When looking for ways to improve your health, we often think first of asking our doctor. Fortunately, nature has provided us with many plants that can give us the same benefits as man-made medicine, with few side effects. The benefits and uses of rosemary essential oil are long and varied, which is why it was considered a sacred herb in the ancient world. There are many ways for you to use it in your own life as well.
Many people suffer from hair loss, either due to skin conditions or other health issues. Men and women will appreciate the benefits and uses of rosemary essential oil when it comes to assisting with keeping the hair you have or keeping it naturally healthy.
Pharmaceutical treatments for hair loss can result in many undesirable side effects. However, using a natural mixture, which includes rosemary essential oil, can work just as well and as quickly as the standard medical treatment. (1) Rosemary can promote a healthy scalp and relieve any inflammation due to itching.
It is even used on patients suffering from Alzheimer's disease to improve memory recall. This could be an excellent complementary therapy to any pharmaceutical treatments. (4) Rosemary has anti-inflammatory properties which help the brain produce the needed chemicals and soothes the irritated neurons so they can take in the chemicals and hormones to improve memory.
It seems that with our work and personal schedules, we live in a constant state of stress. We feel fatigued and operate under a brain fog that keeps us from performing at our best.
Many essential oils are known for several properties that bring about pain relief, and rosemary is no exception. Many of the symptoms that accompany pain, such as inflammation, are also improved.
With the stress relieving properties found when rosemary is inhaled, you can also relax, further allowing a lessening of the pain and allowing healing to continue. Add about 2-3 drops of rosemary to a teaspoon of carrier oil and rub directly on the painful area.
Acne isn't just relegated to teenagers. These skin problems are caused by a number of problems, such as an overproduction of natural oil, which then clogs the pores in the skin, trapping dead cells inside and allowing bacteria to fester.
It also makes a better alternative to the chemicals that fill our cleaning products as well. Add 10 drops rosemary, eucalyptus, and peppermint to filtered water, and you have a spray that you can use directly on your countertops, floors, and even the air to kill airborne illnesses. Rosemary is also used to make homemade hand sanitizers without the drying effect of alcohol. Good for keeping you healthy and better for your skin.
I love rosemary. It has to be the most fragrant herb in my kitchen cupboard, and I use on just about anything, from hamburgers to lamb. Employees at the garden center in the home improvement store follow me around because of my strange habit of touching every rosemary plant I see and then sniffing my fingers. I admit I'm weird but happy. Must be some of that mood lifting and mind enhancing properties, even when not concentrated as an oil.
The oil has been added to my formula for focus, along with eucalyptus and a few drops of lavender for relaxation. 10-20 of rosemary and eucalyptus in my diffuser and I'm ready to work for hours without stopping or losing focus. I only add about 5 drops of lavender. I find that even a little bit can put me to sleep, but I like the relaxing properties that boost the memory enhancement benefits of rosemary.
Not only does it improve my thinking, but it also sanitizes the air with the incredible anti-bacterial properties. The mist also helps disinfect any surface it lands on, so my office is naturally germ-free. I've made a spray with rosemary, eucalyptus and orange oil for really getting my surfaces clean in both the office and the kitchen, where it can kill food-borne infections like salmonella.
I also make my own hand sanitizer. While I like hand sanitizer for its convenience when you can't wash your hands, I've found that the alcohol dries my skin to the point of bleeding. A recipe of aloe vera gel, vitamin E, witch hazel and an oil blend including clove, rosemary, cinnamon, eucalyptus, and lemon is my new go-to. I leave out the rosemary and make a mix for my kids to use as well.
A long list of essential oils with anti-fungal, anti-bacterial, and anti-inflammatory properties makes up the ingredients of this shampoo. Rosemary is used in conjunction with tea tree oil which is good for skin infections and includes vitamin E to keep the skin healthy.
It is meant to keep your hair healthy and promote hair growth as well. Since rosemary has been shown to have many of the same effects as a popular medical treatment for hair loss, this shampoo may be key to keep what you have, even if genetics are to blame.
Rosemary has been shown to help you keep the hair you have, and can even fight scalp infections that can cause dandruff or hair loss. This product is a mix of peanut oil and other essential oils that can soothe the skin as well as help make hair healthier.
We tend to do damage to our hair with all the dyeing, blow-drying, and styling we like to do. It can become dry and brittle as we age or if our diet is poor. This oil promises to help keep hair smooth and silky, without drying out your scalp.
If your children play with other children, you are always in danger of picking up a lice infestation. And once an infestation hits a classroom, it tends to spread very rapidly from household to household. It's not caused by dirty hair, but if you'd like to prevent the social awkwardness that comes with being dismissed for lice, this shampoo could avoid the whole mess.
Its made with a combination of oils that repel undesirable pests such as lice but is gentle on the scalp and hair like lavender and the carrier oil jojoba, making it gentle and effective.
Children 4 and under should not use rosemary. Try frankincense for the same results.
Do not use rosemary if pregnant. It could cause uterine bleeding.
Use in recommended amounts. Large amounts may be toxic.
May cause an allergic reaction in people who have an aspirin allergy.
May cause bleeding in persons with blood disorders.
Rosemary may cause seizures in persons with a history of seizures or epilepsy. Consult a physician before using.
Decreased sperm motility has been observed and may affect fertility in men.
Can cause skin irritation if applied directly to the skin. Blend with carrier oils for best results.
People with diabetes should use rosemary in moderation as it can raise blood sugar.
I hope you find rosemary to not just be an herb to season your dinner. Rosemary was once considered sacred and modern science has helped to back up that claim, showing it is good for your hair and your memory. Please be sure to share this with any students you may know. They may find it helpful as they try to pass their exams.


Video watches were not long ago viewed as sci-fi and beyond this era, but now the first MP4 video watch has been launched. This gadget exhibits a 128x128 pixels screen accompanied by a 1Gb storage capacity. Whilst not recommended for watching blockbuster movies, it can prove useful for small video files to keep you up to date, or amused, on the go.


Submitter Brad said: A kite store goes online! They offer tons of products from kites ,banners, windsocks and even some ggag gifts. They have easy online ordering. Pretty neat graphics I think. Course I did most of them thats probably why I think they are neat. I would a review so I can give to my boss and maybe one day he will pay me for all this work!
* Reviewer says: The site loaded quickly (always a plus). Although the initial page offered little information, the second page was informative. The navigation within the site was easy to follow. The links were all working. The colors were bold and bright leaving the impression that the product offered also contains bright colors.
__ The only concern on this website was the animated clock which rotates on the second page at the upper left corner of text. It is distracting and difficult to read. Also, the various text sizes and bright colors on the new products page compete for the eye's attention making it difficult to scan down the page. Perhaps same size type or same color type would be less distracting?
__ Thank you for letting me visit the site. Knowing that the owners were native Washingtonians made me homesick yet again... (insert heavy sigh here).
* WD&R Comments: Thank you Cherie Yannone-Hasemann for your comments on this site!
I have to agree with Cherie -- and I'll add that this site has a lot of potential to really be a lot of fun, and sell some product too. Just about everyone loves kites, even if they don't get to participate!


text:
«Опівнічна спека» () — американський трилер 1992 року.

Сюжет
Повернувшись у Лос-Анджелес після довгої відсутності, фотожурналіст Ерік «потрапляє у халепу». Він зупиняється в Малібу в будинку свого друга Денні, який вплутався в мафіозні справи, вкравши у гангстерів мільйон доларів. Оскаженілий бандитський бос Карл Медсен, разом з яким до від'їзду з Лос-Анджелеса Ерік торгував наркотиками, віддає наказ убити Денні, бере в заручниці кохану Еріка і дає йому 24 години, щоб знайти і повернути викрадені гроші.

У ролях
 Майкл Паре — Ерік Райт
 Адам Ент — Денні Роллінз
 Денніс Гоппер — Карл Медсен
 Дафна Ешбрук — Джулі
 Чарлі Шлеттер — Девід
 Трейсі Туід — Лена
 Літтл Річард — Брендон
 Лука Берковічі — детектив Кук
 Стефанос Мільцакакіс — Арк
 Тоні Тодд — Друкер
 Шеріл Фріман — жінка-поліцейський
 Джо Лара — Тодд
 Майкл Телботт — бармен
 Сінді Валентайн Леоні — Холлі
 Дейв Дерошер — охоронець Карла
 Джулі Стрейн — дівчина зі сніданком / срібна статуя
 Трейсі Делі — дівчина у басейні
 Пол Бен-Віктор — житель Нью-Йорка
 Бріджет Батлер — леді в Нью-Йорку
 Боб Ларкін — старик
 Кліффорд Далтон — Вейн
 Джефф Дженсен — мрець у доках
 Елена Сахагун — модель
 Керрі Кларк — модель
 Сенді Чунг — модель
 Белінда Беррі — модель
 Сара Крамлет — модель
 Консуела Ненс — модель
 Лайат — модель
 Лені Фаас — Harley Guy
 Норм «Клатч» Дженнінгс — Harley Guy
 Джим Біслі — Harley Guy
 Девейн Ньюман — Harley Guy
 Хет — група Холлі
 Лес Джулі — басист
 Покет Оноре молодший — гітарист
 Тадеус Коріа — барабанщік
 Метт Вітмор — клавішик
 Крістін МакГроу — кокетка (в титрах не вказана)

Посилання

Фільми англійською мовою
Фільми-трилери США
Фільми про Малібу
Фільми про Лос-Анджелес

redpajama_set_name: RedPajamaWikipedia


All jokes aside, I really do enjoy this outfit regardless of whether I look like mustard and ketchup. It's so bright and airy. You can really get use out of your bright things during the summer months. I especially enjoy wearing bright colors when it is an overcast/rainy day like the one we are having today.
I was looking around in Walmart and my eye caught on this gorgeous, laced, red top. I have a total of two red tops in my entire closet. I felt like I "needed" a dressy one. That's what I told myself anyways, so I decided to get it. You really can dress it up or down. I could throw this top on with some jeans and flip flops and transform it into a casual look.
Do you like dressing up like various condiments? Haha! Let me know!
When I firstly saw your outfit I thought - what a great summer combination! Red and yellow reminds so much the sun!
Thank you! I'm all about the brights in the summer time.
I laughed too! You are so funny!


It's that time of the year! Can you believe it?! Although the lead up to Christmas is my favourite time of year, it can often be the most stressful. Usually each year I brace the chaos of the shops, the crowds and all the mayhem that comes with it, but this year I've decided to do the most of my shopping online. I just find there are better deals, it saves you a world of exhaustion and you can do it from the comfort of your own home, drinking eggnog and watching Christmas movies. Does it really get anymore festive?
So where do you even begin? Every year I put together gift guides featuring what I consider to be the best buys, gift sets and deals, to ultimately make the experience less stressful for you. Do you have any beauty lovers in your life? Perhaps they would appreciate some of the gifts here – or at least give you some inspiration!


When life throws us lemons, we have to make the best lemonade! After being laid off from her medical job, Keonta Ramsey knew it was time to do life differently. She turned a childhood passion for writing into a business that has helped several clients make A's in courses and even receive their dream jobs! Listen in to find out more about this gift and the story that led up to the creation of Eloquence Unlimited, LLC! They specialize in all of your writing needs from resumes to email correspondence. She will empower you to be confident in writing because we all have something to say while also dropping why black girl magic took some time to grow on her!
Need help boosting your resume? Editing a research paper? Calligraphy work? Be sure to contact the experts at Eloquence Unlimited by calling or texting 843.507.3011, or email Eloquenceunlimited@gmail.com. Be sure to follow @eloquence_unlimitedllc on Instagram! Website coming soon!


Hello! Do you need to reach us?
The Service Member Support Division offices are open Monday – Friday from 7:00 am until 5:00 pm.
Even though we have regular business hours, that does not mean you have to wait to get help or have an urgent/important question answered by a real, live person.
Call our support line, it is staffed 24/7/365.
You can even send us an email if that works better for you. Click here!
Believe it or not, there is a real, live human being that maintains this website. I sincerely hope you enjoy the information put together for you. Sometimes, I do make mistakes and links break from time to time. If you see/find something that is "off", please send me an email.


text:
selfies pussy ass finger » Hidden Cam » New country music september 2017
New country music september 2017
In , Billboard magazine published two main charts ranking the top-performing country music songs in the United States. The Hot Country Songs chart ranked songs based on digital downloads , streaming , and airplay not only from country stations but from stations of all formats, a methodology introduced in In the issue of Billboard dated February 25, singer Sam Hunt reached number one with the song " Body Like a Back Road ", which would remain in the top spot through the issue dated October In August the song broke the record for the most weeks spent at number one on the Hot Country Songs listing, surpassing the 24 weeks spent in the top spot by Florida Georgia Line 's " Cruise " in and Lynch tied with Blake Shelton for the highest total number of weeks at number one on that chart, both artists spending five weeks in the top spot.
An ever-changing collective of Texas studio musicians, an adolescent Appalachian prodigy and a duo that tempers soft ballads with irreverent humor make up the 10 country and Americana artists you need to hear this month. Why You Should Pay Attention: A loosely collected group of studio musicians from Dallas, Texas, that counts somewhere around 25 people among its members, the Texas Gentlemen usually perform as a five- or six-piece group. The core members — organist Beau Bedford, guitarist Nik Lee, bassist Matt McDonald, keyboardist Daniel Creamer, bassist Scott Lee and drummer Ryan Ake — played together in different capacities for years before making things official in , taking their cue from legendary house bands like the Wrecking Crew and Muscle Shoals Rhythm Section.
The following albums placed on the Top Country Albums charts in From Wikipedia, the free encyclopedia. This is a list of notable events in country music that took place in See also: List of number-one country singles of U. Notes [ edit ] "—" denotes releases that did not chart. See also: List of number-one country albums of U.
And the nonmember spouse may just put pressure on the member spouse to spend more time with them. I know my husband appreciates me looking into it because he knows I am doing it to gain an understanding into the culture he was raised in. What if you are sexually incompatible. Never marry someone with the goal of a post-marriage conversion. Obviously don't make any commitments further in the relationship because you do not want to be married into an insane orthodox LDS family because it will cause alot of troubles. I'm glad he's upfront about the difficulty in dating for him. How church discipline works.
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redpajama_set_name: RedPajamaCommonCrawl


Sometimes, you need to look deep in the past to understand the present. It's definitely true about art.
If something was chosen to represent the pride of Russia, it would definitely be the beauty, intelligence, resourcefulness, resilience of Russian women. And luckily, the modern women's prose is well translated.


Measuring the parameters of the environment without the intervention of physical contact and power dissipation is not an easy task. Application requirements for point detection, in the micro-, or even the nano-scale, are becoming very stringent when combined with the need for a plurality of detection points, multi-sensoric outputs and minimal cost. Specific areas of deployment spun from agriculture and forestry, urban and industrial pollution control, safety at workplace, biomedical diagnostics, security and defense.
Existing sensor technologies, both electronic and optical, suffer from several impediments in terms of technology complexity, instrument size, power budget, capital and running costs.
The engineered photonic nanocomposites of our interest are offering innovative tools for environmental and biomedical sensing. The design and implementation of advanced composite materials designs in the form of thin films or coatings opens up new approaches for the implementation of novel interactions of light and matter and the acquisition of useful environmental data through them. Indeed, the physical and the chemical microenvironment affect the nanocomposite structure to a degree higher to that of, for example, a pure crystalline medium. In the specific embodiments pursued and demonstrated here, chemical vapors induce nanocrystallite complexation. This effect is optically interrogated by a laser beam thus providing remote, contactless means for detection and quantitative monitoring.
Enhanced performances are implemented by designer photonic structures of interferometric, diffractive / holographic nature produced by structural and morphological tailoring. Respective methodologies in free-space and optical waveguide configurations are also implemented to demonstrate.
Sensors and Integrated Photonic Information Processing is a further objective aiming towards future systems for environmental control, biomedicine, safety and security. Prototype Photonic Devices are optoelectronically integrated and tested in the unique Photonic Sensor Environmental Testing Platform established in the Photonics clean-room (Class 1000) laboratory.
Development of optical and photonic techniques for optical inspection, measurement and photonic quality monitoring. Emphasis is placed on optical interferometric, holographic and imaging methods for the precise measurement of physical dimensions, physical/chemical parameters and process control. The objectives focus on the implementation of specifically developed non-destructive schemes and certification of products of industrial production, and on the control of the industrial processes and the environment.
Systems developed for specific applications include radiometric monitors, high-precision instruments for mechanical engineering manufacturing, three-dimensional profilers and security controls.


Sci-fi Fantasies is a blog about science fiction, fantasy, and science, mostly television but books and movies sometimes, too. I'm Lynn, and this is my site.
One of the first things you need to know about Sci-fi fantasies is that it's organized with tags. Categories are broad and if you want to narrow down what you're looking at, you need to drill down with tags.
Although others may contribute from time to time, this blog reflects my own personal interests when it comes to science fiction, fantasy, and science topics.
Those things that interest me will make it onto the site eventually. Those that don't, won't.


Copyright (c) 2006, Nick Curtis. All Rights Reserved. Distributed under the 1001Fonts Free For Commercial Use License (FFC) www.1001fonts.com/licenses/ffc.html - PayPal donations in any amount may be made at nicksfonts.com.


Size Guide(in Inches): 1-2 Years: Length: 21" Chest: 19" Waist: 17" 2-3 Years: Length: 23" Chest: 20" Waist: 18" 3-4 Years: Length: 24" Chest: 21" Waist: 19" 4-5 Years: Length: 27" Chest: 22" Waist: 20"
Buy online in India the stylish and beautiful pale pink wedding dress for cute baby girl. It comes with high quality net straps and net flare along with a heavily sequenced floral bodice. Dress your toddler in this exquisite special occasion clothing crafted with high quality fabric and make your girl look like a princess.


To stop the British invasion of the New England Colonies during the American Revolution, Peter Townsend manufactured a Great Chain at Sterling Forest for the Continental Army. The chain was placed across the Hudson River at West Point. Please join Doc Bayne on Thursday, January 10 at 7 p.m. for an eye opening presentation on how he discovered the forge in Sterling Forest that made the chain.
Doc will share the history of the iron industry that started in 1736 in Sterling Forest and how the Sterling Forge was used to create the Great Chain that was placed across the Hudson. Donald "Doc" Bayne has been interested in history since the age of 8, after retiring from Minolta, Doc became a Forest Ranger for Sterling Forest State Park, and later accepted the position of Environmental Educator and Historian for the park. Doc has acquired a vast knowledge of the forest, animals, Native Americans, and iron history.
In his position he planned and conducted history and nature hikes in both Sterling Forest and Bear Mountain State Parks. He has lectured on many aspects of the environment such as the iron history of New York State. Doc is a passionate researcher and educator with the ability to feel the history of the land and transmit it to the people.


Oscar has one funny dad…I should start a blog for all the funny things he says, but in all honesty, most of the quotes are TMI 🙂 One favorite that I was just replaying in my head was when we went to visit our friends The Stevens' and they had this amazing aromatherapy soap from Bath and Bodyworks. In the car on the way home, Jerry was so excited about how good his hands smelled he was going on and on about the soap and finally sighed and said, "man, we'll never have soap like that". The next day I went to Bath and Bodyworks and we've been smelling our hands ever since! Oscar, I just want you to know that one day, you will use that soap and smell your hands. And when you do, you can thank your dad.
When do you find your Calling?
That is a personal favorite of mine. 🙂 I support the Jerryisms blog or website. Let's do it.
that soap is incredible. I'm pretty sure that it's made by angels in a heavenly factory…same place where those turkey meatballs are churned out!
Why not? I have Roan Quotes. I am CERTAIN I would enjoy Jerry Quotes.
just laughing out loud at at my husband right now… that's all.
Angie, i just told Andrea "i'm not 6…i don't need a quotes page". thank you for reinforcing my stance.
Jen, you can start your Jonchak quote page with "heavenly meatballs".


text:
\section{Introduction}\label{sec1}

General relativity, being fundamentally a geometric theory, relies heavily in geometrically defined objects to make physical predictions. In fact, many theoretical predictions depend on defining suitable geometric objects associated with physical concepts and then prove geometrical relations among them. As an already classical and crucial example we have the positivity of mass, $m\geq0$, for isolated systems \cite{Witten81}, \cite{ShoenYau81}. An important family of such relations is formed by the so called geometrical inequalities. They are predictions of the theory and allow us to understand relevant properties of physical systems. For black holes they tend to relate the area of the black hole and physical parameters, such as the mass, charge and angular momentum. As example we have that for axially symmetric black holes
\begin{equation}
 \sqrt{|J|}\leq m,
\end{equation}
proved in \cite{Dain08}, where $J$ is the angular momentum of the black hole. Also in this category we have the Penrose inequality \cite{Penrose73},
\begin{equation}
 m\geq\sqrt{\frac{A}{16\pi}},
\end{equation}
which presents still a very important open problem. Crucially this last inequality and part of the motivation for the former (and other inequalities) depend on the cosmic censorship conjecture. For an up to date and thorough review of geometrical inequalities in general relativity the reader is referred to \cite{DainGabachClement18} and for the present status of the Penrose inequality to \cite{Mars09}.

A problem that turned out to be extremely challenging is to find geometrical inequalities for ``ordinary objects'', that is, regular matter objects. One of the reasons for such difficulty is that ordinary objects do not have geometrically distinguished boundaries as black holes do. After the firsts struggles to find geometric relations or conditions on matter objects it was realized that simple attempts to relate things like the mass and area or length of an object were bound to fail unless spherical symmetry was present. In this sense it became clear that just the length of an object or its area was not a good measure of its ``size'', as it was possible to make the area of an object go to zero without making its mass zero, or it was possible to make an arbitrarily long object with fixed mass. A much used example of this, an the main concern of the present article, is the spacetime presented in \cite{Bonnor98}. Progress was made once it was realized that an extremality condition was lacking, which was something that the black holes naturally had. To the rescue came trapped surfaces for the spacetime and isoperimetric surfaces for initial data. A stable isoperimetric surface is a surface whose area is a minimum  with respect to nearby surfaces that enclose the same volume. In this sense, the area of the smallest stable isoperimetric surface enclosing an object is seen as a better representative of the size of the object than the area of the object itself. Please refer again to \cite{DainGabachClement18} for the state of the art and the discussion of possible measures of size for ordinary objects.

The problem of finding the stable isoperimetric surfaces in a given metric manifold, so called isoperimetric problem, has a long and fruitful history in mathematics. Of particular importance in general relativity are the results showing that for initial data that is asymptotic to Schwarzschild there exists a unique foliation by stable isoperimetric surfaces in the asymptotic region. In this regard please refer to \cite{HuiskenYau96}, \cite{EichmairMetzger2013a} and \cite{EichmairMetzger2013b} (this last work contains also an interesting appendix with an overview of results on isoperimetric regions).

Back to geometrical inequalities, it was proved  in \cite{DainJaramilloReiris21} that for a stable isoperimetric surface in an electro-vacuum maximal initial data with a non-negative cosmological constant
\begin{equation}\label{desProbada}
 A\geq \frac{4}{3}\pi Q^2,
\end{equation}
where $A$ is the area of the surface and $Q$ is its electric charge. This result is purely quasi-local and therefore charged matter could be present inside or outside the surface. To explore this inequality in \cite{AcenaDain13} the super-extreme regime of the Reissner-Nordstr\"om family of spacetimes was considered. Due to the staticity and spherical symmetry the isoperimetric profile was obtained and then it was possible to see that equality in \eqref{desProbada} was never attained. This led to conjecture the more stringent inequality
\begin{equation}\label{desConjetura}
 A \geq \frac{16}{9}\pi Q^2.
\end{equation}

Continuing with the idea of testing the inequality \eqref{desProbada}, in the present work we focus on the family of spacetimes presented by Bonnor in \cite{Bonnor98}. These are solutions of the Einstein-Maxwell field equations where the matter content is a spheroid of electrically counterpoised dust (ECD). These solutions are striking in the way the mathematical properties of ECD are exploited. This allows to modify the parameters of the spacetimes in order for example to test the hoop conjecture \cite{Thorne72}. Also, the area of the matter spheroid can be made arbitrarily small while keeping its mass (and charge) constant. This is a counterexample to the idea that the area of an object can be bounded by its mass.  Our main interest is to analyze these spacetimes in relation to the inequality \eqref{desProbada}. So we want to find the isoperimetric profile for a maximal initial slice and obtain the quotient between area and charge. From the perspective of  the conjecture \eqref{desConjetura}, we are interested in seeing if the spacetime presents a challenge to it.

To find the stable isoperimetric surfaces in a metric manifold is in general quite complicated. A necessary condition for a surface to be stable isoperimetric is that its mean extrinsic curvature has to be constant \cite{BarbosaDoCarmoEschenburg88}. Such a surface is said to be of constant mean curvature (CMC). Even finding CMC surfaces is in general complicated, and it is necessary to use algorithms as the one developed in \cite{Metzger04}. We have the benefit that the spacetime we consider is static and axially symmetric, which allows us to reduce the problem to the integration of a second order ODE with a parameter to be determined. Therefore with standard numerical methods we are able to find candidates for stable isoperimetric surfaces, calculate their area and compare with the inequalities \eqref{desProbada} and \eqref{desConjetura}.

The article is organized as follows. In Section \ref{sec2} we describe the family of spacetimes found in \cite{Bonnor98}. Then, in Section \ref{sec3}, we calculate the ODE satisfied by CMC surfaces and discuss the particularities of its integration and the numerical scheme. The results on the relation between area an charge are discussed in Section \ref{sec4} This leads to an interesting limit manifold that is analyzed in Section \ref{sec5}. Finally the conclusions are presented in Section \ref{sec6}.

\section{The metric for the ECD prolate spheroid}\label{sec2}

In \cite{Bonnor98} Bonnor presents a family of static, axially symmetric, asymptotically flat solutions of the Einstein-Maxwell field equations. The matter content of the spacetimes corresponds to a prolate spheroid of ECD surrounded by vacuum. The metric in prolate spheroidal coordinates is
\begin{equation}\label{metric4}
 ds^2=-U^{-2}dt^2+a^2U^2\big(X(du^2+d\theta^2)+\sinh^2u\cos^2\theta d\phi^2\big),
\end{equation}
where $a$ is a constant and
\begin{equation}
 X=\cosh^2u-\sin^2\theta.
\end{equation}
The boundary between the matter and vacuum regions is defined by choosing a positive constant $u_0$, with $u<u_0$ corresponding to the region where the matter is, and $u>u_0$ corresponding to the vacuum region. The metric function $U$ is
\begin{equation}
 U = \left\{ \begin{array}{l l}
              1+\frac{m}{a}\ln\coth\frac{u}{2}, & u > u_0,\\
              1+\frac{m}{a}\Big(\ln\coth\frac{u_0}{2}+\frac{u_0^5-u^5}{5u_0^4\sinh u_0}\Big), & u < u_0.
             \end{array}\right.
\end{equation}
We refer the reader to \cite{Bonnor98} for details regarding the field equations. The parameter $m$ is the ADM mass of the spacetime, and as we are dealing with ECD it is also the total electric charge, $Q=m$. The parameter $a$ comes from the definition of prolate spheroidal coordinates, as in fact such coordinates are not a single system of coordinates but a family. It is interesting that changing this parameter changes the spacetime, as it changes the coordinates on which the spacetime is constructed.

In \cite{Bonnor98} the geometric properties of the ECD spheroid are discussed. If we consider $u_0$ as a parameter defining a family of spacetimes, while the other parameters are kept constant, then it is shown that the equatorial perimeter and area of the spheroid go to zero as $u_0$ goes to zero, while the polar perimeter diverges. This implies that given any positive number $k$, there is always possible to choose $u_0$ such that
\begin{equation}
 A_{u_0} < k\,m^2,
\end{equation}
or in terms of the total charge
\begin{equation}\label{ineqFail}
 A_{u_0} < k\,Q^2,
\end{equation}
where $A_{u_0}$ is the area of said spheroid. This is used in \cite{Bonnor98} as a counterexample to the conjecture that any mass distribution whose area is small enough with respect to its mass should form a black hole.

\section{CMC surfaces}\label{sec3}

As the maximal initial hypersurface we simply take a $t=constant$ slice. The extrinsic curvature vanishes and the induced metric is
\begin{equation}
 ds^2=a^2U^2\big(X(du^2+d\theta^2)+\sinh^2u\cos^2\theta \,d\phi^2\big).
\end{equation}
If we define the parameter
\begin{equation}
 \mu = \frac{m}{a}
\end{equation}
we see that $a^2$ is just an overall constant factor in the metric, which in fact is also an overall factor in the spacetime metric if we rescale the coordinate $t$. Therefore we concern ourselves with the metric
\begin{equation}\label{metric3}
 ds^2=U^2\big(X(du^2+d\theta^2)+\sinh^2u\cos^2\theta \,d\phi^2\big)
\end{equation}
and powers of $a$ can be restated later whenever necessary. As we only need to consider the vacuum region or the surface of the spheroid we have
\begin{equation}
 U=1+\mu\ln\coth\frac{u}{2}.
\end{equation}

In order to see why the inequality \eqref{ineqFail} is possible, we calculate the mean extrinsic curvature, $\chi$, of the $u=constant$ spheroids. A lengthy but straightforward computation gives
\begin{equation}
 \chi = \frac{U\cosh u (2\sinh^2u+\cos^2\theta)-2\mu X}{U^2X^\frac{3}{2}\sinh u}.\label{chispheroid}
\end{equation}
This shows explicitly that the $u_0$ spheroid is not an isoperimetric surface. We indirectly knew this because such spheroids can be made to violate the inequality \eqref{desProbada}.

As noted, a necessary condition for a surface to be isoperimetric is that its mean extrinsic curvature has to be constant. We describe a generic axisymmetric surface by the embedding $(u,\theta,\phi)=(s(\theta),\theta,\phi)$, where $s(\theta)$ is a function of $\theta$ only and we have made an abuse of notation by denoting also by $\theta$ and $\phi$ the coordinates on the surface.
The mean extrinsic curvature for such a surface is
\begin{eqnarray}\label{eqMean}
 \chi & = & -\frac{1}{U\sqrt{X(1+s'^2)}}\Bigg[\frac{s''}{1+s'^2}-\frac{1}{2}s'\sin(2\theta)\Big(\frac{1}{X}+\frac{1}{\cos^2\theta}\Big) \\
 && -\frac{1}{2}\sinh(2s)\Big(\frac{1}{X}+\frac{1}{\sinh^2s}\Big)+\frac{2\mu}{U\sinh s}\Bigg],
\end{eqnarray}
where
\begin{equation}
 X = \cosh^2 s-\sin^2 \theta, \qquad U = 1+\mu\ln\coth\frac{s}{2},
\end{equation}
and prime denotes derivative with respect to $\theta$.
In the special case $s(\theta)=constant$ we recover the formula for the spheroids \eqref{chispheroid}. Equation \eqref{eqMean} can be written in a more suggestive form as a differential equation for $s$, if we consider $\chi$ as a constant parameter,
\begin{eqnarray}\label{isSurfEq}
 s'' & = & (1+s'^2)\Bigg[-\chi U \sqrt{X(1+s'^2)}+\frac{1}{2}s'\sin(2\theta)\Big(\frac{1}{X}+\frac{1}{\cos^2\theta}\Big) \\
 && +\frac{1}{2}\sinh(2s)\Big(\frac{1}{X}+\frac{1}{\sinh^2 s}\Big)-\frac{2\mu}{U\sinh s}\Bigg].
\end{eqnarray}
A solution of \eqref{isSurfEq} corresponds to a CMC surface and hence we want to integrate it from $\theta=-\frac{\pi}{2}$ to $\theta=0$. The first thing to consider is that the solution needs to represent a smooth enough surface and this means that at least $s'\left(-\frac{\pi}{2}\right)=s'(0)=0$. Also, the differential equation \eqref{isSurfEq} is singular at $\theta=-\frac{\pi}{2}$, that is, the r.h.s. formally diverges at that point. This is a coordinate problem due to the spheroidal coordinates being singular there. This issue can be remedied, as discussed below, and the r.h.s. has a well defined limit if $s'\left(-\frac{\pi}{2}\right)=0$, coincident with one of the previous conditions.

Due to the complicated nature of \eqref{isSurfEq} we integrate it numerically using a shooting method. We fix the initial conditions $s_0=s\left(-\frac{\pi}{2}\right)$ and $s_1=s'\left(-\frac{\pi}{2}\right)=0$, and make a guess for $\chi$. We can then integrate the differential equation. We use as error function the value of $s'$ at the end point of the integration, that is, $s'(0)$. We update the guess for $\chi$ using the Newton-Raphson method,
\begin{equation}
 \chi_{k+1}=\chi_{k}-\frac{s'(0)}{\dot{s}'(0)},
\end{equation}
where dot means derivative with respect to $\chi$. We iterate until the value of the error function is small enough. After this process we obtain the function $s(\theta)$ and the corresponding $\chi$. By varying $s_0$ we change the surface found and by varying $\mu$ in \eqref{isSurfEq} we change the metric in which the surface is embedded, correspondingly we denote by $s_{s_0,\mu}$ the solution and by $\chi_{s_0,\mu}$ its mean extrinsic curvature.

As said, the differential equation \eqref{isSurfEq} is singular at $\theta=-\frac{\pi}{2}$. Although the limit is well defined, the singularity poses problems for the numerical integration. In order to circumvent this issue, before integrating we extrapolate the initial conditions from $\theta=-\frac{\pi}{2}$ to $\theta=-\frac{\pi}{2}+\delta$, where $\delta$ is the size of the first step on the integration grid. The extrapolation is done via a Taylor expansion to second order
\begin{equation}
 s(\theta) \approx s_0+s_1\left(\theta+\frac{\pi}{2}\right)+\frac{1}{2}s_2\left(\theta+\frac{\pi}{2}\right)^2
\end{equation}
The coefficients $s_0$ and $s_1$ could in principle be prescribed, but due to \eqref{isSurfEq} being singular only $s_0$ can be freely prescribed. In order for \eqref{isSurfEq} to have a well defined limit at $\theta=-\frac{\pi}{2}$ we need
\begin{equation}
 s_1=0.
\end{equation}
Once this is ensured, the r.h.s. of \eqref{isSurfEq} has a well defined limit that depends on $s_2$, and equating this with the l.h.s., i.e. $s_2$, we obtain
\begin{equation}
 s_2=-\frac{1}{2}\chi U_0 \sinh s_0 + \coth s_0 -\frac{\mu}{U_0\sinh s_0},
\end{equation}
where
\begin{equation}
 U_0 = 1+\mu\ln\coth\frac{s_0}{2}.
\end{equation}
Summarizing, the new initial conditions are
\begin{equation}
 s\left(-\frac{\pi}{2}+\delta\right) = s_0 + \frac{1}{2}s_2\delta^2, \qquad s'\left(-\frac{\pi}{2}+\delta\right) = s_2\delta,
\end{equation}
and the integration is performed from $\theta=-\frac{\pi}{2}+\delta$ to $\theta=0$.

An accompanying strategy to help with the singular limit is to use a grid with unevenly spaced points, in order to have more resolution close to the singular end. After some trials we decided to use a grid where the point $i$ is at position
\begin{equation}
 \theta_i = -\frac{\pi}{2}+\frac{\pi}{2}\left(\frac{i}{n}\right)^{1.4},\quad 0\leq i \leq n.
\end{equation}

Once we have obtained $s_{s_0,\mu}$ we calculate its area, which is given by
\begin{equation}
 A_{s_0,\mu} = 4\pi\int_{-\frac{\pi}{2}}^{0}U^2\sqrt{X(1+s'^2)}\sinh s\cos{\theta}\,d{\theta}.
\end{equation}
To perform the ODE integration we use the Runge-Kutta-Fehlberg method, and for the area integration the  composite Simpson's rule. Both methods are already implemented in SageMath \cite{SageMath}. To test the accuracy of the numerical solution we use the $\mu=0$ case, which is simply Euclidean space and where we know that the isoperimetric surfaces are spheres, which in prolate spheroidal coordinates have the expression
\begin{equation}
 s_E(\theta)=\mbox{arccosh}\sqrt{\cosh^2 s_0+\cos^2\theta},
\end{equation}
and for which
\begin{equation}
 \chi_E = \frac{2}{\cosh s_0},\qquad A_E = 4\pi\cosh^2(s_0).
\end{equation}
Comparing the numerical solution to the exact solution we decided to use a grid with $n=2^{10}$ points for $s_0> 0.005$ and with $n=2^{11}$ points for $s_0\leq 0.005$ which ensures enough accuracy. The relative error in the area, which is our main concern in the numerical scheme, is shown in Figure \ref{fig0}.

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig0.pdf_tex}
  \caption{Relative error in the area for the Euclidean case.}
  \label{fig0}
\end{figure}

In Figure \ref{fig1} we have plotted several solutions to \eqref{isSurfEq} with varying $s_0$ and $\mu$, which illustrates the general tendency of the CMC surfaces. As expected from the $\mu=0$ case, each $s_{s_0,\mu}(\theta)$ is an increasing function of $\theta$. Also expected, if we fix $\mu$, then $s_{s_0,\mu}(\theta)$ is an increasing function of $s_0$ for every $\theta$ and therefore the solution $s_{s_0=0,\mu}(\theta)$ bounds from below all the other solutions. Finally, if we fix $s_0$, then $s_{s_0,\mu}(\theta)$ is a decreasing function of $\mu$, and the solution does not go to zero but there exists a limit solution as $\mu\rightarrow\infty$.

\begin{figure
  \centering
  {{}}\def.8\textwidth{\textwidth}
  \input{Fig1.pdf_tex}
  \caption{CMC surfaces.}
  \label{fig1}
\end{figure}

In Figure \ref{fig2} we show the mean extrinsic curvature of the CMC surfaces as a function of $s_0$ for several values of $\mu$. In general, as expected, $\chi_{s_0,\mu}$ is a decreasing function of $s_0$, although for some values of $\mu$ there is a range in $s_0$ where $\chi_{s_0,\mu}$ is an increasing function. In all cases the mean extrinsic curvature goes to zero as $s_0\rightarrow\infty$. Also, if we fix $s_0$, then $\chi_{s_0,\mu}$ is a decreasing function of $\mu$ and goes to $0$ as $\mu\rightarrow\infty$.

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig2.pdf_tex}
  \caption{Mean extrinsic curvature.}
  \label{fig2}
\end{figure}

\section{Relation between area and charge}\label{sec4}

Our main interest in this work is to analyze the relation between area and charge for the surfaces we have integrated, and compare with the inequalities \eqref{desProbada} and \eqref{desConjetura}. All the surfaces we consider enclose the ECD spheroid and therefore their charge is the charge of the spacetime. To make the comparison easier we define the quantity
\begin{equation}
 q_{s_0,\mu} = \frac{A_{s_0,\mu}}{4\pi\mu^2}.
\end{equation}
This quotient is the same as $A/(4\pi Q^2)$ once we reinstate the factors of $a$. We know that $q_{s_0,\mu}$ is not bounded above, as the spacetime is asymptotically flat and then $A_{s_0,\mu}$ can be made as large as we want by taking $s_0$ big enough. On the other hand, $q_{s_0,\mu}$ has to be bounded below away from zero if $s_{s_0,\mu}$ is a stable isoperimetric surface. In order to compare with the inequalities \eqref{desProbada} and \eqref{desConjetura} we note that if they are satisfied by $s_{s_0,\mu}$ then $q_{s_0,\mu}\geq k$ with $k=\frac{1}{3}$ for \eqref{desProbada} and $k=\frac{4}{9}$ for \eqref{desConjetura}.

In Figure \ref{fig3} we have plotted $q_{s_0,\mu}$ as a function of $s_0$ for several values of $\mu$. We see that $q_{s_0,\mu}$ is an increasing function of $s_0$, as expected, and that there is a well defined limit for $q_{s_0,\mu}$ as $s_0$ goes to zero, which can be quite large if $\mu$ is small. We plot again $q_{s_0,\mu}$ as a function of $s_0$ in Figure \ref{fig4}, but for higher values of $\mu$. We observe the same behavior as before, although the curves get closer as $\mu$ increases and there is a limiting curve. We see already that the minimum of $q_{s_0,\mu}$ seems to be above $0.96$, a value that is far from $\frac{1}{3}$ or $\frac{4}{9}$.  There is a subtlety regarding the case when $s_0$ is close to zero. In Figure \ref{fig5} we have zoomed into the region close to $s_0=0$ for $\mu=28$. We see that the minimum of $q_{s_0,\mu}$ is not attained at $s_0=0$ but at around $s_0=0.0021$. Analyzing the results of the integrations we conclude that such minimum first appears for $\mu\approx 1$, although we have not tried to find exactly when this happens. Said minimum moves to the right and settles at around $s_0=0.0026$ with increasing $\mu$.

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig3.pdf_tex}
  \caption{Area-charge quotient.}
  \label{fig3}
\end{figure}

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig4.pdf_tex}
  \caption{Area-charge quotient for large $\mu$.}
  \label{fig4}
\end{figure}

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig5.pdf_tex}
  \caption{Area-charge quotient for small $s_0$.}
  \label{fig5}
\end{figure}

From the plots we note that $q_{s_0,\mu}$ is a decreasing function of $\mu$ if one keeps $s_0$ constant. To analyze this we show in Figure \ref{fig6} $q_{s_0,\mu}$ as a function of $\mu^{-1}$, which highlights its behavior for large $\mu$. We see that it is an increasing function of $\mu^{-1}$. To see the limit as $\mu^{-1}\rightarrow 0$ we zoom in in Figure \ref{fig7}, showing that $q_{s_0,\mu}$ has a well defined limit there and that said limit does depend on $s_0$. As already noted we have $q_{s_0,\mu}>0.96$. The behavior of $q_{s_0,\mu}$ suggest taking the limit $\mu\rightarrow\infty$, which we do in the following section.

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig6.pdf_tex}
  \caption{Area-charge quotient.}
  \label{fig6}
\end{figure}

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig7.pdf_tex}
  \caption{Area-charge quotient for large $\mu$.}
  \label{fig7}
\end{figure}

To close this section we point out that there are other CMC surfaces besides those considered so far. In Figure \ref{fig11} we have plotted five CMC surfaces, all with $s_0=0.005$ and for $\mu=10$. The one in red corresponds to a candidate for a stable isoperimetric surface, while the other four are not candidates, as they are concave and therefore they are not stable isoperimetric surfaces. It is interesting that these surfaces can violate both \eqref{desConjetura} and \eqref{desProbada}, which again shows that the stability requirement is crucial.

\begin{figure
  \centering
  {{}}\def.8\textwidth{\textwidth}
  \input{Fig11.pdf_tex}
  \caption{Other CMC surfaces.}
  \label{fig11}
\end{figure}

\section{The limit $\mu\rightarrow\infty$}\label{sec5}

From the results so far it is clear that the lowest possible value for $q_{s_0,\mu}$ is attained in the limit $\mu\rightarrow \infty$ and for a CMC surface with $s_0$ close to zero. It is quite interesting that the isoperimetric problem can be analyzed in the limit $\mu\rightarrow\infty$ as we show in the present section. We start by defining a limit metric,
\begin{equation}
 d\hat{s}^2 = \lim_{\mu\rightarrow\infty} \frac{ds^2}{\mu^2} = \hat{U}^2 \left(X(du^2+d\theta^2)+\sinh^2u \cos^2\theta d\phi^2\right),
\end{equation}
where
\begin{equation}
 \hat{U} = \ln\coth\frac{u}{2}.
\end{equation}
The quantities that we calculated for $ds^2$ can be obtained for $d\hat{s}^2$ by performing the analogous calculations or simply by multiplying the adequate factors of $\mu$ and then taking the limit. In particular, the equation corresponding to a CMC surface is
\begin{eqnarray
 s'' & = & (1+s'^2)\Bigg[-\hat{\chi} \hat{U} \sqrt{X(1+s'^2)}+\frac{1}{2}s'\sin(2\theta)\Big(\frac{1}{X}+\frac{1}{\cos^2\theta}\Big) \\
 && +\frac{1}{2}\sinh(2s)\Big(\frac{1}{X}+\frac{1}{\sinh^2 s}\Big)-\frac{2}{\hat{U}\sinh s}\Bigg],
\end{eqnarray}
where
\begin{equation}
 \hat{\chi}=\lim_{\mu\rightarrow\infty}\mu\chi.
\end{equation}
For the numerical integration, the Taylor approximation coefficients are
\begin{equation}
 s_1 = 0,\qquad s_2=-\frac{1}{2}\hat{\chi} \hat{U}_0 \sinh s_0 + \coth s_0 -\frac{1}{\hat{U}_0\sinh s_0}.
\end{equation}
Also
\begin{equation}
 \hat{A}_{s_0} = \lim_{\mu\rightarrow\infty}\frac{A_{s_0,\mu}}{\mu^2}  = 4\pi\int_{-\frac{\pi}{2}}^{0}\hat{U}^2\sqrt{X(1+s'^2)}\sinh s\cos{\theta}\,d{\theta},
\end{equation}
and the quotient between area and charge takes the form
\begin{equation}
 \hat{q}_{s_0} = \frac{\hat{A}_{s_0}}{4\pi} = \lim_{\mu\rightarrow\infty}q_{s_0,\mu}.
\end{equation}

It is worth noticing that the limit metric can be written in spherical coordinates as
\begin{equation}
 d\hat{s}^2 = \hat{U}^2(dr^2+r^2 d\Omega^2).
\end{equation}
If we consider $r$ large, then
\begin{equation}
 d\hat{s}^2 \approx \frac{dr^2}{r^2} + d\Omega^2,
\end{equation}
with the relative error in the metric functions being of order $r^{-1}$. If we define $\hat{r} = \ln{r}$ then
\begin{equation}
 d\hat{s}^2 \approx d\hat{r}^2 + d\Omega^2,
\end{equation}
which shows that the metric is asymptotically cylindrical and that for $r$ large the surfaces $r=constant$ are approximate isoperimetric surfaces, with area $\hat{A}_{s_0\rightarrow\infty}= 4\pi$, which gives $\hat{q}_{s_0\rightarrow\infty} = 1$.

For the integrations corresponding to this section we increased the number of grid points to $n=2^{12}$ for $s_0\leq0.005$, in order to have better accuracy. From the numerical results, we first plot $\hat{\chi}_{s_0}$ in Figure \ref{fig8}. We see that it is a decreasing function that goes to zero. To analyze the area-charge quotient, in Figure \ref{fig9} we have plotted $\hat{q}_{s_0}$, and we zoom in close to $s_0=0$ in Figure \ref{fig10}. We find that the minimum of $\hat{q}_{s_0}$ is attained at $s_0=0.00259$ and with a value $\hat{q}_{s_0}=0.9628862930603$.
From this we conclude that all CMC surfaces that are candidates to be stable isoperimetric surfaces satisfy
\begin{equation}
 q_{s_0,\mu} \geq 0.9628862930603,
\end{equation}
which as noted before is sufficiently above $\frac{1}{3}$ and $\frac{4}{9}$ as not to present a challenge for the inequalities \eqref{desProbada} and \eqref{desConjetura}.

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig8.pdf_tex}
  \caption{Mean extrinsic curvature for $\mu\rightarrow\infty$.}
  \label{fig8}
\end{figure}

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig9.pdf_tex}
  \caption{Area-charge quotient for $\mu\rightarrow\infty$.}
  \label{fig9}
\end{figure}

\begin{figure
  \centering
  {{}}\def.8\textwidth{.8\textwidth}
  \input{Fig10.pdf_tex}
  \caption{Area-charge quotient for $\mu\rightarrow\infty$ close to $s_0=0$.}
  \label{fig10}
\end{figure}

\section{Conclusions}\label{sec6}

We have studied the spacetime found by Bonnor \cite{Bonnor98} in the light of the geometrical inequality \eqref{desProbada}. Through a shooting method we have obtained numerically a foliation of part of the maximal initial slice by CMC surfaces which are candidates to be stable isoperimetric surfaces. By the results in \cite{HuiskenYau96}, \cite{EichmairMetzger2013a} and \cite{EichmairMetzger2013b} we know that for $s_0$ large enough they are indeed stable isoperimetric surfaces, and although we do not know how large $s_0$ needs to be it seems that the foliation gets quite close to the ECD spheroid even when $\mu$ diverges.

With these CMC surfaces we tested the inequalities \eqref{desProbada} and \eqref{desConjetura}, showing that for the family of spacetimes
\begin{equation}\label{desECD}
 q_{s_0,\mu} \geq 0.9628862930603.
\end{equation}
So the bound on $q_{s_0,\mu}$ is far from $\frac{1}{3}$ and $\frac{4}{9}$, and therefore does not present a challenge to the geometrical inequalities. This not being close to saturate the inequalities can be interpreted as the spacetime being far from extremality in terms of its charge density. An interesting consequence of searching for \eqref{desECD} is that we were led naturally to consider a limit metric, which instead of an asymptotically flat end has a cylindrical end, and were the minimum of \eqref{desECD} is attained.

We also found CMC surfaces that are not stable isoperimetric, showing that some of them do not satisfy \eqref{desProbada} or \eqref{desConjetura}, illustrating that the stability requirement is fundamental for the inequalities to be valid.

We have not analyzed several interesting properties of the surfaces, most notably their stability, but it is a complicated problem that did not add to  the main objective of the work, as the inequalities \eqref{desProbada} and \eqref{desConjetura} were far from being challenged. Also, we did not investigate the reasons why the minimum of $q_{s_0,\mu}$ is achieved for a positive value of $s_0$ for $\mu$ big enough, the increasing value of $\chi_{s_0,\mu}$ as a function of $s_0$, or the relation between the isoperimetric surfaces and the spacetime, if there is any. Finally, and far more reaching, is the question of finding a good measure of the ``size'' of an object. We have not tried to analyze other proposed measures of size and compare to the isoperimetric surfaces.

\section{Acknowledgments}

I would like to dedicate this article to the memory of Sergio Dain, he suggested this problem, generous as he was with ideas, and discussions with him were always enlightening.

The numerical computations were performed and the figures produced in SageMath \cite{SageMath}.

redpajama_set_name: RedPajamaArXiv


text:
package controllers

import (
	"github.com/astaxie/beego"
	"mywork/api"
	"mywork/models"
)

type LoginController struct {
	beego.Controller
}

//显示登录的主页面
func (this *LoginController) Index() {
	this.Data["title"] = "用户登录"
	this.Layout = "tpl/login_layout.tpl"
	this.TplNames = "login/index.html"
}

//检测用户名密码是否正确
func (this *LoginController) Check() {
	var err error
	if _, err = models.CheckLogin(this.Ctx); err == nil {
		this.SetSession("uid", int(1))
		this.SetSession("username", this.Input().Get("username"))
	}
	this.Data["json"] = api.Output("", err)
	this.ServeJson()
}

//用户退出
func (this *LoginController) Out() {
	this.DestroySession()
	this.Data["json"] = api.Output("", nil)
	this.ServeJson()
}

redpajama_set_name: RedPajamaGithub


The Caten brothers (that would be Dean and Dan) once again bring us a merry mix of seemingly disparate elements forged into an intoxicating brew. They double up on singular charm by combining military, Victoriana, and other winsome themes and genres to produce quirky yet covetable ensembles.
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Toreador pants without the need to torture a critter. These can go casual OR upscale akin to tuxedo pants. Or hell, go nuts and wear with the embellished black cape in the collection.
Tried and true wearable silhouettes made opulent and dramatic by virtue of the fabrications, detail work, and whimsical combinations. Throw in some latter day armor and we have quite the tour de force spectacle.
Red and Blue is always a winning combination. Think of this combo as the new neutral.
Many of these pieces would work well at any glamorous soiree or gala opening. And then could be worn again over casual togs and jeans and such.
Thanks Dean and Dan for another spellbinding collection!
JODHPURS are the new black!


H.E.R. continues to captivate audiences around the country and on television.
The rising R&B artist appeared on Tuesday's episode of "The Tonight Show" Starring Jimmy Fallon, and performed her sultry song, "As I Am." Rocking an all black with sunglasses, H.E.R. launched her performance behind a keyboard with the backing of two background singers before picking up a guitar and setting up shop at center stage. DJ Scratch accompanied the R&b songstress and added some hip-hop flavor to the performance.
H.E.R. will launch the 21-date "I Used To Know HER Tour" on November 10 in Atlanta, GA. The trek will make stops in major cities like New York, Chicago, San Francisco, and Las Vegas, before commencing on December 20 in San Francisco.


We are living in one of the most exciting times in the history of humankind. Our world is now filled with information abundance, surplus, and access. The result is synergy whereby the human mind plus our current technologies far exceed the sum of these individual parts.
(Gerstein, Jackie The Educator as a Maker Educator) See Maker Educator Thinglink below.
To identify digitally driven, and other innovative practices that work, then scale them up.
To inspire teachers and students, empowering both to amplify their learning through emerging technologies and state-of-the-art student engagement activities.
Corporations and industry are uniquely designed to robustly respond to dizzying cultural changes and adapt to emerging technologies. Education, however, burdened by bureaucracy and financial constraints, in many cases, is incapable of leveraging freely available tools to maximize teacher workflow, student learning and enhanced productivity for both.
In the 21st Century, a teacher's role is no longer the "Sage on the Stage," but the "Guide on the Side."
Teachers must lead all learners to not only develop digital literacy skills but at the same time, inspire a new generation of intellectual risk takers, critical thinkers, communicators, collaborators and innovators who will ensure America's future prosperity and tackle the pressing problems facing this planet.
Despite a boundless supply of both compelling digital resources and hands-on, "unplugged" materials that promote engineering and creativity, the lack of substantive staff development to both train and provide teachers adequate time to internalize new learning, has created a crises-gap between what teachers should know and can do to promote 21st Century Skills.
To fill this teacher-knowledge gap, communities and all stake holders, need to work together to ensure all teachers have the tools, training and adequate time to effectively process and implement their new learning, so they can empower students to become change agents of the future.
Stanford's "You Cubed" website titled 'Everyone Can Do Math", provides evidence that learning is the inalienable right of every child; that it is a result of engagement, a positive mindset, and believing in the "power of failure". Technology-engagement provides a safe place to fail and try again until mastery.
TED-ED and TED Talks a resource of human inspiration and hope.
TEDEd provides a broad scope of short engaging educational topics, which include question feedback, deeper thinking options, and options to modify lesson. Click on image to link to lessons.
, Upon leaving the 2019 Computer User Education Conference in Palm Springs, the presentations reinforced the utter "Simplexity" of school districts' abilities to generate a "butterfly effect" of pedagogical and technological transformations in every classroom, thus creating a critical mass of highly effective teachers who would positively alter the school culture, amplify visible learning and guarantee enhanced student achievement.
To achieve this vision, it will require a radical mind-shift on ensuring quality staff development, a model built upon implementation and accountability systems. A true innovative shift in staff development needs to re-think the pressures of time and the negative impact on teacher wellness, and as such, offer teacher stipends and/or incentives to motivate and reward new learning.
After teaching 48 years, taking risks alone, with no help, thus stumbling and falling all over the technology learning curve, I am passionately committed toward designing a better, more efficient system to ensure teachers effectively implement new methodologies and technologies to positively impact student learning. For those who join me, you are helping me inspire a positive teaching culture, an educational "climate change" rooted in respecting teachers.
TED Talks: Provocative ideas presented by renowned scientists, entrepreneurs, engineers, professors, artists, that explore BIG IDEAS and inspire curiosity.


text:
Hydroklortiazid är ett diuretikum (urindrivande medel).
Hydroklortiazid ingår i ett stort antal läkemedel i kombination med blodtryckssänkande substanser.

Referenser

Tiazider
Bensotiadiaziner


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Home > > 05/14/2018
Volume 265 Issue 20 05/14/2018
Sponsored by Sourcebooks
No One Is Illegal: Spotlight on Eoin Colfer
A graphic novel by Eoin Colfer, author of the Artemis Fowl books, and Andrew Donkin puts a human face to the European migrant crisis
Eoin Colfer and Andrew Donkin are perhaps best known for their graphic novel adaptations of Colfer's Artemis Fowl fantasy-adventure series. Their latest project marks a clear departure for the duo. Illegal is a middle grade graphic novel about a Ghanaian orphan named Ebo who follows his older brother, Kwame, on a brutal journey in pursuit of asylum in Europe. The narrative alternates between the present—in which Ebo has reunited with his brother but the two are adrift in the Mediterranean, awaiting uncertain rescue—and the past, to Ebo's trek into Niger to find his brother.
After collaborating on four graphic Artemis Fowl adaptations, Colfer, who lives in Wexford, Ireland, and Donkin, based in London, felt drawn to embark on an original work on a pressing topic. About four years ago, as the two sought out the right subject for their project, Donkin found himself deeply affected by frequent news reports on the sinking of vessels carrying migrants fleeing humanitarian crises. "We'd wait for a follow-up report and a list of names, but they never came," he says.
Colfer was similarly impacted by the loss of migrant lives and the tragic anonymity of the news reports. In conceiving their story, he drew from an earlier experience he had working with Tunisian orphans in a volunteer orphanage. "The stories of those children were heartbreaking," Colfer says. "This issue is so sensitive that we wanted to make our story as truthful and real as possible."
Colfer and Donkin began researching in earnest, attending conferences and connecting with London-based charities Migrant Voice and Women for Refugee Women to hear refugee stories firsthand. For Colfer, the graphic format was a powerful way to tell Ebo's story. "The beauty of the graphic novel is that it can be poured over a dozen times, and each time the reader will find something they missed," he says. The authors turned to Italian illustrator Giovanni Rigano, who also created the art for the Artemis Fowl graphic novels, to illustrate Illegal.
"Giovanni has done a stunning job with the artwork, which really brings out the epic nature of their struggles and their long and dangerous journey," Donkin says. "This is the perfect medium for this story because we can show you what happens to Ebo and his brother without having to overly comment on it and pass judgment ourselves."
The book's title is arguably provocative, however. "Illegal is quite a controversial word in this context," Colfer says. "Often migrants are referred to as illegal, but the children cannot understand how they can be illegal for simply existing on planet Earth." Colfer adds that he and Donkin took the title from a quote by author and Holocaust survivor Elie Wiesel, which begins, "You who are so-called illegal aliens must know that no human being is 'illegal.' That is a contradiction in terms."
Since the book's U.K. release last year, the authors have heard from many readers. "The most powerful reactions have been from people who have made the journey and gave us their seal of approval," Colfer says. "It was very emotional for some of those people to read this book, and it meant a lot to us that Illegal moved them."
Donkin says, "The reaction to the book has been fantastic, especially from people who have completed that terrible journey." After speaking at an exhibition about the book in Como, Italy, Donkin was approached by a young man who could personally relate to Ebo's experience. "He was so happy we'd written it for others to read," Donkin says. "That was a really touching moment."
The authors are hopeful that American readers will be similarly moved by Ebo's story. "I hope that U.S. readers will focus in on the children who are stranded at sea through no fault of their own and forget the politics surrounding the issue," Colfer says. "The question is: should we help children in trouble? The answer to that question should always be yes."
A version of this article appeared in the 05/14/2018 issue of Publishers Weekly under the headline: No One Is Illegal
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Hemp Foods Australia Named Finalist in Premier's 2016 NSW Export Awards
By Paul Benhaim
Hemp Foods Australia has been named a finalist in Premier's 2016 NSW Export Awards. The company will be recognized for its achievements at a gala dinner and award ceremony at The Star, Pyrmont on 26 October 2016.
"We are excited and honored to be a finalist in the NSW Export Awards." said Paul Benhaim, founder and CEO of Hemp Foods Australia. "Our company has put forth a tireless effort to bring the best quality hemp products to the people of our great home country and internationally, and it is great to see our hard work paying off."
Hemp Foods Australia is the largest hemp food wholesaler, retailer, manufacturer and exporter in the Southern Hemisphere. In addition to its popularity across Australia, the company's high-quality hemp seeds, hemp oils and hemp protein powder are distributed in South Korea and in Japan through its sister company Hemp Foods Japan. In July 2016, Paul Benhaim held a highly publicized discussion with First Lady of Japan Akie Abe regarding the use of hemp as a viable alternative in Japanese industry. The meeting, which took place at the Kyoto Hemp Forum, included high-profile hemp industry entrepreneurs and thought leaders from around the world.
The Premier NSW Export Awards is an annual celebration of best-in-class exporters of goods and services from the New South Wales region. Each year, the Export Council of Australia picks finalists from 12 industries in tandem with the NSW government. The award ceremony promotes excellence in Australian industry and also serves as a promotional tool for nominees to showcase their achievements.
"The NSW Export Awards are a great display of the surging success of Australian business owners," Paul Benhaim stated. "We hope that Hemp Foods Australia can serve as a case study of success for entrepreneurs across the country. In addition, the NSW Export Awards are a great forum to continue the conversation about the incredible benefits of increasing the usage of hemp in our national economy."
For more information about Hemp Foods Australia, please visit http://www.hempfoods.com.au/.
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Julian Burnside on Tampa, Turnbull and the 'unthinkably awful' Peter Dutton | Daily Review: Film, stage and music reviews, interviews and more.
Fotis Kapetopoulos speaks to Julian Burnside QC who will be delivering the annual Walter Lipmann Oration on Thursday, September 13 at the Melbourne Town Hall presented by the Ethnic Communities Council of Victoria.
It is a cold, wet and dark afternoon at the lawyers' end of Melbourne's CBD. The office of human rights advocate and barrister Julian Burnside QC is warm and welcoming, like an old wood-lined library.
Burnside may look professorial but he's a voluble annoyance to the architects of Australia's cruel regime of processing irregular arrivals and those who dog-whistle racial fears.
Burnside gained prominence in the 1990s acting for the people of Ok Tedi against BHP; Alan Bond in fraud trials; Rose Porteous against Gina Rinehart; and the Maritime Union against Patrick Stevedores.
The Tampa Affair in 2001 was a defining moment for Burnside. The Howard Government sent SAS troops onto the Norwegian tanker Tampa to stop it from landing on Christmas Island with 434 refugees it had rescued off the sinking wooden boat Palapa. The government's response began to coarsen our collective attitude towards refugees.
"The Tampa Affair was John Howard's last hurrah, he was on the skids electorally," says Burnside.
Burnside recalls how a solicitor who had briefed him on a complex commercial case thought of a "clever case theory for ending the standoff".
"He asked me to act and I said yes, not because I knew anything about maritime law, which I didn't, and not because I knew of anything about refugee policy or law, because I didn't, but because I feel the heat," he says.
Human rights are not complex for Burnside; they are premised on simple human feeling.
Burnside imagined how it must feel on "that steel deck in the tropical sun; so that very simplistic empathy brought me in the area".
The judgement was handed down in Melbourne on the afternoon on September 11, 2001.
Paintings and photographs hang and rest against the walls of his office. Burnside's love for the arts is equal to his passion for human rights. Books, papers, reports, magazines and cluster around him and on a bookshelf behind his large wooden desk, as he occasionally swiping across his iPad.
He will be talking tomorrow night about multiculturalism in honour of the late Walter Lippmann, one of the designers of multicultural policy, a founder of the ECCV and a prominent advocate in Victoria's Jewish Community in the 70s.
But Burnside is not a policy boffin.
"I am not interested in politics – I grew up in Melbourne in the '50s and I remember how mono-cultural we were and how boring it was" he says.
"Sunday lunch was meat and three veg, all over-cooked. I remember when post World War II immigrants came from Greece and Italy, the people of my parents' generation – not my parents – would call them 'refos', 'wogs', 'i-ties'.
"They complained about how these new immigrants 'dress differently, they have too many children, they are too religious' the same as we hear now about Muslims, Africans and others," he says.
"I remember a time when there was nothing more unthinkable than eating squid and the Italians and Greeks were buying it at a dollar a kilo in the '70s," he laughs.
I tell him stories of my father being harassed for having a moustache and my mother being called a 'whore' for wearing off the shoulder dresses, having long hair and not wearing a pillbox hat. And me growing up being with the word 'wog' etched on me.
Australians, I argue, may be harsh but we are soft compared to places in some European nations where the migrant is a migrant forever.
Burnside takes time, thinks and responds, purposefully, openly and simply.
"True, we do not have long standing hatreds, but we need someone to pick on, maybe because we think our hold on this land is tenuous having taken it off the Aboriginals," he counters.
He highlights how before World War II this divide was "Christians against the Jews" referring to the 1938 Conference of Evian when delegates from 32 nations and representatives from relief organisations met to discuss the German-Jewish refugees.
"Thomas White, the Australian representative at the Conference famously said 'We do not have a racial problem in Australia and have no intention of importing one,'" says Burnside.
Like many of us, Burnside says he had great hopes for Malcolm Turnbull but "he turned out to be disappointing".
And yet, like many of us he too was relieved Scott Morrison became PM, instead of Peter Dutton.
"Morrison was a terrible immigration minister, but Dutton was unthinkably awful," he qualifies.
Julian Burnside QC will be speaking at the ECCV Walter Lippmann Oration on Thursday 13 September at 6pm Melbourne Town Hall Supper Room.
Next Post 'Crudo' by Olivia Laing book review: Is this a novel I see before me?
Politics certainly brings out the opportunists, hey, but I'm terribly cynical, I believe that behaviour probably was well under way before humans stood upright. I don't believe the far right have cornered the market.
The fact that the cunning far right have harnessed the 'accent' of the battler so successfully only proves to me how far the so called left has lost it's way. The only way to counter it in my opinion is to expose it for the fakery it is, by allowing the real battler to speak. I certainly tire of hearing of the strugglers circumstances via an aloof, intellectualized debate. I cannot count the times on the ABC when while talking of extreme hardship, panelists break out in laughter about one thing or another someone has said that has tickled their funny bone.
I believe a lot of people do have the best of intentions, but lack the perspective of experience. Labor has lost perspective. Their track record hasn't been flash either, and their voting with the LNP on policy is disgusting but luckily for them, often hidden from view. And I think they are quite happy to have the LNP do some of their dirty work done for them, regardless of what they say.
Julie, I absolutely agree. And the worst of it is that this has been caused since Tampa – by Govt. Party Policy….. This brought to mind the money that has been put into armaments (as an example) by successive Governments. Take the submarines for example. 12 submarines for $billions and we have only enough sub-mariners to have two available at the one time currently – and how much of this Industry therefore the money, has been "shifted" to the few wealthy dealers of this mass destruction – and the personal wealth that has been amassed by the few in the need of the Parties of the Right to bomb out of existence the people that that Right wing Party – now your Govt., doesn't "like". "But under/unemployment is only going to get worse, housing stress is only going to get worse, and people already resent immigration into areas that previously there was none. The haters are back and have multiplied." ALL of this could be quenched if the dollars created by our Govt. that pays for just these armaments – would go to the Social Welfare bill instead uplifting the drowning numbers of poverty stricken Australian citizens . It also DOESN'T mean we sacrifice our own defense capabilities either. We ARE a monopoly currency issuing Govt. BOTH can be achieved. But again – it is only the Far Right party policy that demonises the poor, encourages racism, creates the victims – like the German Jews of WWII, and enriches an individual at the expense of the millions who can't even get a response from their local Govt members – but the war lobbyists and haters of the media – can. Politics.
There has been significant changes since the early immigrations to Australia. There was the same dog whistling, true. 'They're taking your jobs, they're buying your houses, they have it better than you do, they don't assimilate, they're criminals' baa baa baa baa.
But then, importantly, there was a massive boom in employment. There was a huge boom in housing. 'They don't assimilate' was easily solved by moving into areas low in migrants, and huge numbers could and did. As a result, some of that early racism toward new aussies seemingly faded into the background as they revelled in the new dog whistles, that of the land of the fair go and the lucky country.
But under/unemployment is only going to get worse, housing stress is only going to get worse, and people already resent immigration into areas that previously there was none. The haters are back and have multiplied. First Nations people are still as under threat as they've ever been and on so many levels are treated as bad, if not worse, than immigrants. For over two centuries they've been telling us Australia is racist. I have eyes, I have ears, I believe it. I believe it takes a special kindof ignorance not to. Racism is left and right. It's behind and in front of you. It's above you and below you. It's everywhere. Hard times are coming, and that rarely brings out the warm and fuzzies in anyone, let alone racists.