CORRECTION: Groundwater contaminants were found in Annapolis at 1000x safe limits in what is now a residential development on top of a former Naval Weapons Facility.
A March 2018 report by the United States Department of Defense shows test results of military sites in Anne Arundel County and other national and international locations to have man-made chemical contaminants in drinking water supplies that are believed to cause cancer, birth defects and other diseases.
According to the Environmental Protection Agency (EPA), the two contaminants, perfluorooctane sulfonate (PFOS) and perfluorooctanoic acid (PFOA), are products of industrial processes and are known to bioaccumulate in humans and wildlife. They are extremely persistent in the environment and cannot be mitigated by standard city and county water treatment methods.
In the DoD study, which was presented as a briefing to the House Armed Services Committee in March, four wells were tested in areas surrounding Fort Meade in 2017. While the EPA Lifetime Health Advisory (LHA) level for PFOS/PFOA is 70 parts per trillion (ppt) in water, the wells tested have between 300 and 87,000 parts per trillion PFOS/PFOA. The locations of the wells tested were not listed in the report.
At a former United States weapons facility in Annapolis, drinking water supplies were also tested. In 54 out of 68 wells tested, concentrations of PFOS/PFOA were between 70 ppt (the upper limit of LHA) and 70,000 ppt, which is 1000 times the EPA lifetime limit levels.
Both the City of Annapolis and the Naval Academy pump drinking water from the Patapsco Aquifer.
Although Anne Arundel County and the City of Annapolis list man-made organic chemical contaminants including "synthetic and volatile organic chemicals which are byproducts of industrial processes and petroleum production and can also come from gas stations, urban stormwater runoff, and septic systems," as an issue in groundwater, the City does not test for these contaminants.
Barry Zvimbleman, an environmental remediation specialist for over 30 years with a company in Naples Florida called Onion Equipment, works on installing treatment systems for water on military installations that have been found to that contain PFOS/POFA. Zvimbleman was not aware of the DoD report and has not worked on sites in Maryland. Zvimbleman said that the concentration of PFOS/PFOA in the Naval Academy, Fort Meade and Chesapeake Beach groundwater samples are extremely high and very concerning.
The problem, Zvimbleman said, is not only for those who are drinking from well-water; standard water treatment facilities do not remove PFOS/PFOA.
The County lists only three man-made contaminants in its water quality report for 2016: Ethylbenzene, Tetrachloroethylene, and Diphthalate. However, only 2 of 24 sites were tested. Anne Arundel County Program Manager for Water Operations Eddie Cope said that the county does not currently test for PFOS and PFOA and he was unaware of the DoD report.
The Naval Academy, which treats its own water independent of the City water treatment system, also did not address any volatile organic man-made chemicals in its testing. The Naval Academy 2016 water quality report can be found here.
Two other military facilities in Maryland tested above the EPA's LHA limit. In Chesapeake Beach in Calvert County, 9 of 18 wells tested between 190 ppt and 241,110 ppt, far exceeding safe limits. In Silver Spring, 8 of 16 wells at the Former Naval Surface Warfare Center Dahlgren Division Detachment in White Oak tested above LHA limits.
PFOS/PFOA were developed in the 1970s and used in many industrial and consumer products to make the products resist heat, stains, water, and grease. Examples include Teflon cookware, waterproofing fabric, carpeting and coating on fast food wrappers. On military bases, the most common use is in firefighting foams at airfields and in other industrial processes. Zvimbleman said that the chemicals are sprayed to put out fires and then washed off with water into the environment, sometimes stored in leaky containers, or even dumped into the environment.
According to the DoD report, limited human studies show PFOS and PFOA may be associated with developmental delays in fetuses and children, decreased fertility, increased cholesterol, changes to the immune system, increased uric acid levels, changes in liver enzymes, as well as prostate, kidney, and testicular cancers.
The EPA reports that the compounds are readily absorbed after oral exposure and accumulate primarily in the blood serum, kidney, and liver. Toxicological studies on animals indicate potential developmental, reproductive and systemic effects. Potential exposure pathways include ingestion of food and water, use of consumer products, or inhalation of PFOS/PFOA-containing particulate matter (e.g., soils and dust).
In 2015 studies, the EPA and the Agency for Toxic Substances and Disease Registry found PFOS and PFOA in the blood samples of the general human population and wildlife, indicating that exposure to the chemicals is widespread. Reported data indicate that blood serum concentrations of PFOS and PFOA are higher in workers and individuals living near facilities that use or produce PFOS/PFOA than for the general population.
The chemical company 3M was the primary manufacturer of PFOS. 3M began a voluntary phase-out of production in 2000 following the release of studies that showed a significant accumulation in the environment. By 2006, eight other companies followed suit and agreed to end production and use of PFOS and PFOA, but the chemicals were still in use as of 2015.
According to the EPA, there is no way to treat groundwater contaminated with PFOS and PFOA in situ. After removal, the contaminated water is resistant to most chemical and microbial conventional treatment technologies.
The most common water treatment method for PFOS/PFOA is extraction and filtration through granular activated carbon filters and ion exchange resins, according to Zvimbleman, who says a typical home costs $3000 for a filtration system.
The City of Annapolis water treatment process does not use either of these methods because of cost, and PFOS/PFOA are not regulated by the EPA, so costly carbon filter or ion exchange technology was not implemented when the water treatment facility was upgraded last year, according to Jarrell. The county also does not use carbon filter or ion exchange technologies in water treatment.
The DoD report said that the EPA has so far failed to address a Maximum Contaminant Level for PFOS/PFOA (MCL) which is the highest level of a contaminant allowed in drinking water. The Lifetime Health Advisories for PFOS and PFOA concentrations at 70 ppt are non-enforceable and non-regulatory. They serve only to provide technical information to state agencies and other public health officials.
Water systems should quickly undertake additional sampling to assess the level, scope and localized source of contamination to inform next steps.
If water sampling results confirm that drinking water contains PFOA and PFOS at individual or combined concentrations greater than 70 parts per trillion, then water systems should promptly notify their State drinking water safety agency (or with EPA in jurisdictions for which EPA is the primary drinking water safety agency) and consult with the relevant agency on the best approach to conduct additional sampling.
Drinking water systems and public health officials should also promptly provide consumers with information about the levels of PFOA and PFOS in their drinking water. This notice should include specific information on the risks to fetuses during pregnancy, and to breastfed and formula-fed infants from exposure to drinking water with an individual or combined concentration of PFOA and PFOS above EPA's health advisory level of 70 parts per trillion.
In addition, the notification should include actions being taken and identify options that consumers may consider to reduce risk, such as seeking an alternative drinking water source, or in the case of parents of formula-fed infants, using formula that does not require adding water.
The DoD study tested 2,668 groundwater wells on military installations and found 1,621 to be above safe levels of PFOA and PFOS. The DoD also tested 2,445 public and private drinking water systems adjacent to military bases with 564 drinking water systems testing above the EPA LHA maximum.
Maureen Sullivan, Deputy Assistant Secretary of Defense (Environment, Safety & Occupational Health) and Author of the March 2018 report.
Anthony Brown, Congressman Maryland District 4 and a minority member of the House Armed Services Committee. (Brown Congressional aids sent an email on Monday saying they would have a comment but the Arundel Patriot has not been given a comment at press time. We will update this article when we receive comments from Congressman Brown).
California, Maine, New York, New Hampshire, Texas, South Carolina, Massachusetts, Illinois, Louisana, Mississippi, Washington, Florida, Mississippi, Georgia, Colorado, Wisconsin, Indiana, Deleware, Oklahoma, Rhode Island, Arizona, Arkansas, South Dakota, Wyoming, and Utah.
Carmen Skarulpka contributed to this report.
This article is a correction from the previous article which cited the U.S. Naval Academy as the location of the Annapolis contaminated wells tested by the DoD. According to Ed Zeigler, spokesperson for the U.S. Navy, the location is in Annapolis near the Woods Landing development in the St. Margarets area which was a former Naval Weapons Facility. Drinking water was not tested at the U.S. Naval Academy for PFOS/PFOA as part of the DoD report. The Academy is approximately 7 miles from Woods Landing, by the Department of Defense.
The Arundel Patriot is continuing to follow this story and will update with developments on precise well locations and further testing.
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text:
Q: Cannot read property 'map' of undefined on useState value I'm new to react, I'm getting this error constantly and after google some I can't find the reason why the useState value can't be read as array :( ... this the error I'm getting: 'TypeError: team.map is not a function'
    import React, { useEffect, useState } from "react";

    const SportTeams = () => {
      const [team, setTeam] = useState([]);

      useEffect(() => {
        const getSports = async () => {
          const response = await fetch("https://www.thesportsdb.com/api/v1/json/1/all_sports.php");
          const data = await response.json();
          setTeam(data);
          console.log(data);
        }
        getSports();
      }, []);

      return (

            {team.map((sport, index) => {
              return <li key={`${sport.strSport}-${index}`}>{sport.strSport}

            })}

      );
    };
    export default SportTeams;

A: Just update setTeam like following, your error will be resolved.
setTeam(data.sports);

A: It is because you are setting the team state with the data without checking if its undefined. If the data is undefined your state team become undefined as well. So make sure to check the data.
    import React, { useEffect, useState } from "react";

        const SportTeams = () => {
          const [team, setTeam] = useState([]);

          useEffect(() => {
            const getSports = async () => {
              const response = await fetch("https://www.thesportsdb.com/api/v1/json/1/all_sports.php");
              if (response) {
                const data = await response.json();
                if (data) {
                  setTeam(data);
                }
              }
              console.log(data);
            }
            getSports();
          }, []);

          return (

                {team.map((sport, index) => {
                  return <li key={`${sport.strSport}-${index}`}>{sport.strSport}

                })}

          );
        };
        export default SportTeams;

There might also be the chance that your response is not what you expected and the actual data might be inside your response. In that case you need check what your response first then proceed to set the data.

A: As I said in my comment. the value you are setting to teams isn't an array.

const data = await response.json();
setTeam(data.sports);

redpajama_set_name: RedPajamaStackExchange


text:
You are here: Home / Profiles / Interviews / A Mix of Sarah Bareilles Meets Adele: Interview with Up-and-Coming Singer Samantha Aurelio
A Mix of Sarah Bareilles Meets Adele: Interview with Up-and-Coming Singer Samantha Aurelio
February 6, 2013 Collaj
Filed under Profiles / Interviews
By Amanda Deltuvia —
Hailing from the East Coast, Grammy nominated singer Samantha Aurelio is petite but she can hit those notes with strength and prowess. With a Sarah Bareilles-infused piano style synced with a voice comparable to Adele's amazing pipes, it's clear that Aurelio is a tour de force.
Samantha Aurelio received a Grammy nomination for her work with the well-known jazz organist Joey DeFrancesco on his album "Never Can Say Goodbye" in 2011, and has been on the move ever since. The 5-foot-tall performer has been actively singing and performing for the last eight years. Recently, she released her first self-titled EP with producer Joe Buscema and is gaining fans from coast-to-coast. Here is Aurelio in her own words.
AD: You just released an EP. Which is your favorite track on it and why?
SA: My favorite track is "Fly Away," because I didn't trust that song when I first wrote it. So the creation of that song means a little more by seeing the transformation process. I'd like to call it "The Little Song that Could."
AD: What're your top three favorite songs of all time?
SA: I'd probably have to go with "Don't Stop Me Now," by Queen. That's a really hard question, I like the craziest music. Let's see, "Fire and Rain" by James Taylor. "Blackbird" by The Beatles. Those are definitely top three. Little eclectic, old school. Newer stuff would be "Let the Rain" by Sarah Bareilles.
AD: Are there any new artists that people may not know about that have tickled your fancy lately?
SA: I am on a huge Ellie Goulding kick lately. I'm going to see her when I go out to L.A. And Allen Stone.
AD: Speaking of L.A., when are you going?
SA: February 6th.
AD: Where will you be playing?
SA: I am playing Feb 11th, which is a Monday, at 8pm at Room 5 in West Hollywood. And I believe that there is a "Songwriter's Night" after my set. It's my set, then open mic after. If you go to my Facebook page, you can pull up the address.
AD: What are your favorite things about L.A. and Hollywood?
SA: Besides the weather? I love the life of it. The dream of it all. It's like the "Goldenland." It's a little more packaged than New York is. New York is the promised struggle, and L.A. is all wrapped in gold, always sunny, a little bit happier.
AD: What are some of your favorite spots in the L.A. area?
SA: I'm pretty fond of the Starbucks in LAX. I go there every time I fly (laughs). I have to stop at the beach every time I go out to the West Coast, either Santa Monica Pier or Manhattan Beach. Frida Mexican Cuisine I believe is the restaurant I went out to before the Grammys. I also love Malibu Seafood and Health Nut.
AD: What is an interesting fact about you that not many people would know?
SA: Hmm… I really love Olympic lifting and gymnastics. I've been doing Crossfit for about four years and before that I was a runner and did karate. Basically, my mom wanted me to be really tough for my size!
AD: Do you have a favorite quote?
SA: "I'm bigger than my body gives me credit for." I feel like John Mayer wrote that about me.
AD: Top three passions in life?
SA: Music, writing and cooking. I love cooking.
AD: You always have a slew of love songs and breakup songs, are these solely based off of your experiences or have you pulled interesting relationship stories from friends into your music?
SA: The stuff that I released is all personal. I have stuff that I have not released, that is in the making that is of other peoples' relationships.
AD: Do you find it easier to write about your own relationship experiences or other peoples'?
SA: Me. 100%.
Samantha Aurelio with her band crew
Well, it depends on where I start. Because sometimes I start at the piano and sometimes I start with the words. Lately, I'd say I end up in a coffee shop for a couple of hours and write a whole lot. Sometimes you'll catch me singing quietly into my phone recording melodies and then, coming back later to my piano and work from there. Usually it involves a lot of writing before I do any musical accompaniment. Lots of time in the coffee shop. (laughs) They know me there, it's cool.
AD: When you get stumped on music or lyrics, what do you do to get inspired?
SA: Spotify everything.
AD: Spotify?
SA: Because there's so much music there! Usually where I hear the melody in my head, is usually the genre of music I start to listen to. Because if I try to write an upbeat song, I'm not gonna listen to a ton of really slow stuff. (laughs). In a perfect world I'd like to go see a show whenever I'm stuck. That's really inspiring. Every time I leave a show, I'm like "I wanna write an album!"
AD: What's the next step? Are you going to record an album?
SA: We are writing the album. That's what's happening. My producer and I are going to co-write and produce a full-length masterpiece. It's very exciting. We're in the writing process now, so it's just a little baby. We have to nurture it and let it grow. Just like a seed.
For more information on Samantha and to listen to her music, check out her website, or purchase her EP on iTunes
Tags: interview with singer, samantha aurelio, up and coming singer, young creative professional

redpajama_set_name: RedPajamaCommonCrawl


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Iam working on Report which will transfer the data to Application server .
My selection screen contains the Language option in which the user want to see the role descriptions.
when i try to download the data with Chinese language ,i could see '#' or junk values , as the Code Page conversion was not happening.
So i have changed my "open Dataset " to OPEN DATASET lv_path FOR OUTPUT IN LEGACY TEXT MODE CODE PAGE 8404.
As Code page of Chinese is 8404.
Still i could not see the correct text of chinese even after this change.
Please guide me where iam wrong.
do you still get hashes (#) in this case (legacy mode) ?
I assume your system is based on Unicode - please confirm.
I will go through this Note and will get back to you .


Almost right on queue, as soon as a proposal for a new bike trail is on the table, disclaimers immediately follow. This particular network of trails was jointly announced with the disappointment that the trail couldn't be built to full width.
The greenway is proposed to be a 10- to 12-foot-wide, ADA-accessible trail, though this may not be feasible in some sections of the corridor due to environmental, right-of-way, and topographical constraints.
This needs to stop. I'm all for protecting sensitive lands and being as environmentally friendly as possible, and we all understand that building through such areas come at a cost. But we also build six lane super-highways above & through environmentally sensitive areas, so we should be able to build a simple 12 foot wide path that would ultimately be more useful than the six lane highway 25 years from now. I'm thinking about the ICC where the bike lane was promised for the full length of the toll road, but remains unbuilt on account that it would cause too much environmental damage. We need to look at the big picture and stop cutting these really small corners. If the ICC right-of-way, for example, was such an environmentally sensitive area, perhaps they should have only built four lanes and allowed for the bike lanes, saving more than 24 feet of roadway instead of just 12 feet of bike trail.
The above quote is from the "concept" plans for the Patapsco Regional Greenway. Concept, to me, means it should be time to dream and plan what the network should be like, without restrictions and short changing bicyclists. Bike and pedestrian networks should be planned and implemented with the same priorities as large roadway projects, including public input that would have a process of vetting the concept ideas and selecting the most sensible. All of this needs to be supported with investment to make the project a success. This is no time for dismissing and skimping on trail design. Make a concept that would serve the needs today and 25 years from now.


The Gutenberg Cave is regarded as one of the most beautiful dripstone caves in the Swabian Alb. Just like the Gußmann Cave nearby, this is also a fissure cave, although it is located in the higher transitional level between bedded limestones and massive limestones of the Lower Chalk formation. There are six fairly large chambers in the cave which are connected to one another by narrow, high passageways. There is a remarkable collection of stalactites, stalagmites and sinter deposits, particularly at the back of the cave.
May to October: Sat von 1 p.m. - 5 p.m., Sun and public holidays 10 a.m. - 5 p.m.
The Gutenberger cave is a geopoint since September 2016.


Hospitals that are aiming at improving their postoperative pain therapy and that are honestly interested in evaluating their own patients' outcome compared to national averages are our project's target group.
As QUIPS includes all patients who have undergone surgery (and not only those who are cared for by acute pain units or who are equipped with PCA-pumps), the hospitals' persons in charge of the project should not be members of the particular departments (e.g. anesthesiology, surgery, nursing) but build a team out of all clinical partners who are involved in postoperative patient care (for example, an interdisciplinary task force 'acute pain' could be established).
From experience we know that the best way to start QUIPS is to choose two or three surgical departments with no more than 5 - 6 wards at the beginning.


text:
//------------------------------------------------------------------------------
// <auto-generated>
//     This code was generated by a tool.
//
//     Changes to this file may cause incorrect behavior and will be lost if
//     the code is regenerated.
// </auto-generated>
//------------------------------------------------------------------------------

namespace Scada.Web {

    public partial class WFrmEvents {

        /// <summary>
        /// EventsForm control.
        /// </summary>
        /// <remarks>
        /// Auto-generated field.
        /// To modify move field declaration from designer file to code-behind file.
        /// </remarks>
        protected global::System.Web.UI.HtmlControls.HtmlForm EventsForm;

        /// <summary>
        /// lblEvents control.
        /// </summary>
        /// <remarks>
        /// Auto-generated field.
        /// To modify move field declaration from designer file to code-behind file.
        /// </remarks>
        protected global::System.Web.UI.WebControls.Label lblEvents;

        /// <summary>
        /// rbEvAll control.
        /// </summary>
        /// <remarks>
        /// Auto-generated field.
        /// To modify move field declaration from designer file to code-behind file.
        /// </remarks>
        protected global::System.Web.UI.WebControls.RadioButton rbEvAll;

        /// <summary>
        /// rbEvView control.
        /// </summary>
        /// <remarks>
        /// Auto-generated field.
        /// To modify move field declaration from designer file to code-behind file.
        /// </remarks>
        protected global::System.Web.UI.WebControls.RadioButton rbEvView;

        /// <summary>
        /// chkEvPause control.
        /// </summary>
        /// <remarks>
        /// Auto-generated field.
        /// To modify move field declaration from designer file to code-behind file.
        /// </remarks>
        protected global::System.Web.UI.WebControls.CheckBox chkEvPause;

        /// <summary>
        /// lblEvPause control.
        /// </summary>
        /// <remarks>
        /// Auto-generated field.
        /// To modify move field declaration from designer file to code-behind file.
        /// </remarks>
        protected global::System.Web.UI.WebControls.Label lblEvPause;
    }
}

redpajama_set_name: RedPajamaGithub


text:
Q: How to use listing, tikz and tikzmark packages together to annotate source code listing? I'd like to annotate code listing something like this:

Below is what I've attempted so far. I am a little worried about having to use raisebox so that the arrow tip doesn't point to the base of the line. How can I avoid this hardcoding? I would also appreciate any advice on improvements so that it's easier to handle a few varieties of annotations as seen in the screenshot.
It would be nice, to get the desired results, if I can just specify the following:

*

*the distance between the end of source line and the arrow tip

*the length of the horizontal line and the length of the vertical line
of the arrow (and whether the vertical line goes upwards or downwards)

*and the position of the text node (whether right or left of the vertical line and vertical alignment of text node with the top or bottom.
\documentclass[twoside, openright, 10pt]{book}
\usepackage{listings}
\usepackage{tikz}
\usetikzlibrary{arrows.meta, tikzmark}

\begin{document}

\chapter{TiKz}

\begin{lstlisting}[caption={[MeetKarel]{MeetKarel}}, label={lst:meet_karel}, escapechar=ß]
import stanford.karel.Karel;
public class MeetKarel extends Karel {
        public void run() {
                move();
                move();
                move();
                ß\tikzmark{b}ßpickBeeper();ß\raisebox{2.6pt}{\tikzmark{a}}ß
                turnLeft();
                move();
                move();
                turnLeft();
                turnLeft();
                turnLeft();ß\raisebox{2.6pt}{\tikzmark{c}}ß
                move();
                putBeeper();
                move();
        }
}
\end{lstlisting}
\begin{tikzpicture}[remember picture,overlay]
\draw([shift={(12ex,10ex)}] pic cs:a) ++ (0.05, 0) % shift just a little to the right
  % set inner and outer to 0 so that text is alighed with the beginning of the vertical line
  node[inner sep=0,outer sep=0, fill=yellow!80!black,text width=5cm, anchor= north west]
  {Shifted a little above so that the arrow head points to the middle of the line.};
\draw[thin, gray, arrows = {-Stealth[inset=0pt, angle=45:7pt]}]
  ([shift={(12ex,10ex)}] pic cs:a) --
  ([shift={(12ex,0ex)}] pic cs:a) --
  ([shift={(0ex,0ex)}] pic cs:a);
\draw([shift={(12ex,-10ex)}] pic cs:c) ++ (0.05, -0.05) % shift just a little to the right and down
  % set inner and outer to 0 so that text is alighed with the beginning of the vertical line
  node[inner sep=0,outer sep=0, fill=yellow!80!black,text width=5cm, anchor= south west]
  {I want to align base line of this text to the `c` node nicely. };
\draw[thin, gray, arrows = {-Stealth[inset=0pt, angle=45:7pt]}]
  ([shift={(12ex,-10ex)}] pic cs:c) --
  ([shift={(12ex,0ex)}] pic cs:c) --
  ([shift={(0ex,0ex)}] pic cs:c);
\end{tikzpicture}
\end{document}

Result:

A: Here's a slightly simplified version of your code.

*

*By using the tikzmark special listings library then you don't need to specify tikzmarks in your code, they are all provided for you.

*The arrows start at (0.5,.5ex) away from the corresponding tikzmarks.  The .5ex is half the height of an x, and looks a good vertical height to me.

*The lines and nodes are drawn together and the -| path construction is used to make the line bend nicely.

*A little bit is added to the outer xsep of the label nodes to move them away from the joining line.  Other ways of achieving the same effect do seem to cause issues with the arrow placement.

All of this contrives to make the code much shorter.  Various numbers could be hard-coded into a style to make it even more simple and a bit more flexible.
\documentclass[twoside, openright, 10pt]{book}
%\url{https://tex.stackexchange.com/q/657375/86}
\usepackage{listings}
\usepackage{tikz}
\usetikzlibrary{
  arrows.meta,
  tikzmark,
  calc,
  positioning
}
\usetikzmarklibrary{listings}

\begin{document}

\chapter{Ti\emph{k}Z}

\begin{lstlisting}[
  caption={[MeetKarel]{MeetKarel}},
  label={lst:meet_karel},
  name=karel,
  escapechar=ß
]
import stanford.karel.Karel;
public class MeetKarel extends Karel {
        public void run() {
                move();
                move();
                move();
                pickBeeper();
                turnLeft();
                move();
                move();
                turnLeft();
                turnLeft();
                turnLeft();
                move();
                putBeeper();
                move();
        }
}
\end{lstlisting}

\begin{tikzpicture}[
  remember picture,
  overlay,
  annotation/.style={
    inner sep=0pt,
    outer sep=0pt,
    outer xsep=1mm,
    fill=yellow!80!black,
    text width=5cm
  },
  >={Stealth[inset=0pt, angle=45:7pt]}
]
\draw[<-] (pic cs:line-karel-7-end)  ++(.5,.5ex) -| ++(2,1.5)
node[annotation, below right]
{Shifted a little above so that the arrow head points to the middle of the line.};

\draw[<-] (pic cs:line-karel-13-end) ++(0.5,.5ex) -| ++(2,-1)
node[annotation, above right]
{I want to align base line of this text to the `c` node nicely. };
\end{tikzpicture}
\end{document}


"You got some time off from flying then?" Gibson cocked his head with a knowing grin, probably having seen the direction of Maxwell's eyes.
This entry was posted in Uncategorized and tagged announcements, book tour, contests, gay romance, giveaway, GLBTQ, guest blog, male male romance, promo, Sarah Madison by Sarah Madison. Bookmark the permalink.


This isn't a recipe post, but it's still a great one because trust me when I say you'll want this cleanser in your life! Today, I bring you my review of the Algenist Anti-Aging Melting Cleanser: This is an oldie but a goodie! I used this cleanser for a few months last year & re-incorporated it into my morning routine a little over a month ago & I" mso happy that I did!
For me, this product is a "kill two birds with one stone" sitch. Not only does it leave my skin smooth & soft immediately after I use it, but overtime, I've seen an improvement in the clarity & brightness of my skin.
It's specifically designed to non-drying (unlike a lot of other cleansers, which are full of soapy ingredients that actually dry out the skin).
It's made with alguronic acid, micro algae oil (so you get the benefits of an oil cleanser: washes away impurities but leaves behind the skin's natural oils so it won't strip your skin of moisture), It also has tons of nourishing anti-inflammatory, skin-glowing & healing fatty acids from oils, such as sweet alone, chlorella, avocado, bilberry & olive oil (the oleic acid in olive oil is amazing for preventing moisture loss also).
What sold me on this cleanser initially was the texture. It starts off as a gel, turns into a silky lightweight oil & when you add warm water, it turns into a milky formula & leaves my skin feeling refreshed, clean & smooth.
PSA: It contains no parabens or sulphates, it's soap-free, non comedogenic, hypoallergenic & dermatologist tested.
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text:
Q: How to get number of matching colums count in the same table as another column? I have a table like below.
    +----+----------+---------+--------+----------+---------+---------------------+
    | id | box_name | diIndex | diMode | diStatus | status  | last_updated        |
    +----+----------+---------+--------+----------+---------+---------------------+
    |  7 | boxa     |       0 |      0 |        0 |    1    | 2017-03-02 10:49:35 |
    |  8 | boxa     |       1 |      0 |        1 |    0    | 2017-03-02 10:49:35 |
    |  9 | boxa     |       2 |      0 |        0 |    1    | 2017-03-02 10:49:36 |
    | 10 | boxa     |       3 |      0 |        0 |    1    | 2017-03-02 10:49:36 |
    | 11 | boxa     |       4 |      0 |        0 |    0    | 2017-03-02 10:49:36 |
    | 12 | boxa     |       5 |      0 |        0 |    2    | 2017-03-02 10:49:36 |
    | 13 | boxa     |       6 |      0 |        0 |    2    | 2017-03-02 10:49:36 |
    | 14 | boxa     |       7 |      0 |        0 |    3    | 2017-03-02 10:49:36 |
    +----+----------+---------+--------+----------+---------+---------------------+

Now I want to add a new column in the table which will get me the total number of each matching record of status column like below.
+----+----------+---------+--------+----------+---------+---------------+---------------------+
| id | box_name | diIndex | diMode | diStatus | status  | status count  | last_updated        |
+----+----------+---------+--------+----------+---------+---------------+---------------------+
|  7 | boxa     |       0 |      0 |        0 |    1    |       3       | 2017-03-02 10:49:35 |
|  8 | boxa     |       1 |      0 |        1 |    0    |       2       | 2017-03-02 10:49:35 |
|  9 | boxa     |       2 |      0 |        0 |    1    |       3       | 2017-03-02 10:49:36 |
| 10 | boxa     |       3 |      0 |        0 |    1    |       3       | 2017-03-02 10:49:36 |
| 11 | boxa     |       4 |      0 |        0 |    0    |       2       | 2017-03-02 10:49:36 |
| 12 | boxa     |       5 |      0 |        0 |    2    |       2       | 2017-03-02 10:49:36 |
| 13 | boxa     |       6 |      0 |        0 |    2    |       2       | 2017-03-02 10:49:36 |
| 14 | boxa     |       7 |      0 |        0 |    3    |       1       | 2017-03-02 10:49:36 |
+----+----------+---------+--------+----------+---------++--------------+---------------------+

Here you can see that for status value 1 there are 3 records so value for status_count for columns having status as 1 will be 3 and so on..
How can I achieve this?

A: With window functions, this would be almost trivial to add as a column in a query:
COUNT(*) OVER (PARTITION BY status) AS status_count

Since MySQL hasn't implemented them (you'll have to wait, they may be in the next version), you'll need something more complex now. It can be done with a derived table - to calculate these counts - and then join to the base table:
SELECT
    t.id, t.box_name, t.diIndex, t.diMode, t.diStatus, t.status,
    g.status_count, t.last_updated
FROM
    tableX AS t
  JOIN
    ( SELECT status, COUNT(*) AS status_count
      FROM tableX
      GROUP BY status
    ) AS g
  ON
    t.status = g.status ;


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text:
\section{Introduction}
\noindent The vertical dynamics of a free falling ball on a moving racket is considered. The racket is supposed to
move periodically in the vertical direction according to a regular periodic function $f(t)$ and
the ball is reflected according to the law of elastic bouncing when hitting the
racket. The only force acting on the ball is the gravity $g$. Moreover, the mass of the racket is assumed to be large with respect to the mass of the
ball so that the impacts do not affect the motion of the racket.

\noindent This model has inspired many authors as it represents a simple model exhibiting complex dynamics, depending on the properties of the function $f$. The first results were given by Pustyl'nikov in \cite{pust} who studied the possibility of having motions with velocity tending to infinity, for $\df$ large enough. On the other hand, KAM theory implies that if the $C^k$ norm, for $k$ large, of $\df$ is small then all motions are bounded. On these lines some recent results are given in \cite{ma_xu,maro4,maro6}. Bounded motions can be regular (periodic and quasiperiodic, see \cite{maro3}) and chaotic (see \cite{maro5,maro2,ruiztorres}). Moreover, the non periodic case is studied in \cite{kunzeortega2,ortegakunze}, the case of different potentials is considered in \cite{dolgo} and recent results on ergodic properties are present in \cite{studolgo}.

In this paper we are concerned with $(p,q)$-periodic motions understood as $p$-periodic with $q$ bounces in each period. Here $p,q$ are supposed to be positive coprime integers. In \cite{maro3} it is proved that if $p/q$ is sufficiently large, then there exists at least one $(p,q)$-periodic motion. This result comes from an application of Aubry-Mather theory as presented in \cite{bangert}. Actually, the bouncing motions correspond to the orbits of an exact symplectic twist map of the cylinder. The orbits of such maps can be found as critical points of an action functional and the $(p,q)$-periodic orbits found in \cite{maro3} correspond to minima. Here we first note that a refined version of Aubry-Mather theory (see \cite{katok_hass}) gives, for each couple of coprime $p,q$ such that $p/q$ is large, the existence of another $(p,q)$-periodic orbit that is not a minimum, since it is found via a minimax argument. This gives the existence of two different $(p,q)$-periodic motions for fixed values of $p,q$, with $p/q$ large.

We are first interested in the stability in the sense of Lyapunov of such periodic motions. This is related to the structure of the $(p,q)$-periodic orbits of the corresponding exact symplectic twist map, for fixed $p,q$. It comes from Aubry-Mather theory that the $(p,q)$-periodic orbits that are minima can be ordered and if there are two with no other in the middle then they are connected by heteroclinic orbits. In this case they are unstable. On the other hand, $(p,q)$-periodic orbits can form an invariant curve. In this case they are all minima but their stability cannot be determined as before since we are in a degenerate scenario. However, if we suppose to be in the real analytic case, a topological argument (see \cite{ortega_fp,ortega_book}) can be used to deduce instability. More precisely we will use the fact that for a real analytic area and orientation preserving embedding of the plane that is not the identity, every stable fixed point is isolated. Therefore, the hypothesis of $f$ being real analytic comes here into play.

Concerning the structure of the set of $(p,q)$-periodic motions we prove that in the real analytic case they can only be either isolated or in a degenerate case, in the sense that the corresponding orbits form an invariant curve that is the graph of a real analytic function. As before, in the isolated case at least one is unstable and in the degenerate case they all are minima and unstable. Note that this result differs from Aubry-Mather theory since we are not requiring the orbits to be minima of a functional. To prove this result we need the $q$-th iterate of the map to be twist. For $q=1$ this is true for every real analytic $f$, while for the general case $q>1$ we need to restrict to $\norm{\ddf}$ being small.

The paper is organized as follows. In Section \ref{sec:theory} we recall some known facts about exact symplectic twist maps together with the results for the analytic case. In Section \ref{sec:tennis} we introduce the bouncing ball map and describe its main properties. Finally, the results on the existence of two $(p,q)$-periodic motions, the instability and the structure of the set are given in Section \ref{sec:per}.

\section{Some results on periodic orbits of exact symplectic twist maps}\label{sec:theory}
Let us denote by $\Sigma=\RR\times(a,b)$ with $-\infty\leq a<b\leq +\infty$ a possibly unbounded strip of $\RR^2$. We will deal with $C^k$ ($k\geq 1$) or real analytic embeddings $\tilde{S}:\Sigma \rightarrow \RR^2$ such that
\begin{equation}\label{def_cyl}
\tilde{S}\circ\sigma=\sigma\circ \tilde{S}
\end{equation}
where $\sigma:\RR^2\rightarrow\RR^2$ and $\sigma(x,y)=(x+1,y)$. By this latter property, $\tilde{S}$ can be seen as the lift of an embedding $S:\Sigma\rightarrow\AA$ where $\AA = \TT\times \RR$ with $\TT = \RR/\ZZ$ and $\Sigma$ is now understood as the corresponding strip of the cylinder. We denote $\tilde{S}(x,y)=(\bar{x},\bar{y})$ and the corresponding orbit by $(x_n,y_n)_{n\in\ZZ}$.

 We say that $\tilde{S}$ is exact symplectic if there exists a $C^1$ function $V:\Sigma\rightarrow \RR$ such that $V\circ\sigma=V$ and
\[
\bar{y} d \bar{x} -y dx = dV(x,y) \quad\mbox{in }\Sigma.
\]
Moreover, by the (positive) twist condition we understand
\[
\frac{\partial \bar{x}}{\partial y} >0 \quad\mbox{in }\Sigma.
\]
A negative twist condition would give analogous results. The exact symplectic condition implies that $\tilde{S}$ preserves the two-form $dy\wedge dx$ so that it is area and orientation preserving.
An equivalent characterization is the existence of a generating function, i.e. a $C^2$ function $h:\Omega\subset \RR^2\rightarrow \RR$ such that $h(x+1,\bar{x}+1) = h(x,\bar{x})$ and $h_{12}(x,\bar{x}) <0$ in $\Omega$ and for $(x,y)\in\Sigma$ we have $\tilde{S}(x,y) = (\bar{x},\bar{y})$ if and only if
    \[
    \left\{
    \begin{split}
      h_1(x,\bar{x})&=-y \\
      h_2(x,\bar{x})&=\bar{y}.
    \end{split}
    \right.
    \]
Moreover, $\tilde{S}$ preserves the ends of the cylinder if, uniformly in $x$,
\[
\bar{y}(x,y) \rightarrow \pm\infty \quad\mbox{as }y\rightarrow \pm\infty
\]
and twists each end infinitely if, uniformly in $x$,
\[
\bar{x}(x,y)-x \rightarrow \pm\infty \quad\mbox{as }y\rightarrow \pm\infty.
\]
Finally we will say that an embedding of the cylinder $S:\Sigma\rightarrow\AA$ satisfies any of these properties if so does its corresponding lift.

These maps enjoy several properties and many interesting orbits are proved to exist. Here we recall some results concerning periodic orbits. We start with the following
\begin{definition}
  Fix two coprime integers $p,q$ with $q\neq 0$. An orbit $(x_n,y_n)_{n\in\ZZ}$ of $\tilde{S}$ is said $(p,q)$-periodic if $(x_{n+q},y_{n+q})=(x_n+p,y_n)$ for every $n\in\ZZ$. Moreover, we say that it is stable (in the sense of Lyapunov) if for every $\varepsilon>0$ there exists $\delta>0$ such that for every $(\hat{x}_0,\hat{y}_0)$ satisfying $|(x_0,y_0)-(\hat{x}_0,\hat{y}_0)|<\delta$ we have $|\tilde{S}^n(\hat{x}_0,\hat{y}_0)-({x}_n,{y}_n)|<\varepsilon$ for every $n\in\ZZ$.
\end{definition}

\begin{remark}\label{rem_periodic}
  Note that $(q,p)$-periodic orbits correspond to fixed points of the map $\sigma^{-p}\circ \tilde{S}^q$. This follows from the fact that $\tilde{S}$ is a diffeomorphism defined on the cylinder. Each point of the orbit is a fixed point of $\sigma^{-p}\circ\tilde{S}^q$ and a fixed point of $\sigma^{-p}\circ\tilde{S}^q$ is the initial condition of a $(p,q)$-periodic orbit. Note that different fixed points may correspond to the same orbit but not viceversa. Moreover, if an orbit is $(q,p)$-periodic then it cannot be also $(q',p')$-periodic unless $p/q=p'/q'$. Actually, let $\xi=(x,y)$ and suppose that $\xi=\sigma^{-p}\circ\Phi^q(\xi)=\sigma^{-p'}\circ \Phi^{q'}(\xi)$. Then $\sigma^{p}(\xi)=\Phi^q(\xi)$ and $\sigma^{p'}(\xi)=\Phi^{q'}(\xi)$ from which $\Phi^{qq'}(\xi)=\sigma^{pq'}(\xi)=\sigma^{p'q}(\xi)$ and $pq'=p'q$.
  Finally, the stability of a $(q,p)$-periodic orbit corresponds to the stability in the sense of Lyapunov of the corresponding fixed point of the map $\sigma^{-p}\circ\tilde{S}^q$.
\end{remark}

A particular class of periodic orbits are the so called Birkhoff periodic orbits.
\begin{definition}
  Fix two coprime integers $p,q$ with $q\neq 0$. An orbit $(x_n,y_n)_{n\in\ZZ}$ of $\tilde{S}$ is said a Birkhoff $(p,q)$-periodic orbit if there exists a sequence $(s_n,u_n)_{n\in\ZZ}$ such that
  \begin{itemize}
  \item $(s_0,u_0)=(x_0,y_0)$
  \item $s_{n+1}>s_n$
  \item $(s_{n+q},u_{n+q})=(s_{n}+1,u_{n})$
  \item $(s_{n+p},u_{n+p})=\tilde{S}(s_{n},u_{n})$
    \end{itemize}
 \end{definition}
  \begin{remark}
    Note that a Birkhoff $(p,q)$-periodic orbit is a $(p,q)$-periodic orbit since
    \[
(x_{n+q},y_{n+q})=(s_{np+qp},u_{np+qp})=(s_{np}+p,u_{np})=\tilde{S}^n(s_0,u_0)+(p,0)=(x_{n}+p,y_{n}).
    \]
    \end{remark}

The existence of Birkhoff $(p,q)$-periodic orbits comes from Aubry-Mather theory. Here we give a related result \cite[Th. 9.3.7]{katok_hass}

\begin{theorem}\label{birk_orbits}
  Let $S:\AA\rightarrow\AA$ be an exact symplectic twist diffeomorphism that preserves and twists the ends infinitely and let $p,q$ be two coprime integers. Then there exist at least two Birkhoff $(p,q)$-periodic orbits for $S$.
\end{theorem}
\begin{remark}
The Theorem is proved via variational techniques. The periodic orbits correspond to critical points of an action defined in terms of the generating function. One of this point is a minimum and the other is a minimax if the critical points are isolated.
  \end{remark}

In the analytic case, something more can be said on the topology of these orbits.

\begin{proposition}\label{unstable}
Let $\tilde{S}:\Sigma\rightarrow\RR^2$ be an exact symplectic twist embedding satisfying condition \eqref{def_cyl} and admitting a $(p,q)$-periodic orbit. Then there exists at least one $(p,q)$-periodic orbit that is unstable.
\end{proposition}
\begin{proof}
  The proof is essentially given in \cite{maroTMNA,ortega_fp,ortega_book}. We give here a sketch. It is enough to prove that there exists at least one unstable fixed point of the area and orientation preserving 1-1 real analytic map $\sigma^{-p}\circ \tilde{S}^q$. Let us first note that since $\tilde{S}$ is twist, the map $\sigma^{-p}\circ \tilde{S}^q$ is not the identity. Actually, it is known (see for example \cite{herman})) that if $\tilde{S}$ is twist, then the image of a vertical line under $\tilde{S}^q$ is a positive path, i.e. a curve such that the angle between the tangent vector and the vertical is always positive. This implies that $\tilde{S}^q$ cannot be a horizontal translation.\\
By hypothesis the set of fixed points of $\sigma^{-p}\circ \tilde{S}^q$ is not empty so that applying \cite[Chapter 4.9, Theorem 15]{ortega_book} we deduce that every stable fixed point is an isolated fixed point.\\
Hence, if there exists some non isolated fixed point, it must be unstable. Finally, suppose that we only have isolated fixed points that are all stable. From \cite[Chapter 4.5, Theorem 12]{ortega_book} they must all have index $1$. On the other hand, the Euler characteristic of the cylinder is null, and by the Poincar\'e-Hopf index formula we have a contradiction. Hence, there must exists at least one fixed point that is unstable.
   \end{proof}

\begin{corollary}
  In the conditions of Theorem \ref{birk_orbits}, if $S$ is real analytic then there exists at least one unstable $(p,q)$-periodic orbit.
\end{corollary}

In the analytic case, the twist condition gives information on the structure of the set of $(p,q)$-periodic orbits. Actually the following result has been proved in \cite{maroTMNA,ortega_pb}

\begin{theorem}\label{maro_teo}
  Consider a $C^1$-embedding $\tilde{S}:\Sigma\rightarrow\RR$ satisfying property \eqref{def_cyl} and suppose it is exact symplectic and twist. Fix a positive integer $p$ and assume that for every $x\in\RR$ there exists $y\in (a,b)$ such that
  \begin{equation}\label{maro_cond}
\bar{x}(x,a)<x+p<\bar{x}(x,y).
  \end{equation}
Then the map $\sigma^{-p}\circ\tilde{S}$ has at least two fixed points in $[0,1)\times (a,b)$. Moreover, if $\tilde{S}$ is real analytic then the set of fixed points is finite or the graph of a real analytic $1$-periodic function. In the first case the index of such fixed points is either $-1$, $0$, $1$ and at least one is unstable. In the second case, all the fixed points are unstable.
  \end{theorem}

\begin{remark}
	Aubry-Mather theory gives a description, for fixed $p,q$ of those $(p,q)$-periodic orbits that are global minimizers. They can be ordered and if two of them are neighbouring, in the sense that there is no other minimal $(p,q)$-periodic orbit in the middle, then there are heteroclinic connections between them (\cite{bangert,katok_hass}). In this case, the $(p,q)$-periodic orbits are unstable.  On the other hand, they can form an invariant curve. We stress that in the analytic case Theorem \ref{maro_teo} gives the description of the set of all $(p,q)$-periodic orbits, not only those that are action minimizing.
\end{remark}

\section{The bouncing ball map and its properties}\label{sec:tennis}

Consider the motion of a bouncing ball on a vertically
moving racket. We assume that the impacts do not affect the racket  whose vertical position is described by a
$1$-periodic $C^k$, $k\geq 2$, or real analytic function $f:\RR\rightarrow\RR$. Let us start getting the equations of motion, following \cite{maro5}. In an inertial frame, denote by $(\to,w)$ the time of impact and the corresponding velocity just after the bounce, and by
$(\Pto,\bar w)$ the corresponding values at the subsequent bounce.
From
the free falling condition we have
\begin{equation}\label{timeeq}
f(t) + w(\Pto-\to) - \frac{g}{2}(\Pto -\to)^2 = f(\Pto) \,,
\end{equation}
where $g$ stands for the standard acceleration due to gravity.
Noting that the velocity just before the impact at time $\Pto$ is $w-g(\Pto-\to)$, using
the elastic impact condition and recalling that the racket is not affected by the ball, we obtain
\begin{equation}
  \label{veleq}
\bar{w}+w-g(\Pto-\to) = 2\dot{f}(\Pto)\,,
\end{equation}
where $\dot{}$ stands for the derivative with respect to time. From conditions (\ref{timeeq}-\ref{veleq}) we can define a bouncing motion given an initial condition $(t,w)$ in the following way. If $w\leq\df(t)$ then we set $\bar{t}=t$ and $\bar{w}=w$. If $w>\df(t)$, we claim that we can choose $\bar{t}$ to be the smallest solution $\bar{t}> t$ of \eqref{timeeq}. Bolzano theorem gives the existence of a solution of \eqref{timeeq} considering
\[
F_t(\bar{t})=f(t)-f(\Pto) + w(\Pto-\to) - \frac{g}{2}(\Pto -\to)^2
\]
and noting that $F_t(\bar{t})<0$ for $\Pto-\to$ large and $F_t(\bar{t})>0$ for $\Pto-\to\rightarrow 0^+$. Moreover, the infimum $\bar{t}$ of all these solutions is strictly larger than $t$ since if there exists a sequence $\bar{t}_n\rightarrow t$ satisfying \eqref{timeeq} then,
\[
 w - \frac{g}{2}(\Pto_n -\to) = (f(\Pto_n)- f(t)) /(\Pto_n-\to)
\]
that contradicts $w>\df(t)$ using the mean value theorem.
For this value of $\bar{t}$, condition \eqref{veleq} gives the updated velocity $\bar{w}$.

For $\Pto-\to>0$, we introduce the notation
\[
f[\to,\Pto]=\frac{f(\Pto)-f(\to)}{\Pto-\to},
\]
and write
\begin{equation}
  \label{w1}
\Pto = \to + \frac 2g w -\frac 2g f[\to,\Pto]\,,
\end{equation}
that also gives
\begin{equation}
  \label{w2}
\bar{w}= w -2f
[\to,\Pto]
+ 2\dot{f}(\Pto).
\end{equation}
Now we change to the moving frame attached to the racket, where the velocity after the impact is expressed as $v=w-\dot{f}(t)$,
and we get
the equations
\begin{equation}\label{eq:unb}
  \left\{
  \begin{split}
\Pto = {} & \to + \frac 2g \vo-\frac 2g f[\to,\Pto]+\frac 2g \df(\to)\textcolor{blue}{\,}
\\
\Pvo = {} & \vo - 2f[\to,\Pto] + \df (\Pto)+\df(\to)\textcolor{blue}{\,.}
\end{split}
\right.
\end{equation}
 By the periodicity of the
function $f$, the coordinate $t$ can be seen as an angle. Hence, equations \eqref{eq:unb} define formally a map
\[
\begin{array}{rcl}
\tilde\Psi:
\RR & \longrightarrow & \RR \\
(\to,\vo) & \longmapsto & (\Pto, \Pvo),
\end{array}
\]
satisfying $\tilde\Psi\circ\sigma=\sigma\circ\tilde\Psi$ and the associated map of the cylinder $\Psi:\AA\rightarrow\AA$.

This is the formulation considered by Kunze and Ortega
\cite{kunzeortega2}. Another approach was considered by Pustylnikov in
\cite{pust} and leads to a map that is equivalent to
\eqref{eq:unb}, see \cite{maro3}.
Noting that $w>\df(t)$ if and only if $v>0$, we can define a bouncing motion as before and denote it as a sequence $(t_n,v_n)_{n\in\ZZ^+}$ with $\ZZ^+=\{n\in\ZZ \::\: n\geq 0\}$ such that $(t_n,v_n)\in \TT\times [0,+\infty)$ for every $n\in\ZZ^+$.

The maps $\Psi$ and its lift $\tilde{\Psi}$ are only defined formally. In the following lemma we state that they are well defined and have some regularity.
Let us introduce the notation $\RR_{v_*}=\{v\in\RR \: :\: v>v_* \}$,  $\AA_{v_*} = \TT\times \RR_{v_*}$ and $\RR^2_{v_*}=\RR\times\RR_{v_*}$. We will denote the $\sup$ norm by $\norm{\cdot}$ and recall that $f\in C^k(\TT), k\geq 2$ or real analytic.

\begin{lemma}
  \label{well_def}
There exists $v_*>4\norm{\df}$ such that the map $\Psi:\AA_{v_*}\rightarrow \AA$ is a $C^{k-1}$ embedding. If $f$ is real analytic, then $\Psi$ is a real analytic embedding.
\end{lemma}
\begin{proof}
The proof is essentially given in \cite{maro5}. We give here a sketch.
To prove that the map is well defined and $C^{k-1}$ we denote $v_{**}=4\norm{\df}$ and apply the implicit function theorem to the $C^{k-1}$ function $F :\{(\to,\vo,\Pto,\Pvo)\in \AA_{v_{**}} \times \RR^2 \: :\:\to\neq\Pto   \} \rightarrow \RR^2$
given by

\begin{equation*}
 F(\to,\vo,\Pto,\Pvo):=
\left(
\begin{split}
& \Pto - \to - \frac 2g \vo + \frac 2g f[\to,\Pto]-\frac 2g \df (\to) \\
& \Pvo - \vo + 2f[\to,\Pto] - \df(\Pto)-\df(\to)
\end{split}
\right),
\end{equation*}
This gives the existence of a $C^{k-1}$ map $\Psi$ defined in $\AA_{v_{**}}$ such that $F(\to,\vo,\Psi(\to,\vo) )=0$. If $f$ is real analytic, we get that $\Psi$ is real analytic applying the analytic version of the implicit function theorem. \\
One can easily check that $\Psi$ is a local diffeomorphism since
\[
\det \Dif_{\to,\vo} \Psi (t,v) =-\frac{\det (\Dif_{\to,\vo} F(\to,\vo,\Psi(\to,\vo) ))}{ \det (\Dif_{\Pto,\Pvo} F(\to,\vo,\Psi(\to,\vo) ))} \neq 0 \quad\mbox{on }\AA_{v_{**}}.
\]
To prove that $\Psi$ is a global embedding we need to prove that it is injective in $\AA_{v_*}$ for $v_*$ eventually larger than $v_{**}$. This can be done as in \cite{maro5}.
\end{proof}

\begin{remark}
  Note that we cannot guarantee that if $(\to_0,\vo_0) \in \AA_{v_*}$ then $\Psi(\to_0,\vo_0) \in \AA_{v_*}$. This is reasonable, since the ball can slow down decreasing its velocity at every bounce.

  However, a bouncing motion is defined for $v\geq 0$
\end{remark}

\begin{remark}
  From the physical point of view, the condition $\Psi^n(\to_0,\vo_0)\in\AA_{v_*}$ for every $n$, implies that we can only hit the ball when it is falling. To prove it, suppose that $\to_0 =0$ and let us see what happens at the first iterate. The time at which the ball reaches its maximum height is $t^{max}=\frac{\vo_0}{g}$. On the other hand, the first impact time $\Pto$ satisfies,
  \[
\Pto \geq \frac{2}{g}\vo_0 - \frac{4}{g}\norm{\df}= t^{max}\left(         2-\frac{4}{\vo_0}\norm{\df} \right) > t^{max},
\]
where the last inequality comes from $\vo_0\in\RR_{v_*}$ and $v_*>4\norm{\df}$.
\end{remark}

The map $\tilde\Psi$ is exact symplectic if we pass to the variables time-energy $(\to,\Eo)$ defined by
\[
 (\to,\Eo) = \left(\to,\frac{1}{2}\vo^2\right),
\]
obtaining the conjugated map
\[
\Phi :\AA_{\Eo_*}
\longrightarrow  \AA, \qquad \Eo_*=\frac{1}{2}v_*^2
\]
defined by
\begin{equation}\label{eq:unbe}
  \left\{
  \begin{split}
\Pto =  & \to + \frac 2g \sqrt{2\Eo}-\frac 2g f[\to,\Pto]+\frac 2g \df(\to)
\\
\PEo =  & \frac{1}{2}\left( \sqrt{2\Eo} - 2f[\to,\Pto] + \df (\Pto)+\df(\to) \right)^2,
\end{split}
\right.
\end{equation}
that by Lemma \ref{well_def} is a $C^{k-1}$-embedding or real analytic if $f$ is real analytic. More precisely, we have the following
\begin{lemma}
  \label{lemma:exact}
  The map $\Phi$ is exact symplectic and twist in $\AA_{e_*}$.

  Moreover, $\Phi$ preserves and twists infinitely the upper end.

\end{lemma}

The map $\Phi$ is not defined in the whole cylinder. However, it is possible to extend to the whole cylinder preserving its properties. More precisely:
\begin{lemma}
  \label{extension}
There exists a $C^{k-2}$ exact symplectic and twist diffeomorphism $\bar{\Phi}:\AA\rightarrow\AA$ such that $\bar{\Phi} \equiv \Phi$ on $\AA_{e_*}$ and $\bar{\Phi}\equiv\Phi_0$ on $\AA\setminus\AA_{\frac{e_*}{2}}$ where $\Phi_0$ is the integrable twist map $\Phi_0(t,e)=(t+e,e)$. Moreover, $\bar{\Phi}$ preserves the ends of the cylinder and twists them infinitely. If $f$ is real analytic, then the extension $\bar{\Phi}$ is $C^\infty$.
\end{lemma}

Due to Lemma \ref{well_def} and the fact that the maps $\Phi$ and $\Psi$ are conjugated we can consider the lift $\tilde{\Phi}:\RR^2_{e_*}\rightarrow\RR^2$ and give the following
\begin{definition}
  A complete bouncing motion $(t_n,e_n)_{n\in\ZZ}$ is a complete orbit of the map $\tilde{\Phi}$.
  \end{definition}

In the following section we will study the existence and properties of periodic complete bouncing motions as orbits of the map $\tilde{\Phi}$ defined in \eqref{eq:unbe}.

\section{Periodic bouncing motions}\label{sec:per}
The existence of periodic complete bouncing motions follows from an application of Aubry-Mather theory. In this section we prove it and in the analytic case we give some results on the structure of such motions and their stability.

We start saying that a complete bouncing motion is $(q,p)$-periodic if in time $p$ the ball makes $q$ bouncing before repeating the motion, more precisely:
\begin{definition}
  Given two coprime integers $q,p\in\ZZ^+$, a complete bouncing motion $(t_n,e_n)_{n\in\ZZ}$ is $(q,p)$-periodic if the corresponding orbit of $\tilde{\Phi}$ is $(p,q)$-periodic. Moreover, we say that it is stable if the corresponding orbit is stable.
\end{definition}

The existence of two $(q,p)$-periodic complete bouncing motions comes from an application of Theorem \ref{birk_orbits}.

\begin{theorem}\label{pre_bouncing}
For every $f\in C^3$ there exists $\alpha>0$ such that for every positive coprime $p,q$ satisfying $p/q>\alpha$ there exist two different $(q,p)$-periodic complete bouncing motions. Moreover, if $f$ is real analytic, then at least one of the $(q,p)$-periodic complete bouncing motion is unstable.
  \end{theorem}
\begin{proof}
  By Lemma \ref{lemma:exact}, the map $\Phi$ defined in \eqref{eq:unbe} is a $C^2$ exact symplectic twist embedding in $\AA_{e_*}$ for some large $e_*$ depending on $\norm{\df}$. Moreover $\Phi$ preserves and twists infinitely the upper end. Its extension $\bar{\Phi}$ coming from Lemma \ref{extension} satisfies the hypothesis of Theorem \ref{birk_orbits} and admits for every coprime $p,q$ two Birkhoff $(q,p)$-periodic orbit. Consider the Birkhoff $(q,p)$-periodic orbits for $p,q$ positive and $p/q$ large enough such that
  \begin{equation}\label{choice_pq}
  \frac{p}{q}-1-\frac{4}{g}\norm\df>\frac{2}{g}\sqrt{2e_*}.
  \end{equation}
  Since Birkhoff periodic orbits are cyclically ordered, from \cite[lemma 9.1]{gole} we have that they satisfy the estimate $t_{n+1}-t_n>p/q - 1$. On the other hand, from \eqref{eq:unbe},
  \[
  t_{n+1}-t_n\leq\frac{2}{g}\sqrt{2e_n}+\frac{4}{g}\norm\df
  \]
  so that it must be
  \[
\frac{2}{g}\sqrt{2e_n}+\frac{4}{g}\norm\df>\frac{p}{q}-1.
  \]
By the choice of $p/q$ in \eqref{choice_pq} we have that $e_n>e_*$ for every $n\in\ZZ$ so that these Birkhoff periodic orbits are all contained in $\AA_{e_*}$ and so they are orbits of the original map $\Phi$. If $f$ is real analytic the result on the instability follows from Proposition \ref{unstable}.
\end{proof}

Theorem \ref{pre_bouncing} gives the existence of $(p,q)$-periodic bouncing motions but does not give information on the topological structure of the set of $(p,q)$-periodic bouncing motions for fixed values of $(p,q)$. This is a complicated issue and some results comes from Aubry-Mather theory. However, here we will see which results can be obtained using Theorem \ref{maro_teo}. To state this result we give the following
\begin{definition}

  We say that the set of $(p,q)$-periodic complete bouncing motions is (analytically) degenerate if there exists a real analytic curve $(t(s),e(s))$ such that $(t(s+1),e(s+1))=(t(s)+1,e(s))$ for every $s\in\RR$, the function $t(s)$ is bijective for $s\in[0,1)$ and $(t_n,e_n)_{n\in\ZZ}$ is a $(p,q)$-periodic complete bouncing motion if and only if there exist $n_0,s_0$ such that $(t_{n_0},e_{n_0})=(t(s_0),e(s_0))$.
  \end{definition}

The following result is a quite direct consequence of Lemma \ref{lemma:exact}.
\begin{proposition}
If $f$ is real analytic, then there exists $\alpha>0$ such that for every $p>\alpha$ the set of $(p,1)$-periodic complete bouncing motions is either finite or degenerate. In the first case at least one $(p,1)$-periodic complete bouncing motion is unstable. In the degenerate case, all $(p,1)$-periodic complete bouncing motion are unstable.
  \end{proposition}
\begin{proof}
  By Lemma \ref{lemma:exact} the map $\tilde{\Phi}$ is exact symplectic and twist on $\RR^2_{e_*}$. Moreover, let us choose $a$ such that $e_*<\sqrt{2a}$ and $p$ such that
  \[
\frac{gp}{2}-2\norm{\dot{f}}>\sqrt{2a}.
\]
Let us start with the following estimates for the lift $\tilde{\Phi}$ that can be easily proved by induction on $n$ from \eqref{eq:unbe}:
  \begin{equation}\label{stim_t_e}
  	|\sqrt{2e_n}-\sqrt{2e}|\leq 4n\norm{\dot{f}}, \qquad \left|t_n-t-\frac{2}{g}n\sqrt{2e}\right|\leq 4n^2\frac{\norm{\dot{f}}}{g}.
  \end{equation}
  These give
  \[
\bar{t}(t,a)-t\leq \frac{2}{g}\sqrt{2a}+4\frac{\norm{\dot{f}}}{g}<p.
\]
On the other hand, Lemma \ref{lemma:exact} also gives that $\tilde{\Phi}$ twists the upper end infinitely, i.e. $\lim_{e\rightarrow +\infty}\bar{t}(t,e)-t=+\infty$ uniformly in $t$. Hence, condition \eqref{maro_cond} is satisfied in the strip $\Sigma=[a,+\infty)$ for every $p$. The conclusion comes from the application of Theorem \ref{maro_teo} and the fact that $(p,1)$-periodic complete bouncing motions corresponds to the fixed points of the map $\sigma^{-p}\circ\tilde{\Phi}$.
  \end{proof}

This result is not trivially extended to $(p,q)$-periodic motions for $q\geq 1$ since $\Phi^q$ need to be exact symplectic and twist. The twist condition is in general not preserved by composition, while the exactness is, as shown in the following result, inspired by \cite{bosc_ort}
\begin{lemma}\label{lemma_isot_exact}
For every $q>0$ there exists $e_\#\geq e_*$ such that for every $p>0$ the map $\sigma^{-p}\circ\tilde{\Phi}^q:\RR^2_{e_\#}\rightarrow\RR^2$ is exact symplectic
  \end{lemma}
\begin{proof}
  Since the map $\tilde{\Phi}$ is defined in $\RR^2_{e_*}$, the image $\tilde{\Phi}(\RR^2_{e_*})$ could not be contained in $\RR^2_{e_*}$ so that the iterate could not be defined. From \eqref{eq:unb} we have that $|\bar{v}-v|\leq 4\norm{\dot{f}}$ from which, the map $\tilde{\Psi}^q$ is well defined in $\RR^2_{v_\#}$ with $v_\#=v_* + 4 q \norm{\dot{f}}$. Hence passing to the variables $(t,e)$, the map $\tilde{\Phi}^q$ is defined in $\RR^2_{e_\#}$ with $e_\#=\frac{1}{2}v_\#^2$.

  Since $\Phi$ is exact symplectic, there exists $V:\RR^2_{e_\#}\rightarrow\RR$ such that, defining $\lambda=e dt$ we have $\tilde{\Phi}^*\lambda-\lambda=dV$. Hence, denoting $V_1=V+V\circ\tilde{\Phi}+\dots+V\circ\tilde{\Phi}^{q-1}$ it holds that $V_1\circ\sigma=V_1$ on $\RR^2_{e_\#}$  and
  \begin{align*}
    dV_1 &= dV+\tilde{\Phi}^*dV+\dots+(\tilde{\Phi}^{q-1})^*dV \\
    & = \tilde{\Phi}^*\lambda-\lambda + (\tilde{\Phi}^2)^*\lambda-\tilde{\Phi}^*\lambda             +\dots+(\tilde{\Phi}^q)^*\lambda-(\tilde{\Phi}^{q-1})^*\lambda \\
    &= (\tilde{\Phi}^q)^*\lambda-\lambda
    \end{align*}
  from which $\tilde{\Phi}$ is exact symplectic. Finally, we conclude noting that by the definition of $\sigma^{-p}$,  $(\sigma^{-p}\circ\tilde{\Phi}^q)^*\lambda = (\tilde{\Phi}^q)^*\lambda$.
\end{proof}

Concerning the twist condition the following technical result holds.
\begin{lemma}\label{twist_q}
  Let $f$ be $C^2$. For every $q\geq 1$ there exist $\epsilon_q>0$, $e^q>e_\#$, such that if $\norm{\ddf}<\epsilon_q$ then
  \[
\frac{\partial t_q}{\partial e}=\frac{2q}{g\sqrt{2e}}(1+\tilde{f}_q(t,e))
  \]
where $|\tilde{f}_q(t,e)|< 1/2$ on $\RR^2_{e^q}$.
  \end{lemma}

\begin{proof}
  To simplify the computation, let us perform the change of variables $y=\sqrt{2e}+\df(t)$ so that \eqref{eq:unbe} becomes
\begin{equation}\label{eq:unby}
  \left\{
  \begin{split}
\Pto =  & \to + \frac 2g y-\frac 2g f[\to,\Pto]
\\
\bar{y} =  & y  - 2f[\to,\Pto] + 2\df (\Pto).
\end{split}
\right.
\end{equation}
Since $\partial t_q/\partial e=(\partial t_q/\partial y) (\partial y/\partial e)$ it is enough to prove that for every $q\geq 1$ there exist $\epsilon_q>0$ and $y^q$ large, such that if $\norm{\ddf}<\epsilon_q$ then
  \begin{equation}\label{new_th}
\frac{\partial t_q}{\partial y}=\frac{2q}{g}(1+\tilde{f}_q(t,y))
\end{equation}
where $|\tilde{f}_q(t,y)|< 1/2$ on $\RR^2_{y^q}$.

Let us start with some estimates that hold for every $q\geq 1$. It comes from \eqref{eq:unby} that
\begin{equation}\label{y_q}
y_q=y+2\sum_{i=1}^{q}\df(t_i)+2\sum_{i=1}^{q}f[t_{i-1},t_{i}]
\end{equation}
so that
\[
|y_q-y|\leq 4q\norm\df.
\]
Using it,
\begin{equation}\label{t_q}
|t_q-t_{q-1}|\geq \frac{2}{g}y-\frac{2}{g}(4q+1)\norm\df,
\end{equation}
from which there exists $y^q$ large enough and $C_q$ such that
\begin{equation}\label{fqq-11}
\left|\partial_{t_q}f[t_{q-1},t_q]\right|=\left|\frac{\dot{f}(t_q)-f[t_{q-1},t_q]}{t_q-t_{q-1}}\right|\leq
\frac{g\norm{\dot{f}}}{y-(4q+2)\norm{\dot{f}}}<\frac{C_q}{y} \qquad \mbox{on } \RR^2_{y^q}
\end{equation}
and analogously
\begin{equation}\label{fqq-12}
\left|\partial_{t_{q-1}}f[t_{q-1},t_q]\right|<\frac{C_{q-1}}{y} \qquad \mbox{on } \RR^2_{y^{q-1}}
\end{equation}
  Now we can start the proof by induction on $q\geq 1$. For $q=1$ we have, differentiating the first equation in \eqref{eq:unby}
  \begin{equation}\label{t_1_y}
\frac{\partial t_1}{\partial y}\left(1+\frac{2}{g}\partial_{t_{1}}f[t,t_1]\right)=\frac{2}{g}y
\end{equation}
  from which, using \eqref{fqq-11} we get the initial step taking a suitably larger value of $y^1$.\\
For the inductive step, let us suppose \eqref{new_th} to be true for $i=1,\dots,q-1$. By implicit differentiation

\begin{equation}\label{t_q_e}
\frac{\partial t_q}{\partial y}\left(1+\frac{2}{g}\partial_{t_{q}}f[t_{q-1},t_q]\right)=\frac{2}{g}\frac{\partial y_{q-1}}{\partial y}+\frac{\partial t_{q-1}}{\partial y}\left(1-\frac{2}{g}\partial_{t_{q-1}}f[t_{q-1},t_q]\right)
\end{equation}
From \eqref{y_q} and the inductive hypothesis we have
\begin{align*}
  \frac{\partial y_{q-1}}{\partial y}&=1+2\sum_{i=1}^{q-1}\left(\ddf(t_i) \frac{\partial t_i}{\partial y}-\partial_{t_{i}}f[t_{i-1},t_{i}]\frac{\partial t_i}{\partial y} -\partial_{t_{i-1}}f[t_{i-1},t_{i}]\frac{\partial t_{i-1}}{\partial y}\right)\\
   &=1+2\sum_{i=1}^{q-1}\left(\ddf(t_i) (1+\tilde{f}_i)-\partial_{t_{i}}f[t_{i-1},t_{i}](1+\tilde{f}_i) -\partial_{t_{i-1}}f[t_{i-1},t_{i}](1+\tilde{f}_{i-1})\right).
  \end{align*}
Since by (\ref{fqq-11}-\ref{fqq-12}) for every $i$ $|\partial_{t_{i}}f[t_{i-1},t_{i}]|$ tends to zero uniformly as $y \rightarrow +\infty$ and $|\tilde{f}_i|<1/2$ for $y$ large, we can find new constants $C_{q-1}$ and $y^{q-1}$ such that on $\RR^2_{y^{q-1}}$,
\begin{equation}\label{stim_y}
\frac{\partial y_{q-1}}{\partial y} = 1 + \bar{f}_{q-1}(t,y)  \qquad \mbox{with } |\bar{f}_{q-1}|\leq C_{q-1}\norm\ddf.
\end{equation}
Using it and the inductive hypothesis in \eqref{t_q_e} we get
\begin{align}\label{final}
  \frac{\partial t_q}{\partial y}\left(1+\frac{2}{g}\partial_{t_{q}}f[t_{q-1},t_q]\right)&=\frac{2}{g}(1 + \bar{f}_{q-1}(t,y))+\frac{2(q-1)}{g}(1+\tilde{f}_{q-1}(t,y))\left(1-\frac{2}{g}\partial_{t_{q-1}}f[t_{q-1},t_q]\right)\\
  &=\frac{2q}{g}\left(1+ \tilde{f}_q(t,y)\right)
\end{align}
where,
\[
\tilde{f}_q(t,y)=\frac{1}{q}\bar{f}_{q-1}(t,y)+\frac{q-1}{q}\tilde{f}_{q-1}(t,y)+\frac{2(q-1)}{gq}\partial_{t_{q-1}}f[t_{q-1},t_q](1+\tilde{f}_{q-1}(t,y)).
\]
Now (\ref{fqq-11}-\ref{fqq-12}) and \eqref{stim_y} imply
\[
|\tilde{f}_q|<\frac{C_{q-1}}{q}\norm\ddf+\frac{q-1}{2q}+\frac{C'_{q-1}}{y}
\]
so that we can find $\epsilon_q$ and $y_q$ such that if $\norm\ddf<\epsilon_q$ then $|\tilde{f}_q|<\frac{1}{2}-\frac{1}{2q}$ on $\RR^2_{y^{q}}$. Plugging it into \eqref{final} and using again (\ref{fqq-11}-\ref{fqq-12}) we get the thesis, eventually increasing $y^q$.

\end{proof}

This is used to prove the following result
\begin{proposition}
Suppose that $f$ is real analytic. For every $q>0$ there exist $\alpha>0$ and $\epsilon_q>0$ such that if $p>\alpha$ and $\norm{\ddf}<\epsilon_q$ then the set of $(p,q)$-periodic complete bouncing motion is either finite or degenerate. In the first case at least one $(p,q)$-periodic complete bouncing motion is unstable. In the degenerate case, all $(p,q)$-periodic complete bouncing motion are unstable.
\end{proposition}

\begin{proof}
  We would like to apply Theorem \ref{maro_teo} to the map $\tilde{\Phi}^q$, noting that $(p,q)$-periodic bouncing motions correspond to fixed points of the map $\sigma^{-p}\circ\tilde{\Phi}^q$. Let us fix $q>0$. In Lemma \ref{lemma_isot_exact} we proved that $\tilde{\Phi}^q$ is exact symplectic in $\RR^2_{e_\#}$ for some $e_\#$ depending on $q$. Moreover, by Lemma \ref{twist_q}, there exist $\epsilon_q$ and $e^q>e_\#$ such that if $\norm{\ddf}<\epsilon_q$ then $\tilde{\Phi}^q$ is also twist on $\RR^2_{e^q}$. Now choose $p>0$ such that
  \[
  \frac{gp}{2q}-2q\norm{\dot{f}}>e^q.
  \]
   Hence, there exist $b>a$ such that
  \[
  e^q<\sqrt{2a}<\frac{gp}{2q}-2q\norm{\dot{f}}<\frac{gp}{2q}+2q\norm{\dot{f}}<\sqrt{2b}.
  \]
  This choice for $a,b$ gives condition \eqref{maro_cond} on the strip $\Sigma=\RR\times (a,b)$. Actually, from \eqref{stim_t_e},
  \begin{align*}
  t_q(t,b)-t & \geq\frac{2}{g}q\sqrt{2b}-4q^2\frac{\norm{\dot{f}}}{g}>p \\
  t_q(t,a)-t & \leq\frac{2}{g}q\sqrt{2a}+4q^2\frac{\norm{\dot{f}}}{g}<p.
  \end{align*}
  This concludes the proof.
  \end{proof}

redpajama_set_name: RedPajamaArXiv


Judoka Dex Elmont is European Champion 2014 U73kg and won three World Championships medals, but the gold is missing. He participated at three Olympic Games. He competed U66 and U73kg. Dex is younger brother of former world champ Guillaume Elmont. Father was judoka for Suriname. Club: Kenamju. Dex Elmont (NED) was number 1 of the IJF World Ranking for seniors U73kg in 2014 and 2015.


text:
Q: How can I correct my war application (Tomcat 8)? I made a Web Java Application, on JDK 1.8, with the next libraries:
 - Hibernate 4.3.x
 - bootstrap 1.0.10
 - commons codec 1.10
 - commons logging 1.2
 - poi 3.12-20150511
 - poi ooxml 3.12-20150511
 - poi ooxml-schemas 3.12-20150511
 - xmlbeans 2.6.0
 - gson 2.3.1
 - bson4jackson 2.7.0
 - jackson annotations 2.7.3
 - jackson core 2.7.3
 - jackson databind 2.7.3
 - jongo 1.3.0
 - mongo java driver 3.2.2
 - postgresql 9.4.1208jre6
 - primefaces 6.0
 - commons fileupload 1.3.1
 - commons io 2.4

I developed my application on Netbeans 8.0 and finally I generated a war file. After I downloaded and installed Tomcat 8 in my computer (with Windows 8.1 to 64 bits) to 32 bits, and when I mount my war file on Tomcat, and I accessed to http://localhost:8080/MyApplication the page respond with HTTP STATUS 404 message.
As I don't know what is the file with the specific exception, I show all the files of the log folder:
catalina.2017-03-20.log
20-Mar-2017 19:31:57.589 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Server version:        Apache Tomcat/8.5.12
20-Mar-2017 19:31:57.616 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Server built:          Mar 8 2017 17:41:47 UTC
20-Mar-2017 19:31:57.637 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Server number:         8.5.12.0
20-Mar-2017 19:31:57.660 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log OS Name:               Windows 8.1
20-Mar-2017 19:31:57.661 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log OS Version:            6.3
20-Mar-2017 19:31:57.662 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Architecture:          x86
20-Mar-2017 19:31:57.662 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Java Home:             C:\Program Files (x86)\Java\jre1.8.0_101
20-Mar-2017 19:31:57.663 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log JVM Version:           1.8.0_101-b13
20-Mar-2017 19:31:57.663 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log JVM Vendor:            Oracle Corporation
20-Mar-2017 19:31:57.663 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log CATALINA_BASE:         C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.664 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log CATALINA_HOME:         C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.665 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dcatalina.home=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.665 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dcatalina.base=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.666 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.io.tmpdir=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\temp
20-Mar-2017 19:31:57.666 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.util.logging.manager=org.apache.juli.ClassLoaderLogManager
20-Mar-2017 19:31:57.666 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.util.logging.config.file=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\conf\logging.properties
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: exit
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Xms128m
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Xmx256m
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.core.AprLifecycleListener.lifecycleEvent La biblioteca nativa de Apache Tomcat basada en ARP que permite un rendimiento óptimo en entornos de desarrollo no ha sido hallada en java.library.path: C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\bin;C:\WINDOWS\Sun\Java\bin;C:\WINDOWS\system32;C:\WINDOWS;C:\ProgramData\Oracle\Java\javapath;C:\Program Files (x86)\Intel\TXE Components\TCS\;C:\Program Files\Intel\TXE Components\TCS\;C:\WINDOWS\system32;C:\WINDOWS;C:\WINDOWS\System32\Wbem;C:\WINDOWS\System32\WindowsPowerShell\v1.0\;C:\Program Files\nodejs\;C:\Program Files\MongoDB\Server\3.2\bin;C:\Program Files\PostgreSQL\9.3\bin;C:\tas-8.3-1\multiserver\enhydra\bin; C:\Program Files\PostgreSQL\9.3\bin;C:\Python27;C:\Python27\Scripts;C:\Program Files (x86)\Skype\Phone\;;.
20-Mar-2017 19:31:58.005 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.init Initializing ProtocolHandler ["http-nio-8081"]
20-Mar-2017 19:31:58.593 INFORMACIÓN [main] org.apache.tomcat.util.net.NioSelectorPool.getSharedSelector Using a shared selector for servlet write/read
20-Mar-2017 19:31:58.599 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.init Initializing ProtocolHandler ["ajp-nio-8009"]
20-Mar-2017 19:31:58.605 INFORMACIÓN [main] org.apache.tomcat.util.net.NioSelectorPool.getSharedSelector Using a shared selector for servlet write/read
20-Mar-2017 19:31:58.606 INFORMACIÓN [main] org.apache.catalina.startup.Catalina.load Initialization processed in 2024 ms
20-Mar-2017 19:31:58.680 INFORMACIÓN [main] org.apache.catalina.core.StandardService.startInternal Arrancando servicio Catalina
20-Mar-2017 19:31:58.680 INFORMACIÓN [main] org.apache.catalina.core.StandardEngine.startInternal Starting Servlet Engine: Apache Tomcat/8.5.12
20-Mar-2017 19:31:58.761 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployWAR Despliegue del archivo C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\MyApplication.war de la aplicación web
20-Mar-2017 19:32:15.612 GRAVE [localhost-startStop-1] org.apache.catalina.core.ContainerBase.addChildInternal ContainerBase.addChild: start:
 org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/MyApplication]]
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:167)
    at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:752)
    at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:728)
    at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:734)
    at org.apache.catalina.startup.HostConfig.deployWAR(HostConfig.java:952)
    at org.apache.catalina.startup.HostConfig$DeployWar.run(HostConfig.java:1823)
    at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)
Caused by: java.lang.IllegalArgumentException: El mapeo de filtro especifica un nombre desconocido de filtro PrimeFaces FileUpload Filter
    at org.apache.catalina.core.StandardContext.validateFilterMap(StandardContext.java:2987)
    at org.apache.catalina.core.StandardContext.addFilterMap(StandardContext.java:2950)
    at org.apache.catalina.startup.ContextConfig.configureContext(ContextConfig.java:1275)
    at org.apache.catalina.startup.ContextConfig.webConfig(ContextConfig.java:1190)
    at org.apache.catalina.startup.ContextConfig.configureStart(ContextConfig.java:775)
    at org.apache.catalina.startup.ContextConfig.lifecycleEvent(ContextConfig.java:299)
    at org.apache.catalina.util.LifecycleBase.fireLifecycleEvent(LifecycleBase.java:94)
    at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5114)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
    ... 10 more

20-Mar-2017 19:32:15.615 GRAVE [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployWAR Error durante el despliegue del archivo C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\MyApplication.war de la aplicación web
 java.lang.IllegalStateException: ContainerBase.addChild: start: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/MyApplication]]
    at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:756)
    at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:728)
    at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:734)
    at org.apache.catalina.startup.HostConfig.deployWAR(HostConfig.java:952)
    at org.apache.catalina.startup.HostConfig$DeployWar.run(HostConfig.java:1823)
    at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)

20-Mar-2017 19:32:15.621 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployWAR Deployment of web application archive C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\MyApplication.war has finished in 16.856 ms
20-Mar-2017 19:32:15.625 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\docs de la aplicación web
20-Mar-2017 19:32:15.899 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\docs has finished in 274 ms
20-Mar-2017 19:32:15.900 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\examples de la aplicación web
20-Mar-2017 19:32:16.762 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\examples has finished in 862 ms
20-Mar-2017 19:32:16.762 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\host-manager de la aplicación web
20-Mar-2017 19:32:16.833 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\host-manager has finished in 71 ms
20-Mar-2017 19:32:16.834 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\manager de la aplicación web
20-Mar-2017 19:32:16.954 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\manager has finished in 120 ms
20-Mar-2017 19:32:16.955 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\ROOT de la aplicación web
20-Mar-2017 19:32:16.999 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\ROOT has finished in 44 ms
20-Mar-2017 19:32:17.008 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.start Starting ProtocolHandler [http-nio-8081]
20-Mar-2017 19:32:17.047 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.start Starting ProtocolHandler [ajp-nio-8009]
20-Mar-2017 19:32:17.054 INFORMACIÓN [main] org.apache.catalina.startup.Catalina.start Server startup in 18447 ms

commons-daemon.2017-03-20.log
[2017-03-20 19:31:55] [info]  [ 1908] Commons Daemon procrun (1.0.15.0 32-bit) started
[2017-03-20 19:31:55] [info]  [ 1908] Running 'Tomcat8' Service...
[2017-03-20 19:31:55] [info]  [ 4584] Starting service...
[2017-03-20 19:31:57] [info]  [ 4584] Service started in 1292 ms.

host-manager.2017-03-20.log
[is empty]

localhost.2017-03-20.log
20-Mar-2017 19:32:16.740 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.core.ApplicationContext.log ContextListener: contextInitialized()
20-Mar-2017 19:32:16.741 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.core.ApplicationContext.log SessionListener: contextInitialized()

localhost_access_log.2017-03-20.txt
0:0:0:0:0:0:0:1 - - [20/Mar/2017:19:32:27 -0500] "GET /MyApplication/ HTTP/1.1" 404 994
0:0:0:0:0:0:0:1 - - [20/Mar/2017:19:32:29 -0500] "GET /MyApplication/ HTTP/1.1" 404 994
0:0:0:0:0:0:0:1 - - [20/Mar/2017:19:32:29 -0500] "GET /favicon.ico HTTP/1.1" 200 21630
0:0:0:0:0:0:0:1 - - [20/Mar/2017:19:32:30 -0500] "GET /MyApplication/ HTTP/1.1" 404 994
0:0:0:0:0:0:0:1 - - [20/Mar/2017:19:32:30 -0500] "GET /favicon.ico HTTP/1.1" 200 21630

manager.2017-03-20.log
[Is empty]

tomcat8-stderr.2017-03-20.log
2017-03-20 19:31:55 Commons Daemon procrun stderr initialized
20-Mar-2017 19:31:57.589 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Server version:        Apache Tomcat/8.5.12
20-Mar-2017 19:31:57.616 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Server built:          Mar 8 2017 17:41:47 UTC
20-Mar-2017 19:31:57.637 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Server number:         8.5.12.0
20-Mar-2017 19:31:57.660 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log OS Name:               Windows 8.1
20-Mar-2017 19:31:57.661 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log OS Version:            6.3
20-Mar-2017 19:31:57.662 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Architecture:          x86
20-Mar-2017 19:31:57.662 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Java Home:             C:\Program Files (x86)\Java\jre1.8.0_101
20-Mar-2017 19:31:57.663 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log JVM Version:           1.8.0_101-b13
20-Mar-2017 19:31:57.663 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log JVM Vendor:            Oracle Corporation
20-Mar-2017 19:31:57.663 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log CATALINA_BASE:         C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.664 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log CATALINA_HOME:         C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.665 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dcatalina.home=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.665 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Dcatalina.base=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5
20-Mar-2017 19:31:57.666 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.io.tmpdir=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\temp
20-Mar-2017 19:31:57.666 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.util.logging.manager=org.apache.juli.ClassLoaderLogManager
20-Mar-2017 19:31:57.666 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Djava.util.logging.config.file=C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\conf\logging.properties
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: exit
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Xms128m
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.startup.VersionLoggerListener.log Command line argument: -Xmx256m
20-Mar-2017 19:31:57.667 INFORMACIÓN [main] org.apache.catalina.core.AprLifecycleListener.lifecycleEvent La biblioteca nativa de Apache Tomcat basada en ARP que permite un rendimiento óptimo en entornos de desarrollo no ha sido hallada en java.library.path: C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\bin;C:\WINDOWS\Sun\Java\bin;C:\WINDOWS\system32;C:\WINDOWS;C:\ProgramData\Oracle\Java\javapath;C:\Program Files (x86)\Intel\TXE Components\TCS\;C:\Program Files\Intel\TXE Components\TCS\;C:\WINDOWS\system32;C:\WINDOWS;C:\WINDOWS\System32\Wbem;C:\WINDOWS\System32\WindowsPowerShell\v1.0\;C:\Program Files\nodejs\;C:\Program Files\MongoDB\Server\3.2\bin;C:\Program Files\PostgreSQL\9.3\bin;C:\tas-8.3-1\multiserver\enhydra\bin; C:\Program Files\PostgreSQL\9.3\bin;C:\Python27;C:\Python27\Scripts;C:\Program Files (x86)\Skype\Phone\;;.
20-Mar-2017 19:31:58.005 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.init Initializing ProtocolHandler ["http-nio-8081"]
20-Mar-2017 19:31:58.593 INFORMACIÓN [main] org.apache.tomcat.util.net.NioSelectorPool.getSharedSelector Using a shared selector for servlet write/read
20-Mar-2017 19:31:58.599 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.init Initializing ProtocolHandler ["ajp-nio-8009"]
20-Mar-2017 19:31:58.605 INFORMACIÓN [main] org.apache.tomcat.util.net.NioSelectorPool.getSharedSelector Using a shared selector for servlet write/read
20-Mar-2017 19:31:58.606 INFORMACIÓN [main] org.apache.catalina.startup.Catalina.load Initialization processed in 2024 ms
20-Mar-2017 19:31:58.680 INFORMACIÓN [main] org.apache.catalina.core.StandardService.startInternal Arrancando servicio Catalina
20-Mar-2017 19:31:58.680 INFORMACIÓN [main] org.apache.catalina.core.StandardEngine.startInternal Starting Servlet Engine: Apache Tomcat/8.5.12
20-Mar-2017 19:31:58.761 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployWAR Despliegue del archivo C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\MyApplication.war de la aplicación web
20-Mar-2017 19:32:15.612 GRAVE [localhost-startStop-1] org.apache.catalina.core.ContainerBase.addChildInternal ContainerBase.addChild: start:
 org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/MyApplication]]
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:167)
    at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:752)
    at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:728)
    at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:734)
    at org.apache.catalina.startup.HostConfig.deployWAR(HostConfig.java:952)
    at org.apache.catalina.startup.HostConfig$DeployWar.run(HostConfig.java:1823)
    at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)
Caused by: java.lang.IllegalArgumentException: El mapeo de filtro especifica un nombre desconocido de filtro PrimeFaces FileUpload Filter
    at org.apache.catalina.core.StandardContext.validateFilterMap(StandardContext.java:2987)
    at org.apache.catalina.core.StandardContext.addFilterMap(StandardContext.java:2950)
    at org.apache.catalina.startup.ContextConfig.configureContext(ContextConfig.java:1275)
    at org.apache.catalina.startup.ContextConfig.webConfig(ContextConfig.java:1190)
    at org.apache.catalina.startup.ContextConfig.configureStart(ContextConfig.java:775)
    at org.apache.catalina.startup.ContextConfig.lifecycleEvent(ContextConfig.java:299)
    at org.apache.catalina.util.LifecycleBase.fireLifecycleEvent(LifecycleBase.java:94)
    at org.apache.catalina.core.StandardContext.startInternal(StandardContext.java:5114)
    at org.apache.catalina.util.LifecycleBase.start(LifecycleBase.java:150)
    ... 10 more

20-Mar-2017 19:32:15.615 GRAVE [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployWAR Error durante el despliegue del archivo C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\MyApplication.war de la aplicación web
 java.lang.IllegalStateException: ContainerBase.addChild: start: org.apache.catalina.LifecycleException: Failed to start component [StandardEngine[Catalina].StandardHost[localhost].StandardContext[/MyApplication]]
    at org.apache.catalina.core.ContainerBase.addChildInternal(ContainerBase.java:756)
    at org.apache.catalina.core.ContainerBase.addChild(ContainerBase.java:728)
    at org.apache.catalina.core.StandardHost.addChild(StandardHost.java:734)
    at org.apache.catalina.startup.HostConfig.deployWAR(HostConfig.java:952)
    at org.apache.catalina.startup.HostConfig$DeployWar.run(HostConfig.java:1823)
    at java.util.concurrent.Executors$RunnableAdapter.call(Unknown Source)
    at java.util.concurrent.FutureTask.run(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor.runWorker(Unknown Source)
    at java.util.concurrent.ThreadPoolExecutor$Worker.run(Unknown Source)
    at java.lang.Thread.run(Unknown Source)

20-Mar-2017 19:32:15.621 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployWAR Deployment of web application archive C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\MyApplication.war has finished in 16.856 ms
20-Mar-2017 19:32:15.625 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\docs de la aplicación web
20-Mar-2017 19:32:15.899 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\docs has finished in 274 ms
20-Mar-2017 19:32:15.900 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\examples de la aplicación web
20-Mar-2017 19:32:16.762 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\examples has finished in 862 ms
20-Mar-2017 19:32:16.762 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\host-manager de la aplicación web
20-Mar-2017 19:32:16.833 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\host-manager has finished in 71 ms
20-Mar-2017 19:32:16.834 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\manager de la aplicación web
20-Mar-2017 19:32:16.954 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\manager has finished in 120 ms
20-Mar-2017 19:32:16.955 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Despliegue del directorio C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\ROOT de la aplicación web
20-Mar-2017 19:32:16.999 INFORMACIÓN [localhost-startStop-1] org.apache.catalina.startup.HostConfig.deployDirectory Deployment of web application directory C:\Program Files (x86)\Apache Software Foundation\Tomcat 8.5\webapps\ROOT has finished in 44 ms
20-Mar-2017 19:32:17.008 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.start Starting ProtocolHandler [http-nio-8081]
20-Mar-2017 19:32:17.047 INFORMACIÓN [main] org.apache.coyote.AbstractProtocol.start Starting ProtocolHandler [ajp-nio-8009]
20-Mar-2017 19:32:17.054 INFORMACIÓN [main] org.apache.catalina.startup.Catalina.start Server startup in 18447 ms

tomcat8-stdout.2017-03-20.log
2017-03-20 19:31:55 Commons Daemon procrun stdout initialized

And the web.xml of my application is:
<?xml version="1.0" encoding="UTF-8"?>
<web-app version="3.1" xmlns="http://xmlns.jcp.org/xml/ns/javaee" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://xmlns.jcp.org/xml/ns/javaee http://xmlns.jcp.org/xml/ns/javaee/web-app_3_1.xsd">
    <context-param>
        <param-name>primefaces.THEME</param-name>
        <param-value>bootstrap</param-value>
    </context-param>
    <context-param>
        <param-name>javax.faces.PROJECT_STAGE</param-name>
        <param-value>Development</param-value>
    </context-param>
    <context-param>
        <param-name>facelets.LIBRARIES</param-name>
        <param-value>/WEB-INF/tsp.taglib.xml</param-value>
    </context-param>

    <context-param>
        <param-name>primefaces.FONT_AWESOME</param-name>
        <param-value>true</param-value>
    </context-param>

    <context-param>
        <param-name>javax.faces.DATETIMECONVERTER_DEFAULT_TIMEZONE_IS_SYSTEM_TIMEZONE</param-name>
        <param-value>true</param-value>
    </context-param>

    <mime-mapping>
        <extension>ttf</extension>
        <mime-type>application/x-font-ttf</mime-type>
    </mime-mapping>
    <mime-mapping>
        <extension>woff</extension>
        <mime-type>application/x-font-woff</mime-type>
    </mime-mapping>
    <mime-mapping>
        <extension>woff2</extension>
        <mime-type>application/x-font-woff2</mime-type>
    </mime-mapping>
    <mime-mapping>
        <extension>eot</extension>
        <mime-type>application/x-font-eot</mime-type>
    </mime-mapping>
    <filter-mapping>
        <filter-name>PrimeFaces FileUpload Filter</filter-name>
        <servlet-name>Faces Servlet</servlet-name>
    </filter-mapping>
    <servlet>
        <servlet-name>Faces Servlet</servlet-name>
        <servlet-class>javax.faces.webapp.FacesServlet</servlet-class>
        <load-on-startup>1</load-on-startup>
    </servlet>
    <servlet-mapping>
        <servlet-name>Faces Servlet</servlet-name>
        <url-pattern>/faces/*</url-pattern>
    </servlet-mapping>
    <session-config>
        <session-timeout>
            -1
        </session-timeout>
    </session-config>
    <welcome-file-list>
        <welcome-file>faces/index.xhtml</welcome-file>
    </welcome-file-list>
</web-app>

Could you help me to understand and solve the error?
Thank you very much!!