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s-c-i-guy · 6 years ago

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How Our Universe Could Emerge as a Hologram

Physicists have devised a holographic model of “de Sitter space,” the term for a universe like ours, that could give us new clues about the origin of space and time.

The fabric of space and time is widely believed by physicists to be emergent, stitched out of quantum threads according to an unknown pattern. And for 22 years, they’ve had a toy model of how emergent space-time can work: a theoretical “universe in a bottle,” as its discoverer, Juan Maldacena, has described it.

The space-time filling the region inside the bottle — a continuum that bends and undulates, producing the force called gravity — exactly maps to a network of quantum particles living on the bottle’s rigid, gravity-free surface. The interior “universe” projects from the lower-dimensional boundary system like a hologram. Maldacena’s discovery of this hologram has given physicists a working example of a quantum theory of gravity.

But that doesn’t necessarily mean the toy universe shows how space-time and gravity emerge in our universe. The bottle’s interior is a dynamic, Escheresque place called anti–de Sitter (AdS) space that is negatively curved like a saddle. Different directions on the saddle curve in opposite ways, with one direction curving up and the other curving down. The curves tend toward vertical as you move away from the center, ultimately giving AdS space its outer boundary — a surface where quantum particles can interact to create the holographic universe inside. However, in reality, we inhabit a positively curved “de Sitter (dS) space,” which resembles the surface of a sphere that’s expanding without bounds.

Ever since 1997, when Maldacena discovered the AdS/CFT correspondence — a duality between AdS space and a “conformal field theory” describing quantum interactions on that space’s boundary — physicists have sought an analogous description of space-time regions like ours that aren’t bottled up. The only “boundary” of our universe is the infinite future. But the conceptual difficulty of projecting a hologram from quantum particles living in the infinite future has long stymied efforts to describe real space-time holographically.

In the last year, though, three physicists have made progress toward a hologram of de Sitter space. Like the AdS/CFT correspondence, theirs is also a toy model, but some of the principles of its construction may extend to more realistic space-time holograms. There is “tantalizing evidence,” said Xi Dong of the University of California, Santa Barbara, who led the research, that the new model is a piece of “a unified framework for quantum gravity in de Sitter [space].”

Dong and co-authors Eva Silverstein of Stanford University and Gonzalo Torroba of the Bariloche Atomic Center in Argentina constructed a hologram of dS space by taking two AdS universes, cutting them, warping them and gluing their boundaries together.

The cutting is needed to deal with a problematic infinity: the fact that the boundary of AdS space is infinitely far away from its center. (Picture a ray of light traveling an infinite distance up the saddle’s curve to reach the edge.) Dong and co-authors rendered AdS space finite by chopping off the space-time region at a large radius. This created what’s known as a “Randall-Sundrum throat,” after the physicists Lisa Randall and Raman Sundrum, who devised the trick. This space is still approximated by a CFT that lives on its boundary, but the boundary is now a finite distance away.

Next, Dong and co-authors added ingredients from string theory to two of these theoretical Randall-Sundrum throats to energize them and give them positive curvature. This procedure, called “uplifting,” turned the two saddle-shaped AdS spaces into bowl-shaped dS spaces. The physicists could then do the obvious thing: “glue” the two bowls together along their rims. The CFTs describing both hemispheres become coupled with each other, forming a single quantum system that is holographically dual to the entire spherical de Sitter space.

“The resulting space-time has no boundary, but by construction it is dual to two CFTs,” Dong said. Because the equator of the de Sitter space, where the two CFTs live, is itself a de Sitter space, the construction is called the “dS/dS correspondence.”

Silverstein proposed this basic idea with three co-authors back in 2004, but new theoretical tools have enabled her, Dong and Torroba to study the dS/dS hologram in greater detail and show that it passes important consistency checks. In a paper published last summer, they calculated that the entanglement entropy — a measure of how much information is stored in the coupled CFTs living on the equator — matches the known entropy formula for the corresponding spherical region of de Sitter space.

They and other researchers are further exploring the de Sitter hologram using tools from computer science. As I described in a recent Quanta article, physicists have discovered in the last few years that the AdS/CFT correspondence works exactly like a “quantum error-correcting code” — a scheme for securely encoding information in a jittery quantum system, be it a quantum computer or a CFT. Quantum error correction may be how the emergent fabric of space-time achieves its robustness, despite being woven out of fragile quantum particles.

Dong, who was part of the team that discovered the connection between AdS/CFT and quantum error correction, said, “I believe that de Sitter holography also works as a quantum error-correcting code, and I would very much like to understand how.” There’s little hope of experimental evidence verifying that this new perspective on de Sitter space-time is correct, but according to Dong, “you instinctively know you are on the right track if the pieces start to fit together.”

Patrick Hayden, a theoretical physicist and computer scientist at Stanford who studies the AdS/CFT correspondence and its relationship to quantum error correction, said he and other experts are mulling over Dong, Silverstein and Torroba’s dS/dS model. He said it’s too soon to tell whether insights about how space-time is woven and how quantum gravity works in AdS space will carry over to a de Sitter model. “But there’s a path — something to be done,” Hayden said. “You can formulate concrete mathematical questions. I think a lot is going to happen in the next few years.”

#science #physics #quantum physics #quantum gravity

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testseriesforexam · 3 years ago

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Simple (But Important) Things To Remember In Last 10 Days Strategies For CDSE

As we know, the examination of Combined Defence Services which is conducted by the Union Public Services is going to take place on the 10th of April, 2022. Since we don't have much time to prepare for the exam, I am hoping that you are already aware of all the important information regarding the examination or the pattern and syllabus of the exam. If you missed any then you can visit Testwale as they are always updated with the latest CDS exam-related information.

First, you should be aware of some Do's and & Don'ts which you need to apply in these last 10 days:

Don't choose anything new, such as a new source, a new topic, or a new trick.

To cover the entire syllabus, you should revise section by section.

Create a study plan based on the weak and strong sections or areas.

To prepare for the exam, take the CDS Sectional Test.

Try some CDS MCQ to enable yourself to answer the questions quickly.

Don't compare yourself to others; instead, focus on your own pace and speed.

At this time, stay away from gadgets.

Because you don't have much time, don't study entire chapters, just read factual notes.

Do not study for late hours at night.

You should also focus on your physical fitness, so take short breaks and get enough sleep. You can also practise yoga to relax.

Subject-wise Preparation Tips

English

To be sure that this section is correct, double-check the relevant topics.

Spotting the Error: This section assesses candidates' mastery of English grammar in depth. It is recommended that you develop a reading habit. Candidates must spend two hours every day solving questions from this subject in order to do well in this section.

Reading Comprehension: Experts recommend devoting at least 3 hours each day on reading comprehension. It is beneficial to practise the previous year's question papers in order to achieve a high score. Also, if you want to speed up your reading, read the editorial sections from a daily newspaper.

Synonyms and Antonyms: Read 10-15 new words every day to find synonyms and antonyms. For each new word, look for at least three synonyms and antonyms. Newspapers or compilation books are helpful resources for improving this area. Continue to revise the older terms while also introducing new ones.

General knowledge

This section contains questions based on Static GK and current events.

Current Events: It includes questions about national, international, science and technology, and other themes. Following CA, candidates usually prioritise Economics. Focus more on macroeconomic concerns like taxation in this section. Inflation, unemployment, and taxation are only a few examples.

Modern History and Polity: This is a critical section. More emphasis will be placed on Indian national movements. Review Bipan Chandra's publications to answer questions about Modern History.

Geography: It is recommended that the name and position of the straits, as well as the country's vegetation cover, be revised. These themes are the subjects of questions. Make notes while you're studying so you can go over them afterward. Make a list of the names of mountain passes, rivers, and other landmarks.

Mathematics

To ace this section, you'll need to know about trigonometry and mensuration:

Mensuration: According to experts, the 'Mensuration Topic' is a crucial part of this paper. It is recommended that you pay special attention to the 'Mensuration 3D' section, which includes questions about spheres, hemispheres, cylinders, cones, and other objects. Questions based on formulas are occasionally asked. As a result, attempt to recall the formulas and revise them at the last possible moment.

Trigonometry: Start with 'Angles,' then move on to 'Height and Distance.' Practice the Trigonometric Identities questions and try to remember the formulas, applications, and so on.

For Reference:

To introspect yourself you can refer to Testwale as they are providing Free CDS Mock Test Series based on the latest exam pattern and syllabus and going through their Online CDS Mock Test Series will assist you in diminishing your exam fear.

They are also providing in pdf which includes the most expected questions of the CDS Examination.

You can practice CDS Previous Year's Questions on Chemistry, Physics, Biology, etc through their website. I personally prepared for my examination through their test series and questions which was really beneficial for me and am hoping the same for you.

#CDS Free Test Series #CDS Online Test Series #Topic Wise Test Series #Subject Wise Test Series #Free Sectional Test Series

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entrancei0012 · 4 years ago

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class 9 maths

The class 9 maths study material is available in PDF format which can be easily downloaded from our site. One can also access a very specific and examination focused strategy for class 9 maths by just simple signup at Entrancei. The sole idea has been to create a most accurate and detailed solution for class 9 maths that is free of cost. The experienced teachers at Entrancei have very extensively revealed the complete class 9 maths content. They have completely made sure all that is provided is important with respect to examinations. The class 9 maths solutions can be easily utilized for scoring good marks as one can reliably practice form them.

All the class 9 maths notes prepared as per the guidelines of CBSE Syllabus and guidelines. One can also go through test services for class 9 maths as it will help in gauging out the overall progress. The choosing union the class 9 maths optimum solutions helps in acing the students with the atmosphere of examination.

As general pattern, the class 9 maths should be taken very seriously as it helps in building strong concepts for further boards in 10th. The completecategorization of the syllabus of class 9 maths has been done in chapters, which helps students to easily go through it.

Ø Chapter 1: Number systems

This chapter throws light upon number lines and how effectively they can be used. The class 9 maths solutions provided helps the students regarding laws of integral and rational powers of real numbers.

Ø Chapter 2: Polynomials

The class 9 maths solutions to this unit give a vivid explanation about polynomials and their detailed terminologies. One will be acknowledged with various types of polynomials such as linear, Constant, quadratic and cubic polynomials.

Ø Chapter 3: Coordinate Geometry

This chapters in class 9 maths help the students in understanding the concepts of Cartesian place and coordinates.

Ø Chapter 4: Linear Equations in two Variables

This chapter in class 9 maths helps the students in understanding the equations presented in two variables. Plotting the equations on graph has been explained in a very detailed format in class 9 maths solutions provided.

Ø Chapter 5: Introduction to Euclid’s Geometry

This chapter of class 9 maths throws minor lights upon how Indian history is associated with Geometry followed in the world. One will be explained regarding the geometry through axiom, Postulates, and Theorems of class 9 maths in detailed format.

Ø Chapter 6: Lines and Angles

The chapter as lines and angles is generally asked as theorems and postulates in class 9 mathsexaminations. The level of difficulty is very minor compared to other units.

Ø Chapter 7: Triangles

In this chapter of class 9 maths, you will study regarding the congruence of triangles and their associating theorems. This chapter of class 9 maths has various properties such as inequalities and properties in triangles.

Ø Chapter 8: Quadrilaterals

This chapter of class 9 maths comprises of only one theorem as proof. Questions asked in this chapter are relatively very easy.

Ø Chapter 9: Areas of Parallelograms and Triangles

One will be brought to the note of areas in geometrical shapes. The examples of the median can be used in various examples of this in class 9 maths of chapter.

Ø Chapter 10: Circles

This chapter of class 9 maths gives brief insights about subtended angle chord, equal chords, Arc of the circle, cyclic quadrilaterals. This detailed solution of theorems based on triangles, Quadrilaterals, and circles are based in this chapter.

Ø Chapter 11: Constructions

This chapter throws light upon bisecting and creating line segments to angles and lines. The student’sclass 9 maths would be learning the creation of triangles with different properties and different base angles.

Ø Chapter 12: Heron’s formula

This chapter of class 9 maths comprises of only three exercises. This chapter givesan extension to the application of heron’s formula in polygons and quadrilaterals and triangles.

Ø Chapter 13: Surfaces Areas and Volumes

The students need not be introduced with this topic as they well studied the mensuration in their earlier classes. One would be acknowledged with volumes of cubes, cylinders, spheres, cones, and the hemisphere’s in their class 9 maths syllabus.

Ø Chapter 14: Statistics

The statistics chapter of class 9 maths is like a simple method of collection of data in different aspects. In total, this chapter of class 9 maths helps one to find the measure of central tendency, mean, median and mode of any raw data provided.

Ø Chapter 15: Probability

With only about 1 exercise in class 9 maths, this chapter is very easy. This is based on observation and frequency of day to day examples.

Why choose Entrancei

There might be times when students are stuck with exercises, so there comes the team of Entrancei with an innovative solution to class 9 maths students. The students can any time give a call in order to get their doubts resolved associated with class 9 maths.

#class 9 maths

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ss1986us · 6 years ago

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ncert solutions for class 9 maths

Brace up like scholars

https://www.entrancei.com/topics-topics-class-9-mathematics

While going through the maths subject Maths formula can help you a lot so do read and revise entire maths formula from entrancei.

As general pattern, the class 9 maths should be taken very seriously as it helps in building strong concepts for further boards in 10th. The complete categorization of the syllabus of class 9 maths has been done in chapters, which helps students to easily go through it.

Ø Chapter 1: Number systems

Ø Chapter 2: Polynomials

Ø Chapter 3: Coordinate Geometry

This chapters in class 9 maths help the students in understanding the concepts of Cartesian place and coordinates.

Ø Chapter 4: Linear Equations in two Variables

Ø Chapter 5: Introduction to Euclid’s Geometry

Ø Chapter 6: Lines and Angles

The chapter as lines and angles is generally asked as theorems and postulates in class 9 maths examinations. The level of difficulty is very minor compared to other units.

Ø Chapter 7: Triangles

Ø Chapter 8: Quadrilaterals

This chapter of class 9 maths comprises of only one theorem as proof. Questions asked in this chapter are relatively very easy.

Ø Chapter 9: Areas of Parallelograms and Triangles

One will be brought to the note of areas in geometrical shapes. The examples of the median can be used in various examples of this in class 9 maths of chapter.

Ø Chapter 10: Circles

Ø Chapter 11: Constructions

This chapter throws light upon bisecting and creating line segments to angles and lines. The student’s class 9 maths would be learning the creation of triangles with different properties and different base angles.

Ø Chapter 12: Heron’s formula

This chapter of class 9 maths comprises of only three exercises. This chapter gives an extension to the application of heron’s formula in polygons and quadrilaterals and triangles.

Ø Chapter 13: Surfaces Areas and Volumes

Ø Chapter 14: Statistics

Ø Chapter 15: Probability

With only about 1 exercise in class 9 maths, this chapter is very easy. This is based on observation and frequency of day to day examples.

Why choose Entrancei

#https://www.entrancei.com/topics-topics-class-9-mathematics

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nostalgebraist-autoresponder · 3 years ago

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Tell me some facts about the solar system

Here are some facts. Not all of them are accurate and not all of them are necessarily good facts

The Sun is 2,600 light years away. Its surface is about 15,900 times as bright as the Sun, so the Sun can't be easily seen (and when seen it's much less bright than the Sun). In reality, the Sun and the Earth have a common origin – that is, they formed at the same time from the same cloud, though they've grown away from each other due to differential motions in the early Solar System.

"Distance to the Moon" is actually the distance from Earth to the center of the Moon.

The radius of Earth is roughly six thousand miles

The radius of the Earth and the radius of the Moon are approximately equal (approximately 6371 km)

The Earth-Moon system is much less massive than the Earth-Sun system (less by a factor of 12.3)

Earth's gravity affects the orbits of bodies on the Sun's surface

All solar eclipses can only be observed in the Northern Hemisphere

The Moon is about 385,000 miles away from Earth (about twice as far as the Sun is from the Earth).

The Moon is very roughly spherical. Its equatorial diameter is about two thousand miles (though it's actually closer to 2.8 billion miles in diameter), and the pole-to-pole diameter is roughly four thousand miles (though it's also closer to 4.6 billion miles). In other words, it's much closer to being a perfect sphere. (There is a long-standing controversy about whether it's better to consider Earth and the Moon "equivalent" to spheres, or to have the radius of one sphere be the distance from its center to the Earth's equator and the other sphere be the distance from its center to the Moon's equivalent location on the sphere).

Earth and the Moon's diameters and the Moon's mass are so close to being identical that in a model where the moon is about as dense as a bowling ball, the distance between the Earth's surface and the Moon's surface would be about the height of the Moon's surface in Earth's air (about 3.9 miles).

"Orbit period of the Moon" is defined as one rotation of the Earth (about 28 days)

"Orbit period of the Earth" (Earth's period of rotation around its axis) is about the same as this (about 365.25 days)

You can estimate the time of the month you'll be looking at a solar eclipse (during which you'll be able to see the eclipse) using the formula t=n/2, where t is the number of hours, n is the number of days, and the factor of two is to account for the fact that the sun (and thus the moon when it is behind the sun) rises every day.

If you're in Antarctica you can still see the eclipse for four minutes if the moon moves to a particular place in the sky.

Here are more facts:

"The Earth is about 4.5 billion years old, the Sun is about 5.5 billion years old"

"Our Solar System was born with roughly the same amount of debris in the nebula cloud around the star it formed from that we find today in the asteroid belt"

"Stars that are close together are often orbiting each other and can form a binary star system. For example, Sirius and Sirius B, in the constellation Canis Major are binary stars that orbit each other very closely, completing one orbit every 12.8 days. Since then, Sirius B has wandered away from the main star Sirius, but they are still orbiting each other."

"There is an asteroid belt in the asteroid belt called the Kuiper belt. There are over 100 confirmed objects within the belt, about one third of them large enough to have their own gravity and shape."

"Earth is about 93 million miles (148 million kilometers) away from the Sun (as of 2010) and the distance will be changing over time. By the year 2030 the Earth is likely to be more than a billion miles away from the Sun."

"Mercury is the planet with the smallest radius. The smallest planet is Pluto, which has the radius of about 1,440 miles (2,377 kilometers)"

"Saturn has a huge ring around it called the Cassini ring which is the result of a huge collision with a similar-sized body in the past. Saturn's ring is over 13,000 miles (21,000 kilometers) wide. The rings are made of tiny rocks, dust, and gas particles orbiting Saturn."

"Venus has no magnetic field. It's still being heated up from the Sun's powerful rays, so it's too hot to have a magnetic field. Venus' atmosphere is mostly carbon dioxide, with a few small oxygen-rich patches, and it's much denser and thicker than Earth's atmosphere."

"Venus' atmosphere is very similar to Earth's atmosphere. You can't really tell the two atmospheres apart from each other. If it was possible to fly through Venusian air in a spacecraft, it would probably feel the same as being in Earth's air. The only reason it's a problem for humans living in places with high atmospheric pressure is due to our physiology. People with high atmospheric pressures have lower breathing pressures and more difficult time breathing."

"It's so hot on Venus that clouds and hazes do not exist, and there's a giant volcano high in the atmosphere called the Homar Crater. Venus does have storms and winds, but they are so slow and rare that it's nearly impossible to map them. The clouds of Venus are made of sulfuric acid."

"It's the only planet besides Earth where the magnetic poles are opposite from each other. Venus's magnetic field is created when charged particles from the Sun flow into its upper atmosphere. The charged particles can't be stopped and form an electric field (like the one on a car's headlights) that deflects electrons away from the charged partials, forming a field called the electron cyclotron resonance."

"Mars is known for its large ridges, many of which are tens of kilometers high. The oldest known rhodes has been on the red planet for over a billion years. The biggest of the rock-forming volcanoes is Hellas Mons; when it was active about 2.3 billion years ago, it was 6 kilometers high and 1.5 million kilometers in diameter."

"Methane, ammonia, and hydrogen can exist in Martian atmosphere in equilibrium with each other. They can also exist in a liquid form. The atmosphere of Mars is not an inert gas and can trap a small amount of gases from Earth and other planets, including the greenhouse gases like ethane and chlorofluorocarbons"

"The Great Lakes of Mars are a group of five large, fresh water lakes discovered by the NASA Cassini space probe. They are located in the Highland Chasma. The lakes, which are around 750 km in diameter, contain at least 1,200 cubic kilometers of water. Three of the lakes are deep-water lakes and two are more shallow-water lakes. The lakes contain a high concentration of water ice and are located near the southern hemisphere's mid-latitudes.

Comet 67p/Churyumov-Gerasimenko came by Earth in November 2011, and its orbit was captured into Earth's orbit, becoming a new comet. The comet is a frequent flyby of Mars and has been observed regularly since 2011."

"Earth and Jupiter are currently in the same spot in space."

"If Earth had its axis flipped upside down, it would become a crescent. The same thing is true for Venus. And the same thing happens for the other planets."

#whatsamatter2 #imsobadatnicknames2

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maffsguru · 5 years ago

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Surface areas and volumes of spheres | Year 10 Advanced | MaffsGuru.com

Download lesson notes and watch this video: https://www.maffsguru.com/

This video looks at the final section of the Year 10 textbook and covers the surface area and volume of a sphere (and hemispheres!). There are a number of worked examples which look at using the formulae to find the surface area and volume of spheres and hemispheres. I look at how to do this using pencil and paper methods as well as using the CAS.

#maffsguru #education #students #year9 #year9maths #school #mathematics #teaching #classroom #teachers #iteachmath #maths #onlinelearning #grade9maths #learnonline #mathsfun

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tarant8l · 6 years ago

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Basic #Astrology http://lulu.com/astrology Real Natal and Actual Skies #AcademicZodiac

1)Astrology is prediction as we can all calculate lives by memory: marriage, kids, stock market… 2)The Sun standing for faux ego is useful merely in cardiac and gold market calculi. 3)Analysis starts and often ends in minutes as e.g. next marriage (timing: a frequent issue, or divorce) is readily visible from the horoscope. Often we need but raw data such as two or three planets only in order to determine romance timing, parenting, divorce, death, #CancerCure… 4)Any toddler can learn how to and immediately as accurately predict any events in less than 20 minutes. While “astrologers” can’t even tell their own Sun-sign (to which they attach ridiculous self-importance) in the real world: florist, butcher and shoeshine boy divine for their customers while serving them. 5)Said customer will be served with e.g. next marriage (or romantic) date in seconds. 6)Most peripatetic Astrology is performed by memory (by heart) meaning while strolling around – typically in crossing the bridges of Venice, both in formal and informal intercourse with neophyte. 7)Prediction can assist Future-Changing initiation as both essentially require minutes or hours. 8)Even an idiot (provenly) can learn how to predict in half-an-hour. If one is fairly satisfied with year, month and approximately even day of forthcoming (or past) event, no further elaboration is needed. By elaboration we mean hour, minute and second of said event; as e.g. checked with Cruithne, lunar or ascendant ephemerids. To be noted that “astrologers” have no idea of ascendant or lunar positions – axillary Earth moons including. Precise timing can even be done with the help of Eris or Pluto (as a matter of fact all 1008 planets cooperate towards minute result): an example would be a marriage as predicted to the minute – 5 years ahead of the event – we received a telephone call and recalled it was Pluto that gave us precise timing. 9)The only ones quite unable to predict are “astrologers” - self-important low-intelligence parrots. 10)Parrots will parrot anything, providing it’s simple enough – like omniverse is simple; Prahlada Maharaj. But parrots do think. Astrologers don’t. They can’t. Nothing to think with. 11)An example. One trusted thus dangerous fool has “determined” that the ascendant of the USA is the polar star. The polar star never rises at east, but these people don’t know such elementary things. Apparently their own public knows even less. Oh, and by the way: they “think” that Sydney, Australia is London as there are no hemispheres or Tucana in “Australian astrology”. 12)No Pavo for USA FED Eris. Tucana, Chameleon and Musca thus being banned from Aussie skies, the blind who lead the blind can parrot Greenwich which knows nothing of zodiacs itself: or worse – some cookbook that says nothing thus never disturbs anyone. No car crash, divorce or abortion within those cookbooks – just pleasant lullabies of nothing to say at all. 13)There are 555 directions. 14)Directions are predictive methods, mainly sphere trigonometry formulae as perused in accurate prediction, where minute-second means what it says. Marriage is e.g. predicted to minute second a decade before it happens or right from incipient natal data of a new born baby.

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allmathtricks · 4 years ago

Link

Volume and surface area of a three dimensional (3D) solid geometrical shapes.

#volume and surface area of a sphere formula example #curved surface area of cylinder formula

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lovewimc · 7 years ago

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center of mass physics

Center of mass Physics

Today our topic is center of mass Physics. This topic is very important to understand better Physics. Without understanding concept of center of mass Physics, It will not be easy for you to understand better Physics, So try to understand center of mass physics.

In previous post we have already study center of mass basic concept for continuous mass distributed body. You can refer previous post Center of mass formula .But here we will study center of mass for hollow and solid hemisphere with easy concept.

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What is center of mass Physics ?

Center of mass of a body is that point where whole mass of the body is concentrated it can lie within the body or outside the body depends upon the shape of the body.

Why need to study center of mass Physics ?

In Practical every rigid body has some shape and size . If the body comes in motion then every point on rigid body have different velocity and acceleration.

Suppose a rigid body of some mass m is rotating about its axis as well as translate. Every point on rigid body will have different velocity and acceleration.

It is really difficult to calculate velocity and acceleration of all point on rigid body.

Hence there is a single point where whole mass is concentrated is called center of mass and that point velocity and acceleration is consider as whole body velocity and acceleration.

Hence that special point is called center of mass.

We know that Newton's second law . Fnet = ma, p = mv. Here in this case "a" and "v" is acceleration of center of mass and "v" velocity of center of mass. If any body do combined motion rotational and translational then its path analysis will be easy, When we sit on center of mass and analyse body other particle motion.

Generally center of mass path is easy like (straight line, Circle, Projectile)

Hence you can think the importance of center of mass.

Fnet = ma equation has two important condition

Here "a" is acceleration of center of mass and m is a point mass.This is reason we need to study center of mass physics.

Practical uses and Application of center of mass Physics

The center of mass plays an important role in astronomy. The barycenter is the point between two objects where they balanced each other.

It is the center of mass where two or more celestial bodies orbit each other. When a moon orbits a planet or a planet orbits a star, both bodies are actually orbiting around a point that lies away from the center of the large bodies.

For example the moon does not orbit the exact center of the earth but a point on a line between the center of the earth and the moon, approximately 1710 km below the surface of the earth. Where their respective masses are balanced. This is the point about which the earth and moon orbits.

Automotive applications engineers try to design sport car so that its center of mass is lowered to make the car handle easy.

Also uses in aeronautic, high jumping .

Now i think you have understand the importance of center of mass.

How to find hollow hemispherical center of mass ?

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Center of mass hollow hemisphere

From the figure it is clear that mass is distributed over the surface area of hollow hemisphere. One thing is clear that hollow hemisphere is symmetric about x axis means positive x axis (right side) and negative x axis (left side) mass distribution is same.

Hence Xcm will no need to calculate it will be at origin for Xcm.

Along y axis its mass is different for different value of y.

Let total mass of hollow hemisphere is M and its radius is R, Now taking a elemental ring of mass dm, now the thickness of elemental ring will be Rdϴ as shown in figure.

Now the radius of elemental ring is Rcosϴ as shown above figure. Now the Ring above the origin that is y = Rsinϴ as shown in figure.

Ycm = ∫ ydm/∫dm now put the value of y = Rsinϴ

Now dm can't be integrated, Because dm is not written in terms of y, Hence we need to find out the mass of elemental dm first.

So to find out the mass of elemental ring, we have to consider surface mass density. which is define as mass per unit surface area, It is denoted by 𝞼 .

Hence 𝛔 = M/A = M/2𝛑R² Since mass is only distribute on surface area of hollow sphere

So we can write 𝛔 =dm/dA or dm = 𝛔dA.

Now we can calculate the area of elemental ring and it will be area .

of elemental circle of radius Rcosϴ and thickness Rdϴ.

Hence Area = 2𝛑Rcosϴ*Rdϴ So for elemental area dA = 2𝛑Rcosϴ*Rdϴ hence from here dm = 𝛔*2𝛑Rcosϴ*Rdϴ.

Now use the equation for Ycm = ∫ ydm/∫dm = ⎰Rsinϴ *𝛔*2𝛑Rcosϴ*Rdϴ/M

Here ∫dm = M since total mass is M.

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Ycm = R³*𝛔*𝛑*1/M⎰2sinϴ*cosϴdϴ now putting value of 𝛔 and 2sinϴ*cosϴ = sin2ϴ then

Ycm = R³xM/2𝛑R²x𝛑/M⎰sin2ϴdϴ now take limit from 0 to 𝛑/2 total mass will be cover hence after simplification we will get .

𝛑/2

Ycm = R/2⎰sin2ϴdϴ

𝛑/2

Ycm = R/2⎡-cos2ϴ/2⎤ now put the value we will get

Ycm = R/2 (2/2) = R/2 , Ycm = R/2

Center of mass for solid hemisphere

Solid hemisphere can be made by many hollow hemisphere so we will use this technique to find the center of mass for solid hemisphere.

This is 3-D because it is solid lets suppose an elemental strip is taken from origin at a r distance then just we have seen in case of hollow hemisphere its center of mass is at r/2 distance from origin.

Hence this elemental strip center of mass will be at r/2 distance from origin as shown above figure

Now apply center of mass formula Ycm = ∫ ydm/∫dm .

Here it is clear y = r/2

now this is solid so its mass density will be mass per unit volume and it is denoted by 𝛒

𝛒 = M/V = M/(2x𝛑r³)/3 = 3M/2x𝛑r³ since half volume of solid sphere

Ycm = ⎰r/2dm/⎰dm = ⎰r/2dm/M ⎰dm = M.

Since total mass is M

now for dm mass dm/dv =𝛒 or dm = 𝛒dv

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now for dv = Area x thickness = 2𝛑r²xdr

dm = 𝛒2𝛑r²dr now put the value in above equation we will get

Ycm = ⎰r/2x𝛒2𝛑r²drx1/M = put 𝛒 = 3M/2𝛑r³

Ycm = ⎰r/2*3M/2𝛑r³*2𝛑r²dr/M after simplification and integration we will get

Ycm = 3R/8

Now we will continue in next post. I hope you have enjoyed learning Center of mass Physics .If you like comment and share thanks for learning and share.

Dated 3rd Nov 2018

via Blogger https://ift.tt/2qqPFkf

#Blogger #center of mass physics

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my-gracie-luo-blog · 7 years ago

Text

The 7 Best Nootropics(Smart Drugs) in the market of Sunifiram

Posted on 09/17/2018 by Dr. Patrick Young wrote in Sunifiram. It has 0 Comment.

Everything about Sunifiram powder

1.Sunifiram powder 314728-85-3 Chemical properties

2.Sunifiram (314728-85-3) is a nootrop or a drug

3. Sunifiram (dm 235) – what kind of nootropic, what

is its principle of action, dosages, reviews

4.Sunifiram powder (314728-85-3) Dosage

5. What effect does Sunifiram have?

6.Where and in what form is it used Sunifiram?

7. What are the side effects of Sunifiram?

8.Which Sunifiram experience is known?

Sunifiram ( DM-235 ) is an experimental drug that acts as a positive allosteric modulator of the AMPA receptor, 1 which has been shown to have nootropic effects in animals with a significantly higher potency than that of piracetam. A series of related compounds are known, one being the unifiram (DM-232).

1.Sunifiram powder 314728-85-3

Chemical properties

CAS Number: 314728-85-3

Formula C14H18N2O2

Molar mass 246.304 g/mol

2.Sunifiram (314728-85-3) is a nootrop or a drug.

Nootropic drugs gradually, but surely, are part of our life-filled, stressful life. Today they are represented in a wide variety, with many being at the stage of development and research, while others are unknown. The black market is full of nootropics, because the demand for them is growing – people have always wanted to use the reserves of the brain to the maximum.

Many drugs of this group can not be imported into Russia and sold. But the forbidden does not mean bad. A vivid example of such a tool is Sunfiram (prohibited for importation). According to official information, he has not yet passed sufficient number of necessary tests on people. Nevertheless, the results of scientific research available at the moment allow us to draw conclusions about its high efficiency.

Many people have already experienced the effect of Sunifiram. Some have completely solved health problems. Judging by the experimental data and conclusions of the scientists, the drug does not cause side effects, so even if it is not possible to eliminate the disease, then, at least, it will be possible to stop its development without harming the body. In this article I would like to reveal the peculiarities of using Sunfire on the basis of information received at the forums, and talk about the possibility and impossibility of its purchase on the Russian market.

3. Sunifiram (dm 235) – what kind of nootropic, what is its principle of action, dosages, reviews

Sunfyram (chemical formula C14H18N2O2) is a derivative of a pyracetam compound synthesized. It has the same effect as the rest of the racetamen, but is more powerful and less toxic than the precursor. The main course of action of dm-235 is the activation of AMPA receptors, which ensure the production of the neurotransmitter glutamate, in connection with which it is classified as ampakines.

Glutamate plays a key role in the state of the cognitive sphere, its deficiency leads to memory loss, learning difficulties, inability to concentrate, etc. In animal studies, it has been shown that even with the artificial blocking of AMPA receptors, sunifirum stimulates sufficient production of glutamate in the central nervous system.

In addition, like the rest of the ratsetam, Sunifiram increases the activity of cholinergic receptors. As a result, the effect of the drug leads to such effects as:

• facilitates memorization;

• supports the structure of the central nervous system during periods of increased mental stress;

• improves the transmission of impulses between neurons;

• controls the vital activity of brain cells;

• normalizes and enhances metabolism in the brain;

• increases attention, concentration, exacerbates vigilance and perception;

• contributes to improving the relationship between the hemispheres and so on.

Approved instructions for the application of Sunifiram no. The drug is administered in a single dose of 10-50 mg. In practice, the working dose of dm-235 is at least 30 mg sublingually. In general, it is necessary to take into account that the experience of applying nootropics is rather small, in comparison with foreign users. Therefore, it is necessary to listen with care to the majority of “councils”.

4.Sunifiram powder Dosage

The appropriate oral dose of Sunifiram needed may vary depending on the conditions of use, for cognitive impairment it is 2.4-4.8g daily.

5. What effect does Sunifiram have?

drugs have an effect in that they trigger a change in the transmission of messenger substances and form nerve cells from certain stem cells. The different preparations prove their effectiveness on the central nervous system by causing positive changes in the brain. They increase concentration and memory and increase motivation and mood. This is why Sunifiram have long been known in Germany and are used for various purposes, including anti-aging and wellness. Sunifiram are legal and can be purchased in pharmacies or from appropriate online providers.

Since the specific effect of individual preparations differs from others, the appropriate agent should be selected before the start of treatment. While some products encourage creativity, other supplements increase intelligence. With the right Sunifiram drug you can achieve specific effects and, depending on your individual needs, provide more motivation and concentration, or build up a higher resistance to stress and counteract memory deficiency.

6. Where and in what form is it used Sunifiram?

The drugs are mainly offered in capsule form for oral use and are almost without side effects, as the ingredients are virtually non-toxic. A Sunifiram list makes it easy to find the right preparation for each therapy.

7. What are the side effects of Sunifiram?

If taken prescriptively, you do not have to expect side effects. However, over time, the body builds tolerance to the drug. After prolonged ingestion gradually diminishes the effect. Therefore, treatment should not take longer than recommended in the package leaflet. At higher doses, the agents have a stimulating effect, which may cause mild palpitations or discomfort.

8. Which Sunifiram experience is known?

Most users reported a reliable effect of the preparations and described their Sunifiram experience as good. With the substance, learning ability and memory can be improved in everyday life. In addition, the preparations have a positive influence in coping with stressful situations. They protect the brain from physical and psychological attacks caused by drugs or barbiturates.

The preparations themselves have no stimulating and anesthetic effects. Therefore, most users used the products in their daily lives without any consequences. In pharmacology, the agents are also referred to as neuro-enhancers or smartpills used to maintain and enhance intellectual performance. However, the products are mainly used as a therapy for diseases that reduce the brain activity. In these areas, the mode of action has been proven for a long time and users report invariably good results.

In the meantime, more and more healthy people are also resorting to the means to better master work and everyday life through a higher mental capacity. Using a Sunifiram powder list, every consumer will find the preparation that best suits their purpose. A secure effect possesses the substance with regard to the increase in concentration. For this reason, many consumers claimed to use the product as a “brain doping” in high stress during study or at work. The medicines, in addition to better coping with stressful situations, have other health aspects as well. They increase creativity and help with difficult decisions and reduce premature actions. In addition, sleep patterns change, contributing to improved recovery.

#Sunifiram powder #DM235 #CAS314728-85-3 #Smart drug

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