$$
6. The results about the nonlinear stability of the
coupled nonlinear system for the two special Lagrangian models (1) and (2) are given in
this article.
7. The results about the nonlinear stability of the coupled nonlinear
system for the two special Lagrangian models (3) and (4) are given in this article.
8.
The results about the nonlinear stability of the coupled nonlinear system for the two
special Lagrangian models (5) and (6) are given in this article.
This article is
distributed under the terms of the Creative Commons Attribution Noncommercial License
which permits any noncommercial use, distribution, and reproduction in any medium,
provided the original author(s) and source are credited.
We wish to thank the
technical staff of the Department of Mathematics for their technical assistance. This
article is divided into sections (i)–(d). Section ii) is the first part of this
article, and section iii) is the main part. In each section the author is mainly
interested in numerical stability of the coupled nonlinear system, which were
previously studied by many mathematicians. Sections iv) and v) show that the coupled
nonlinear system with equation $\lambda u+uv=0$ does not satisfy a simple linear
algebra analysis.
Numerical stability of coupled nonlinear systems
{ssec:num}
===============================================
The coupled nonlinear
system has the following form $$\label{N-D-O-1}
u=\alpha_1(\lambda^2)\,,\quad
\alpha_2(x)=x^2+\lambda^2x+2\lambda
x+\lambda^2\sqrt{(\alpha_1\alpha_2)^2-x^2}\,,$$
$$\label{N-D-O-2}
u=\alpha_0\,,\quad
\alpha_0\neq 0\,.$$
Let us briefly recall the following general idea of the coupled
nonlinear system, which we have introduced in the previous sections. The solution
$\xi(\cdot,\lambda)\,$ of the coupled nonlinear system is given by
$$\xi(\lambda)=\alpha_0(\lambda^2)\,\sqrt{\lambda^3+\lambda^2\,\alpha_0\lambda
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