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To derive his 1917 cosmological model, Einstein made three assumptions that lay outside the scope of his equations.1- The universe is homogeneous and isotropic in the large (i.e., the same everywhere on average at any instant in time).2- The total volume of a three-dimensional space with uniform positive curvature would be finite but possess no edges or boundaries (to be consistent with the first assumption).3- The universe as a whole is static - i.e., its large-scale properties do not vary with time.When Einstein first studied the universe at large using the General Theory of Relativity he discovered that his equations predicted a universe which was either expanding or contracting and this was contradicted with the best astronomical observations at the time. He then modified his equations to satisfy the observations. This modification corresponds to the assumption that the whole universe is permeated with a constant pressure (which in his case balanced the expansion yielding a steady universe).Einstein's static universe is closed and contains uniform dust and a positive cosmological constant lambda as follow:At almost exactly the same time, Friedmann carefully revised the Einstein's cosmological equations and he published his classic relativistic cosmology. His key realization was that isotropic world models had to have isotropic curvature everywhere. In the paper of 1922, Friedmann found the solutions for expanding the universe models with closed spatial geometries, including those that expand to a maximum radius and then collapse to a singularity. Friedmann showed that there exist expanding solutions that are unbounded with hyperbolic geometry.“In 1929, Hubble announced a further dramatic discovery which completely turned astronomy on its ear. With the benefit of improved telescopes, Hubble started to notice that the light coming from these galaxies was shifted a little towards the red end of the spectrum due to the Doppler effect (known as “redshift”), which indicated that the galaxies were moving away from us.”The Friedman differential equations that he derived were:In other words, Friedmann raised the possibility of a dynamic universe, which changes in size over time. In fact, Friedmann introduced the expression “expanding universe.” Moreover, one of his solutions modeled a cosmos which began in a singularity – an infinitesimally small point. It even had an expansion rate which increased over time, just as modern observations indicate. Einstein wrote a short note in the German Physics Journal, Zeitschrift fur Physik, calling Friedmann’s non-stationary world “suspicious.” Friedmann immediately sent the great physicist an extended letter detailing his work. Six months later, Einstein wrote in the journal:”. . . my criticism . . . was based on an error in my calculations. I consider that Mr. Friedmann’s results are correct and shed new light.”In the 1990s, experimental observations showed that the expansion of the universe is accelerating and dark energy is tending to accelerate the expansion of the universe.Accelerated expansion of universe and evolving ideas about gravityThe Big Bang theory is an effort to explain what happened at the very beginning of our universe. According to the standard Big Bang theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a ‘‘singularity’’ and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of ‘‘black holes.’’ Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called ‘‘singularities.’’ Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know.With several issues being raised in the late twentieth century, modern physics was challenged and while quantum mechanics and relativity did not have the ability to respond and resolve issues also they cannot do it todays. Despite such problems, physicists are trying to find an appropriate and convincing response only on the scope of quantum physics and relativity and in this respect need to pay attention to the classical mechanics. Series of failures exist in some categories of these theories, that prior to their use, they should be clarified and resolved. In CPH theory, regarding on review of Newton's second law, we have been attempted to enter to the sub-quantum space by crossing the border of quantum mechanics then to survey of counteracting Newton's second law and the universal gravitation law and finally we can be analyzed and investigated the results. In sub-quantum space, we passed across the black hole and signNow the formation of the absolute black hole by specifying the limits of Newton's second law and gravitation law, then the singularity will be explained in the explosion of an absolute black hole. In this review we will be forced to change their attitude towards the singularity and the general conclusion in the singularity state is: volume will not be zero, density will be limited.Read more on my answer to question: Where did the energy for the Big Bang come from?

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As you have lost your PAN and you are not aware of your PAN details, the first thing you should do is search for your PAN number from Know Your PAN facility of income tax website and after you are aware of your PAN details you should make an application at NSDL website or by submitting a physical form. Both the process are explained below in details- It is possible to search the details of your Pan Card on the income tax website. To check your PAN card details Online, you can use “Know Your PAN” service provided by Income Tax Department. Steps to know your pan details.- * Browse to income tax website * Click on know your PAN as shown in the image below. * Fill in the required details ( Surname, Status Date of Birth and mobile numbers are mandatory) . Mobile number registered with the PAN Card is to be given. * Enter the OTP received on the registered mobile number. * You can get the detail of your PAN and Jurisdiction as shown in the image. You can make an application for E-Pan card which will be sent to you by mail or you can also apply for a physical PAN card. The applicant is only required to fill and submit the online application form along with online payment of the respective processing fee Steps to apply for PAN card * Visit the NSDL website * Select "Request for New PAN Card or/and Changes or Correction in PAN data" as Application type ( if PAN number has already been issued to you and want a fresh Pan/E-pan or want to make correction) and fill your status. * Fill in rest of the information asked such as name, and date of birth. Information marked with an asterisk sign has to be filled in mandatorily. It is mandatory to mention the email id in case of application for an E-PAN card. * A token number will be generated and same will be sent to your email id (But the same must be noted ). Click on continue with your Application. * A new page will appear on your screen. There will be three options asking you how you want to proceed with your application. To apply for E-PAN you must select No to the question “Whether Physical Pan is required?”. ( as shown in the image) ( Please check Note) * Enter your details such as Aadhaar number, parents name, etc. Aadhaar number is mandatory if you have choosed e sign and e KYC as an option. * Once you have filled all the relevant data, click on 'Next'. A new page will appear asking you to fill in Contact & Other details . * After you have filled the same you will be asked for document that you will submit as proof. As a proof of PAN you can submit Copy of PAN Card , Allotment letter. In case you have lost your PAN you must select no documents. * You will be required to give a declaration . Then you have to click submit. * You will be ask to recheck your application and you will be asked to make payment .You can pay using your debit or credit cards, Net banking . * Once you have made the payment, you will be required to undergo the Aadhaar authentication process. If your Aadhaar authentication process is successful,then a 15 digit unique acknowledgement number will be generated. * You will receive E PAN on your email after your application is processed or the physical PAN will be sent to your address Note- * There is a paperless facility called e-KYC and e-sign where your Aadhaar details will be used. You don't have to upload images such as photo, signature or other supporting documents. Your Aadhaar photograph will appear in your PAN if you use the e-KYC and e-sign facility. * There is a second method which is a standalone e-sign facility where you are required to upload your photograph, signature (in black ink) and specified supporting documents in a prescribed format.

I speak two languages: English and Japanese.The word that describes turning nouns into verbs in English is declension. The easiest way to declense a noun in English is to add “to” to the beginning of it. For example, party → to party. Then, you just treat it as a regular verb with standard conjugation.Party: to party, partied, parties, will party, has partied, etc..Knife (meaning “to stab with a knife”): to knife, knifed, knifes, will knife, etc..Declension is a pretty rudimentary skill in English—anyone can do it, I believe. However, Japanese is much more fascinating.In Japanese, there is an entire verb class dedicated to declension called group III verbs, or する (suru) verbs. する (suru) is the Japanese verb for “to do” in English. In Japanese, there is a class of nouns called “action” nouns, or -する (-suru) nouns. To declense a -する (-suru) noun, all you have to do is add する (suru) to it. From there, you can conjugate it to whatever tense/form you need.Examples:勉強 (べんきょう, benkyou): Study/studies (as in, scholarly study, Japanese studies, etc.)勉強する (benkyou suru): To study or I/you/he/she/etc. studies (informal)勉強します (benkyou shimasu): To study or I/you/he/she/etc. studies (formal)勉強しない/しません (benkyou shinai/shimasen): I/you/he/she/etc. doesn’t study (informal/formal)勉強できる/できます (benkyou dekiru/dekimasu): Can study (informal/formal)And so on.If you have a noun in Japanese and you want to make it into a verb, there’s a really high chance that all you have to do is add a conjugation of -する onto it and you’ll have the verb you need.Furthermore, there are many nouns to which there are related verbs.Examples:諦め (akirame): resignation/quitting; 諦める (akirameru): to resign/quit光 (hikari): light; 光る (hikaru): to shine/glow笑い (warai): laughter; 笑う (warau): to laugh数 (kazu): a number; 数える (kazoeru): to count答 (kotae): an answer; 答える (kotaeru): to answer痛み (itami): pain; 痛む (itamu): to ache, to feel painAnd so on.All in all, I find Japanese declension really interesting, and once I started learning the language, this one rule expanded my Japanese reservoir of verbs to easily twice or three times its size. To anyone learning Japanese, this will be one of the most, if not the most important grammar rules past the very basics.

Yes , it is mandatory to report your foreign bank accounts if your total balance(of all accounts) are over $10000 at any given time,It is a simple form and would not take more than 30 mins to complete. My tax consultant does this for me every year, but it’s pretty simple and you can do it yourself . If you fail to submit FBAR before deadline (Usually June 30) they may impose $10000 penalty per year delinquent.Also, if you are a US resident( i.e physically present in the U.S. during the year for 183 days or more.) it is required to open NRE account and convert your regular savings account to...

Our grade-school textbooks teach that laser light is “monochromatic,” and also that it’s “coherent.” Monochromatic isn’t hard to understand. It just means “single color,” where the light has a single pure frequency, like the note from a flute, but made of E&M.What then does “coherent” mean? You’ll find all sorts of confusing explanations, mostly wrong. (Either they’re wrong, or they’re correct but aimed at high-level education, and expressed as math-language rather than simple sentences.) But don’t worry, the simple sentence version does exist.To understand coherence, first ask, “what is INcoherent light?” That’s easy. It’s light that comes from a bunch of independent sources. The hot atoms in an electric heating element, or in a tungsten light bulb filament, they spew out incoherent light. So does the sun. So does the fluorescent coating on a mercury-vapor tube. Important: when we look into incoherent light, we see an object with an “extended” shape. Look backwards into an incoherent beam, and we’ll see a coiled filament, or a glowing cylinder-tube, or a lit candle. Or for the sun, an intensely bright disk. Incoherent sources look like a sheet of white paper. Or red paper, etc., a broad diffuse object.Incoherent light comes from fancy shapes. Coherent light then is *single-source light.” When we gaze into coherent light, we don’t see any shape. Instead, we see an intensely-brilliant dot. A pinpoint. A “point source” of light. Not a small disk. Instead, it’s more like seeing a single atom, but intensely bright.For incoherent light, whenver we focus the light with a lens, and let the focused image land upon a white screen, what do we see? We’ll see a little upside-down light bulb. Or perhaps a coiled, glowing tungsten filament, or a spiral CCFL tube, always upside-down. But if we do the same with coherent light, instead we’ll only see a brilliant pinpoint. (It might even burn a tiny hole through our screen.)Coherent light is the light from pinholes.To convert an incoherent source into a coherent source, just pass its light through an extremely tiny pinhole. Coherent light looks like perfect sphere-waves, or perfect plane-waves. This makes perfect sense, since the light from a pinhole is going to be an electromagnetic sphere-wave. (Or, if you’re far from the pinhole, then it looks like a plane-wave.) It’s a single pinpoint source, so there aren’t any swerving interference patterns or out-of-phase regions. Just a perfect sphere-wave.Here’s a bit of odd trivia. Light from the sun is quite incoherent. The sun looks like a white, glowing disk. However, starlight is extremely coherent. Starlight is far more coherent than the light from the best lasers ever made! But but but …the stars are distant enormous suns! That’s right. As light travels away from an incoherent source, it becomes more and more coherent. If we look at the sun we see a disk, but if we look at the stars, we only see geometric points, and this point-source appearance is the signature of all coherent light sources. As starlight travels, all the waves combine, adding or canceling, to form single spherical ripples. Close to a sun its light is incoherent, but let it travel for a lightyear and it becomes more coherent than laser light.We could try looking at conventional coherent light. Just get a laser tube that’s ten feet long and about a foot wide. Gaze into its beam. (First better turn the power down to far below 1/1000 watt!!) What do you see in the foot-wide laser beam? A brilliant spark! An intensely bright star. The light from lasers has no image. It’s dangerous to look at, because the lens in your eye will concentrate the light into a tiny pinpoint on your retina. Remember that we can easily look at 100watt light bulbs? A light bulb doesn’t look like an infinitely-small spark. It’s image is safe to look at, because it’s spread out to form an extended shape.But even a one-watt laser, even with its beam spread out, can easily punch a permanent hole in your vision.Back in the early 60s, Winston Kock of Bell Labs said: laser light is sharper light. It’s a sharp tool. He got that exactly right. With coherent light, lenses can focus it down to form an incredibly sharp cutting tool. But if you only have a thousand-watt light bulb, then those same lenses will only produce a small, upside-down image of the bulb, and that won’t punch any holes through steel razor blades.

As John A. Wheeler famously said, matter tells space how to curve and space tells matter how to move. The way matter tells space how to curve is expressed in the Einstein’s gravitational field equations of General Relativity:G = 8πT,where on the right side, we have the energy momentum tensor of matter, T (the source of gravity), and, on the left side, we have Einstein tensor G (expressing the curvature of space). (This equation is written for simplicity in geometrical units.) So there you have – Einstein tensor G describes the curvature of Riemannian space (or, more precisely, curvature of pseudo-Riemannian spacetime) in response to the presence of matter (described by the energy momentum tensor T).The Einstein tensor, by definition, is:G = R – ½ Rg,Where R is the Ricci tensor, R is the scalar curvature, and g is the metric tensor. In components, this definition can written asGμν = Rμν – ½ R gμνDespite its deceptive simplicity, the Einstein tensor is a non-linear function in second partial derivatives of the metric tensor g, which is why Einstein field equations (unlike Newtonian equations of gravity or Maxwell equations of electrodynamics, which are all linear) are non-linear and notoriously difficult to solve.An important property of the Einstein tensor is that is divergence vanishes as the expression of the Bianchi identities:∇G =0This assures the energy conservation for matter, which follow from the Einstein field equations∇T =0In fact, the Einstein tensor is the only tensor function of the metric with identically vanishing divergence, which was what led Einstein to his field equations of gravity.

I own a small online business, and my operational costs are mainly due to marketing demands. Digital marketing is supposed to be cheaper than traditional marketing, but for some reason, I had to deal with high costs at one point.It was due to my lack of creativity and resourcefulness in marketing content and managing social media campaigns. Those two aspects are signNow in increasing my sales and making sure more and more people are introduced to my brand.What I've learned from my struggles with high operational costs is that you have to look at what's available there for free and utilize it as much as possible. That's the key, and many things are surprisingly accessible for free or at a low cost to boost your marketing.For example, many small-time social media influencers have enough followers and the right crowd for your brand. You don't have to go out of your way to collaborate with big names.It's a two-way street when partnering with these new influencers who at least have a more focused group of consumers. Just make an effort in searching for these people on Instagram.This method gave my social media marketing a signNow improvement in less than two weeks. I didn't even have to spend much as the influencer agreed to receive free products instead.Pure resourcefulness like this can help you a lot in managing your funds. Also, instead of hiring in-house employees for creative content, you can hire freelancers instead. Outsource the tasks from different corners of the world.For small to medium-sized businesses, employing people to build a team is a big part of the expenses. Eliminating that through collaborating with outsourcing agencies or scouting skilled workers on different online platforms is the wisest move that has kept my business on great ranks.