%% IMPORTANT NOTE: Please read carefully all information preceded by % sign
%% This is a Sample File showing the right templates
%% for all AIMS Journals Prepared in AmSTeX
\input amstex
\documentstyle{amsppt}
\input graphicx
% \input psfig.sty
%% add this line only if you have pictures
%% pictures should be in esp format
%For pictures: screened artwork should be set up with an 85 or 100 line screen
\nologo
\pageno=1
\loadbold
\leftheadtext{{\smc Author Names}} % List authors here
\rightheadtext{{\smc Running heading with forty characters or less}}
%put here running heading with forty characters or less
\hsize=5 true in
\vsize=8.2 true in
\hoffset=.65 in
\voffset= 30 pt
\TagsOnRight
\NoBlackBoxes
\def\cal#1{\fam2 #1}
\def\eps#1{{#1}_{\varepsilon}}
\def\ep{\varepsilon}
\font\twelvebf cmbx12
\font\twelvern= cmr12
\font\eightbf=cmbx8
\font\eightit=cmti8
\font\eightrm=cmr8
\font\sevenrm=cmr7
%%Please use equation numbers only when they provide essential convenience
%%Try to avoid defining your own macros
%Do not make any changes in the following block
\topinsert\vskip-1.5
\baselineskip
{\vbox{\sevenrm\baselineskip 7pt
\noindent Manuscript submitted to\hfill doi:10.3934/xx.xxxxxxx \break
\noindent AIMS journals\hfil\break
\line {Volume {\sevenbf X}, Number {\sevenbf X},
XX {\sevenbf 200X}\hfil
\eightpoint pp. X--XX}}
}\endinsert
%Please supply information in the next two foot notes, they both are required.
\footnote""{ {\it 2020 Mathematics Subject Classification}.
Primary: 35C20, 35P20; Secondary: 93D15.}
\footnote""{ {\it Key words and phrases}. Dimension theory, Poincar\'e
recurrences, multifractal analysis.}
\footnote""{This research was partially supported by NSF.}
\footnote""{ } %%Please leave this line as it is.
\bigskip
\document
\vglue 1\baselineskip
\centerline{\bf Sample \AmSTeX\ File for AIMS Journals}
\bigskip
\medskip
%% Enter the first author's name and address:
\centerline{\smc First-name1 last-name1}
\medskip
{
\eightpoint
\centerline{First line of the address of the first author}
\centerline{Other lines, Springfield, MO 65801-2604, USA}
} % Do not forget to end the \eightpoint by the sign } here
\medskip
%% Enter the second author's name and address:
\centerline{\smc First-name2 last-name2}
\medskip
{
\eightpoint
\centerline{ First line of the address of the second author}
\centerline{Other lines, Springfield, MO 65801-2604, USA}
} % Do not forget to end the \eightpoint by the sign } here
\bigskip
\centerline{(Communicated by Aim Sciences)}
\medskip
\bigskip
{
\eightpoint
{\narrower\smallskip
\noindent
{\bf ABSTRACT.}
This fictitious paper is meant to serve only as the template for
AIMS' journals: DCDS-A, DCDS-B, CPAA, JIMO, NHM, JMD, AMC, IPI and
ERA-MS. Please read the instructions in the tex file very carefully.
The sample file for MBE may be downloaded at
http://www.mbejournal.org/.
\smallskip
}
}
\bigskip
\noindent
{ \bf 1. Introduction.}
With the setting of the template, automatically the text is set in
10 point fonts, while the abstract and references are in 8 point
fonts. All formulas and pictures must be within the limit of {\bf 5}
inches in width. An abstract is needed and not exceeding {\bf 200}
words. Also needed are some {\bf key words} and {\bf AMS subject
classifications}. Here are some important instructions on how to
prepare your final \TeX\ files. Please pay special attention to the
following:
\smallskip
1. All texts in a theorem, lemma, proposition, corollary, conjecture
environment should be automatically {\bf\sl slanted}.
\smallskip
2. However all texts in a definition, remark, or notation
environment should be automatically {\bf normal}.
\smallskip
3. Please try to avoid defining your own macros.
\smallskip
4. Make sure all {\bf lines}, {\bf math formulas} and {\bf figures}
are {\bf within the limit of 5 inches in width}. In particular,
formulas can not run to the right of equation numbers. Never run out
of the bound.
\smallskip
5. The following seven items all address the exact {\bf reference
style}. Please also follow very closely the reference samples at the
end of this article.
\smallskip
\medpagebreak i). List papers in alphabetic order according to first
authors.
\medpagebreak ii). Always place the first name (or first name initial) first,
then the middle name initial (optional), followed by the last name.
If there are multiple authors, use the word `and` to connect the last two authors.
See references [1], [2] and [3] for details.
\medpagebreak iii). If a reference is a paper in a journal,
the title of the paper should be {\bf \sl slanted},
Only the first character in a paper's title is in capital.
When you list a paper from a journal,
please ignore the issue number since the page numbers and
volume number yield sufficient information to identify the paper.
Finally, please pay attention to the correct way
for {\bf volume number} (in bold face), {\bf year},
{\bf starting page}--{\bf ending page}.
See references [2] and [3] for details.
\medpagebreak iv). If the reference is a book, one should quote the title
of the book, the first letter of each word should be capitalized.
See reference
[4] for details.
\medpagebreak v). If the reference is a paper in a conference proceeding,
please see the sample reference [5].
\medpagebreak vi). If the reference is a thesis, please see the sample reference [6].
\medpagebreak vii). Please don't list any references you never cited in your
paper.
\smallskip
Please use the AIMS template to prepare your tex file after the
paper is accepted by an AIMS journal. Thank you for your
cooperation.
\medskip
\noindent {\bf 2. Examples in AIMS standards.} In this section,
please pay attention to the style of the Definition, Proposition,
Theorem, Proof and the alignments of the mathematics formulas:
\demo{\bf Definition 2.1} The content of your definition. For
example, A is call {\sl standard} if it satisfies $\cdots$.
\enddemo
\demo{\bf Proposition 2.2} {\sl The content of your proposition}
\enddemo
\medskip
\noindent{\it Proof. }
Assume that
$$\int_0^1(|y_n|^2 + \gamma^2|y_{nx}|^2)dx =1,)
$$
then we find that
$$
\align
\eps{\theta} \wedge d\eps{\theta}^{n-1} &= (\theta_0 + \ep \alpha)
\wedge (d(\theta_0 + \ep \alpha))^{n-1} \quad \text{ since } d\alpha = 0\\
&= (\theta_0 + \ep \alpha) \wedge
(d\theta_0)^{n-1} + \theta_0 \wedge d\theta_0^{n-1} - \ep d(\alpha \wedge
\theta_0 \wedge d\theta_0^{n-2})\\
& \quad + \theta_0 \wedge d\theta_0^{n-1} + \ep \alpha \wedge
d\theta_0^{n-1} \\
&= \theta_0 \wedge d\theta_0^{n-1} - \ep d(\alpha \wedge
\theta_0 \wedge d\theta_0^{n-2}) \tag2.2
\endalign
$$
Using (2.2) and Poincar\'e's
inequality, we complete the proof.
\hfill $\square$
\medskip
\demo{\bf Theorem 2.3} {\it $A$ has at least $2n$ real eigenvalues
if the following condition holds:
$$\alpha^2 > n^2\pi^2\big(\gamma^2 +{1\over \pi^2}\big).\eqno(2.5)$$
} \enddemo
\noindent{\it Proof. }We see that under the condition
(2.5), the equations
$$\big(\gamma^2+ {1\over \pi^2}\big)\lambda^2 +2\alpha\lambda
+ k^2\pi^2 =0; \qquad \gamma^2\lambda^2 +2\beta\lambda +
(k-1)^2\pi^2= 0$$ admit negative roots $\alpha_k^\pm$ and
$\beta_k^{\pm}$. Therefore the theorem is proved.
\hfill $\square$
\medskip
\demo{\bf Remark 1} Please place the content of your remarks Here.
\enddemo
%below is an example of including figures in your paper
\centerline{\includegraphics[width=1in]{aims_logo.eps}}
%\midinsert
% \centerline{\hbox{\psfig{figure=1.eps,width=10cm}}}
\centerline{Fig. 1. Put the caption here} \vskip 10pt
%\endinsert
\medskip
Please follow the below {\bf instructions on figures}:
\smallskip
1. Notice that all color graphics will be printed in black and white
in the AIMS journals, {\bf make sure that a black and white printout
of your figure is legible}.
\smallskip
2. All figures should be placed in the body of your paper and before
your Reference.
\smallskip
3. In a page with figures, there should be no unnecessary spare
space. Be sure that a page should be fully occupied by figures and
texts.
\smallskip
4. Reduce the physical size of your figures if possible, while keep
your figures {\bf clearly visible}. For example, an eps figure file
with size bigger than 1MB is usually unacceptable.
\smallskip
5. Pictures should be in eps format and scalable.
\smallskip
6. Again, be sure that all {\bf figures} are {\bf within the limit
of 5 inches in width}. Never run out of the bound.
\medskip
\noindent{\bf Acknowledgments.} We would like to thank the
referees very much for their valuable comments and suggestions.
\Refs
\ref\key 1
\by FirstNameInitial. MiddleInitial. LastName
\paper\rm Title of the paper
\jour\it Name of the journal
\pages {\bf Volume} (Year), StaringPage--EndingPage
\endref
\ref\key 2
\by D. Aifindel
\paper\rm Dynamical characteristics of solutions of certain
partial differential equations
\jour\it Discrete Continuous Dynam. Systems
\pages {\bf 12} (2005), 27--54
\endref
% Example of multiple authors:
\ref\key 3
\by Y. Benoist, P. Foulon and F. Labourie
\paper\rm
Flots d'Anosov a distributions stable et instable differentiables
\jour\it J. Amer. Math. Soc.
\pages {\bf 5} (1992), 33--75
\endref
% Example of a book in the reference: quote the book tile, the first letter of each word should be capitalized.
\ref\key 4
\by R. Bott
\book Differential Forms in Algebraic Topology
\publ Springer-Verlag, New York, 1986
\endref
\ref\key 5
\by J. Serrin
\paper\rm Gradient estimates for solutions of nonlinear elliptic
and parabolic equations
\inbook in
\it Contributions to Nonlinear Functional Analysis
\bookinfo
(eds. E. H. Zarantonello and Author 2)
\publ Academic Press, 1971, 33--75
\endref
\ref\key 6
\by FirstNameInitial. LastName
\book Torsion Cycles and Set Theoretic Complete Intersection
\publ Ph.D thesis, Washington University in St. Louis, 2006
\endref
\endRefs
\medskip
Received XXXX 2006; revised XXXX 2007.
\medskip
{\it E-mail address}: email1\@smsu.edu \par
{\it E-mail address}: email2\@aimSciences.org
\enddocument