Skip to content

Black holes without a singularity

I know I’ve been too busy to post anything here for a while now, but I came across something recently that I found so cool that I had to share it. Usual disclaimer: This is a very handwavey explanation.

Most people think of black holes as “a thing that nothing can escape from, not even light”. And this is correct, modulo some quantum stuff. You also may know that general relativity tells us that the gravitational force is actually a warping of space-time itself, and that at the centre of a black hole the spacetime is so curved that it becomes singular.

Has anybody seen that movie Tron?

Obviously you’ve spotted the contradiction to Fermat’s last theorem there too, right?

A curvature singularity is thought of like the hole in ground in the above image from Homer’s trip into 3D land; it becomes infinitely curved. It is generally assumed that inside a black hole there is always one of these singularities, and in fact the standard picture of gravitational collapse tells us that this should always be the case.

However, some recent work by Prof. Dr. Frans Klinkhamer from the Institute for Theoretical Physics at Karlsruhe Institute of Technology has come up with some unusual solutions to Einstein’s equations corresponding to black holes without singularities. Now this in itself is not entirely new, because people have found similar solutions by inserting some weird “exotic matter” into their models. However Klinkhamer has come up with solutions to Einstein’s equations corresponding to black holes without singularities, without introducing weird matter. In fact, these solutions have NO matter in them; they’re entirely empty universes.

There is however something peculiar about his universes, which allows for these black holes. The difference is in what mathematicians call the topology of the universe. Inside the event horizon, the universe twists around itself; not entirely unlike a pretzel.

As I mentioned above,  this kind of black hole is a perfectly valid solution to Einstein’s equations but it doesn’t agree with the standard picture of gravitational collapse. There is no proposed mechanism for this weird twisting of the universe to occur naturally from the gravitational collapse of a massive object, and in fact there are theorems saying that when gravitational collapse occurs the end result is actually a singularity. But who knows? Perhaps when we have a working theory of quantum gravity, we will come up with a mechanism to avoid the singularity and end up with one of these solutions instead. Or perhaps this is just a mathematical quirk and nothing more?

The most recent paper on this stuff can be found here (not for the faint of heart):

Highlight Reel

The Feynman Sprinkler
Dead Mathematicians Society
Risk-free gambling with math!
Abbott’s Cabinet: What’re the chances?
Probabability Paradox* — part 2
The pi is a lie!
My infinity is bigger than yours!
real theorem!

Asking Stupid Questions

An oft-quoted line from teacher to student is “There is no such thing as a stupid question”, which I think is a good sentiment to alleviate the fear of asking questions. Although I believe a good deal more than that is required to ensure that students are comfortable asking and answering questions in class, this is not what I plan on talking about today.

Today we’re going to talk about a special kind of stupid question. Of course there are stupid questions; Why did you lock your keys in the car? Would you like free upgrade to first class?  What’s your star sign? Should I go to grad school? What’s that smell? And many more… Then there are things like these beauties from the Australian Academy of Science. But if you’re observationally gifted, you may have noticed that this post was filed under education. Today we complain about education again.

Far too often, I’ve seen test questions that I don’t remotely agree with. I don’t disagree with the solutions — I just don’t believe that the questions achieve their purposes. Since I’m not nearly at a point in my career when I can carelessly insult specific questions that I’ve come across, I won’t. But this kind of stupid question is so prevalent that it wouldn’t be fair to isolate any particular culprits anyway. The kind of stupid question that I’m talking about is one requiring unnecessary complicated calculations or assuming that the student is familiar with some particular example. And here I’m referring to test questions only — timed tests should be approached differently to assignments, where plenty of unstressed thinking time is available. Let me illustrate what I mean with some fictional examples:

  • Testing l’Hôpital’s rule with an example that requires 6 iterations before getting an answer. That is, the student must perform the same technique 6 times over before arriving at an answer.
  • Testing primary school geometry by asking what the interior angles of a stop sign are. Not knowing the shape of a stop sign is different to not knowing what an octagon is.
  • A separable first order ODE that requires a page of working to evaluate the integral.
  • Asking students to reproduce a proof that was included as an optional exercise earlier in the semester. Students will do a different random selection of problems each; you’ll just be measuring which students picked the same question that you did.
  • Having a needlessly ugly solution to a problem — Like 4736\sqrt{17}-Log_e (7)\pi^{1/4}. Many students will assume it’s wrong and either start again or abandon the problem entirely.
Credit to this dude, who has a page full of these drawings.

These problems don’t only cause students who understand the concepts to get the questions wrong, they can also make students waste time and become unnecessarily stressed. And just to reiterate the point, I think these are terrible test questions but perfectly good assignment questions. Test questions should test concepts, not who was listening to the example given in lecture 17 or who can perform pages of computations the fastest.

Pick a number!

Dear readers,
sorry for being such a useless blogger lately. I started off posting as often as a few times a week and now it’s been over a month since my last post! It could be the three distinct talks that I’ve had to give recently, or that my PhD is reaching crunch time, or the fact that I now have a girlfriend; somehow I’ve not found the time to blog though. As I’m currently visiting a GR program at MSRI and staying in a house in Berkeley Hills, away from distractions, I can type up a post I had sitting in the ideas pile.

Pick a number – any number…

What did you pick? Was it 7? Or pi? or 1+e^{i\pi}? I mean, pick ANY number. It doesn’t have to be a whole number, or even a rational number. If you were to choose a random number — a truly random number — out of all of the real numbers, then the probability that it was a whole number, or even a rational number, is zero. Take a look at My Infinity is Bigger Than Yours to figure that one out, because that’s not exactly the problem I’ll be talking about today. What I’m going to convince you of today, is that the number will certainly contain a 7 as a digit — 100%.

Let me explain.
The random number can – and will be – arbitrarily large so it will have many many digits. If I had a 100 digit number then the probability that the first digit is not a 7 is 9/10, the same for the second digit and the same for the rest. So the probability that none of the digits are 7 is given by the product of the individual probabilities — (9/10)^{100}=0.00003. That’s a 3 in 100,000 chance. And if we start looking at numbers with 10000000000000 digits, then this probability quickly goes to zero.

Alternatively, you could consider how many numbers less than 10 have a 7; then how many less than 100 have a 7, etc. and you would see that this ratio approaches 1 as you start including higher and higher numbers.

Then again, does it even make sense to “pick a random number”?

Abbott’s Cabinet: What’re the chances?

Read more…

What the deuce?! (Guest post)

It seems I’ve been way too busy lately to actually post anything here, so today we’ve got a guest post from David Hartley.

With Australia making it back into the world group of the Davis Cup after six years and Steve taking the week (month?) off, I thought this would be a great opportunity to write a guest blog. Now I will try to keep this in the same vein as Steve’s blogs but I suspect I won’t be able to stop myself including some equations (the worst ones I will provide links to instead of including in the text).

As a mathematician and sportsfan I often find myself checking out various statistics (for example F1 sector and lap differentials) and trying to predict what will happen and the end of the match/race. One of the most interesting sets I’ve found are tennis statistics, especially since you can win more points than another player but still lose in straight sets. And because most games end with only slightly different amounts of points won but again are over in straight sets. In this blog we will see why this is so.

A while ago (nine and a half years apparently) I came across a maths question in an interesting probability book. It asked: If the probability of you winning a point is p, what is the probability of you winning a game of tennis? Having just completed high school and therefore knowing some basic binomial theory, I thought I should tackle this.

Firstly p will be a number between 0 and 1 and represents the likelihood you win a point (For example if you win 55% of points then p=0.55). Next the probability of two (or more) events happening is the product of their probabilities, for example the probability of you winning a game of tennis to love (nil) is p\times p\times p\times p=p^4 – that is, the probability of winning four straight points.

The next best way to win a game of tennis is by winning a point after being up 40-15 (or 3-1 if tennis had a sensible scoring system). This sort of game can occur four ways, since your opponent can win their point on the first, second, third or fourth points of the game (this is often written as the binomial coefficient \binom{4}{1}). Therefore the probability of you winning to 15 (scoring a point from being 40-15 up) is 4p^4(1-p), since you lose one point with a probability 1-p but win four points each with a probability p.

Likewise to win a game to 30 the probability is 10p^4(1-p)^2, since there are ten different ways they can win 2 out of the 5 points (or ten ways you can win 3 out of 5 points if, like me, you prefer to keep track of the points you win).

So far, so good but what happens next? You can’t win from 40-40, instead you would need to win the next two points. Therefore the probability of winning is 20p^5(1-p)^3. Unfortunately/fortunately this isn’t the end of the story. If you only win one of the next two points you are not out of the game but back at deuce, thus we seem to be trapped in a loop. To get out I’m afraid we need to use math(s) (Note to editor: go to hell Steve it’s maths!).

We know that the probability of getting to deuce is 20p^3(1-p)^3, if we let d be the probability of winning from deuce then d is given by the sum of the probability of winning both points and wining one of the next two points then winning from deuce. Mathematically it is written as:

This can be solved for d to give:

With that little trick of algebra the problem is solved and the probability of you winning the game is:

To get a feel for the formula assume you win 55% points on average against another player (a relatively small difference considering a tight set might have around 60 points), then the probability they win a game is 62.3%. A steep increase indeed (the slope has a maximum value of 2.5 when p=0.5). Figure 1 shows the probability curve.

The probability curve for winning a game of tennis. Sexy, huh?

The situation gets worse if you consider a set of tennis. For this we need some extra formulas such as those for the probability of winning a tie-break and both tie-break set and advantage set. The probability curves for an advantage set (Figure 2) shows that if you have a 55% chance of winning a point, you get a 82% chance of winning the set. Remember if there are 60 points in the set that means on average the points won would be 33-27.

The probability curve for winning an advantage set. Mmmmm Matlab.

The probability curve for winning an advantage set. Mmmmm Matlab.

The curves for the probability of winning a match can also be done and they show that for a five set match where the last set goes to advantage, a person who wins 55% of points has over a 95% chance of winning the match.

The probability curve for winning a five set advantage match. Wowwee, don't bother showing up unless you win more than a third of the points on average.

The probability curve for winning a five set advantage match. Wowwee, don’t bother showing up unless you win more than a third of the points on average.

Of course this analysis is very simplified. For instance if anyone remembers Wayne Arthurs then they will know that the probability you win a point on serve, 73% for Arthurs in 1999 leading to 91% of service games won (our model gives 93%), can be vastly different to the probability you win a point while receiving, 29% in the same year with 8% of receiving games won (8.8% by the model). Including both parameters will change the formulas for the probability of winning a tie-break game or either type of set; since mathematically it makes no difference if you serve first or second in the set, the match formulas don’t change. Using those formulas the data tells us he had a ~59% chance of winning; his actual winning percentage that year was 51% (he only played 27 matches so the data set is small). However, the moral of the story is that even if your favourite player has a scoreline that looks like they were easily beaten, this may just be a result of compounding probabilities.

Probabability Paradox* — part 2

You may see this title and immediately think that this is the second part of a two part post; you’d be wrong. This title is an example where intuition can be wrong — or an example of sneaky buggery. Or something? This is to prepare you for a little probability problem. At first, probability sounds like it must be the most intuitive thing ever; if something happens 50% of the time then there’s a good chance that it will happen in around 50 of 100 trials. But it turns out that probability can actually be quite the sneaky bugger. We’ve already seen the Monty Hall problem here, which seemed like quite a simple little probability problem but turned out to be quite counter-intuitive. Today we’ll look at another little probability paradox* that I was recently reminded of.

*Not actually a paradox.

*Not actually a paradox.

First let’s look at a simple problem.

Mrs Robinson — here’s to her — has two children; at least one of whom is a son. What’s the probability that she has two sons?

How stupidly simple does this problem sound? It’s about 50%, right… We know that one of them is a son, so the other one has a 50-50 chance?
Of course not! Probability is far too sneaky for that.

Since we know that she’s got at least one son, there are three possibilities:

  • She has two sons,
  • The older sibling is a son while the younger is a daughter,
  • Or the older is a daughter while the younger is a son.

We’re assuming here that they weren’t at the the exact same time, but this is only so that I can easily talk about the different scenarios. You can convince yourself that these outcomes are equally likely by considering the 4th possibility; if we didn’t know about one of her sons then she could have two daughters. These 4 outcomes are clearly equally likely before we have any knowledge of a son. By saying that at least one is indeed a son, all we’ve done is rule out the fourth option.

Since there are three equally likely outcomes, there is a one in three chance that she has two sons! Take that, intuition!

So now let’s change the problem ever so slightly.

Mrs Robinson has two children; at least one of whom is a son who was born on a Tuesday. What’s the probability that she has two sons?

Oh get stuffed! What does Tuesday have to do with anything? These are probably things that you’re thinking to yourself. The answer is obviously the same as before… right… isn’t it?

Ha! Probability and it’s swift kick to the brainbits strikes again.

Let’s write down all of the (equally likely) possible cases again:

  • The older is a son born on a Tuesday and the younger is a daughter.
  • The older is a son born on a Tuesday and the younger is a son born on a Wednesday.
  • The older is a son born on a Thursday and the younger is a son born on a Tuesday.
  • The older is a son born on Tuesday and the younger is a son born on a Thursday.
  • … There appears to be a whole lot of other possibilities in this scenario.

The difference here, is that we are being more specific about the boy now. If we had said “This is Johnny, Mrs Robinson’s son; he’s got one sibling.” then it would be obvious that there was a 50-50 chance of his sibling being a brother. The more specific we are about her son, the closer the probability gets to a 50-50. If we add up all of the cases in the Tuesday example, we’d actually find that there is a 13/27 chance of Mrs Robinson having two sons.

Convince yourself! Write up a table of the possibilities and check it out.


Essential resources and expertly-authored materials
Essential resources and
expertly-authored materials
designed to support your teaching

The casebook you want.
The digital learning tools your students need.

When you adopt the CasebookPlus version of your chosen text, your students can test their understanding of the material as they are learning it in class.

What adopters and students are saying about CasebookPlus:

90 Percent Pie Chart

90% of faculty who adopted CasebookPlus would adopt it again or recommend it.

94 Percent Pie Chart

94% of students said CasebookPlus helped them understand the subject matter.

85 Percent Pie Chart

85% of students would recommend it to a peer.

Law Faculty

We are dedicated to providing you with trusted content, useful digital tools and personalized service.


Did DD change the image processing technique or did I change something?

We flew the same mission twice, one year apart. The conditions of lighting and the subject were identical- forested, leaf-off, snow cover, overcast skies. Last year, the resolution was astounding- you could easily see snowshoe prints in the snow, and trees had a high level of detail. This year, the ground is much more blurry and DD seems to have interpreted the canopy differently- trees are more like blurry blobs, rather than just a straight up image.

Is this a setting that I should’ve been able to control? Did we inadvertently try to process the images as a 3d model instead of a 2d map? I don’t recall doing anything differently, which is why we are wondering if DD is using a different technique or setting on their end.

3 posts were merged into an existing topic: Mavic out of focus?


Depression in Men

Depression is a thief

MythDepression is a sign of personal weakness

RealityDepression is a real illness

Myth‘Real men’ are in control of their emotions and don’t let things get to them

Reality‘Real strength’ is facing whatever challenges arise

MythFeeling sad or down is not manly

RealitySadness is an emotion all humans feel, including men

MythAnyone with enough willpower ought to be able to ‘snap out of it’

RealityDepression isn’t overcome by willpower alone, you have to learn and acquire new skills and tools to beat it

MythMen should not ask for help; they should be able to cope on their own

RealityConsulting others for direction and guidance really means taking control and it’s the smartest thing you can do

Because of these myths, men will often talk about feeling angry or irritable rather than sad or down. These myths can also feel like handcuffs for men, preventing them from reaching out to others for even a little support. This contributes to many men not seeking support until their depression is very severe, if at all. This can place men at an increased risk of taking their own lives – the greatest risk factor for suicide is untreated depression.

Man with depression

Men are taking action

Fortunately, more and more men, including professional athletes, musicians, actors, lawyers, businessmen, writers, tradesmen, teachers, men in the military, and everyone in between, are ‘going public’ about depression and taking control of their health.

The myths are breaking down, freeing guys to talk about and tackle their depression.

Depressed man looking at camera

Depression can be treated

Ignoring or hiding the pain of depression only makes things worse. This site will provide you with tips and tools, information about professional services, and stories of success that show you how depression can be overcome.

It starts with you recognizing depression and then making important changes in your life to overcome it. It takes courage. It takes strength. It takes work. But know that it can be done.


soorappa babu nithya menon director ks ravikumar sudeep birthday,

User Rating: 0 / 5

Star inactiveStar inactiveStar inactiveStar inactiveStar inactive
sudeep birthday celebration image
sudeep birthday celebration

On Sunday there was surprise on the set of Sudeep's new film. The actor's birthday was celebrated by the team. The shooting schedule was packed up on Saturday and therefore the team decided to celebrate Sudeep's birthday on Sunday night itself. Sudeep.'s birthday is on September 2.

On the birthday cake the film's tentative title Production No 4 was mentioned. The shooting the film will resume after Sudeep completed his commitments in the Karnataka Cricket League tournament between September 3 and September 20.

The set for the KS Ravikumar directed Kannada-Tamil bilingual was put up at the Kanteerava Studios.


• Stormwater Management

Stormwater Management

New developments in built-up conurbations and the unstoppable urbanization of areas have exacerbated the potentially damaging effects of conventional surface-water drainage.

Traditional drainage of stormwater run-off was designed to rapidly convey rainwater from where it has fallen to a soakaway or watercourse. This old method increases the risks of flooding, environmental damage, and urban diffuse pollution, as run-off water usually carries contaminants including oils, heavy metals, pesticides, fertilisers, chemicals, and other organic matter.

GreenBlue’s stormwater management solutions provide a sustainable and effective approach to low impact development.

Stormwater Storage

Structural support modules for stormwater storage are a cost-effective option that meets maximum load-bearing requirements.

RootRain Linear Drain

A fully customized linear strip drain stormwater solution for installation in hardscape surfaces.

Closable stormwater inlet for incorporating into road side tree pit designs or other stormwater management projects.


International short-term medical service trips: guidelines from the literature and perspectives from the field.

The increasing interest in practising medicine overseas has outpaced research conducted to evaluate its effectiveness and the development of guidelines from evidence-based best practices. Short-term medical teams regularly travel to provide medical care, yet there is little research on the impact or practices of these missions. This study assessed current… (More)

  • Presentations referencing similar topics


Book Review | Hiroshima in the Morning

Title: Hiroshima in the Morning

Author: Rahna Reiko Rizzuto

My Review:

This is a story about a wife and a mother who sets out on a journey to learn more about history and her own family’s heritage, and ultimately learns more about herself and her own abilities. Even though Rahna is a successful author, she had never been on her own or taken on anything as challenging or life-changing as leaving her family and travelling to Japan for six months. She has challenges fitting in and finding people in Japan who want to share their stories with her, or the stories seem to lack an emotional connection and just sound like rehearsed facts. Her marriage starts to fall apart during her absence, and she struggles with her role as wife and mother. Then, 9/11 happened and changed everything. The fear for her family’s safety and reality of how life can change in an instant repairs the damage to her marriage. The stark reality of the attack on the US and the International heartache the followed helped people to open up and share their stories from Hiroshima. She has used her experiences and interviews from this trip to write another book called “Shadow Child” that has not yet been released.

I found the story hard to connect with in the beginning, but eventually was consumed by it. The memories of 9/11 are vivid for me, like for most people, so the story became personal and I really connected to it. I’m looking forward to reading the fictional story based on her interviews and experiences that these memoirs are based on.

more by Sheri »


Language of Light [Hibiru]

Zep Tepi Language of Light The Emrald Tablets of Thoth and The Keys of Enoch "The lost Enochian knowledge reveals the mother tongue as a "language of Light". Known to the ancients as HIBURU, it is the primal seed language, introduced at the beginning of this time cycle. Modern research confirms, the most ancient form Hebrew to be a natural language, the alphabetic forms emerging from the phosphene flare patterns of the brain. The same shapes, in fact, born of a spinning vortex. It is a true language of light, coursing through our very nervous system.....Encoding the natural waveform geometries of the physical world, Hiburu is a harmonic language, mimicking the waveform properties of light. The "keys" Enoch speaks of, turn out to be sound keys, keys to be vibratory matrix of reality itself, the mythic "Power of the World". The Enochian knowledge describes sonic equations, encoded within the ancient mantras and god names, capable of directly affect the nervous system and producing profound effect of healing and higher consciousness states....As the ancient texts declare, "If you would speak with the gods you must first learn the language of the gods."

Alchemy and Magic

Zep Tepi is also known as an alchemist which makes him a Magician, Magi, Master, he who can bend the light to create illusion in the electromagnetic program or our reality - magnetics and illusion. He is known to the Egyptians as Thoth, (thought) the "Lord of Magic and Time" - to the Greeks as Hermes, 'Messenger of the Gods" - and to the Celtics as the enigmatic wizard Merlin, who disappears up an apple tree to mythic Avalon, seeking the secret of immortality and vowing to return.

Discoveries emerging from Egypt, describe the existence of a world wide pyramid temple system in prehistory, mounted like antennae on the key energy meridians, which were employed by ancient priest-scientists as a musical system to stabilize the tectonic plates of the planet... cataclysmic geology at it's finest. From the mother tongue word Jedaiah, meaning 'the way of the Word' or 'The power of the Word', the ancient Jedai priests used the Language of Light to tune the planet like a giant harmonic bell. Much is being rediscovered in the last days of this time cycle.

Esoteric and Metaphysical Secrets

In my metaphysical dream I once had this voice told me 'Keep Reading Those Books, You'll Attain More Insight", I will never ever forget that day.It happend in May 2007AD

The Sphinx was a monument built to a hybrid sphinx presit who survived the flood of Atlantis or died and was remember by the egyptians who are the remnants of Atlantis, Egyptian gods were orginally presit, kings and queens of Atlantis.

Mayan gods also were priest kings,queens of the ancient civilization of Lemuria [MU]. Genesis means 'Genes' of Isis. Translators of the bible meaning the free masons took the hebrew words and currupted them into a non hebrew beleif or meaning.

The ancient Black Americans who are called Israelites claim direct children of the constellation of Orion, they are the orginal Sumerians and Babylonians. Who are descendents of the Lemurians (Mu) and the Atlanteans.

The name Jehovah was created in 1518 it is latin and is not the name of the God of Israel.The name Yahweh contians the language of light.The langugage of Light is classifed as 'hibiru'. It consist of a electronic magnetic harmaic sound and power.

The keys of Enoch,The emrald Tablets of Thoth,The sword of Moses all these ancient books reveal the language of light and it's connection with ancient beings from other worlds who I consider as angels of Yahweh.

The Nephilim/Anunnaki built the civilization or city of Atlantis and thier children dwelled thier shortly after more ancient civilizations rose from that one. in 1 Enoch Chapter 7 and Genesis 6 it explains this, Tablet 13 of the ancient book of Thoth who was Enoch speaks of this civlization as well.

DNA came from Yahweh he put it into a cannister and flew to our planet with his angels inside spaceships thousands of years ago.

Gilgamesh came from Lemuria [MU] reason I know this is because him and his firend Enkidu a hybrid had to walk across the great sea to see the father figure of men who's name was Utnapishtim, Utnapishtim was the same Noah of the Genesis in the Old Testament.

Mayans claimed they were the remnants of the children of Lemuria [Mu]).they say that the "Giants" built ....... more coming soon.

Ancient Art of Atlantis

Technology of Atlantis

Michael Tsarion interviewed by Dr. Patrick Bailey about Astro-Theology from "Technology Trends."

Wireless Engery Grid

13TH LOCATION DISCOVERED!!Energy grids have been founded in the most stragest spot most shockingly right in the location where lost civilizations of the Nephilim and Giants settled thier civilizations I can cleary see Atlantis and Mu!

Maybe these energy grids were used for the electricty in the city of these lost ancient civilizations or could it be so that it was used to recharge spaceships that either the advanced giants had or the 'gods' of the creation of man who came with Yahweh the creator! Does this signigfy that Prophet Enoch was a Atlanteans you can cleary see how a grid was right in the spot of the pyramid of Giza who the prophet Enoch is said to be a modifier and Alchemist of it thousands or years ago. Thoth is said to be this Preist teaching around 35,000 BCE in Egypt.

I know it is giving into the prophet Enoch because a pyramid wrighting said: 'Pa-Hanok' this is egyptian for 'the house of Enoch' so this literally means he had a mystery school in egypt, could this be the schools the Sumerians and Egyptians learned in also the Hebrew prophet Moses aswell! Since they did live in Egypt for 400years!

Ancient Lost City of Atlantis & Mu

Every year some nation claims they have found Atlantis ..Atlantis was apart of West Africa.It was on the edge of Morocco. Lemuria is apart of South America and the Bahamas region...thats another lost civilizations that sprung off after the creation of Atlantis.The giants lived their...they were renowned and advanced such as their nephilim fathers. Atlantis has nothing to do with Greek Caucasian people homer learned about the tale from Egyptian black people.In the epic of Gilgamesh he visited their and said that the gods dwelled their meaning the 'nephilim' 'or anunnaki'.

Gilgamesh also talks about how the gods had a landing place their at (Atlantis) and that the gods would ascend and descend in their Shem's and eagles among the firmaments of the wind... Shem means Fiery Space Vehicle. In the 'The Epic Of Gilgamesh' and do research on Enkidu , Adapa, Etana and Enoch these are all Sumerians survivors of the flood who came from Atlantis ohhh yeah also Noah they all talk about gods taking them on journeys to outer space. Atlantis had a crystal board that would shine in the costellation Orion it was beacon and a navigator for gods who rode in flying vehicles such as the pyramid of Giza same ordeal... Heaven is constellation Orion.

The Old Testament is history of Atlantis also. The Old Testament is the aftermath of the flood and so on...what went on after. Read books such as 'the emerald tablets of Thoth' and the keys of Enoch they were Ethiopians and Egyptians who wrote about visits to their also Enoch and Thoth are the same person he was really Enoch the Egyptians just called him Thoth.

Human Origins Part I

Zecharia Sitchin, Archeologist presents evidence to show that humans were the creation of beings from another planet. The Sumarian Origins of Humans shows the beginings of human civilization in the Sumarian culture. Art and ancient text provide thought-provoking clues and supportive data to Zecharia Sitchin's theory.

A Throne For Giants

Monoliths that as if they had been pre-cast like mordern concrete, Thrones for giants? Did the 'gods' destroy thier base at Sacsayhuaman when they had carriedout thier mission? My theory is that Nephilim 'Giants' suvivors of Mu migrated to that area 13,000 years ago and built them a city when thier Mighty Structure died out thier children the Inca's then dwelled thier in machhu Pachhu in the home of thier ancestors. The Incan epic speaks about Mighty Men and Women building the city they were tan skinned people with black hair similar to a mayan's shade but not a caucausin who came from the city where the gods dwelled which I assume to be Lemuria/Mu!

8,000 Year Old Underwater Building Off Of Japan

This story was originally revealed by Laura Lee nearly a year ago. For her update on this amazing discovery, see link at end of this article. A STRUCTURE thought to be the world's oldest building, nearly twice the age of the great pyramids of Egypt, has been discovered. The rectangular stone ziggurat under the sea off the coast of Japan could be the first evidence of a previously unknown Stone Age civilisation, say archeologists.The monument is 600ft wide and 90ft high and has been dated to at least 8000BC. The oldest pyramid in Egypt, the Step Pyramid at Saqqara, was constructed more than 5,000years later. The structure off Yonaguni, a small island southwest of Okinawa, was first discovered 75ft underwater by scuba divers 10 years ago and locals believed it was a natural phenomenon.

Robert Schoch, professor of geology at Boston University, dived at the site last month. "It basically looks like a series of huge steps, each about a metre high. Essentially, it's a cliff face like the side of a stepped pyramid. It's a very interesting structure," he said. "It's possible that natural water erosion combined with the process of cracked rocks splitting created such a structure, but I haven't come across such processes creating a structure as sharp as this."

Further evidence that the structure is the work of humans came with the discovery of smaller underwater stone mounds nearby. Like the main building, these mini-ziggurats are made of stepped slabs and are about 10m wide and 2m high.

"This could only have been done by a people with a high degree of technology, probably coming from the Asian continent, where the oldest civilisations originate. There would have to have been some sort of machinery involved to have created such a huge structure."

British archeologists are, however, cautiously enthusiastic about the discovery which will be featured this summer in a Channel 4 documentary.

Ancient Astrology

Astrology goes back to the times of the Sumerians, who settled in Mesopotamia around 30,000 BC. This marks the first example of a people who worshipped the sun, moon, and Venus. They considered these heavenly bodies gods, or the homes of gods. The priests of the time who communicated with the gods were the first rulers. There were High Priests and lesser priests - much like the way things were in Atlantis. They carried the teachings with them from one civilization to another. In the 6th century B.C. the scribes of Enuma Anu Enlil were a group of men at the Babylonian court who were experts in astronomy and astrology. Texts refer to this group of scribes, but we do not know exactly who they were, what they did and how they were trained. However, for hundreds of years the scribes kept accurate records of natural events on the earth and in the sky in order to predict the future.

10,000 BC

Hall of Amenti

Hall of Records The site finally selected for the safekeeping of all records and for the great symbol of the esoteric content of the law was the fertile plains of Gizeh, which had stood firm during the flood that had swept over so much of the land some thousands of years ago. This site was situated even higher than was the Temple of Isis.
It was calculated that this area was also approximately the mathematical centre of the land areas of the earth, where there might be the least disturbance by future earthquakes or floods. Here the record vaults were to be hidden, in a small pyramid between the Sphinx and the Great Pyramid, connected to both. Other large pyramids were also to be constructed in the vicinity.

The Sphinx had already been started, then work was discontinued, then restored and added to, after the return of the High Priest, Ra. Originally it was intended to be a memorial to Araaraat, but after the recall of Ra the meaning was changed to symbolize the relation of man and the animal, or carnal world, to those changes which must come about in his spiritual evolution - changes which were already coming about, in the fading of falling away of imperfections of man's bodily pattern.

The base of the Sphinx had been laid out in channels, and in the corner facing the Great Pyramid the story was inscribed as to how all these were begun and built, giving the history of the first invading ruler and the ascension of Araaraat. From the right forepaw, a passage was made to lead to the entrance of the Record Chamber, or Pyramid of Records. This was to remain undiscovered until man overcame his ego and reached true spiritual understanding, at the beginning of the fifth root race.

The Hall of Records was enclosed in a pyramid of its own, also to stay hidden for many thousands of years. It is situated between the Sphinx and the Great Pyramid. Hidden in the northeast corner were thirty-two tablets, buried with the remains of King Araarat. This was the first of the pyramids to be constructed from the shifting sands.

The Great Pyramid of Gizeh was one hundred years in the building: from 10,490 to 10,390 B.C. Ra himself made extensive studies of the terrain, and great care was taken in figuring the geometrical location in relation to the Sphinx and the four cardinal points of the compass.

Although it was planned by Ra, the actual construction and engineering were worked out by Hermes, a descendant of Hennes Trismegistus, who had returned with the Priest from the Nubian land of exile.

The Great Pyramid was built as a hall of initiation, the 'House Initiate', for those dedicating themselves to special services in the secrets of the mystery religion of Egypt. Here the masters performed their vows, consecrating themselves to holy service. Its purpose, therefore, was far greater than that of a burial place.

It was erected by the application of those universal laws and forces of nature which cause iron to float. By the same laws, gravity may be overcome, or neutralized, and stone made to float in air. The Pyramid was thus built by levitation, abetted by song and chanting, much in the same manner in which the Druids of England set up their huge stones at a later period.

Material for erection of the Pyramid was brought from as far away as Nubia; many different kinds of stone being used. Highly polished white limestone was placed on the four sides, in slabs whose joints were cemented together so imperceptibly that the work may be compared to the jeweller's precision. This casing stone was later stripped off and pieces may still be found in buildings in Cairo. Portions still lie buried below the sand, A few are still in place at the foundation line on the north side.

The Pyramid's capstone was composed of an alloy of copper, brass and gold, pounded into a covering for the top of the Pyramid. This eventually was desecrated,. by the sons of Heth, on orders of the Pharaoh, under whom the children of Israel suffered in bondage. In certain seasons a cosmic fire was lighted on top of the Pyramid, for symbolic purposes, by a method known only to the Atlanteans..

A long and elaborate ceremony marked the dedication of the Pyramid after the capstone was put into place. The event was announced to the people by a loud clanging of metal. From this ringing-out has arisen the call to prayer, thanksgiving and worship, as symbolized in the church bell. It is also the origin of the trumpet call to arms, and the ringing-in of the New Year.

The Great Pyramid is a record in stone of the history and development of man from the time of Araaraat and Ra to the end of the present earth cycle in 1998. Its records are written in the language of mathematics, geometry and astronomy, as well as in the lands of stone used, with their symbology.

At the end of the cycle, there is to be another change in the earth's position, with the return of the Great Initiate for the culmination of the ancient prophecies. All changes that have come and are yet to come are shown there in the passages from the base to the top. Changes are signified by the layer of stone, the colour of it, and the direction in which the turns are made. There are no undiscovered rooms, as such, in the Great Pyramid.

In the smaller Pyramid of Records, yet to be uncovered, there is a vault sealed with heavy metal, containing the prophecy for the period from 1958 to 1998. Here were secreted the records of the People of the One God, from the beginning of man's entrance into the earth. The occasion of this sealing was attended by Araaraat, Ra and the priests and priestesses of the Temples.

In the Great Pyramid, current history is symbolized by the low ceiling at the entrance of the passage leading to the King's Chamber, as it is called. This low passage or depression shows a downward tendency, as indicated by the variations in the land of stone used. The present period, therefore, may be termed the Crucitarian Age, or the age in which preparations are made for the beginning of the new sub-race. Astronomical and numerical factors indicate this date began in the Autumn of 1932.

When the gradual change taking place in the position of the North Star, Polaris, became noticeable as calculated from the entrance of the pyramid, there will be evidence of the incoming of the new race, with a greater influx of souls from the Atlantean, Lemurian, La, Ur or Da civilizations. These conditions are indicated by the turn in the passage through the Pyramid. The empty sarcophagus in the King's Chamber is itself a symbol of the enlightenment of man as to the meaning of death - as a transition from one plane of existence to another.

The length, breadth, height and various directions of the many layers of stone in the passages and chambers of the Pyramid accurately depict the events of significance in the spiritual evolution of man on planet earth. The birth and death of Jesus of Nazareth are indicated to the year, day and hour, at the turn of the passageway leading to the Queen's Chamber.

At one point in the low passage, 1936 is prophesied as a year of disturbances and turmoils, including wars, storms and land upheavals; with a resulting unrest among groups and masses. After 1956 a time of adjustment follows, and then the world enters a new period as shown in the King's Chamber - some time between 1938 and 1958.

This era is the beginning of developments of an unusual nature in many ways, terminating in the year 1998. It will be a time of preparation for the coming of the Master of the world - not necessarily His actual coming, the time of which no man can ever work now. It will be a period of greater spiritual reawakening and enlightenment; of new understanding, new life and new faith. There will be marked advancements in the field of science and new knowledge concerning the balancing of the forces of gravity by which the Pyramid itself was built.

The present age of mankind is rapidly approaching a peak in its development. At the crest of the wave there will be a breaking, a clash between the material-minded and the spiritual-minded. Many will fall away; but those who stand firm will be guided in finding the records and interpreting them for the benefit of men everywhere. The important thing lies not in just their discovery but their interpretation!!

The Great Pyramid of Gizeh stands as an historical monument to the present root race. It records the story of man's struggle for spiritual wisdom, and for many ages it was used as a temple of initiation for many of the world's great teachers and leaders. It was here that the Great Initiate of the Hebrew Moses was taught by his dad Amram or his relatives.

Where Do We Come From

The Sumerian cuneiform deciphering skills of Zecharia Sitchin, a linguist in command of many ancient languages who has set the scientific world on its ear with his astounding interpretations of ancient writings. In 1976, Sitchin’s first book, The Twelfth Planet, began an odyssey that has literally transformed the field of ancient history; in 1993 came the sixth book in his Earth Chronicle series, When Time Began. Among other mind boggling assertions, this book links the complex calendar of Stonehenge and the puzzling ruins of Tiahuanacu in Bolivia, to the ancient culture of the Sumerians, and by extension, to the Nibiruans, who are also called the Anunnaki. These are the folks Sitchin insists not only created the Sumerian culture, but who also genetically created human beings as we know them. And yes, they live on this mysterious 12th planet, Nibiru.

To date, Sitchin has deciphered more then 2,000 clay cylinders from that ancient land on the Persian Gulf that existed some 6,000 years ago. Some of these fragments, which date to 4,000 B.C., are in museums around the world. One fragment in particular, presently in Germany, indicates that Earth is the seventh planet, counting in from Pluto. The time frame here is four millennia before modern astronomy confirmed the existence of Pluto as an actual planet in our solar system. So how did an ancient race of people know this fact? Sitchin says it is because these ancient people did not come from Earth, but from Nibiru. Profound family squabbles eventually caused the Nibiruans to abandon planet Earth, leaving human beings to fend for themselves. These early humans would never possess the ability to travel among the stars like their creators, nor would they possess the immortality of their creators. Eons later, however, we humans finally have sent an intelligently designed satellite probe beyond the confines of our solar system. Are we repeating our past? This is but one of the perplexing questions Sitchin investigates in the Earth Chronicles. Not only an eminent archaeologist, Sitchin is also a formidable analyst of ancient cultures, in fact, perhaps the best ever.

His explicative comparisons of similar but disparate mythologies provide a fuller understanding of world religions. Among other things, Sitchin’s investigations indicate that there may be an outpost in orbit around Mars preventing current humans from getting there (a fact verified by both U.S. and Russian space probe problems in that neighborhood). But the primary focus of this impressive research is ancient Sumer. The decipherment of that culture’s clay tablets, buried for millennia, reveals roots that stretch all the way back to 450,000 B.C. The reason Sitchin was motivated to learn to read cuneiform tablets was his initial curiosity as a boy concerning the meaning of "Nefilim", an enigmatic group mentioned in the Old Testament. Translated, "Nefilim" means "those who came down."

Cuneiform tablets

It would be impossible to do justice to his research in such a brief review as this one; however, there are some very significant findings on the existence of this other race of people. Perhaps the most compelling is the "face on Mars," the structure in the area called Cydonia on the Red Planet. What is it? If the relationship of the face on Mars is analyzed for its distance to other pyramidal structures also discovered on Mars, the geometric relationship is found to be identical to the distances of the Egyptian Sphinx and the pyramids in the surrounding areas of Egypt. Sitchin concluded the placement of these pyramids indicates that they served as landing markers for the Nibiruans after they entered the Earth’s atmosphere from outer space. Sitchin also has asserted that the early pyramids were not designed by the Egyptians. NBC-TV aired a program on Nov.10, 1993 entitled "The Mystery of the Sphinx", indicating that the Sphinx is 2,000 years older than previously thought. This corroborates Sitchin’s findings that someone other than the Egyptians designed the pyramids.

One astounding assertion after another has made Sitchin the most controversial writer of our time because he challenges everything we thought we knew about human civilization. It’s easy to dismiss Sitchin’s research in the same way that other people dismiss UFO’s, Eric Von Daniken and countless other researchers who claimed to have found evidence for extraterrestrial visitors to this planet. But Sitchin is well aware of this devil’s advocacy, and vaporizes the arguments of skeptics with solid scholarship, including the most rigorous translations of Sumerian text, Vedic tales and excerpts from the original Greek and Hebrew versions of the Bible. This ability to translate many languages is no small achievement. Those of us who will never possess the ability to decipher 6,000-year-old clay tablets must trust that Sitchin has done his job accurately. But his sources reveal an utter integrity, including the finest, most respected citations and references imaginable.

The two most recent individuals to pay attention to Sitchin were Colin Powell and Norman Schwarzkopf, the American Generals who were key figures in the recent Gulf War. The landing place of the Nibiruans was in an area once called Eridu, now called Southern Iraq. The main reason Saddam Hussein was not captured was because he was holding out in an ancient step pyramid constructed by one of those early civilizations mentioned by Sitchin, and which the Americans were loathe to bomb, because of their inestimable historical value. Once the gloss of the media is removed from consensus reality, an entirely new picture emerges as to who knows what concerning what Sitchin has uncovered. This writer may never know who knows what, but the circumstantial evidence in the Earth Chronicles concerning the Nibiruans is absolutely compelling.

Where does one look for their arrival?

Many of us will never travel all over the world to visit the ancient observatories. However, Sitchin has, and what he has found concerning the placement of these observatories on the surface of the Earth also is startling. All the observatories are inclined to the Southern hemisphere. They also are on the same Earth latitude. In his latest book, we learn that many of these observatories measure exact lunar and solar rising and settings with an accuracy unmatched by any modern measuring equipment. The field of astronomy and astrology are made completely understandable by Sitchin, who shows that the concept of "Divine Time" was something these ancient astronomer priests created to predict the arrival of their creators. Farfetched, to be sure, but when logic and patience are afforded to Sitchin’s conclusions, one comes away with the realization that humanity has been misled in regards to our actual origins.

The biochemical research is especially haunting. Our entire DNA structure is like a Contact time-release capsule. When we were originally programmed, our basic DNA structure was limited to a double-helix strand. The triggering mechanism that enables us to function as we do is affected by stellar radiation. We are now at a place in the orbit around our central galaxy where the radio frequencies of the center of the galaxy, as well as many other star systems, are communicating new information to us. The release of this information, according to Sitchin, coincides with the next arrival of the 12th planet. The government’s attempt to construct a Freedom Space Lab will be aimed to ascertain the whereabouts of Nibiru (the 12th planet).

The big question, of course, is what will these beings whom we have confused with gods think of us now? In the past we were not granted the same powers they had, but as a result of thousands of years of genetic selection, we have in some ways become like gods. Most all of the ancient languages have now been deciphered, and the 22 Hebrew letters have been found to contain information based on light generating systems. Our understanding of torodial force fields, fibonacci series, fractals and open topological vector spaces have been expressed in the language of mathematics. Star fields begin to look more like computer generated printouts than random points of light in the night sky. If there is one thing Sitchin has definitely accomplished, it has been to expand the human imagination.

The legendary cultures of Atlantis and Lemuria no longer appear fantastic, but as efforts of other races to survive on planet Earth. The SETI project, the government’s official Search for Extraterrestrial Intelligence has been cancelled, and then reactivated by a private consortium of companies. The most recent Mars probe completely disappeared. The answer given to these enigmas are unsatisfactory, when weighted against the evidence that another race of people is about to visit our planet, as they apparently have many times in the past. Remember, it takes Earth one year to orbit the sun. It takes Nibiru 3,600 years, according to Sitchin. Therefore, one year for the Nibiruans is equal to 3,600 Earth years. He has completed all this research, he says, to prepare us, the human race, for the return of our creators.

Quantum Entanglement

The possibility of paradoxes

Time travel and the anthropic principle

Time Travel and Religion
Prophecy and theology

Transcending time through ancient wisdom.

The Destruction Of Atlantis [Michael Tsari...

The ... quality of the video is not so good, but the information and images are so rich with knowledge and wisdom!

The Legend of The Star Man

Vitruvian Man The pentacle was once revered for the perfection with which the human form fits enigmatically into a five pointed star. Today it is a symbol that resurfaces time and again, but without the purity that was originally intended to be its message. The ‘evolved’ and altered image shown here is all that has survived human interference over the ages. Few if any have given any thought to its origins. Wayne Herschel believes that before this symbol was usurped by all kinds of bizarre followings, it was the ultimate representation of humankind. Humankind, whom he believes from all his research, came from the stars so to speak! Humankind created under a supreme Creator’s perfect mathematical design code.

So why has this symbol of perfection been so blatantly confused with evil? Why has a unique representation of this symbol become the object of desecration and Satanism, to be feared when it was once so pure?

The story of the universal mathematical blueprint of the human form seems to originate around the time of Christ.

A man by the name of Vitruvious lived during this period. We all know how Da Vinci referred to this ancient scholar in his rendition of ‘Vitruvian Man’. What most people don’t realise is that Vitruvious not only delved into advance drawings and the mechanics of machines like Da Vinci, but he had originally represented a universal mathematical code of the human form that was once more defined.

2000 years ago, Vitruvious had recognised the navel as the important central axis for a circle and a square when the human form has legs together and arms outstretched above the head. He also had a second rendition of the human form with legs and arms apart. But here is where something crucial seems to have been forgotten or intentionally omitted. Vitruvious originally interpreted the arms quite differently to Da Vinci in two distinct positions with arms outstretched above the head and arms outstretched far apart. (matching the exact leg positions being together and far apart).

This is exactly how Wayne has interpreted the two arm positions in his human codex theory in ‘The Hidden Records’.

Da Vinci thought the point where the square and the circle intercept was a sacred arm position (see position ‘x’ in the image below). It is also amazing that while Da Vinci published his perhaps ‘censored’ Vitruvian man 1500 years later… another great scholar in Germany at virtually the same moment in time as Da Vinci published the complete Vitruvious human form rendition. His name was Heinrich Agrippa. The churches in Germany were so horrified by this mans occult publication that he was arrested and subsequently burned at the stake.

Here is a combination depiction of Agrippa’s reproduction of Vitruvious’ 2000 year old human code and his two original sketches are shown in an overlay. Note the ‘all seeing’ eye positioned above the head like a crown. It suggests that Vitruvious himself might be repeating an ancient Egyptian source of lost knowledge. One must also consider the possibility that it was not at all safe 2000 years ago for Vitruvious to show the once sacred human icon as complete, i.e. the connection between the human form and the stars.

Over time, the true meaning of the once sacred icon suddenly became embroiled in witchcraft during the Renaissance era, and was henceforth interpreted as ‘the occult’. The ‘sacred’ symbol became a target for desecration by evil groups and cult followers. The way to show disrespect for its godliness and purity was simple… it was unceremoniously turned upside down and desecrated in rituals and utterances, perhaps motivated by the intention to scare people away from the wonderful 'secret'. The icon became something churches believed should be feared.

And fear one must, but for other reasons as Wayne Herschel explains: Humanity has taken our most precious icon of whom we are and where we come from and violated it.

Once you have had the opportunity to read 'The Hidden Records', you will notice that the symbol above has evolved from a very sacred codex that not only makes its appearance at Stonehenge and Giza, some of humanity’s oldest sites, but as bizarre as it may sound, it can even be found on another planet. To get an idea of what the author is getting at, browse through the thumbnail images on this website, then go to the book for the all important reasoning.

This is how the author believes this sacred symbol became distorted. It would appear that over time the human genitalia were seen to be a more appropriate focal point of the ‘star man’ than the navel (as in Da Vinci’s Vitruvian Man), which was once the central point from where all the geometrical proportions emanated. Wayne says it not surprising this distortion of the original came about. In the case of the age old Cerne Giant found at Dorset (shown lower down), it seems the genitalia form the cosmic pointer to the area of the sky that repeats the solution to all the star maps that have been found by the author. The same is true for a similar painting of a man in the Lascaux caves that dates back 17 000 years, where the human anatomy acts as a cosmic pointer to the celestial bull. In both instances the genitalia have mistakenly been confused with the ‘sacred geometric centre’ of the human form… hence the distortion of the meaning of the pentacle in later years.


Download A concise course on stochastic partial differential by Claudia Prévôt PDF

By Claudia Prévôt

These lectures pay attention to (nonlinear) stochastic partial differential equations (SPDE) of evolutionary variety. every kind of dynamics with stochastic impact in nature or man-made complicated structures could be modelled by means of such equations.
To maintain the technicalities minimum we confine ourselves to the case the place the noise time period is given by way of a stochastic crucial w.r.t. a cylindrical Wiener process.But all effects could be simply generalized to SPDE with extra basic noises akin to, for example, stochastic quintessential w.r.t. a continual neighborhood martingale.

There are essentially 3 methods to research SPDE: the "martingale degree approach", the "mild answer technique" and the "variational approach". the aim of those notes is to provide a concise and as self-contained as attainable an advent to the "variational approach". a wide a part of priceless heritage fabric, akin to definitions and effects from the speculation of Hilbert areas, are incorporated in appendices.

Show description

Read Online or Download A concise course on stochastic partial differential equations PDF

Similar differential equations books

Bitangential Direct and Inverse Problems for Systems of Integral and Differential Equations (Encyclopedia of Mathematics and Its Applications Series, Volume 145)

This principally self-contained remedy surveys, unites and extends a few twenty years of study on direct and inverse difficulties for canonical structures of vital and differential equations and similar platforms. 5 uncomplicated inverse difficulties are studied within which the most a part of the given info is both a monodromy matrix; an enter scattering matrix; an enter impedance matrix; a matrix valued spectral functionality; or an asymptotic scattering matrix.

Solution Techniques for Elementary Partial Differential Equations, Third Edition

Answer strategies for user-friendly Partial Differential Equations, 3rd version is still a best choice for the standard, undergraduate-level direction on partial differential equations (PDEs). Making the textual content much more hassle-free, this 3rd variation covers very important and general equipment for fixing PDEs.

Extra info for A concise course on stochastic partial differential equations

Example text

In this section we give precise conditions on A and B. Let T ∈ [0, ∞[ be ﬁxed and let (Ω, F, P ) be a complete probability space with normal ﬁltration Ft , t ∈ [0, ∞[. e. for every t ∈ [0, T ], these maps restricted to [0, t] × V × Ω are B([0, t]) ⊗ B(V ) ⊗ Ft -measurable. As usual by writing A(t, v) we mean the map ω → A(t, v, ω). Analogously for B(t, v). We impose the following conditions on A and B: (H1) (Hemicontinuity) For all u, v, x ∈ V, ω ∈ Ω and t ∈ [0, T ] the map R λ→ V∗ A(t, u + λv, ω), x V is continuous.

12) follows by Lebesgue’s dominated convergence theorem. Let n, m ∈ N and set ψt (R) := exp(−2αt (R) − |X0 |), t ∈ [0, ∞[. 1. e. 14) + σ(s, X (n) (s) + p(n) (s)) − σ(s, X (m) (s) + p(m) (s)) (n,m) − 2Ks (R)|X (n) (s) − X (m) (s)|2 ds + MR 2 (t), (n,m) where MR (t), t ∈ [0, ∞[, is a continuous local (Ft )-martingale with (n,m) (0) = 0. e. 9) and assumption (i) in the last step. e. for t ∈ [0, γ (n,m) (R)] |X (n) (t) − X (m) (t)|2 ψt (R) (n) (m) 4(1 + R)(λt (R) + λt (n,m) (R)) + MR (t). 15) γ (n,m) (R) and (Ft )-stopping times Hence for any (Ft )-stopping time τ (n,m) σk ↑ ∞ as k → ∞ so that MR (t ∧ σk ), t ∈ [0, ∞[, is a martingale for all 48 3.

Then A + A, ˜ ˜ A both satisfy (H1), (H4) then so does A + A. 2. If A satisﬁes (H2), (H3) (with B ≡ 0) and for all t ∈ [0, T ], ω ∈ Ω, the map u → B(t, u, ω) is Lipschitz with Lipschitz constant independent of t ∈ [0, T ], ω ∈ Ω then A, B satisfy (H2), (H3). Below, we only look at A independent of t ∈ [0, T ], ω ∈ Ω. From here examples for A dependent on (t, ω) are then immediate. 3. V = H = V ∗ (which includes the case H = Rd ) Clearly, since for all v ∈ V 2 V ∗ A(v), v V 2 V ∗ A(v) − A(0), v V + A(0) 2 V∗ + v 2 V , in the present case where V = H = V ∗ , (H2) implies (H3) with c1 > c2 and α := 2.

Download PDF sample

Rated 4.02 of 5 – based on 31 votes

About admin


Achilles Tendon
Achilles tendon ruptures may be divided into full thickness ("total") and partial thickness ruptures. Total ruptures usually occur in formerly active athletes (average age 40) who resume sport activity after having been away from it for some time. In these cases, degenerative changes have weakened the tendon so much that sudden, forceful loading of the tendon causes it to tear. To some extent, these changes in the tendon could have been prevented by regular physical activity. In most cases, the injury mechanism is a strong activation of the posterior lower leg musculature, eccentrically overloading the tendon. A typical mechanism of injury involves pushing off hard with the weight-bearing foot while the knee is extended (e.g., running uphill) or sudden, unexpected dorsal extension of the ankle with reflex contraction of the calf musculature (e.g., falling down into a hole).

Non Surgical Treatment
Achilles Tendonitis

Surgical Treatment
In general, Achilles tendon repair surgery has a much higher success rate and lower incidences of re-rupture than non-surgical methods of treatment. It is preferred by the nation?s leading athletes as the best course of action, allowing them to return to previous activity and performance levels at a much faster rate, with a lower chance or re-injury and less potential muscle loss.

The best treatment of Achilles tendonitis is prevention. Stretching the Achilles tendon before exercise, even at the start of the day, will help to maintain ankle flexibility. Problems with foot mechanics can also lead to Achilles tendonitis. This can often be treated with devices inserted into the shoes such as heel cups, arch supports, and custom orthotics.

創作者 RosauraGosda 的頭像

Rosaura Gosda


The first edition of Stroke was held on 11th December, 2016 at the Symphony Hall in Khar gymkhana.

Kabeer Khurana spoke about Artyculate and their ‘Confidently flawed’ campaign to commence the event at approximately 5:30 in the evening. In good faith, the crowd was asked to write an adjective that is usually considered socially unacceptable next to ‘Confidently…’ on a blackboard with a white chalk and a picture of them with the board was taken by our photographer.

Anu Elizabeth Roche commenced the performances with her beautiful and moving poetry about motherhood and postpartum depression, which are topics that are generally considered taboo by society.  We also had Saineeta on the keyboard who played ‘Imagine’. Rashika Desai,  who is one of TMAC’s writers, performed a piece on the conflict between the heart and the mind.

Then, Ishaan Jajodia, Sasha Kalrani, Adyot Rajadhyaksha and Chintan Modi led the nude art and menstruation art panel discussion, in which Ishaan commenced the discussion by citing a translation of a piece in the Rig veda called the Nasadiya Sukta which talks about how sexual desire was one of the ways the universe was created. Moreover, it promotes intellectualism and inquisitiveness, and it questioned the existence of God.  The panel encouraged the audience to ask questions and share their opinions on the topic as we spoke about a wide range of topics such as censorship, body-shaming, bisexuality, masturbation, mythology, religious art, sexuality education, how a few of the members in our audience were molested and shunned by the police when they tried to ask for help, and a lot more. The panelists were sitting in front of the crowd on mattresses instead of the podium and promoted healthy discussion on all of these issues.

By about 7, we recommenced our performances with Banat on the guitar who sang a melodious song. Next, we had Akshatha Narayan who spoke about depression and anxiety, and Twinkle Kataria, Varun Srinivasan and Shruti Giri also performed marvelous spoken word poetry. Akshath Killa, who was the co-host and creative designing head of TMAC, and Yatika Agarwal, who is a resident writer in the magazine, also performed abstract pieces on colour and self-love respectively.  Rohan Parekh performed some hilarious stand up comedy and Ebrahim and Rutash played their electric guitars and created rock music in an attempt to bring love for rock music back again.


Tiina Myllärinen

Myllärinen's works include Squarcio for ensemble and orchestral works What (2010) and Traces (2013, commissioned by the Pro Musica Foundation, world premiere at the Helsinki Music Centre on 5 June 2014).

Tiina Myllärinen's music has been described as cheerfully inquisitive, vigorous and original. She has recently developed an interest in the application and study of various acoustic phenomena, such as resonance, in her music.


Monthly Disability Benefits| Social Security Disability Benefits for Schizophrenia | SSD | SSDI | SSI

If you suffer from schizophrenia that prevents you from working, you may be entitled to monthly disability benefits from the Social Security Administration. A Social Security attorney or Social Security law firm can help guide you as you apply for SSI or SSDI benefits.

Schizophrenia is a serious and challenging medical illness, an illness that affects well over 2 million American adults, which is about 1 percent of the population age 18 and older.  Although it is often feared and misunderstood, schizophrenia is a treatable medical condition.

More than 2 million Americans suffer from schizophrenia, a serious and challenging mental illness. Schizophrenia is a mental disorder that makes it hard to discern the difference between reality and unreal experiences, to behave normally in public, to think logically and to have normal emotional responses to circumstances. Schizophrenia can be just as disabling as a physical illness.

People who suffer from a serious mental illness like schizophrenia are entitled to disability benefits from the Social Security Administration, just like someone who is prevented from working by a physical disability would be. A licensed mental health professional or physician must evaluate your condition and determine if your schizophrenia is so severe that it will prevent you from working and persist for more than 12 months. A Social Security attorney or law firm can help you file your application for disability benefits and help present the evidence about your schizophrenia in the most compelling way possible.

When evaluating an individual for disability on the basis of a schizophrenia, an applicant may have to provide information from the following sources, including medical evidence, psychiatric information, evidence of work attempts, mental status examination, psychological testing, intelligence testing, personality testing, neuropsychological assessments and evidence of treatment.

The following symptoms, when found in combination, are some of the hallmark signs of schizophrenia:

  1. Delusions or hallucinations;
  2. Catatonic or other grossly disorganized behavior
  3. Incoherence, loosening of associations, illogical thinking, or poverty of content of speech; and
  4. Emotional withdrawal and/or isolation

Mental Illness SSD Attorneys will help you recover benefits

If the above symptoms are present and result in at least two of the following, the Social Security Administration is likely to classify your schizophrenia as being severe enough to qualify you for monthly Social Security disability payments in the form of SSDI or SSI benefits:

  • Marked restriction of activities of daily living;
  • Marked difficulties in maintaining social functioning;
  • Repeated episodes of decompensation, each of extended duration.

If you have a medically documented history of chronic schizophrenia for the past two years and this condition has limited your ability to work, you are likely to qualify for Social Security disability benefits. One of our Social Security lawyers or law firms can evaluate your case and gauge your chances of having your disability claim approved.

For more information about schizophrenia, visit the Social Security Administration's website.

DotCO's Tips when applying for a SSDI or SSI claim for schizophrenia:

  1. Keep detailed records of all hospitalizations. It is important to keep records on any time you are hospitalized as part of your schizophrenia treatment. At a bare minimum, these records should contain discharge records. However, the more comprehensive your records are, the more likely the SSA is to approve your claim for Social Security disability.
  2. Participate in research.Participating in cutting edge schizophrenia research helps establish your diagnosis and can also help identify what is causing your mental illness. Moreover, it demonstrates to the SSA that you are serious about finding a way to address your illness. Oftentimes, research includes testing that is not part of your typical psychiatric evaluation: These tests can include MRI, EEG, fMRI, PET, MMPI, WISC, etc, and can help further document your illness.
  3. Maintain copies of all educational records. Keeping copies of educational records, such as report cards and graded assignments can help show if your schizophrenia is causing your grades to suffer, for instance if your grades dropped from A's to B's or C's to D's. While your application may not ask for this information, it is important to include and helps provide a full picture of an applicant's disability. This is especially true when dealing with cases of childhood schizophrenia, and for all applicants with a history of schizophrenia who are in college.
  4. Ensure your answers are both thorough and concise. You want to ensure you are providing enough information to give the SSA a full picture of how your schizophrenia is impacting your life, but you also want to make sure that information is easily understandable. Using bullet points can be a simply way to break down information into manageable chunks. A Social Security attorney can help review your application to ensure the information is presented in the most compelling way possible.

Social Security Disability Attorneys - Submit your information and be contacted today!


Ten Best Cds Of 1992 MAG

By Unknown, Unknown, Unknown

   1. "More Noise and Other Disturbances" - The Mighty iMighty Bosstones (Taang!) - The odd concoction of ska, pop and hard-core grabs you and brings you into a plaid dimension of omnipotence.

2. "A Picture of Nectar" - Phish (Elektra) - With odd lyrics speaking of "a virile dissector" and "the family berzerker," Phish confuses you into a state that becomes quite comforting with their funk bass grooves and their melodic hippie-esque harmonies. You'll want to crunch along.

3. "Check Your Head" - The Beastie Boys (Capital) - Not as impressive as "Paul's Boutique" and not as sing-a-long-able as "Licensed to Ill" the Beastie Boys' third adventure goes back to the roots using real instruments while mastering the art of sampling.

4. "Honey's Dead" - The Jesus And Mary Chain (Def American) - Most of the grim tales told by the Chain will have you reaping death on others as well as yourself, but you become quickly enlightened with their happy pop numbers that have you singing their songs as you pick flowers in the autumn's dew.

5. "Psalm 69" - Ministry (Sire/Warner Bros.) - The anger generated by this industrial mayhem coup has you lacing up your Doc Martens and moshing with anything in sight (i.e. your couch or younger brother) and then you turn it off and question your sanity.

6. "Weak" - Seaweed (Sub Pop) - Not Nirvana, not Pearl Jam, not Soundgarden, not even Mudhoney, Seaweed is Seattle's finest band. They destroy the definition of grunge and build new boundaries with tunes you hum to and slam to.

7. "Hit to Death in the Future Head" - The Flaming Lips (Warner Bros.) - What is this? I keep replaying it and replaying it and replaying it to search for this ultimate truth. I still haven't found the answer. An enjoyable blend of fusion guitars, sitars and samplers to name a few oddities of this enigma.

8. "Apollo 18" - They Might Be Giants (Elektra) - I love these guys. After accepting the eclectic abilities of these two geniuses, I have found their mesh of accordions and french horns with pop music can produce a wondrous noise.

9. "Slanted and Enchanted" - Pavement (Matador) - This is what R.E.M.'s "Automatic for the People" should have sounded like. It is a perfect collection of alternative rock that will make you say, "This is good stuff."

10. "Hotwired" - Soup Dragons (Big Life/Mercury) - My friends say, "I don't like this album, it all sounds the same." Exactly. The Soup Dragons take an album and make one long song. And it's a great song.

"Dirty" - Sonic Youth (DGC)

"What to do about Them" - Swirlies (Taang!)

"Cracker" - Cracker (Virgin)

"The Predator" - Ice Cube (Priority)

"Daisychain Reaction" - Poster Children (Sire) n

Similar Articles

This article has 1 comment.

i love this so much!

MacMillan Books

Aspiring Writer? Take Our Online Course!


Fed gathers to take U.S. economy's pulse

With the U.S. economy turning a corner, Federal Reserve policymakers will consider whether some programs intended to ease the recession and stem the financial crisis should be extended.

Fed Chairman Ben Bernanke and his colleagues open a two-day meeting Tuesday afternoon, where they will sift through economic data and anecdotal information about how businesses and consumers are faring nationwide. So far, many of those barometers suggest the worst recession since World War II is ending and that the economy has started to grow again, or will soon.

And there are risks lurking.

While unemployment dipped to 9.4% in July, the Fed says it's likely to top 10% this year because companies won't be in a rush to hire. That could restrain the recovery if it crimps spending by already-cautious consumers.

Another danger comes from the troubled commercial real market where defaults on loans are rising. That's a strain on banks holding such loans. The increasing risk is making lenders ever-more stingy about new commercial real-estate loans or refinancing existing ones.

Against that backdrop, the Fed is all but certain to hold a key bank lending rate at a record low near zero when its meeting ends Wednesday. The central bank is also expected to renew a pledge to hold that rate there for an "extended period."

Economists predict the Fed will leave its target range for its banking lending rate at zero to 0.25% through the rest of this year. The rationale: Super-low lending will spur Americans to spend more, which would support the economy.

If the Fed holds its key rate steady, that means commercial banks' prime lending rate, used to peg rates on home equity loans, certain credit cards and other consumer loans, will stay around 3.25%, the lowest in decades.

There have been signs the economy is on the mend.

Many analysts believe the economy, which logged a mild contraction in the second quarter after a dizzying free-fall in the prior six months, is growing now. That makes it more likely the Fed will consider whether some rescue programs should continue, but any decisions might not come at this week's meeting.

"I think they'll let it expire. It seems the mood turned against Treasury purchases in the last couple of months, and there's been some skepticism whether it has worked in bringing rates down," said Michael Feroli, an economist at JPMorgan Economics. There's also been some concern that the program makes the Fed look like it is printing money to pay for Uncle Sam's exploding budget deficits.

Inflation, meanwhile, is expected to stay low.

The government reported Tuesday that workers' productivity grew sharply in the second quarter, while their hourly compensation — adjusted for inflation — fell. Productivity gains helps to tamp down inflationary pressures. While good for the economy, the second-quarter gain came at the expense of layoffs. Companies simply produced more with fewer workers.


Posts from the ‘Classroom Management’ Category

Management vs. Engagement

The Management Side:

The Engagement Side:

Together in Harmony

Social Studies Stations

I had the opportunity to team teach a lesson in a 6th grade Social Studies class today.  The teacher and I decided to use stations for the structure.  The material was not new (ancient Egypt) so we didn’t have to worry about presenting new information.  We wanted to give the students the opportunity to “play” with the content and review what they knew.

We developed three different station activities with four actual stations.  One of the activities was longer and needed a little more time to complete.

The activities were a 9 square game, decoding hieroglyphs, and creating a foldable using Egyptian cartoons.  Each group would have about 11 minutes to complete a station based on the amount of time in the class.

9 square answer key and student copy

9 square answer key and student copy

Student attempt at answering 9 square puzzle.

Student attempt at answering 9 square puzzle.

Decoding Hieroglyphs

Decoding Hieroglyphs

Creating foldable for Egyptian cartoons.

Creating foldable for Egyptian cartoons.

When the students came into the classroom, I had four steps written on the board.  The teacher wanted them to copy down the lesson objective and I wanted them to get out a blank sheet of paper.  I learned a couple of new brain based strategies at the NMSA conference this past week.  One of them that struck me was that we can hold about 10 things in our short term memory at a time.  The speaker (Dr. Kagan) suggested that instead of a warm-up we have students write down everything that is going on in their brain when they first come into class (all the things that are bothering them, what they just learned, what they need to do after school, what they need to remember, ect).  Sort of clear out the short term memory.  I explained to the students why we were doing this and how I would not want the paper.  I gave them one minute to write, but had to extend it as they kept making their list for over two minutes.  I was amazed about how serious they took this activity.  When they finished, I began explaining the stations and they seemed more focused.  I will definitely use this activity again.  I am thinking about having my students do this every day before class.

I then began explaining the various stations.  When I am explaining various activities, I explicitly state what they will and will not do.  I show them the actual materials that they will use to complete the activities.  I make sure that I have an example for them to follow at each station.  I then took them out to their table in the pod area.

Pod area set up for stations

Pod area set up for stations

They immediately began working.  We made sure that we checked in with each station at the beginning of each rotation to make sure that they understood exactly what they needed to do.  The level of engaged conversation was really incredible.  The 9 square game was by far the most difficult activity, but students also had to work hard to find the information from the cartoons and decode the hieroglyphs.  Out of two classes and almost 50 students, I had one student in one class that was not engaged.  It turned out he just didn’t understand exactly what he needed to do and hadn’t asked another group member or a teacher.

Students working in stations.

Students working in stations.

Another view

Another view

At the end of the class period, I had students return to the classroom and write one thing they learned and one question that they still had on the back of their foldable and turn it in.  This was an exit card and a way for us to assess what they knew and what they were still struggling with.  The foldable can also be used as a review for an assessment.

As an additional exit ticket, I asked each student as they left to tell me one thing they learned.

Overall, we were really pleased with the activity.  The students were engaged in meaningful dialog about the topic and were focused for the entire 45 minutes.  This activity just reminded me how much I like stations.  There is a lot of prep work, but when that is finished, you just facilitate during class periods.  It is a great way to teach.

Newspapers – Day 2

I was very happy with the performance of my students both in finding the text features and working in groups.  I wanted to have them discuss their frequency charts as a follow up to the previous activity.  But first, I wanted to see what new information they had learned about text features.  I decided to have them use the same paper for the first “brain dump” to add any new information that they had learned.  I had them draw a line under their first writing and add any new information that they had learned.  I then had them share their new understandings.

I wanted each student to share an answer, so I borrowed some marbles from another teacher and placed a plastic plate in the middle of each table.

Each student selected three marbles of the same color.  Every time they answered a question, they placed a marble in the plate.  It was an easy way for me to see who has shared.  I discovered, however, that marbles (or anything else that rolls), is not the way to go.  I will be purchasing some colored chips to use in the future.  The marbles struggled to stay in the plate and they rolled across the table too easy.

I had my overhead set up in the pod area and I had one complete copy of the newspaper on each table.  I had students move into the area and sit in groups. I displayed one question at a time and had the groups discuss the answer.  After every person had answered, I asked one person to tell me what another group member had said.  I discovered that they struggled with really listening to their group members.  It allowed me to assess their listening and retelling skill levels.

I need to work on group sharing and listening in my future activities.

Classroom Management & Discipline Part 2

Below is the continuation of our Classroom management & discipline series.

Classroom Management & Discipline Part 1

Classroom management and discipline are an essential element of the English language learner classroom. Below is part 1 of 2 Classroom Management & Discipline.


LAHORE – Besides having earned a bad name on diplomatic front due to its underhand lobbying and state-sponsored terrorism across the borders, India has also been recognized as the ‘Namak Haram country’ (treachous country) by Google.

Related – India’s ‘rich’ history of supporting terrorism in neighboring countries

Believe it or not, like majority of Pakistanis, the US-based tech giant considers India as a “Namak Haram country’. The reason is very simple yet interesting: a 1973 Hindi drama film ‘Namak Haraam’ starring Rajesh Khanna, Amitabh Bachchan, Rekha and Simi Garewal.

If you are still curious, type ‘Namak Haram Country’ in Google search bar and get amused.