A public hearing is set for the fourth Thursday of every month before the Zoning Board of Adjustments at which time notices of the public hearing are sent to all property owners within 200' radius of the proposed lot. The city staff will make their recommendation to the Zoning Board. The decision of the Board is final, but any person or persons aggrieved by any decision of the Board may present to a court of record, a petition if due cause is shown.


text:
Arsenal fans in for a treat with new 'pioneering' tech
Premier League club is using artificial intelligence (AI) to give its fans and supporters a more personalised experience
12:19pm 24th Oct 2018
Arsenal FC unveils first official club chatbot
Premier League club Arsenal FC is dipping its toes in the world of artificial intelligence with the launch of its first official club bot.
The technology was developed by AI chat application platform GameOn and will provide fans with personalised and "unique access" to the club, all delivered through the personality of 'Robot Pires', named after Gunners legend Robert Pires.
Available through social media messaging platforms including Facebook Messenger, Slack, Skype, Kik, and Telegram, the Arsenal bot will respond to fans' natural language requests for specific news, scores, stats, videos and more about the team and the games they follow.
"We're constantly looking at ways to bring fans content that makes their match day experience even more entertaining," said Tom Hines, senior content manager for Arsenal.
"Working with GameOn to craft the bot is the next step in us developing a hub for fans that houses the answers to all of their questions – that feels intuitively part of the Arsenal voice and experience.
"Fans feel a personal connection to Arsenal, and AI is more important than ever for us to give fans a personalised experience."
Arsenal is the latest to join the GameOn community, following the success of the Sky Sports' Jeff Bot and Sports Illustrated's Olympics and NFL bots.
GameOn says chatbots are experiencing a surge in pick-up with fans eager to know the latest from their favourite teams.
Arsenal fans will be able to access the latest club news, fixtures, results, videos, player stats and more. Casual supporters can stay informed with match updates and trending news deliveries, while super fans can dig deeper with minute-to-minute match commentary, match previews and post-match reports, all delivered in real-time.
Alex Beckman, founder and CEO of GameOn, said: "As the way fans engage with teams evolves, there are more exciting and dynamic ways we can craft chatbots.
"Football clubs like Arsenal face a tough challenge in that a lot of funding usually goes into the teams – as it should – however that often doesn't leave big budgets for content.
"Chatbots are a great way for clubs to evolve their platforms for speaking to fans, and we're excited to work with Arsenal to help bring shape to the category."
Everton Facebook Live stream reaches 1.5m
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Liga and Serie A matches to air for free in UK
23rd, Nov
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Metapraxis partnership launches scrum analytics first
The financial analytics firm has partnered with Sportable Technologies to…

redpajama_set_name: RedPajamaCommonCrawl


text:
by Michael Butterfield | Aug 9, 2018 | 0 comments
Smartphone App Judged More Reliable Than Eye Witness in Distracted Driving Case.
In a July 16, 2018 court decision, Regina v. Patrick F. Tannhauser, a local Victoria man was able to prove his innocence, beating a distracted driving charge. He was successful, despite eyewitness testimonies of police officers, by using an application on his smartphone. While Mr. Tannhauser was seen holding his phone while driving, in a position that it could be used, he was able to prove that he could not have used his cell phone because software on his phone prohibited its' use while driving.
Had he been found guilty, the fine for a single distracted driving violation ticket would have been $368, and 4 penalty points that will be applied a driver's record, according to the Motor Vehicle Act. On a first infraction, these points would also result in a driver paying a further $175 ICBC Driver Penalty Point premium, for a total of $543 for a first infraction.
Mr. Tannhauser worked for Orkin, a pest control service, and driving was a necessity of his job.
On August 17th, 2017, Cst. Buerfeind and his colleagues were conducting a cell phone and seat belt compliance campaign. The routine was performed in View Royal, at a time when cars would be moving slowly, known as the "Colwood Crawl". Cst. Buerfiend testified that he saw Mr. Tannhauser holding and handling his phone, though he could not see if the screen of the device was lit.
The law states that it is illegal to use an electronic device while driving a vehicle. Use is defined as "holding the device in a position in which it may be used". Mr. Tannhauser, however, argued that because software on his phone prevents its use while driving, he could not have used his phone.
Despite police officers seeing him holding his phone, Justice H.W.Gordon decided that Mr. Tannhauser was innocent of the charge. This was due to the fact that Mr. Tannhauser had reason to believe his phone could not be used, and his story did not directly conflict with eyewitness testimony. His employer issued cell phone had an app disabling its' use during driving.
Victoria Lawyer, Michael Butterfield, stated that "while this is an important case, each case is judged on its own merits".
ICBC is currently operating a pilot project, which could help reduce distracted driving owing to cell phone use. The technology involves a vehicle being fitted with a small device that activates an app installed on the driver's cellphone. The technology disables the phone when the car is being driven. There are several settings on cell phones and cell phone apps that can be used to prevent distracted driving.
Justice H.W. Gordon noted in his decision "that suggests to me that ICBC is alive to the fact that if the potential for distraction is removed, so the device is not in a position in which it may be used, then it will not offended the section".
This case sets an interesting precedent, not only because a man used an app on his smartphone to prove innocence, but because he did so against an officer's eyewitness testimony. This brings about the question of, how far does this go now that the precedent is set? How far can the existence of a smartphone app go to prove your innocence?
Piers Young


Red Sox v. Detroit Tigers at 7:10 p.m.
by BHS Band and Color Guard.
Order your Merchandise HERE! Shirts and Sweatshirts!
Thank you for supporting the Bellingham High School Band and Color Guard for our performance at Fenway Park on Thursday, April 25, 2019. Please complete the order form below to request tickets.
National Anthem performance and Star Wars music before game time by the Bellingham High School Music Program. It's Star Wars Night at Fenway! This will include Grades 9 – 12 Band and Color Guard members.
Check or Money Order payable to Bellingham Friends of Music. Payment must be mailed or dropped off at BHS, instructions will appear when you submit this form on the confirmation page. Payments must be received by Tuesday, March 12, 2019.
SEATING REQUESTS: If you/your family would like to sit with other families/individuals, please combine your ticket order into one to guarantee that you will sit together. Please coordinate this ahead of time BEFORE placing your order to make sure all ticket quantities are correct. There is a space below for seating requests, but we cannot guarantee that all requests will be fulfilled. The best way to sit with others is to submit one combined ticket order.
TICKETS FOR PERFORMING BAND & GUARD STUDENTS: Do NOT purchase tickets for performing music/guard students right now. Ticket and shirt orders for performing music students will be completed using a paper form with permission slip.
Tickets will be EMAILED to each family, you will be able to print as PDF or use the MLB ticket app on your smart device for admission. The ticket prices below include a $10.00 donation to the Bellingham Friends of Music to help offset the cost of our music trip to Boston.
In case the game is postponed due to weather, the tickets will be valid for the rescheduled date. There are no refunds or exchanges.
Thank you for supporting the Bellingham Music Program!
Congratulations to the Bellingham 8th Grade Band, Concert Band and Color Guard on their performance at Fenway Park on Monday, May 9, 2016!


It just doesn't stop this summer!
First, Consumer Reports says that mineral sunscreens just aren't effective after testing 13 of them. I totally disagree with them and elucidate my points rather, ahem, pointedly, right HERE.
Now, a reader sent me this article about the dangers of the sunscreen ingredient avobenzone reacting with chlorine in swimming pools to form toxic compounds! The media has been reporting on research published by Cheng Wang in the journal Chemosphere, and I appreciated the more scholarly breakdown of the research here.
Avobenzone, the most popular UV filter in the world (meaning it's used the most in conventional sunscreens to block UVA light, and in FACT it's the only chemical ingredients that DOES block UVA light!), breaks down into hazardous chemical compounds in water, accelerated by the presence of sunlight.
Opposite of the Actual Research?
So that acidic environment is actually the opposite of a chlorinated pool. What is up with the Daily Mail and Phys.org reporting incorrectly?
Let's explore the research further.
Does Sunlight and Chlorine Degrade Avobenzone in Sunscreens?
It sounds like under UV light, avobenzone's half life is 126 minutes. I'm assuming that at least half the avobenzone has broken down into the other 2 substances at that point, chloro-avobenzone and dichloro-avobenzone. Those are quite unstable under sunlight and especially sunlight and water combined, with half lives of as little as 14 minutes.
Some of what this all turns into include benzoic acids and phenols, which are "quite toxic," according to Albert Lebedev, one of the study's authors – especially when they're chlorinated.
This image from the study shows avobenzone being exposed to NaOCl (sodium hypochlorite) and water, and breaking down into chloro-avobenzone and dichloro-avobenzone – see the extra Cl and 2 extra Cl atoms there in the bottom two figures?
What's also interesting is that sodium hypochlorite isn't the most popular way of chlorinating a pool – calcium hypochlorite is.
So perhaps the reporting wasn't quite as much to call home about (and toss your sunscreens) as it sounded at first.
But – don't stop now. There are still PLENTY of reasons to ditch avobenzone in sunscreens and personal products forever!
Avobenzone, which was FDA approved in 1988 as a UVA filter, used to only be available under a trademarked name Parsol 1789. That meant it was more expensive to use in sunscreens and not seen all that often.
In the last few years, it's able to be used in a generic form as avobenzone, and that coupled with the fact that it's the only non-mineral ingredient approved to filter UVA rays, means that it's in just about every conventional sunscreen you can find.
If it's not, you're not getting broad spectrum UVA/UVB protection anyway, so that's no good.
But if avobenzone is so effective at filtering UVA rays, why ditch it?
It does break down in the sun (drastically, see above) faster in water, and faster yet in chlorinated water (Kalister, 2016).
As avobenzone degrades, which may be in less than two hours, it is no longer effective (or at least far less effective) at protecting you from UVA rays. You'll never know it though, because UVAs don't cause burns. They'll just get you decades later with wrinkled skin and cancer.
Even if avobenzone and all the compounds it degrades into aren't absorbed through the skin (do you want your kids to be the guinea pigs??), I'm almost certain my kids drink gallons of pool water each summer (ew) and most certainly ingest whatever is washing off everyone else in the pool (grrrrrr).
Next time I'm passing out all our sunscreens from our massive natural sun protection review, none of which ever include avobenzone and all are broad spectrum protection.
By the way, if you don't think sunscreens and their active ingredients including avobenzone are getting into the pool water (and hence our general water supply), they are.
All the recommended preservatives for avobenzone are toxic or hormone disruptors or both.
Avobenzone causes awful stains on clothing – even after you swim, if you change into clothes and it rubs off, you'll get nasty rust-looking stains that only show up AFTER the clothing is exposed to water, usually in the wash. If you've ever experienced a load of laundry from your beach trip that was mysteriously ruined, your sunscreen may be at fault.
Even if you're not concerned about health or don't buy into the research as conclusive enough for you, perhaps practicality will win out. Who wants to wreck their clothes, spend a ton of time treating stains (that are really hard to get out) or have to shower before dressing every single time you wear sunscreen?
You'll find avobenzone in an alarming number of products, like lipsticks, creams and other makeup.


Tele2 and Com Hem merger completed November 5, 2018 07.58 Europe/London By Robert Briel The Swedish Companies Registration Office has registered the merger between Tele2 AB and Com Hem Holding AB. The merger between Tele2 and Com Hem Holding is thereby completed and Com Hem Holding has been dissolved. The merged entity will maintain the company name Tele2 AB and will continue to have its registered office in Stockholm, Sweden. Anders Nilsson is appointed President and CEO of Tele2 effective as of today, November 5, 2018. The previously announced members of the new Leadership Team of Tele2 also assume their roles today.


text:
Q: Why does the alert-box keep firing in the following code? I have the following HTML code:

function presence_check(elem) {
  if ($(elem).val() === "") {
    alert("Please enter something");
    $(elem).focus();
  }
}

<input type="text" placeholder="Don't leave this textbox blank" onblur="presence_check(this)">
<input type="text" placeholder="Secon input box">

The code is supposed to alert the user and re-focus on the element if the textbox is empty, but instead, it continuously fires the onblur event. I have seen some answers saying that when the alert-box pops up, it removes the focus on the element, consequently firing the onblur event. However, I don't understand how that is possible since the alert() function is called after the element has already lost focus

A: The issue is because on blur the alert() is shown. You then put the focus back in to the element ready for the blur to fire again when the use clicks a button in the dialog, hence an infinite loop. You can see this happening in the console output in this fiddle
This is a prime example of why you should never use alert() in any system - even for debugging purposes. Use an actual HTML element to display the warning to the user, and console.log() or console.dir() for debugging. Here's an example of how to do this:

$('input.validate').on('blur input', function() {
  var $message = $(this).next('.validation-message');
  if (this.value.trim() === "") {
    $message.show();
    this.focus();
  } else {
    $message.hide();
  }
});
.validation-message {
  display: none;
  color: #C00;
}

  <input type="text" placeholder="Don't leave this textbox blank" class="validate" />
  Please enter something

  <input type="text" placeholder="Second input box" />

I would also strongly suggest you don't force the focus back in to the field when it's invalid as it prevents the user from doing anything else in your page, which is terrible UX.
When you do that the JS can be simplified to just this:
$('input.validate').on('blur input', function() {
  $(this).next('.validation-message').toggle(this.value.trim() === '');
});

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text:
\section{INTRODUCTION}
\label{intro}

From time immemorial, the movements of stars have attracted the interest of the first astronomers. Several decades have been past, since astronomers have turned their interest to the kinematics of stars in galaxies and in galaxy clusters in general. Undoubtedly, galaxies are the basic units of the Universe. An interesting task is to determine the amount of matter in galaxies and, consequently, the amount of matter of the Universe. In particular, there are two key events that are closely associated with this interesting endeavour. The first is the pioneer research of J. Oort who studied the motion of stars in the neighborhood of the Sun and realized that in fact the stars were pulled by forces stronger than those that would be caused only by the visible matter \citep{O24}. On the other hand, the astronomer F. Zwicky discovered that the fast motion of galaxies in clusters cannot be justified only by the visible mass \citep{Z33}. In other words, clusters of galaxies should be scrapped unless the their mass was much greater. The existence of dark matter is the most acceptable scenario to resolve these concerns. Things were clarified when \citet{RF70} presented observational evidence supporting the existence of dark matter in galaxies.

Knowing the rate ratio between luminous and dark matter in galaxies (disk or ellipticals), as well as the relations connecting the fundamental quantities which characterize both components is of great importance, since it allow us to understand how galaxies born and evolve and also how dark matter influences these procedures. Today, it is widely accepted that dark matter is the dominant element in galaxies, taking into account that the vast majority of the total matter of the Universe, 80\% according to today measurements, is indeed dark. Dark matter seems to interacts through gravity. Moreover, apart form gravitational, no other type of dark matter interactions has been observed. This strongly indicates that dark matter interactions should be very weak, probably much more weaker than the particle physics weak interactions. The basic proposed candidates corresponding to dark matter are: (i) neutrinos (Hot Dark Matter), (ii) Warm Dark Matter (WDM), (iii) Cold Dark Matter (CDM) and finally (iv) weak interactive massive particles (WIMPS).

A strong indication for the presence of dark matter in galaxies is derived from their flattened rotation curves at large radii. Using Kepler's third law we have $\Theta(R) = \sqrt{GM(R)/R}$, where $\Theta$ is the rotational velocity at a radius $R$, $G$ is the gravitational constant, while $M(R)$ is the total mass within radius $R$. Conducting observations at large galactocentric distances, where no luminous galactic component was present astronomers found, instead of declining at the expected rate $\Theta(R) \propto R^{-1/2}$, which is true if only $M = const.$, the velocity curves $\Theta(R)$ appear to be flattened. However, $\Theta(R) = const.$, implies that $M(R) \propto R$. This strongly suggests that the mass of galaxies continues to grow, even when there is no luminous component to account for this increase. Moreover, the profiles of the velocity curves indicate that the distribution of light does not match the distribution of mass. In other words, in each galaxy the mass to light ratio $M/L$ increases with the radius $R$. The circular velocity needed for the construction of the rotation curve is obtained, as usually, by measuring the 21 cm emission line from neutral hydrogen HI \citep{RFT80,B81,C85,PS95,HS97}.

The existence of dark matter in elliptical galaxies has been confirmed using observational data derived either from hot gas or their X-ray emission \citep[e.g.,][]{LW99,HBG06,JCOR09,DGCZ10} or even using strong lensing methods \citep[e.g.,][]{RK05,GTR07,KBT09,FAT11}. On the other hand, for the disk galaxies there is a plethora of scenarios describing the formation and the evolution of disk galaxies in correlation with dark matter \citep[e.g.,][]{DSS97,FAH97,AFH98,vdB98,AF00}. A large number of measurements of luminous and dark matter have become available over the last years \citep[e.g.,][]{C06,Cap12,WCT12}. Using these data in combination with dynamically modeling we can reconstruct and therefore study the orbital structure of galaxies.

Today we know that galaxies, contain large amounts of dark matter and, therefore, a further study could provide important information about this invisible matter. A simple way to do this, is to construct models of galaxies containing dark matter. The study of the dynamical properties of these models will provide interesting and useful information, which combined with data from observation will aid significantly in finding a solution for the problem of dark matter. The reader can find interesting information in the field of fitting mass models to the kinematics of disk and elliptical galaxies in a series of papers \citep[see, e.g.][]{BSK04,C07,dB08,GT09}. Another important point, that needs to be emphasized, is the difference between the distribution of dark matter in galaxies and clusters. Observational data \citep[e.g.,][]{S04} suggest that dark matter increases as we move away from the centre to the outer parts of the galaxies. On the contrary in galaxy clusters the dark matter distribution decreases with increasing distance from the galactic centre.

Even today, dark matter is still an open and controversial issue in Astronomy. This is true, because the standard model of cosmology (SMoC) seems to be incompatible with a large amount of data derived from extragalactic observations and modified gravity theories. The reader can find more interesting and detailed information regarding this issue in \citet{K12}.

Taking into account all the above, there is no doubt, that dark matter plays an important role in the dynamical behavior of galaxies. On this basis, it seems of particular interest to build an analytical dynamical model describing the motion of stars both in disk and elliptical galaxies containing dark matter and then study, how the presence and the amount of dark matter affects the regular or chaotic nature of orbits as well as the behavior of the different families of orbits.

The present article is organized as follows: In Section \ref{galmod} we present in detail the structure and the properties of our gravitational galactic model. In Section \ref{compmeth} we describe the computational methods we used in order to determine the character of orbits. In the following Section, we investigate how the parameter corresponding to the fractional portion of the dark matter in galaxies influences the character of the orbits, in both disk and elliptical galaxy models. Our paper ends with Section \ref{disc}, where the discussion and the conclusions of this research are presented.

\section{DESCRIPTION OF THE GALACTIC MODEL}
\label{galmod}

In order to study the dynamical properties of galaxies astronomers often construct galactic models. A galactic model is usually a mathematical expression giving the potential or the mass density of the galaxy, as a function of the distance. The reader can find interesting models, describing motion in galaxies, in \citet{BT08}. Potential density pairs for galaxies were also presented by \citet{VL05}. Over the years, many galactic models have been proposed in order to model the orbital properties in axially symmetric systems. A simple yet realistic axisymmetric logarithmic potential was introduced in \citet{Bin81} for the description of galactic haloes at which the mass density drops like $R^{-2}$ \citep[see also][]{E93}. However, the most well-known model for cold dark matter (CDM) haloes is the flattened cuspy Navarro-Frenk-White (NFW) model \citep{NFW96,NFW97}, where the density at large radii falls like $R^{-1}$ . This model being self-consistent has a major advantage and that's why it is mainly used for conducting $N$-body simulations. Our model, on the other hand, is not self-consistent but simple and contrived, in order to give us the ability to study in detail the orbital behavior of the galactic system. Nevertheless, contrived models can provide an insight into more realistic stellar systems, which unfortunately are very difficult to be studied if we take into account all the astrophysical aspects. Due to the fast that our gravitational model consists of Plummer type potentials, at large galactocentric distances the mass density decreases following the $R^{-5}$ law.

In the present work, we shall investigate how the presence of the dark matter influences the character of the orbits in the meridional plane of an axially symmetric galaxy model with a spherical nucleus and a dark matter halo component. We shall use the usual cylindrical coordinates $(R, \phi, z)$, where $z$ is the axis of symmetry.

The total potential $V(R,z)$ in our model consists of three components: the main galaxy potential $V_{\rm g}$, the central spherical component $V_{\rm n}$ and the dark matter halo component $V_{\rm h}$. The first one is represented by the new mass model introduced in \citet{C12} and is given by
\begin{equation}
V_{\rm g}(R,z) = \frac{-G M_{\rm g}(1 + \delta)}{R_{\rm g}},
\label{Vg}
\end{equation}
where
\begin{equation}
R_{\rm g} = \sqrt{\left(1+\delta\right)\beta^2 + R^2 + \left(\alpha + \sqrt{h^2 + \left(1+\delta^2\right) z^2}\right)^2}.
\label{Rg}
\end{equation}
Here $G$ is the gravitational constant, $M_{\rm g}$ is the mass of the galaxy, $\delta$ is the fractional portion of the dark matter in the galaxy, while $\beta$ represents the core radius of the halo of the disk. The shape of the galaxy is controlled by the parameters $\alpha$ and $h$ which correspond to the horizontal and vertical scale length of the galaxy respectively. Therefore, this potential allow us to describe a variety of galaxy types from a flat disk galaxy when $\alpha, \beta \gg h$ to an oblate elliptical galaxy when $h \gg \alpha, \beta$.

For the description of the spherically symmetric nucleus we use a Plummer potential \citep[e.g.,][]{BT08}
\begin{equation}
V_{\rm n}(R,z) = \frac{-G M_{\rm n}}{\sqrt{R^2 + z^2 + c_{\rm n}^2}},
\label{Vn}
\end{equation}
where $M_{\rm n}$ and $c_{\rm n}$ are the mass and the scale length of the nucleus, respectively. This potential has been used successfully in the past in order to model and therefore interpret the effects of the central mass component in a galaxy \citep[see, e.g.][]{HN90,HPN93,Z12a}. At this point, we must make clear that Eq. (\ref{Vn}) is not intended to represent the potential of a black hole nor that of any other compact object, but just the potential of a dense and massive nucleus thus, we do not include relativistic effects. The dark matter halo is modelled by a similar spherically symmetric potential
\begin{equation}
V_{\rm h}(R,z) = \frac{-G M_{\rm h}}{\sqrt{R^2 + z^2 + c_{\rm h}^2}},
\label{Vh}
\end{equation}
where in this case, $M_{\rm h}$ and $c_{\rm h}$ are the mass and the scale length of the halo, respectively. The spherical shape of the dark halo is simply an assumption, due to the fact that galactic halos may have a variety of shapes.

In this work, we use the well known system of galactic units, where the unit of length is 1 kpc, the unit of mass is $2.325 \times 10^7 {\rm M}_\odot$ and the unit of time is $0.9778 \times 10^8$ yr. The velocity unit is 10 km/s, the unit of angular momentum (per unit mass) is 10 km kpc s$^{-1}$, while $G$ is equal to unity. Finally, the energy unit (per unit mass) is 100 km$^2$s$^{-2}$. In these units, the values of the involved parameters are: $M_{\rm g} = 8200$, $M_n = 400$, $c_{\rm n} = 0.25$, $M_{\rm h} = 7560$ and $c_{\rm h} = 15$. For the disk model we choose: $\beta = 6, \alpha = 3$ and $h = 0.3$, while for the elliptical model we have set $\beta = 2$, $\alpha = 0.5$ and $h = 11.5$. The fractional portion of dark matter $\delta$, on the other hand, is treated as a parameter and its value varies in the interval $0 \leq \delta \leq 0.5$.

\begin{figure*}
\centering
\resizebox{0.9\hsize}{!}{\includegraphics{RotCurs.pdf}}
\caption{A plot of the rotation curve in our (a-left): disk and (b-right) elliptical galactic model. We can distinguish the total circular velocity (black) and also the contributions from luminous matter (green) and that of the dark matter (red).}
\label{rotvel}
\end{figure*}

\begin{figure*}
\centering
\resizebox{0.9\hsize}{!}{\includegraphics{DenNeg.pdf}}
\caption{The evolution of the minimum distance $d_{\rm min}$ where negative density appears as a function of the parameter $\delta$ for (a-left): the disk galaxy model (b-right): the elliptical galaxy model.}
\label{deneg}
\end{figure*}

It is well known, that in disk galaxies the circular velocity in the galactic plane $z=0$,
\begin{equation}
\theta(R) = \sqrt{R\left|\frac{\partial V}{\partial R}\right|_{z=0}},
\label{cvel}
\end{equation}
is a very important physical quantity. A plot of $\theta(R)$ for both disk and elliptical galactic model when $\delta = 0.1$ is presented in Fig. \ref{rotvel}(a-b), as a black curve. Moreover, in the same plot the green curve is the contribution from the luminous matter, while the red line corresponds to the contribution form the dark matter. It is seen, that in both cases, the component of the rotational curve generated by the dark matter remains flat for large galactocentric distances, while on the other hand, the luminous matter component continues to decline with increasing distance form the galactic center. We also observe, the characteristic local minimum of the rotation curve due to the massive nucleus, which appears at small values of $R$, when fitting observed data to a galactic model \citep[e.g.,][]{IWTS13,GHBL10}.

At this point, we must clarify, that the mass density in our new galaxy model obtains negative values when the distance from the centre of the galaxy described by the model exceeds a minimum distance $d_{min}$, which strongly depends on the parameter $\delta$. Fig. \ref{deneg}(a-b) shows a plot of $d_{\rm min}$ vs $\delta$ for the both disk and elliptical galaxy models. We see, that even when $\delta = 0.5$ the first indication of negative density occurs only when $d_{\rm min} > 40$ kpc, that is almost at the theoretical boundaries of a real galaxy. Here, we must point out, that our gravitational potential is truncated ar $R_{\rm max} = 30$ kpc for both reasons: (i) otherwise the total mass of the galaxy modeled by this potential would be infinite, which is obviously not physical and (ii) to avoid the existence of negative values of density.

Taking into account that the total potential $V(R,z)$ is axisymmetric, the $z$-component of the angular momentum $L_z$ is conserved. With this restriction, orbits can be described by means of the effective potential
\begin{equation}
V_{\rm eff}(R,z) = V(R,z) + \frac{L_z^2}{2R^2}.
\label{veff}
\end{equation}
The $L_z^2/(2R^2)$ term represents a centrifugal barrier; only orbits with small $L_z$ are allowed to pass near the axis of symmetry. The three-dimensional (3D) motion is thus effectively reduced to a two-dimensional (2D) motion in the meridional plane $(R,z)$, which rotates non-uniformly around the axis of symmetry according to
\begin{equation}
\dot{\phi} = \frac{L_z}{R^2},
\end{equation}
where of course the dot indicates derivative with respect to time.

The equations of motion on the meridional plane are
\begin{eqnarray}
\ddot{R} &=& - \frac{\partial V_{\rm eff}}{\partial R}, \nonumber \\
\ddot{z} &=& - \frac{\partial V_{\rm eff}}{\partial z},
\label{eqmot}
\end{eqnarray}
while the equations describing the evolution of a deviation vector $\delta {\bf{w}} = (\delta R, \delta z, \delta \dot{R}, \delta \dot{z})$ which joins the corresponding phase space points of two initially nearby orbits, needed for the calculation of the standard chaos indicators (the FLI in our case) are given by the variational equations
\begin{eqnarray}
\dot{(\delta R)} &=& \delta \dot{R}, \nonumber \\
\dot{(\delta z)} &=& \delta \dot{z}, \nonumber \\
(\dot{\delta \dot{R}}) &=&
- \frac{\partial^2 V_{\rm eff}}{\partial R^2} \delta R
- \frac{\partial^2 V_{\rm eff}}{\partial R \partial z}\delta z,
\nonumber \\
(\dot{\delta \dot{z}}) &=&
- \frac{\partial^2 V_{\rm eff}}{\partial z \partial R} \delta R
- \frac{\partial^2 V_{\rm eff}}{\partial z^2}\delta z.
\label{vareq}
\end{eqnarray}

Consequently, the corresponding Hamiltonian to the effective potential given in Eq. (\ref{veff}) can be written as
\begin{equation}
H = \frac{1}{2} \left(\dot{R}^2 + \dot{z}^2 \right) + V_{\rm eff}(R,z) = E,
\label{ham}
\end{equation}
where $\dot{R}$ and $\dot{z}$ are momenta per unit mass, conjugate to $R$ and $z$ respectively, while $E$ is the numerical value of the Hamiltonian, which is conserved. Therefore, an orbit is restricted to the area in the meridional plane satisfying $E \geq V_{\rm eff}$.

\section{COMPUTATIONAL METHODS}
\label{compmeth}

In order to obtain the mass profiles of galaxies, we have to construct dynamical models describing the main properties of the galaxies. These models can be generated by deploying two main techniques: (i) using superposition of libraries of orbits \citep[e.g.,][]{G03,TSB04,C06} or (ii) using distributions functions \citep[e.g.,][]{DBVZ96,GJSB98,KSGB00}. In the literature there are also other more specialized dynamical models combining kinematic and photometric data. For instance, axially symmetric Schwarzschild models were used by \citet{B06}, while \citet{H08} used Jeans models in order to fit observational data in the X-ray potential introduced by \citet{HBG06}. Furthermore, axisymmetric Schwarzschild models were also used by \citet{SG10} to fit data derived from the Hubble Space Telescope (HST).

In the recent years, Schwarzschild's superposition method \citep{S79} has been heavily utilized by several researchers \citep[e.g.,][]{RZCMC97,G03,TSB04,VME04,KCEMd05,TSB05} in order to study dark matter distributions in elliptical galaxies therefore, we deem it is necessary to recall and describe briefly in a few words the basic points of this interesting method. Initially, $N$ closed cells define the configuration space, while $K$ orbits extracted from a given mass distribution construct the phase space. Then, integrating numerically the equations of motion, we calculate the amount of time spent by each particular orbit in every cell. Thus, the mass of each cell is directly proportional to the total sum of the stay times of orbits in every cell. Using this technique we manage to compute the unknown weights of the orbits, assuming they are not negative.

In our study, we want to know whether an orbit is regular or chaotic. Several chaos indicators are available in the literature; we chose the FLI method. The FLI \citep{FGL97,LF01} has been proved a very fast, reliable and effective tool, which is defined as
\begin{equation}
\rm FLI(t) = \log \| {\bf{w}(t)} \|, \ \ \ \ t \leq t_{max},
\end{equation}
where ${\bf{w}}(t)$ is a deviation vector. For distinguishing between regular and chaotic motion, we need to compute the FLI for a relatively short time interval of numerical integration $t_{max}$. In particular, we track simultaneously the time-evolution of the orbit itself as well as the deviation vector ${\bf{w}}(t)$ in order to compute the FLI. The variational equations (\ref{vareq}), as usual, are used for the evolution of the deviation vector. The main advantage of the FLI method is that only one deviation vector is required to be computed, while in the case of other dynamical indicators like SALI \citep{SABV04} or GALIs \citep{SBA07} more than one deviation vectors are needed. Therefore, by using the FLI method we need considerable less computation time for integrating and classifying massive sets of initial conditions of orbits.

\begin{figure}
\includegraphics[width=\hsize]{FLI_evol.pdf}
\caption{Evolution of the FLI of a regular orbit (green color - R), a sticky orbit (orange color - S) and a chaotic orbit (red color - C) in our model for a time period of $10^4$ time units. The horizontal, blue, dashed line corresponds to the threshold value 10 which separates regular from chaotic motion. The chaotic orbits needs only about 130 time units in order to cross the threshold value, while on the other hand, the sticky orbit requires a vast integration time of about 4400 time units so as to reveal its chaotic nature.}
\label{FLIevol}
\end{figure}

The particular time-evolution of the FLI allow us to distinguish fast and safely between regular and chaotic motion as follows: when an orbit is regular the FLI exhibits a linear increase, while on the other hand, in the case of chaotic orbits the FLI evolution is super-exponential. The time evolution of a regular (R) and a chaotic (C) orbit for a time period of $10^4$ time units is presented in Fig. \ref{FLIevol}. We observe, that both regular and chaotic orbits exhibit an increase in the value of FLI but with a complete different rate. Unfortunately, this qualitative criterion is applicable only when someone wants to check the character of individual orbits by plotting and then inspecting by eye the evolution of FLI. Nevertheless, we can easily overcome this drawback by establishing a numerical threshold value, in order to quantify the FLI. After conducting extensive numerical experiments in different types of dynamical systems, we conclude that a safe threshold value for the FLI taking into account the total integration time of $10^4$ time units is the value 10. The horizontal, blue, dashed line in Fig. \ref{FLIevol} corresponds to that threshold value which separates regular from chaotic motion. In order to decide whether an orbit is regular or chaotic, one may use the usual method according to which we check after a certain and predefined time interval of numerical integration, if the value of FLI has become greater than the established threshold value. Therefore, if FLI $\geqslant 10$ the orbit is chaotic, while if FLI $ < 10$ the orbit is regular.

In order to investigate the orbital properties (chaoticity or regularity) of the dynamical system, we need to establish some sample of initial conditions of orbits. The best approach, undoubtedly, would be have been to extract these sample of orbits from the distribution function of the model. Unfortunately, this is not available so, we followed another course of action. For determining the chaoticity of our models, we chose, for each set of values of the parameters of the potential, a dense grid of initial conditions in the $(R,\dot{R})$ phase plane, regularly distributed in the area allowed by the value of the energy $E$. The points of the grid were separated 0.1 units in $R$ and 0.5 units in $\dot{R}$ direction. For each initial condition, we integrated the equations of motion (\ref{eqmot}) as well as the variational equations (\ref{vareq}) with a double precision Bulirsch-Stoer algorithm \citep[e.g.,][]{PTVF92}. In all cases, the energy integral (Eq. (\ref{ham})) was conserved better than one part in $10^{-10}$, although for most orbits, it was better than one part in $10^{-11}$.

Each orbit was integrated numerically for a time interval of $10^4$ time units (10 billion yr), which corresponds to a time span of the order of hundreds of orbital periods but of the order of one Hubble time. The particular choice of the total integration time is an element of paramount importance, especially in the case of the so called ``sticky orbits" (i.e., chaotic orbits that behave as regular ones during long periods of time). A sticky orbit could be easily misclassified as regular by any chaos indicator\footnote{Generally, dynamical methods are broadly split into two types: (i) those based on the evolution of sets of deviation vectors in order to characterize an orbit and (ii) those based on the frequencies of the orbits which extract information about the nature of motion only through the basic orbital elements without the use of deviation vectors.}, if the total integration interval is too small, so that the orbit do not have enough time in order to reveal its true chaotic character. A characteristic example of a sticky orbit (S) in our galactic system can be seen in Fig. \ref{FLIevol}, where we observe that the chaotic character of the particular sticky orbit is revealed after a considerable long integration time of about 4400 time units. Thus, all the set of orbits of the grids of the initial conditions were integrated, as we already said, for $10^4$ time units, thus avoiding sticky orbits with a stickiness at least of the order of a Hubble time. All the sticky orbits which do not show any signs of chaoticity for $10^4$ time units are counted as regular ones, since that vast sticky periods are completely out of scope of our research.

A first step towards the understanding of the overall behavior of our galactic system is knowing the regular or chaotic nature of orbits. Of particular interest, however, is also the distribution of regular orbits into different families. Therefore, once the orbits have been characterized as regular or chaotic, we then further classified the regular orbits into different families, by using the frequency analysis of \citet{CA98,MCW05}. Initially, \citet{BS82,BS84} proposed a technique, dubbed spectral dynamics, for this particular purpose. Later on, this method has been extended and improved by \citet{CA98} and \citet{SN96}. In a recent work, \citet{ZC13} the algorithm was refined even further, so it can be used to classify orbits in the meridional plane. In general terms, this method calculates the Fourier transform of the coordinates of an orbit, identifies its peaks, extracts the corresponding frequencies and search for the fundamental frequencies and their possible resonances. Thus, we can easily identify the various families of regular orbits and also recognize the secondary resonances that bifurcate from them.

Before closing this Section, we would like to make a short note about the nomenclature of orbits. All the orbits of an axisymmetric potential are in fact three-dimensional (3D) loop orbits, i.e., orbits that rotate around the axis of symmetry always in the same direction. However, in dealing with the meridional plane the rotational motion is lost, so the path that the orbit follows onto this plane can take any shape, depending on the nature of the orbit. We will call an orbit according to its behaviour in the meridional plane. Thus, if for example an orbit is a rosette lying in the equatorial plane of the axisymmetric potential, it will be a linear orbit in the meridional plane, etc.

\begin{figure*}
\centering
\resizebox{0.9\hsize}{!}{\includegraphics{Orbs_D.pdf}}
\caption{Orbit collection of the six basic types of orbits in the disk galaxy model: (a) box orbit; (b) 2:1 banana-type orbit; (c) 1:1 linear orbit; (d) 3:2 boxlet orbit; (e) 4:3 boxlet orbit; (f) chaotic orbit.}
\label{orbsD}
\end{figure*}

\begin{figure*}
\centering
\resizebox{\hsize}{!}{\includegraphics{Grids_D.pdf}}
\caption{Orbital structure of the $(R,\dot{R})$ phase plane of the disk galaxy model for different values of the fractional portion of the dark matter $\delta$.}
\label{gridsD}
\end{figure*}

\section{ORBIT CLASSIFICATION}
\label{orbclas}

In this Section, we will numerically integrate several sets of orbits in an attempt to distinguish the regular or chaotic nature of motion. We use the initial conditions mentioned in Sec. \ref{compmeth} in order to construct the respective grids of initial conditions, taking always values inside the Zero Velocity Curve (ZVC) defined by
\begin{equation}
\frac{1}{2} \dot{R}^2 + V_{\rm eff}(R,0) = E.
\label{zvc}
\end{equation}
In all cases, the value of the angular momentum of the orbits is $L_z = 15$. We chose for both disk and elliptical galaxy models such energy levels which correspond to $R_{\rm max} \simeq 10$ kpc, where $R_{\rm max}$ is the maximum possible value of $R$ on the $(R,\dot{R})$ phase plane. Once the values of the parameters were chosen, we computed a set of initial conditions as described in Sec. \ref{compmeth} and integrated the corresponding orbits calculating the value of FLI and then classifying the regular orbits into different families.

\subsection{Disk galaxy model}

\begin{table}
\begin{center}
   \caption{Types and initial conditions of the disk galaxy model orbits shown in Figs. \ref{orbsD}(a-f). In all cases, $z_0 = 0$ and $\dot{z_0}$ is found from the energy integral, Eq. (\ref{ham}), while $T_{\rm per}$ is the period of the resonant parent periodic orbits.}
   \label{table1}
   \setlength{\tabcolsep}{3.0pt}
   \begin{tabular}{@{}llccc}
      \hline
      Figure & Type & $R_0$ & $\dot{R_0}$ & $T_{\rm per}$  \\
      \hline
      \ref{orbsD}a & box        &  2.09000000 &  0.00000000 &          - \\
      \ref{orbsD}b & 2:1 banana &  5.79009906 &  0.00000000 & 1.83668227 \\
      \ref{orbsD}c & 1:1 linear &  5.47170604 & 30.97448116 & 1.23526267 \\
      \ref{orbsD}d & 3:2 boxlet &  1.58031642 & 16.62648333 & 3.54124377 \\
      \ref{orbsD}e & 4:3 boxlet & 11.37966251 &  0.00000000 & 4.83447045 \\
      \ref{orbsD}f & chaotic    &  0.40000000 &  0.00000000 &          - \\
      \hline
   \end{tabular}
\end{center}
\end{table}

For the disk galaxy models we choose the energy level $E = -1200$ which is kept constant. Our investigation reveals that in our disk galaxy model there are six main types of orbits: (a) box orbits, (b) 1:1 linear orbits, (c) 2:1 banana-type orbits, (d) 3:2 resonant orbits, (e) 4:3 resonant orbits and (f) chaotic orbits. Note that every resonance $n:m$ is expressed in such a way that $m$ is equal to the total number of islands of invariant curves produced in the $(R,\dot{R})$ phase plane by the corresponding orbit. In Fig. \ref{orbsD}(a-f) we present an example of each of the five basic types of regular orbits, plus an example of a chaotic one. In all cases, we set $\delta = 0.5$. The orbits shown in Figs. \ref{orbsD}a and \ref{orbsD}f were computed until $t = 100$ time units, while all the parent periodic orbits were computed until one period has completed. The black thick curve circumscribing each orbit is the limiting curve in the meridional plane $(R,z)$ defined as $V_{\rm eff}(R,z) = E$. Table \ref{table1} shows the types and the initial conditions for each of the depicted orbits; for the resonant cases, the initial conditions and the period $T_{\rm per}$ correspond to the parent periodic orbits.

\begin{figure}
\includegraphics[width=\hsize]{Percs_D.pdf}
\caption{Evolution of the percentages of the different kinds of orbits in our disk galaxy model, when varying the fractional portion of the dark matter $\delta$.}
\label{percsD}
\end{figure}

\begin{figure*}
\centering
\resizebox{0.8\hsize}{!}{\includegraphics{FOP_D.pdf}}
\caption{Evolution of the starting position $(R_0,\dot{R_0})$ of the periodic orbits as a function of the fractional portion of the dark matter $\delta$. (a-upper left): 2:1 resonant family; (b-upper right): 4:3 resonant family; (c-lower left): 1:1 resonant family; (d-lower right): 3:2 resonant family.}
\label{FOPD}
\end{figure*}

To study how the fractional portion of the dark matter $\delta$ influences the level of chaos, we let it vary while fixing all the other parameters of our disk galaxy model. As already said, we fixed the values of all the other parameters and integrate orbits in the meridional plane for the set $\delta = \{0,0.1,0.2, ..., 0.5\}$. In all cases, the energy was set to $-1200$ and the angular momentum of the orbits was $L_z=15$. Once the values of the parameters were chosen, we computed a set of initial conditions as described in Sec. \ref{compmeth} and integrated the corresponding orbits computing the FLI of the orbits and then classifying regular orbits into different families.

In Figs. \ref{gridsD}(a-f) we present six grids of orbits that we have classified for different values of the fractional portion of the dark matter $\delta$. Here, we can identify all the different regular families by the corresponding sets of islands which are formed in the phase plane. In particular, we see the five main families already mentioned: (i) 2:1 banana-type orbits surrounding the central periodic point; (ii) box orbits are situated mainly outside of the 2:1 resonant orbits; (iii) 1:1 open linear orbits form the double set of elongated islands in the outer parts of the phase plane; (iv) 3:2 resonant orbits form the double set of islands above the box orbits; and (v) 4:3 resonant orbits correspond to the outer triple set of islands shown in the phase plane. Apart from the regions of regular motion, we observe the presence of a unified chaotic sea which embraces all the islands of stability. The outermost black thick curve is the ZVC defined by Eq. (\ref{zvc}).

Fig. \ref{percsD} shows the resulting percentages of the chaotic orbits and of the main families of regular orbits as $\delta$ varies. It can be seen, that there is a strong correlation between the percentage of most orbits and the value of $\delta$. As the portion of the dark matter increases, there is a gradual decrease in the percentage of chaotic orbit, although this tendency is reversed in models with significant amount of dark matter $(\delta > 0.3)$. In particular, we observe that always chaotic motion is the dominant type of motion and when $\delta > 0.3$ the amount of chaotic orbits grows at the expense of box orbits and 1:1 linear orbits. The meridional 2:1 banana-type orbits, on the other hand, are almost unperturbed by the shifting of the portion of dark matter. Moreover, the 4:3 resonant orbits exhibit a constant increase, while the percentage of the 3:2 resonant orbits remains at very low values. From the diagram shown in Fig. \ref{percsD}, one may conclude that the fractional portion of the dark matter affects mostly the 1:1, 4:3 resonant orbits and chaotic orbits in disk galaxy models.

Of particular interest, is to investigate how the variation in the fractional portion of the dark matter influences the position of the periodic points of the different families of periodic orbits shown in the grids of Fig. \ref{gridsD}. For this purpose, we use the theory of periodic orbits \citep{MH92} and the algorithm developed and applied in \citet{Z13}. In Fig. \ref{FOPD}(a-d) we present the evolution of the starting position of the parent periodic orbits of the four basic families of resonant orbits. The evolution of the 2:1 and 4:3 families shown in Figs. \ref{FOPD}a and Fig. \ref{FOPD}b respectively, is two-dimensional since the starting position $(R_0,0)$ of both families lies on the $R$ axis. On the contrary, studying the evolution of the 1:1 and 3:2 families of periodic orbits is indeed a real challenge due to the peculiar nature of their starting position $(R_0,\dot{R_0})$. In order to visualize the evolution of these families, we need three-dimensional plots such as those presented in Figs. \ref{FOPD}c and \ref{FOPD}d, taking into account the simultaneous relocation of $R_0$ and $\dot{R_0}$. The stability of the periodic orbits can be obtained from the elements of the monodromy matrix $X(t)$ as follows:
\begin{equation}
K = {\rm Tr} \left[X(t)\right] - 2,
\end{equation}
where Tr stands for the trace of the matrix, and $K$ is called the \emph{stability index}. For each set of value of $\delta$, we first located, by means of an iterative process, the position of the parent periodic orbits. Then, using these initial conditions we integrated the variational equations in order to obtain the matrix $X$, with which we computed the index $K$. Our numerical calculations indicate, that in the disk galaxy models, all the different families of periodic orbits remain stable throughout the entire range of the values of $\delta$.

\subsection{Elliptical galaxy model}

\begin{table}
\begin{center}
   \caption{Types and initial conditions of the elliptical galaxy model orbits shown in Figs. \ref{orbsE}(a-h). In all cases, $z_0 = 0$ and $\dot{z_0}$ is found from the energy integral, Eq. (\ref{ham}), while $T_{\rm per}$ is the period of the resonant parent periodic orbits.}
   \label{table2}
   \setlength{\tabcolsep}{3.0pt}
   \begin{tabular}{@{}llccc}
      \hline
      Figure & Type & $R_0$ & $\dot{R_0}$ & $T_{\rm per}$  \\
      \hline
      \ref{orbsE}a & box        &  1.90000000 &  0.00000000 &          - \\
      \ref{orbsE}b & 2:1 banana &  7.18420419 &  0.00000000 &  2.47524161 \\
      \ref{orbsE}c & 1:1 linear &  1.53837422 & 33.45716659 &  1.48665183 \\
      \ref{orbsE}d & 3:2 boxlet &  1.06837848 & 22.64363815 &  4.44068043 \\
      \ref{orbsE}e & 4:3 boxlet & 12.92588226 &  0.00000000 &  5.92689152 \\
      \ref{orbsE}f & 5:3 boxlet &  1.58425772 &  9.55073196 &  7.37479109 \\
      \ref{orbsE}g & 8:5 boxlet & 12.42410864 &  0.00000000 & 11.83080833 \\
      \ref{orbsE}h & chaotic    &  0.40000000 &  0.00000000 &          - \\
      \hline
   \end{tabular}
\end{center}
\end{table}

\begin{figure*}
\centering
\resizebox{0.9\hsize}{!}{\includegraphics{Orbs_E.pdf}}
\caption{Orbit collection of the eight basic types of orbits in the elliptical galaxy model: (a) box orbit; (b) 2:1 banana-type orbit; (c) 1:1 linear orbit; (d) 3:2 boxlet orbit; (e) 4:3 boxlet orbit; (f) 5:3 boxlet orbit; (g) 8:5 boxlet orbit; (h) chaotic orbit.}
\label{orbsE}
\end{figure*}

In the case of the elliptical galaxy model, we choose the energy level $E = -1100$ which is kept constant. Our numerical investigation shows that in our elliptical galaxy model there are seven main types of orbits: (a) box orbits, (b) 1:1 linear orbits, (c) 2:1 banana-type orbits, (d) 3:2 resonant orbits, (e) 4:3 resonant orbits, (f) 5:3 resonant orbits, (g) 8:5 resonant orbits and (h) chaotic orbits. It is worth noticing, that the basic resonant families, that is the 2:1, 1:1, 3:2 and 4:3 are common in both disk and elliptical galaxy models. However, in the case of the elliptical galaxy additional secondary resonances (i.e. 5:3 and 8:5) appears. Again, every resonance $n:m$ is expressed in such a way that $m$ is equal to the total number of islands of invariant curves produced in the $(R,\dot{R})$ phase plane by the corresponding orbit. In Fig. \ref{orbsE}(a-h) we present an example of each of the seven basic types of regular orbits, plus an example of a chaotic one. In all cases, we set $\delta = 0.5$. The orbits shown in Figs. \ref{orbsE}a and \ref{orbsE}f were computed until $t = 100$ time units, while all the parent periodic orbits were computed until one period has completed. Table \ref{table2} shows the types and the initial conditions for each of the depicted orbits; for the resonant cases, the initial conditions and the period $T_{\rm per}$ correspond to the parent periodic orbits.

\begin{figure*}
\centering
\resizebox{\hsize}{!}{\includegraphics{Grids_E.pdf}}
\caption{Orbital structure of the $(R,\dot{R})$ phase plane of the elliptical galaxy model for different values of the fractional portion of the dark matter $\delta$.}
\label{gridsE}
\end{figure*}

In order to study how the fractional portion of the dark matter $\delta$ influences the level of chaos, we let it vary while fixing all the other parameters in our elliptical galaxy model. As already said, we fixed the values of all the other parameters and integrate orbits in the meridional plane for the set $\delta = \{0,0.1,0.2, ..., 0.5\}$. In all cases the energy was set to $-1100$ and the angular momentum of the orbits was $L_z = 15$. Once the values of the parameters were chosen, we computed a set of initial conditions as described in Sec. \ref{compmeth} and integrated the corresponding orbits computing the FLI of the orbits and then classifying regular orbits into different families.

Six grids of initial conditions $(R_0,\dot{R_0})$ that we have classified for different values of the fractional portion of the dark matter $\delta$ are shown in Figs. \ref{gridsE}(a-f). By inspecting these grids, we can identify all the different regular families by the corresponding sets of islands which are produced in the phase plane. In particular, we see the seven main families of regular orbits already mentioned: (i) 2:1 banana-type orbits correspond to the central periodic point; (ii) box orbits situated mainly outside of the 2:1 resonant orbits; (iii) 1:1 open linear orbits form the double set of elongated islands in the outer parts of the phase plane; (iv) 3:2 resonant orbits form the double set of islands; (v) 4:3 resonant orbits correspond to the outer triple set of islands shown in the phase plane; (vi) 5:3 resonant orbits forming the set of the three small islands inside the region of box orbits and (vii) 8:5 resonant orbits producing the set of five islands. It is evident, that the structure of the phase plane in the elliptical galaxy models differs greatly from that of the disk models. We observe, that when the amount of dark matter in the elliptical galaxy is low, almost the entire phase plane is covered by different types of regular orbits. On the other hand, chaotic motion appears, mainly at the outer parts of the phase plane, only when the galaxy possesses a significant amount of dark matter ($\delta \geq 0.4$).

\begin{figure}
\includegraphics[width=\hsize]{Percs_E.pdf}
\caption{Evolution of the percentages of the different kinds of orbits in our elliptical galaxy model, when varying the fractional portion of the dark matter $\delta$.}
\label{percsE}
\end{figure}

In the following Fig. \ref{percsE} we present the resulting percentages of the chaotic orbits and of also the main families of regular orbits as $\delta$ varies. It can be seen, that the motion of stars in elliptical galaxies, is almost entirely regular, being the box orbits the all-dominant type. The percentage of box orbits is however reduced as the portion of the dark matter is increased, although they always remain the most populated family. It is also seen, that the percentages of the 2:1 banana-type orbits exhibits a minor decrease with increasing $\delta$. On the other hand, the chaotic orbits start to grow rapidly as soon as the galaxy contains significant amount of dark matter ($\delta > 0.3$). Moreover, all the other resonant families of orbits are immune to changes of the portion of the dark matter, since their percentages remain almost unperturbed and at very low values (less than 5\%). From Fig. \ref{percsE} one may conclude that dark matter in elliptical galaxies mostly affects box and chaotic orbits. In fact, a portion of box orbits turns into chaotic as the galaxy gains more dark matter.

\begin{figure*}
\centering
\resizebox{0.9\hsize}{!}{\includegraphics{FOP_E.pdf}}
\caption{Evolution of the starting position $(R_0,\dot{R_0})$ of the periodic orbits as a function of the fractional portion of the dark matter $\delta$. (a) 2:1 resonant family; (b) 4:3 resonant family; (c) 8:5 resonant family; (d) 1:1 resonant family; (e) 3:2 resonant family; (f) 5:3 resonant family.}
\label{FOPE}
\end{figure*}

We close this Section, by presenting how the variation in the fractional portion of the dark matter influences the position of the periodic points of the different families of periodic orbits shown in the grids of Fig. \ref{gridsE}(a-f). We follow the same method used previously in the case of the disk galaxy. In Fig. \ref{FOPE}(a-f) the evolution of the starting position of the parent periodic orbits of the six basic families of resonant orbits is given. Once more, the evolution of the 2:1, 4:3 and 8:5 families shown in Figs. \ref{FOPE}(a-c), is two-dimensional since the starting position $(R_0,0)$ of these families lies on the $R$ axis. On the contrary, the evolution of the 1:1, 3:2 and 5:3 families are shown in the three-dimensional plots in Figs. \ref{FOPE}(d-f) thus following simultaneous the relocation of $R_0$ and $\dot{R_0}$ as the fractional portion of the dark matter $\delta$ varies. Our numerical calculations suggest, that all the computed resonant periodic orbits were found to be stable. Furthermore, we should point out that several families of periodic orbits in the case of the elliptical galaxy do not cover the entire range of the values of $\delta$.

\section{DISCUSSION AND CONCLUSIONS}
\label{disc}

There is no doubt, that the determination of the nature of dark matter is one of the most interesting and challenging open problems that scientists try to solve. In the present paper, we used the analytic, axisymmetric, mass model which was introduced in \citet{C12} and embraces the general features of a dense, massive nucleus and a spherical dark matter halo. We made this choice because observations show that the assumption of a spherical halo seems to be reasonable. On the other hand, non spherical and triaxial haloes are also possible in some galaxies \citep[see, e.g.][]{GSKVK04,TdWBK08,VC11}. A galaxy with a dark matter halo is undoubtedly a very complex entity and, therefore, we need to assume some necessary simplifications and assumptions in order to be able to study mathematically the orbital behavior of such a complicated stellar system. For this purpose, our model is simple and contrived, in order to give us the ability to study different aspects of the dynamical model. Nevertheless, contrived models can provide an insight into more realistic stellar systems, which unfortunately are very difficult to be studied, if we take into account all the astrophysical aspects. On the other hand, self-consistent models are mainly used when conducting $N$-body simulations. However, this is entirely out of the scope of the present paper. Once again, we have to point out that the simplicity of our model is necessary; otherwise it would be extremely difficult, or even impossible, to apply the extensive and detailed dynamical study presented in this study. Similar gravitational models with the same limitations and assumptions were used successfully several times in the past in order to investigate the orbital structure in much more complicated galactic systems \citep[see, e.g.][]{Z12b,Z13a}.

In this work, we investigated how influential is the parameter corresponding to the portion of the dark matter $\delta$ on the level of chaos and also on the distribution of regular families among its orbits in both disk and elliptical galaxy models. The main results of our research can be summarized as follows:

\textbf{(1).} In disk galaxy models, the fractional portion of the dark matter affects mostly the 1:1, 4:3 resonant orbits and the chaotic orbits, while the effect on all the other resonant families is very weak compared to them. In particular, chaotic motion is always the prevailing type of motion but when the amount of dark matter is high enough, the amount of chaotic orbits grows at the expense of box orbits and 1:1 linear orbits.

\textbf{(2).} That portion of dark matter in elliptical galaxy models influences mainly the box and the chaotic orbits. In fact, box orbits are the dominant family when the amount of dark matter is low, but the percentage of chaotic orbits quickly grows as the dark matter is being accumulated, by collapsing the percentage of box orbits, although they always remain the most populated family.

\textbf{(3).} The percentage of the observed chaos in disk galaxy models with dark matter is significantly larger compared to that in elliptical galaxy models. This result coincide with similar conclusions obtained using different types of dynamical models in order to model disk and elliptical galaxies \citep[see, e.g.][]{PC05,Z11}.

The outcomes of the present research are considered as a promising first step in the task of exploring the orbital structure in both disk and elliptical galaxy models containing dark matter. Taking into account that our results are encouraging, it is in our future plans to modify properly our dynamical model in order to expand our study in three dimensions.

\section*{Acknowledgments}

We would like to express our warmest thanks to the anonymous referee for the careful reading of the manuscript and for all the aptly suggestions and comments which allowed us to improve both the quality and the clarity of our paper.

redpajama_set_name: RedPajamaArXiv


text:
Houston Dynamo, Dash sold to New York businessman
By Mark Berman
(Photo courtesy of Houston Dynamo via Facebook)
HOUSTON - According to MLS sources, New York businessman Ted Segal has reached an agreement to buy the Houston Dynamo FC and Houston Dash from controlling owner Gabriel Brener.
Segal is the founder and president of New York City-based EJS Group, a real estate development and finance company.
Brener joined the Dynamo ownership group in 2008 as a minority investor. Seven years later he acquired a controlling interest in the Dynamo FC, the Dash, and BVAA Stadium from the original owner, Anschutz Entertainment Group.
Meanwhile, MLS sources confirm Brener, along with minority partners James Harden, Oscar De La Hoya, and Houstonian Ben Guill will remain with the new ownership group, but to a lesser extent.
Another minor partner, Jake Silverstein, will not continue to be involved.
Officials with the Dynamo FC and the Dash released the following statement:
"Our ownership group receives inquiries about the Club from interested parties on a frequent basis and has for quite some time. These inquiries are private in nature, and we respect the privacy of those individuals. Our club will have no comment on any reports."
Budweiser slipping golden cans into beer packs for chance to win $1M
Cy-Fair ISD trustee loses job with IT company following 'racist' comments


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A few months ago it dawned on me that I wasn't feeling great. It wasn't a discernible health issue that I could pop a pill for, or apply cream to. It was something deeper inside me.
My negative self-talk had become very loud and I found myself questioning everything I was doing. My confidence had taken a sudden nose-dive and I couldn't put my finger on why. I wasn't doing anything differently, but suddenly I was feeling really beige. There were tears.
Then I realised, maybe I did need to do something differently. Maybe I needed to look at the way I was thinking. Little things we do and think, often subconsciously, can add up, and drag us down. Before we know it negativity sneaks shackles on you, which prevents you from leaping and bounding through life.
I decided to make a few changes in order to lighten my load, and love myself more.
The bathroom scales have never been my friends. Those suckers could dictate how my whole day went with just a little number in the morning. When the batteries ran out, I decided not to renew them and to kick the scales under the sink where I can't see them.
I know they're there should I have a burning desire to discover my weight, but I've removed the daily temptation to allow a mean old piece of measuring equipment tell me whether I look good today or not.
At first it felt a bit weird to throw a random "You are smart, talented and worthy," at my reflection in the mirror, but soon my morning love words became like a moment with an old friend.
I would look myself square in the eye and say just one nice thing about how I was going to be today ("You are dazzling and engaging") or how I looked ("You are shiny and gorgeous.") I'm totally not above telling myself I look awesome today because let's face it, it's unlikely anyone else is going to.
You know how you often wake up and start the debate about whether or not you should exercise? Yeah, I quit that. I know that my physical, and more importantly mental space, is so much better for the entire day if I do a minimum of 30 minutes exercise in the morning.
I took the debate out of the equation by committing to exercise every weekday. I can pro-crap-stinate to my heart's content on the weekend.
If I don't have time for the gym, I make time to work out in the garden or lounge with kettle bells, skipping rope and a tabata timer on my phone.
I'm 40 and I don't know what I want to be when I grow up. I am a creative. What this means, in my case, is that I don't have a distinct career planned and I have lots of (harebrained) ideas and will follow new paths often.
I used to beat myself up about this and I thought I needed to get a "real" job in order to follow a clear career trajectory and be a SUCCESS. I also measured my own success by what other people were doing, especially, the people on social media.
This is not a good way to gauge yourself so I decided my uncertain, haphazard, colourful career path is simply perfect for me… and social media lives aren't all that.
I was such a Facebook addict that I would check it every 10-15 minutes and scroll perpetually sometimes for moments, or minutes or even hours. I would check it at the traffic lights, while waiting in line, when my date went to the toilet, and even check it on my phone while I was working on my computer where it was opened in a tab anyway.
I haven't given it up, per se, however breaking the habit of checking on my phone made a huge impact on my overall addiction. Basically, I'm too lazy to get off the couch to go to the computer to check it and using Facebook via the internet on the phone is not as satisfying.
The less I saw what whatshername I've not seen since high school was doing, the more I realized it's not important, or relevant, to my life and the time I spent absorbed in that was time stolen from things that could fill my love cup.
I admit, #gratitude is pretty vom inducing, however, a moment's reflection at the end of the day can reveal some interesting things, such as, your life is actually pretty damned great.
I have a handful of caring, inspiring friends, I am strong and healthy, and I am grateful to have an amazing work network that allows me freedom whilst paying for my holidays. The simple act of gratitude is actually not as lame-o as you first may think… But if you want to keep if off Facebook, that's ok by me.


It's been a while since I talked about my skincare routine, so tonight let me share with you new products I've been using for the past few months.
I could say that my skin has been behaving majority of the time. Grease and clogged pores are a problem though and when it's either before or after my period, I do get a zit or two. Good thing, the marks eventually fade.
After washing my face using Kojiesan soap, I apply No-Sebum Toner by Innisfree. I got this from Althea for 530 php.
It has a minty scent and it feels cool on skin. According to the site, the formula is slightly acidic which would lower skin's pH level after washing since that part can strip too much oil. It also has salicylic acid, which is a plus for me because it can contribute to a clearer skin.
As for the oil-control part, it can add another "matte hour" or few more if weather is nice.
For my moisturizer, I'm using this interesting product by Lebaton. It comes with 2 creams so the packaging has 2 compartments.
I apply the whitening cream before sunscreen during daytime. At night, I use the other cream as a regular moisturizer.
The whitening cream is actually hydrating too and what I love most about it is how it brightens the face without the white cast. It's an instant fix to dull skin.
As you can see, my tub is almost empty. Haha!
Btw, Ban Ban in Korean means "half half". So it's kinda self-explanatory why it's called like that. I'm not sure though if Lebaton sells each cream separately.
I think you can also layer both or even mix the two. It's just my preference to use one at day and one at night.
Lebaton Ban Ban Cream retails at 494 php on Althea. That's a good deal because you get two creams already at 50g each.
To get rid of dirt and makeup, I use this facial foam by Aritaum. It lathers nicely but sometimes, I don't find that it cleanses my face enough. I would recommend it though for people with sensitive or dry skin because it seems to be working as a gentle cleanser.
I double cleanse using The Saem Healing Tea Garden Green Tea Cleansing Water (forgot to include this in the first photo). It pretty much works as a micellar water. I tried using it on waterproof and liquid lipsticks and it's good enough.
I also got it from Althea for only 270 php.
Before, I was applying toner as the next step after washing my face but ever since I've used Cosrx BHA Power Liquid, I decided to skip that at night so that the effect of this product would be maximized.
Like I said in my full review of this amazing product, it has made clogged pores more manageable and using this for several months seemed to have resulted to improved overall skin texture.
Once a week, I exfoliate my face using Skin Food Rice Mask Wash Off (310 php on Althea).
I've already tried the black sugar and strawberry sugar version and I could recommend both. However, some would find those abrasive and this rice scrub might be a better option for them.
This can still get rid of roughness though and makes the skin smoother and radiant.
I really like the consistency of this mask. It feels like cream and because of the scent, I almost wanna eat it every time.
Since it's a mild scrub, I sometimes use it twice a week or when I do feel like my skin is getting a bit dull.
Also once a week, I would follow the scrub with this pore clay mask by Innisfree to really give my pores some TLC. Then, once or twice a month, I use nose pack to get rid of the clogs.
I've been using these patches as well to treat stressed eyes and sometimes, pimple marks too. The formula has black pearl collagen, gold powder and amino acids to make that delicate area look less tired and dry.
One tub contains 60 patches. They have a jelly-like feel so they adhere to the skin welll. I love how hydrating these are.
I know this could be a little too extra for some and that's okay. You don't need a lot of products and a lot of layering unless you're into the Korean skincare style. As long as you do the basic stuff, you'd be fine.
How about you? What skincare products are in your current rotation?


If you ask what sort of foundational conviction establishes you as a faithful preacher, it would be this: you believe the Bible is the inspired, inerrant, sufficient, and clear revelation of God. In fact, your preaching will be a direct reflection of what you believe about the Bible.
If you don't preach the Bible then you don't have the right conviction about the Bible. If you think there is some other authority, some better way to communicate, some more clever, or more culturally acceptable, or more psychologically appealing approach than the biblical approach, then you're reflecting a low view of Scripture.
If you don't preach the Bible then you don't have the right conviction about the Bible.
If, on the other hand, you believe that every word of God is pure, as the Bible says, and that all Scripture is given by inspiration of God and is profitable to make the man of God complete, if you believe that God has inspired the Bible in the way that Peter writes about it—that the spirit moved on those who were the writers and they wrote down the very word of God—then it's going to show up in you preaching the Bible.
People might say, "Well, wait a minute. I believe the Bible and I take my truths and my ideas from the Bible, but I sort of frame them up in a cultural way so that people can understand them." Let me speak to that for just a moment.
Looking at the heart of the apostle Paul through 9 convictions found in 2 Corinthians 4, veteran pastor John MacArthur calls church leaders to faithful endurance in ministry.
You've just slipped, and the gold is off and it won't be long before you stop preaching biblical truth in cultural dress and the Biblical truth disappears. Then you've descended into the darkness of just preaching what people want to hear.
You never go from preaching biblical truth in biblical texts to abandoning the Bible. There's a step in between. The step in between is preaching biblical truth in cultural context. God wrote a book and he put truth in biblical contexts and that's how you have to preach it.
Sometimes people say, "Well we need to bring the Bible into modern day life, into modern understanding." That's wrong. What you need to do is take the modern person back to the biblical times. Whatever the Bible meant in its original context is what it means now.
For them to understand what it meant in its original context, you've got to take them back. So the challenge in biblical preaching is not to tamper with the text and try to pull the truth into the modern era, it's to take the modern person back to living in the biblical text, setting the context in which it was revealed originally. That's the challenge of real Biblical preaching in biblical texts and it's the richest way to give people the whole counsel of God.


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I remember once seeing a very interesting chastity device online, and only recently discovered it had at some point actually been made. The first time I saw it it was in some sort of comic, and as I had not been looking for comic-style stuff, I didn't give it more attention than a long curious look before moving on.
Now that I have found out it is an actual device, I've searched using various keywords to try and find a place that sells it. I don't exactly plan on buying it, as I have a metal knockoff cb-6000s and a recently purchased short HolyTrainer v2, but would like to find it for future reference.
It took awhile, but I finally found a comic-style picture with said device. It is not really anything more than a metal tube that has a "cut" from top to bottom, most likely so it's easier to slide on/off and to not keep it super rigid if the wearer becomes aroused. The person putting on the device can use some sort of string to pull the shaft through by the head. At least, that's what was done in the clip that I saw the real thing in. Then some sort of pin was put through two holes at the top of the tube on either side of the cut and then what looks to be a washer is screwed onto the other end of the pin. How exactly this device locks on that way, I'm not sure.
Either way, I am curious to see more of this interesting device. Any knowledge would be appreciated.
Attached is a closeup of the comic image.
NOTE: Avatar is not me.
Centurion used to sell this, but they no longer list it.
the locking pin is a piercing.
As for the locking pin, maybe their version was a piercing, but the one in the clip I saw didn't appear to be. The pin was not placed through any hole in the skin, and there was nothing shown that would prevent the wearer from simply unscrewing the nut/washer, pulling the pin out, and sliding the tube/sleeve off.
The fact that it is no longer listed piques my interest more. Any further information would be much appreciated.


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text:
«Иремель» () — природный парк, находящийся на территории Белорецкого и Учалинского районов Башкортостана, у границы с Челябинской областью. Он окружён тремя блок-постами: со стороны Учалов, со стороны деревни Николаевка Белорецкого района и села Тюлюк Катав-Ивановского района Челябинской области.

География
Горный массив Иремель включает в себя наиболее высокие вершины: Большой и Малый Иремель, разделённые седловиной. Видны горы и хребты Аваляк, Бакты, Ямантау, Зигальга, Нургуш и другие.

Назначение природного парка: сохранение горно-тундровых, таёжных лесных и болотных экосистем, популяций редких видов растений и животных; обеспечение стабильного гидрологического режима истоков крупнейших рек Южного Урала; создание условий для развития регулируемого туризма и отдыха.

Флора и фауна
Парк полностью покрыт лесом, на его территории обитают почти все виды охотничье-промысловых видов животных. Здесь произрастает 553 вида высших споровых и цветковых видов растений, то есть четверть всей флоры Башкортостана, в их числе 57 видов из Красной книги Республики Башкортостан, из которых 15 являются эндемиками, а 33 — реликтами.
Высокогорья массива Иремель богаты растениями горно-тундровой зоны (48 видов). Причем 11 из них – тонконог Ледебура, ива арктическая, ива шерстистая, дриада восьмилепестная, лаготис уральский и др. – встречаются только в данном районе Республики Башкортостан. К настоящему времени в результате хищнических заготовок корневищ упала до критического уровня численность эндемичного вида – родиолы иремельской.

Также, на территории заповедника встречаются около 40 редких и находящихся под угрозой исчезновения видов животных, таких как: летяга, речная выдра, марал, аист чёрный, белая и серая куропатка, травяная лягушка, таймень, европейский хариус, махаон, адмирал и прочие.

Отдых и туризм

Парковая территория разделена на пять зон:
 Заповедник. Вход туристам запрещён.
 Зона регулируемой рекреации. Туристическая территория, поделена на четыре маршрута: Большой Иремель, Малый Иремель, Тюлюкское и Тыгынское болота. Здесь туристам предлагаются пешие, велосипедные и конные маршруты.
 Зона рекреационного посещения отдана под кемпинги и палаточные лагеря. Отсюда открывается вид на истоки реки Белой и панорама на гору Большой Иремель.
 Буферная зона хозяйственной деятельности природного парка, где планируется возведение гостиниц, ресторанов и горнолыжной трассы.
 Коридор миграции зверей между Иремелем и Южно-Уральским государственный природным заповедником.

Экскурсионные маршруты: от п. Тюлюк, д. Новохусаиново, д. Байсакалово, д. Николаевка к подножию горы Большой Иремель.

Все экскурсионные маршруты размечены маркерами и стрелками, имеются оборудованные беседками, туалетами, кострищами и контейнерами твёрдых бытовых отходов, туристические стоянки. По экскурсионному маршруту «Тюлюк — подножье г. Большой Иремель (летний)» имеется гостевой дом. На территории природного парка «Иремель» расположены туристические приюты «Байсакал», «Три медведя», «Горный приют Иремель» и гостевой дом «Божьи коровки». Туристический приют «Байсакал» расположен на берегу Белой, у подножия хребта Аваляк, высочайшим отрогом которого является гора Иремель.

См. также
 Список особо охраняемых природных территорий Башкортостана

Примечания

Ссылки

Заповедники России
Охраняемые природные территории Башкортостана
Туризм в Башкортостане
Природные парки России

redpajama_set_name: RedPajamaWikipedia


text:
Avicenna's Medical Thinking in Colonial Mexico
by Rolando Neri-Vela	Published on: 27th September 2017
4.9 / 5. Votes 177
Avicenna - Ibn Sina - Mexico - Rolando Neri-Vela - South America -
New Spain was a viceroyalty of Spain between 1521 and 1821. In these three centuries, the practice and the teaching of medicine had a great influence from Arabian medicine, and in this way, the thinking of Avicenna and his followers...
A map of the countries under the supervision and appellate jurisdiction of the Viceroy of New Spain, at the Spanish imperial zenith in 1795 (Source)
New Spain was a viceroyalty and part of the great Spanish empire during three centuries, from 1521 to 1821.
After Hernán Cortés conquered the Aztec kingdom, he began a new life studying medicine. This was because European medicine, at the time, was surrounded in superstition.The medical, surgical and pharmacological practices were subpar compared to the medicine of Northern Europe.[1]
Cortés scuttling his own fleet off the coast of Veracruz in order to eliminate the possibility of retreat (Source)
Surely all of the Spanish physicians who crossed the ocean, carried in their luggage the essential bibliographical material for their profession, all of them were faithful to the knowledge of Avicenna. Thanks to these books published by Mexican presses we can see which of Avicenna's books were in circulation.
Francisco Bravo, who arrived in New Spain after he had studied in the Alcalá de Henares and Osuna universities, in Spain, wrote his first medical book, edited in America, named Opera medicinalia,[2] and cited Avicennas works as well as otherauthors like Galen, Avicenna, Rhazes, Hippocrates, Thucydides, Valles and Fracastoro. The works of Galen, Hippocrates and Avicenna were indispensable books for all medical doctors, and were edited many times.
We have a few examples regarding the works of Avicenna that came to New Spain. Avicenna was an author cited by all who wrote medical books in the Viceroyalty, and at the same time, it is rare that a book from the Renaissance period didn't include Avicenna's theories in its texts.
12th-century manuscript of ibn Sina's Canon (Source)
Bravo didn't say which of Avicenna works he consulted, although he did point out treatises and chapters of the most well-known book from Avicenna, Canon. In the 16th century, this book was frequently used by Spanish medical doctors. It was also translated and used in medical schools along with the works of Galen and Hippocrates. There were many editions, of which twenty were in early print, including the classical translation from Gerard of Cremona, in the 12th century.
In the beginning of the 16th century, 1523, Praesens maximus codex est totius scientiae medicine principis Alboali Abinsene was published in Venice. This was a monumental typographical work, and the most commented upon edition from the Persian physician, in whose interpretation supervised the most noted Italian doctors of that times. It was an important book and arrived to almost all Spanish medical centers. A copy of this work was used in the ceremonies at Alcalá de Henares to establish the themes for the grade exam.
During the 16th century in Spain, the Epitome or Compendium of Avicenna was drafted by Miguel Capella, and the Prima primi canonis Avicena section, was written by Miguel Jerónimo de Ledesma, Valencian lecturer. His first book, a translation and commentary on one of Avicenna's texts, was his most successful. It is likely that these two works arrived to New Spain, for the purpose of teaching medicine at the Royal and Pontifical University, founded in 1553, and its Faculty of Medicine, that opened its doors in 1582.
During the middle of the 20th century, Dr. José Joaquín Izquierdo, a very distinguished Mexican physician, found in the National Library of Mexico, a copy of Liber canonis de medicines cordialibus et cantica, from Avicenna. The edition was edited by Joan Hervagios in 1556. The existence of this book in Mexico illustrates works from Avicenna were used in the 16th century by New Spain's doctors. Another book from Avicenna, Disputatione medicae, printed by Pedro García Carrero at Alcalá de Henares by Juan Graciani's press, in 1611, was founded by Izquierdo, too, in the same Library.
Juan de Cárdenas in his work Primera parte de los problemas y secretos maravillosos de las Indias[3] (1591) is sparing when naming his influences, but he does name Avicenna. Agustín Farfán wrote in 1592 Tractado Brebe de Medicina,[4] and in this work he quoted Galen, Hippocrates, Rhazes and Avicenna, in an abstract tone and without interest. Anatomy was studied using the works of Avicenna, complemented with the old authority of Galen and commented upon by Rhazes. The great philosopher and Muslim-Spanish scientist, Farfán said in his Tractado that the bones of the human body are 148, and the muscles 531. In addition, students should study, during the third year, the ninth book of Rhazes Almanzorem.
We have to remember that the medieval therapeutic methods were purges, cupping-glasses, draughts, plasters, cauterizations and various infusions. Then, in those times was used the called soliman water, to cauterize a sweet sublimate of mercury diluted in water, insipid and which first known prescription is founded in Summa perfectionis writed by Geber, Arabian alchemist whose work was known by Avicenna, and too, in New Spain.
Another common medicinal practice, that has its roots in Muslim science, was the use of the bezoar stone. Thought to be an effective antidote, this stone was used as an antidote to all poisons in New Spain. Enrico Martínez, astronomer, but no physician, wrote Repertorio de los tiempos, y historia natural desta Nueva España[5] in 1606, and in the fourth chapter he talks about the applicability of astrology, and in his book he mentions Avicenna and his Canon.
Bezoar stones on display in the German Pharmacy Museum in Heidelberg Castle (Source)
Verdadera medicina, cirugía y astrología, 1607 (Source)
Ships would arrive on American coasts full of books. Some works were forbidden by the Holy Inquisition, however some medical doctors managed to get their hands on some of them. In a list from 1576, Alonso Losa, a bookseller, received two copies of Exposición sobre las preparaciones de Mesue, published in 1569 by Antonio de Aguilera from Alcalá de Henares, in which the author explains the book of Juan Mesue, the Arabian physician whose works were used till the end of the 18th century. Mesue is named with profusion in Juan de Barrios' book, Verdadera medicina, cirugía y astrología (6), published in 1607.
There is another incunabulum in the National Library of Mexico, that is a Latin translation of the works of Serapione, Liber serapionis agregatus in medicines simplicibus translaton Symonis Ianuensis interprete Abraan iudeo tortuosiensi de arabico in latinum inquit Serapion, published in 1473 at Parma by Antonio Zarotum.
In 1648 Juan de Correa, an anatomist of the Real y Pontificia Universidad de México wrote Tratado de la qualidad manifiesta, que el mercurio tiene…,[6] in which he wrote about life in the mines, and the poisoning caused by sulfur. The works of Avicenna and Geber allowed Juan de Correa to write his book.
During the 16th century, in New Spain, the texts for the Faculty of Medicine were various books from Hippocrates, Galen, Ali Abbas, Hunain Ibn Ishaq, Avicenna, Rhazes, Averroes and Mesue. In the third year of studies the students had to study the ninth book of Ad almanzorem, from Rhazes.
Later, when medievalism was substituted for modernism, in Spanish universities, they continued with lectures from Avicenna.[7]
Juan de los Barrios d/1569 (Source)
To summarize these notes, I will mention some ideas from the book Verdadera Medicina, Astrología y Cirugía,[8] from Juan de Barrios, published in Mexico in 1606. Juan de Barrios arrived in New Spain in 1590, after attending the universities of Alcalá, Salamanca and Valencia. His work is probably the most important monument of New Spanish medicine, written in dialogue form.
In chapter 17 of the third treatise of his book, de Barrios illustrates about the headache and hemicranias, saying that Avicenna thought that this disease was so terrible and ferocious that the joints of the head looked dilated, and it opened the head, and it was so tyrannical that sometimes it killed.[9]
When de Barrios talks about cataracts, in chapter 28, mentioning Avicenna, he says that to heal it [cataracts] the physician must use warm and dry air, the patient must not drink wine, only cinnamon or honey water, and they can eat hen, kid, and they must not drink milk nor eat fish.[10]
So, I have exposed briefly the influence and the utility of Arabian medicine and Avicenna's thinking in American medicine, pointing out some of the authors that had more authority on physicians during the three centuries in Colonial Mexico.
Rolando Neri-Vela, MD, MSC
Naval School of Medicine,
Naval University, Mexican Navy
[1] Weckmann, Luis. La herencia medieval de México, II. El Colegio de México. México, 1984. Pp. 669-687.
[2] Bravo, Francisco. Opera medicinalia. Petrum Ocharte. Mexico, 1570.
[3] Cárdenas, Juan de. Primera parte de los problemas y secretos maravillosos de las Indias. Pedro Ocharte. México, 1591
[4] Farfán, Agustín. Tratado breve de anothomia y cirugía. Antonio Ricardo. México, 1579.
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