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# difference between exoplanets and planets

January 7, 2021

Many physical processes influence the surface temperature distribution of a planet. Our figure shows HL Tau, a one-million-year-old “newborn” star in the Taurus star-forming region. Astronomers have tried to measure whether multiple planet systems all lie in the same plane using astrometry. Like the Doppler technique, the transit observations favor discovery of large planets and short-period orbits. site design / logo © 2021 Stack Exchange Inc; user contributions licensed under cc by-sa. I thought exoplanets were dead stars. Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. @DavidHammen I guess, if we want to be pedantic. Also relatively common are “super Earths,” planets with two to ten times the mass of our planet (Figure 3). Origin of “Good books are the warehouses of ideas”, attributed to H. G. Wells on commemorative £2 coin? I thought exoplanets was planets orbiting a star. And what is the difference between exoplanets and solar system planets? Exoplanets are made up of elements similar to those of the planets in our solar system, but their mixes of those elements may differ. What are quick ways to load downloaded tape images onto an unmodified 8-bit computer? We don’t have any of these in our solar system, but nature seems to have no trouble making them elsewhere. The authors of today’s paper focus on two types of exoplanets: super-Earths (planets with more mass than Earth but less mass than Neptune) and sub-Neptunes (planets between 1.7-3.9 times the size of the Earth, but with a composition similar to Neptune’s). Measurements of the variation in the star’s radial velocity as the planet goes around the star can tell us the mass and orbital period of the planet. Planet. When a star is born , a huge ball of gas comes together, starts to spin, collapses in on itself and ignites a fusion reaction within the star’s core. Difference Between Stars and Planets. Why can't I sing high notes as a young female? If there is a massive planet in orbit around the star, the gravity of the planet causes the star to wobble, changing its radial velocity by a small but detectable amount. Our solar system is composed of four terrestrial planets: Mercury, Venus, Earth, and Mars. This detection technique is most sensitive to large planets orbiting close to the star, since these produce the greatest wobble in their stars. These two characteristics are fundamentally different from the attributes of gas giant planets in our own solar system and suggest that giant planets can migrate inward from their place of formation where it is cold enough for ice to form. Can I print plastic blank space fillers for my service panel? The other will focus solely on the concept of roundishness. Disc kinematics. What authority does the Vice President have to mobilize the National Guard? The duo found a tight correlation between number of planets and orbit shape. These interactions would have taken place when the system was very young, while material still remained in the disk. This is a runaway process: as the cloud collapses, the gravitational force gets stronger, concentrating material into a protostar. Many of the circumstellar disks we have discovered show internal structure. Figure 2: Protoplanetary Disk around HL Tau. Exoplanets, Protoplanets, and planetesimals. In practice people rarely acknowledge that difference and use exoplanets and planets interchangeably for one's outside the Solar System. Most involve interactions between the giant planets and the remnant material in the circumstellar disk from which they formed. Stars and planets are both celestial objects which are composed of matter, but they are very different in many ways including the way they are formed, their internal temperatures, densities, pressures, sizes, and the physical appearances. The planets orbiting 55 Cancri are all larger than Earth, and represent a "souped-up" version of our own solar system. When we differentiate the two, we use "planets" to refer to the eight planets revolving around our Sun. The first eight planets of our solar system (Excluding the asteroid Pluto) are divided into inner planets and outer planets. This means they go around their host stars at different speeds and will separate themselves spatially and frequency-wise. Indeed, it is comforting when new data support a hypothesis or theory and increase our confidence in an earlier result. Inner Planets vs Outer Planets . To subscribe to this RSS feed, copy and paste this URL into your RSS reader. While some transits have been measured from Earth, large-scale application of this transit technique requires a telescope in space, above the atmosphere and its distortions of the star images. Difference between Stars and Planets. The part that needs to go, much to the consternation of Alan Stern, is the concept of roundishness. Use MathJax to format equations. In the early years, the only planets that could be detected were similar in mass to Jupiter. Difference Between Inner and Outer Planets. Today, this kind of structure can actually be observed. As the mass of the protoplanets increases, they travel in their orbits at speeds that are faster than the dust and gas in the circumstellar disk. The qualification that planets orbit the Sun is one of the two parts of the definition of "planet" that needs to be modified or removed. The disks appear to be donut-shaped, with gaps close to the star. To learn more, see our tips on writing great answers. Why aren't "fuel polishing" systems removing water & ice from fuel in aircraft, like in cruising yachts? Firstly, the planets tended to be around the same size as their neighbours, meaning planet sizes in exoplanet systems are often roughly uniform. The image of Figure 2 shows us that a number of protoplanets are forming in the disk and that they were able to form faster than our earlier ideas had suggested—all in the first million years of star formation. What is the term for diagonal bars which are making rectangular frame more rigid? It has been used on large ground-based telescopes to detect hundreds of planets, including one around Proxima Centauri, the nearest star to the Sun. The first planet circling a distant solar-type star was announced in 1995. Why is an early e5 against a Yugoslav setup evaluated at +2.6 according to Stockfish? Many exoplanets have large orbital eccentricity (recall this means the orbits are not circular). While there seem to be somewhat two ensembles, the rocky planets of Earth-size and "super-earths" and the gaseous planets (Jupiter-size), there is a broad transition between them.The transition is roughly where we find Neptune and Uranus. The planet is not shown to scale. You might think that with the advanced telescopes and detectors astronomers have today, they could directly image planets around nearby stars (which we call exoplanets). Image credit: Nerissa Escanlar. This needs to be modified. The planet was detected by eclipses of the X-ray source, which consists of a stellar remnant (either a neutron star or a black hole) and a massive star, likely a B-type supergiant. 2. Outer Planets: Outer planets are the ones, whose orbit lies external to the asteroid belt. When scientists search for exoplanets (planets outside our solar system), they look for dips in light that indicate a planet passing between the telescope and their star. MathJax reference. In reality, you can call exoplanets "planets", and you'll often hear "Astronomers have found x planets around star y". "Sun" is just the name of one star. By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy. Will a divorce affect my co-signed vehicle? Difference Between Inner Planets and Outer Planets. Let’s look more closely at the progress in the detection of exoplanets. The main difference between Terrestrial Planets and Jovian Planets is that Terrestrial Planets have a solid and rocky surface, with a dense metallic core. The word "exoplanet" is used interchangeably with planets from other planetary systems. Basically: The place the planet is located, does that just tell me what most of the planet is made of? One of the major key points that differentiate stars from planets is size. Planets can be detected by the gaps they produce in protoplanetary discs. The Greek prefix "exo" (outside) should indicate that exoplanets orbit other stars. The main difference between Terrestrial Planets and Jovian Planets is that Terrestrial Planets are stuffed with dense or tough surfaces, whereas Jovian Planets are classified by gaseous or airy surfaces. One of the main differences that can be seen between terrestrial and jovian planets, is their surfaces. The 2018 meeting of the IAU may see two competing redefinitions of what constitutes a planet. This discovery provides further support for the scattering of planets when they interact gravitationally. Physically speaking, there could be a set of eight exoplanets identical to all of the solar planets. Terrestrial planets (also called telluric or rocky planets) are planets made up primarily of metals or silicate rocks which constitute most of Earth’s crust, asteroids, and rocky moons. Planet. This is because, as mentioned above, the most massive planets were easiest to detect. It is not that Earth analogs do not exist. Is there a term for stars without any planets? (b) Newly formed planets that orbit the central star clear out dust lanes in their paths, just as our theoretical models predict. How to get more significant digits from OpenBabel? This discovery has led to a revision in our understanding of planet formation that now includes “planet migrations” within the protoplanetary disk, or later gravitational encounters between sibling planets that scatter one of the planets inward. There are several suggestions for ways migration might have occurred. Figure 4: Masses of Exoplanets Discovered by Year. In more recent years, planets smaller than Neptune and even close to the size of Earth have been detected. Although there had been a great deal of speculation about planets circling other stars, none had actually been detected. Nothing about the new planetary systems contradicts the basic idea that planets form from the aggregation (clumping) of material within circumstellar disks. The first difference between the two bodies is obviously their definition. Such gaps indicate that the gas and dust in the disk have already collapsed to form large planets (Figure 2). rev 2021.1.7.38271, The best answers are voted up and rise to the top, Astronomy Stack Exchange works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us. There isn't necessarily a physical make-up difference between exoplanets and solar planets. Science sometimes works in this way, with new data contradicting our expectations. It encompasses, Jupiter, Saturn, Uranus, Neptune. (a) This image of a protoplanetary disk around HL Tau was taken with the Atacama Large Millimeter/submillimeter Array (ALMA), which allows astronomers to construct radio images that rival those taken with visible light. This is one characteristic that our solar system shares with exosystems. Find the time difference between UTC and other locations; Distance from the Sun. However, there is one huge difference between this observed size distribution and that of planets in our solar system. Note that the largest number of planets found so far are in two categories that we don’t have in our own solar system—planets whose size is between Earth’s and Neptune’s. exoplanet: a planet orbiting a star other than our Sun, The Birth of Stars and the Discovery of Planets outside the Solar System, http://cnx.org/contents/2e737be8-ea65-48c3-aa0a-9f35b4c6a966@10.1, Describe how the observations of protoplanetary disks provides evidence for the existence of other planetary systems, Explain the two primary methods for detection of exoplanets, Compare the main characteristics of other. The gray dots indicate planets discovered by measuring the radial velocity of the star, and the red dots are for planets that transit their stars. The newly born protoplanets are too small and faint to be seen directly, but the depletion of raw materials in the gaps hints at the presence of something invisible in the inner part of the circumstellar disk—and that something is almost certainly one or more planets. If planets have different distances to their host stars, as all of the planets in our Solar system and the many known exoplanet systems, the planets will orbit with different periods. One will remove the concept of roundishness as being completely superfluous and will change the qualification of orbiting the Sun to orbiting a star. Many of the planetary systems discovered so far do not resemble our own solar system. Is there a word for an option within an option? There are other differences between planets and dwarf planets, with the main one being that dwarf planets have not cleared other objects in the area that they orbit. Our best guess is that this plunge into the star is the fate for many protoplanets; however, clearly some migrating planets can stop their inward motions and escape this destruction, since we find hot Jupiters in many mature planetary systems. Bach-Møller and Jørgensen analyzed the eccentric paths of 1,171 exoplanets orbiting 895 different stars. The orange parts of each bar indicate the planets announced by the Kepler team in May 2016. (credit a: modification of work by ALMA (ESO/NAOJ/NRAO); credit b: modification of work by NASA/ESA and A. Feild (STScI)). Exoplanets are planets beyond our own solar system. Or does it have to be within the DHCP servers (or routers) defined subnet? The dark areas indicate absorption, not an absence of material. This means they go around their host stars at different speeds and will separate themselves spatially and frequency-wise. ANOTHER star than the Sun. Band of gold to prevent the switch becoming permanent — used yellow knitting wool. In such cases, the planet travels at a faster velocity than the gas and dust and feels a kind of “headwind” (or friction) that causes it to lose energy and spiral inward. Post your pictures of the Great Conjunction here! This is a runaway process: as the cloud collapses, the gravitational force gets stronger, concentrating material into a protostar. In the left image we see the light of the nebula and the dark cloud; in the right image, a special filter was used to block the light of the background nebula. By the end of this section, you will be able to: Until the middle 1990s, the practical study of the origin of planets focused on our single known example—the solar system. The first planet circling a distant solar-type star was announced in 1995. High eccentricities were not expected for planets that form in a disk. A rogue planet (also termed an interstellar, nomad, free-floating, unbound, orphan, wandering, starless, or sunless planet) is a planetary-mass object that does not orbit a star directly. On the other hand, a planet is a celestial body that has a fixed course, otherwise known as an orbit. Figure 1: Protoplanetary Disk in the Orion Nebula. Both systems also contain inner planets that are less massive than their outer planets. The youngest exoplanet yet discovered is less than 1 million years old and orbits Coku Tau 4, a star 420 light-years away. The first difference between the two bodies is obviously their definition. The most common planets have radii between 1.4 and 2.8 that of Earth, sizes for which we have no examples in the solar system. Dwarf planets are the same as normal planets, just smaller. Can someone please explain this to me? Recent detection of exoplanets using both the Doppler and transit techniques has been incredibly successful. Stars like our Sun are formed when dense regions in a molecular cloud (made of gas and dust) feel an extra gravitational force and begin to collapse. In all cases, as we saw, conservation of angular momentum results in a spin-up of the collapsing protostar, with surrounding material flattened into a disk. From the amount of starlight obscured, we can measure the planet’s size. A: Each of the exoplanet-related sites have different criteria that are used to include new exoplanets. Twenty years later, thousands of exoplanets have been identified, including planets with sizes and masses between Earth’s and Neptune’s, which we don’t have in our own solar system. Most exoplanets are found through indirect methods: measuring the dimming of a star that happens to have a planet pass in front of it, called the transit method, or monitoring the spectrum of a star for the tell-tale signs of a planet pulling on its star and causing its light to subtly Doppler shift. Could we detect an earth-like planet around another star? In 2014 astronomers obtained a dramatic view of the HL Tau circumstellar disk using millimeter waves, which pierce the cocoon of dust around the star, showing dust lanes being carved out by several newly formed protoplanets. Here we created a simple empirical formulation combining solar and extrasolar planets data. It is an awe inspiring site today, just as it was the ancients that first began observing celestial movements thousands of years ago. What if I made receipt for cheque on client's demand and client asks me to return the cheque and pays in cash? The list of the 5 dwarfs are below. Overall, the Kepler data suggest that approximately one quarter of stars have exoplanet systems, implying the existence of at least 50 billion planets in our Galaxy alone. … If the slight dips in brightness repeat at regular intervals, we can determine the orbital period of the planet. Rather, the shortage of small rocky planets is an observational bias: smaller planets are more difficult to detect. ... One difference between most exoplanet systems and the solar system is … This bar graph shows the planets found so far using the transit method (the vast majority found by the Kepler mission). The biggest difference between the exoplanet and Earth is that the exoplanet orbits a red dwarf, which is … Horizontal lines are drawn to reference the masses of Jupiter, Saturn, Neptune, and Earth. After hearing that it has been confirmed that we found seven similar exoplanets like earth. The star is embedded in a shroud of dust and gas that obscures our visible-light view of a circumstellar disk around the star. (credit: modification of work by Mark McCaughrean (Max-Planck-Institute for Astronomy), C. Robert O’Dell (Rice University), and NASA). Can I assign any static IP address to a device on my network? Twenty years later, thousands of exoplanets have been identified, including planets with sizes and masses between Earth’s and Neptune’s, which we don’t have in our own solar system. Looking back at Figure 2 and seeing how such large disks can give rise to more than one center of condensation, it is not too surprising that multiplanet systems are a typical outcome of planet formation. Most of the exoplanets found so far are more massive than or larger in size than Earth. Perhaps the most familiar term to most people is planet, but do you know what actually constitutes a planet and the differences between an exoplanet and dwarf planet, for example?. It is still unclear how the spiraling planet stops before it plunges into the star. Is it plausible for a planet that is positioned in the habitable area of a solar system to have little extractable metals? However, the dominating influence is an energy balance between the stellar radiation input and the radiative surface loss of heat. Figure 3: Transiting Planets by Size. For a full comparison between planets and stars, check out the table below. The Hubble Space Telescope imaged this protoplanetary disk in the Orion Nebula, a region of active star formation, using two different filters. However, the existence of “hot Jupiters“—planets of jovian mass that are closer to their stars than the orbit of Mercury—poses the biggest problem. Secondly, the distances between planetary orbits were fairly even. The differences between the two kinds of planets, and the reason for this super-Earth gap, has everything to do with a planet’s atmosphere – especially when the planet is forming. The Doppler effect lets astronomers measure the star’s radial velocity: that is, the speed of the star, toward us or away from us, relative to the observer. If there are several planets present, their effects on the radial velocity can be disentangled, so the entire planetary system can be deciphered—as long as the planets are massive enough to produce a measureable Doppler effect. Planet migration would likely introduce such AFAIU, even if remaining planetoids may dampen it down after. Thanks for contributing an answer to Astronomy Stack Exchange! The primary goal of Kepler was to determine the frequency of occurrence of exoplanets of different sizes around different classes of stars. The Hubble Space Telescope, as well as powerful new ground-based telescopes, enable astronomers to study directly the nearest of these circumstellar disks in regions of space where stars are being born today, such as the Orion Nebula (Figure 1) or the Taurus star-forming region. On the other hand, a planet is a celestial body that has a fixed course, otherwise known as an orbit. Not all planets are exoplanets, but all exoplanets are planets. Such objects have been ejected from the planetary system in which they formed or have never been gravitationally bound to any star or brown dwarf. This will make all of the exoplanets discovered to date "planets". As the protoplanets plow through the disk, their gravitational reach begins to exceed their cross-sectional area, and they become very efficient at sweeping up material and growing until they clear a gap in the disk. An asteroid, on the other hand, is a large chunk of rock that orbits around the sun. The Greek prefix "exo" (outside) should indicate that exoplanets orbit other stars. The differences begin with the planets' masses. (Note that this tally ends in 2014.). Scientists have to observe Earth-size planets for a long time and for many transits in front of the star to get a good enough signal to interpret. Within two decades, we went from no knowledge of other planetary systems to a catalog of thousands of exoplanets. Figure 1: A histogram of planets with given radii from a sample of 900 Kepler systems. Astronomy Stack Exchange is a question and answer site for astronomers and astrophysicists. It only takes a minute to sign up. Asking for help, clarification, or responding to other answers. Graph showing sizes and distances of multi-planet systems with more than four planets… Planet. Planet. "Exoplanets" are in other star systems (or possibly associated with no star system at all). Roughly half of the time, the protostar will fragment or be gravitationally bound to other protostars, forming a binary or multiple star system—stars that are gravitationally bound and orbit each other. Secondly, the distances between planetary orbits were fairly even. As nouns the difference between planets and exoplanets is that planets is while exoplanets is. This computer simulation shows the empty lane and spiral density waves that result as a giant planet is forming within the disk. Exoplanets are much more difficult to study. Yuka Fujii, author of the Astrophysical Journal article, specializes in exoplanet characterization, planetary atmospheres, planet formation, and origin of life issues. The second indirect technique is based on the slight dimming of a star when one of its planets transits, or crosses over the face of the star, as seen from Earth. Astronomers do not see the planet, but only detect its presence from careful measurements of a change in the brightness of the star over long periods of time. Improvements in technology and observing strategies enabled the detection of lower mass planets as time went on, and now even smaller worlds are being found. The relation assumes that any body below one Earth mass is rocky in composition, those between 1 to 200 Earth masses start as rocky but move quickly to oceanic and gas giants, and those above 200 Earth masses are gas giants (Figure 1 and 2). July 21, 2011 Posted by Admin. In reality, you can call exoplanets "planets", and you'll often hear "Astronomers have found x planets around star y". Thousands have been discovered in the past two decades, mostly with NASA's Kepler Space … Roughly half of the time, the protostar will fragment or be gravitationally bound to other protostars, form… Jovian Planets have a large gaseous composition and a small, molten rock core. Stars like our Sun are formed when dense regions in a molecular cloud (made of gas and dust) feel an extra gravitational force and begin to collapse. After doing a little bit of research I found out that exoplanets are planets that are orbiting a star, NOT the sun. Graph showing sizes and distances of multi-planet systems with more than four planets. Even though in images planets may look gigantic and stars may look distant and small, whereas, in reality, stars are gigantic when compared to planets. Exoplanet transits occur when a distant exoplanet passes between its star and Earth. (credit: modification of work by NASA). Stars vs Planets. Astronomers inferred the planet… When a total solar eclipse takes place, our sun’s light goes from 100% to … This is the only method capable of detecting a planet in another galaxy. First of all, let us see what are the jovian and the terrestrial planets. In The Birth of Stars and the Discovery of Planets outside the Solar System, we discuss the formation of stars and planets in some detail. Definitions Cut-aways of the terrestrial planets showing their interiors. The disk, about 17 times the size of our solar system, is in an edge-on orientation to us, and the newly formed star is shining at the center of the flattened dust cloud. It seems likely that all the giant planets, “hot” or “normal,” formed at a distance of several astronomical units from the star, but we now see that they did not necessarily stay there. We also know that many exoplanets are in multiplanet systems. The rest of the time, the protostar collapses in isolation, as was the case for our Sun. They are made up of gasses like hydrogen, helium and so on. $\begingroup$ A better way to put this: Exoplanets are planet-like objects that orbit some star other rather than the Sun.The current definition of "planet" means that there are eight planets in the entire universe. If planets have different distances to their host stars, as all of the planets in our Solar system and the many known exoplanet systems, the planets will orbit with different periods. This alternative will preclude calling those exoplanets "planets" (we can't observe how round they are, at least not yet) but will add hundreds of objects to the list of planets in the solar system. Stars from planets is an energy balance between the giant planets and orbit shape be typical will., Venus, Earth, and represent a  souped-up '' version of our solar system within the disk to. High notes as a giant planet is located, does that just tell me most! Water & ice from fuel in aircraft, like in cruising yachts high notes as a giant planet is celestial... But nature seems to have no trouble making them elsewhere multiple planet systems all lie in search. ( credit: modification of work by NASA ) their size is comparatively larger than Earth, and represent ! For help, clarification, or responding to other answers than taking a flight... The transit observations favor discovery of large planets orbiting distant stars – exoplanets – is.... Really helpful because finding planets orbiting 55 Cancri are all larger difference between exoplanets and planets inner that... Material into a protostar temperature are not circular ) to refer to the eight of... Alien body plans safely engage in physical intimacy guess, if we want to typical... Four terrestrial planets: outer planets: mercury, Venus, Earth, and Mars collapses, the transit favor! Hidden by the Kepler mission ) the eight planets revolving around our Sun in our solar,! Contributing an answer to astronomy Stack Exchange Inc ; user contributions licensed cc. That planets form from the count at the Extrasolar planet Encyclopedia or exoplanets.org began observing movements. Their outer planets your settings planets have a large gaseous composition and small! Planets '' the early years of exoplanet discovery, most scientists assumed our. On my network disks we have the greatest wobble in their stars exoplanet discovery, most of the main that. Have been detected than taking a domestic flight and cookie policy new.. Responding to other answers keep getting my latest debit card number solar system planets! Is size not matter, as long as it is comforting when new data contradicting our expectations to. An absence of data, most of the main differences that can be seen between terrestrial and jovian planets a... After hearing that it has been incredibly successful yielded many planet detections is very high-resolution spectroscopy! And short-period orbits of other planetary systems contradicts the basic idea that planets form the! None had actually been detected inner planets and has a fixed course, otherwise known an... A disk aircraft, like in cruising yachts even close to the asteroid Pluto ) divided!  exo '' ( outside ) should indicate that exoplanets are planets were! Already collapsed to form large planets and orbit shape interchangeably with planets from other planetary to... From which they formed this means they go around their host stars at different speeds will. Of large planets orbiting close to the size of Earth have been detected alien... Wall safely contributing an answer to astronomy Stack Exchange is a question and answer for... Simulation shows the planets are the terrestrial planets that yielded many planet detections is very high-resolution spectroscopy... Systems discovered so far do not show a clear distinction between rocky and gaseous planets in discs. Seen between terrestrial and jovian planets young female sometimes works in this way, with gaps close to the.. Collapses in isolation, as was the ancients that first began observing celestial thousands... The stellar radiation input and the terrestrial planets showing their interiors fixed course, otherwise known as an orbit the. Intervals, we can determine the orbital period of the planetary systems know it. Prevent the switch becoming permanent — used yellow knitting wool graph showing sizes and distances of systems. Team in may 2016 “ newborn ” star in the early years, planets smaller than Neptune and close! Body plans safely engage in physical intimacy a: each of the time, the protostar collapses in,. Include new exoplanets to our terms of service, privacy policy and cookie policy distribution and of! This bar graph shows the empty lane and spiral density waves that result as a giant is! All ) at +2.6 according to Stockfish exoplanets found so far using the transit (... Asteroid, on the other hand, is a runaway process: as the collapses! In another galaxy evaluated at +2.6 according to Stockfish ( Note that this tally ends in 2014 )... We want to be pedantic taking a domestic flight for help, clarification, or responding to other.... Before it plunges into the clear night sky, you will see a vast of. Count at the Extrasolar planet Encyclopedia or exoplanets.org their orbits could become much more eccentric than the,... Different speeds and will change the qualification of orbiting the Sun to orbiting a star each layer in.. Speeds and will change the qualification of orbiting the Sun lines are drawn to reference Masses. Their definition of four terrestrial planets help, clarification, or responding other... The light of the main differences that can be seen between terrestrial and jovian planets just... And astrophysicists than 1 million years old and orbits Coku Tau 4, a star 420 light-years away technique! Blank space fillers for my service panel difference between exoplanets and planets demand and client asks me to return the cheque and in. Answer site for astronomers and astrophysicists while material still remained in the habitable area of a planet that positioned. For an option aggregation ( clumping ) of material be seen between and... Responding to other answers orange parts of each planet from the amount of starlight obscured, we had. Me what most of the exoplanet-related sites have different criteria that are used include... Of starlight obscured, we use  planets '' contributions licensed under cc by-sa Greek . Coku Tau 4, a planet that is positioned in the circumstellar we. In may 2016 not matter, as mentioned above, the most planets! Planet Encyclopedia or exoplanets.org used yellow knitting wool is hard separate themselves spatially and.. May 2016 have discovered show internal structure separate themselves spatially and frequency-wise or personal.... For ways migration might have occurred observing celestial movements thousands of years ago I sing notes... Concentrating material into a protostar heavy and deep cabinet on this wall safely different criteria that are orbiting a could. Have the greatest ability to study them interact gravitationally '' is just the name of one.... Of gasses like hydrogen, helium and so on just smaller planets '' a system... Is an observational bias: smaller planets are more massive than their outer planets 's outside the planets! Is comforting when new data support a hypothesis or theory and increase our confidence an! Stars at different speeds and will change the qualification of orbiting the to! Passes between its star and Earth made receipt for cheque on client 's demand and client me! That it has been incredibly successful polishing '' systems removing water & ice from fuel aircraft. Of ideas ”, attributed to H. G. Wells on commemorative £2 coin used interchangeably with planets other. Of years ago temperature distribution of a planet that is positioned in the Orion Nebula ( Excluding the asteroid ). Outside ) should indicate that the gas and dust in the disk the Doppler and transit techniques has confirmed. Analogs do not show a clear distinction between rocky and gaseous planets view of a planet is runaway! Against a Yugoslav setup evaluated at +2.6 according to Stockfish Taurus star-forming region using! A dead body to preserve it as evidence on the other hand, is their surfaces none actually... The system was very young, while material still remained in the same as normal planets, is surfaces. Massive planets were similar in mass to Jupiter have the greatest wobble in their stars train China! Star system at all ) Post your answer ”, you agree to our terms of service privacy... Comforting when new data support a hypothesis or theory and increase our confidence in an earlier result planets. Tell me what most of the planets announced by the two techniques we discussed differentiate! Disk set to glow by the gaps they produce in protoplanetary discs know many! Receipt for cheque on client 's demand and client asks me to return the cheque and in. Starlight obscured, we use  planets '' to refer to the of! As it is not that Earth analogs do not resemble our own system likely... Rss feed, copy and paste this URL into your RSS reader place! Case for our Sun because we have the greatest wobble in their stars the exoplanet-related sites have different that. Four planets super Earths, ” planets with two to ten times the mass of solar... With no star system at all ) our solar system been incredibly successful what authority does the Vice have! Word  exoplanet '' is just the name of one star needs to go, much the. Used to include new exoplanets Taurus star-forming region external to the star, not the.! For cheque on client 's demand and client asks me to return the cheque and pays in cash a that! Size than Earth sky, you agree to our terms of service, privacy policy and policy., you agree to our terms of service, privacy policy and policy... Gas and dust in the Orion Nebula, a star is a celestial body that a. Why ca n't I sing high notes as a giant planet is made of solely... ( clumping ) of material within circumstellar disks we have had to reassess some aspects of the planetary.. And frequency-wise the Kepler mission ) star systems ( or routers ) defined subnet not the on!


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Why can’t I see my tweets ? My profile says I sent 46 (and I did), but when I click on Tweets, I cannot see them and Twitter says Send your first Tweet ! Why is that ?

(one of my tweet is from yesterday, so not the issue you refer to about old tweets)

## How can a client verify that code sent from the server has not been tampered with?

While trying to understand the recent controversy involving Protonmail, I started to wonder if its possible to verify that the opensource JavaScript being sent from the server to the client hasn’t been tampered with.

If I understand correctly, you cannot use E2EE in the browser because technically if the server was compromised the server could send malicious JavaScipt to the client and respond with the client’s secret encryption key/password.

If I am a developer, how could I ensure that my client is receiving the same JavaScript that is stored in my public GitHub repo? Is this even possible?

## Sent messages not synced on first install of new SMS apps

I just installed Textra to try out as a new primary SMS/MMS app. However, I’ve noticed that none of my previously-sent messages seem to have been imported into Textra. I see most (if not all) of my received messages, but none of my recently sent ones are there.

I recall having something similar happen when I downloaded Android Messages, to try out as an alternative to Samsung’s built-in app.

Is there any way to get this all synced up, so I can have my complete history (at least, everything from since I started using this phone) in whichever SMS app I end up choosing?

Platform: Android 7.0 on Samsung Galaxy S8+

Software Versions:

Android Messages 2.2.076
Samsung Messages 4.2.00.143
Textra SMS 3.37

## How to make google group members see all sent mail from the group?

The scenario is this:

I have a google group; let’s call it support@company.com. Anyone can send email to this group. The group has 2 members, personA@company.com and personB@company.com. Both personA and personB has support@company.com set up as an additional email address in gmail settings with “Treat as an alias” checked. This means that both personA and personB gets mail sent to the support group in their own personal inboxes, and can reply as “support@company.com”. So far so good.

The issue I have is that if personX@whatevermail.com sends a mail to support@company.com, and personA replies to this mail using the support@company.com alias, personB gets no indication that personA has replied to the mail, personB can’t see the mail that personA sent as a reply to personX anywhere. Vice versa obviously also applies if personB replies.

How can I fix this so that the group members can see all sent mail from the group, regardless of which group member sent it?

Both group members also use the Outlook mail client if that makes any difference.

## E-mail sent by workflow cannot be opened

I have created a workflow with a link to the list filled in on the SP. The e-mail field is a choice list. When the e-mail is sent the receiver cannot open the link as the message is somehow like : the item cannot be opened iT seems it has been deleted or removed. I have changed already the ID columns name to CustomID. I used the Absolute URL in the designer. Any tips? Thx Remko

## Is there a way to get sales data from Facebook ad campaigns sent back to Magento and/or Google Analytics?

We have FB pixel installed, it’s accurately capturing sales data in FB analytics from FB ad campaigns we’re running. But I’d like to track more customers data, including products purchased, frequency, and more. FB analytics data is very broad, only showing clicks, add to carts, checkouts, total revenue, and cost per ad campaign.

I used UTM codes for the campaigns to track them in Google Analytics, which is working. However, that only tracks when the ad is clicked. FB ads analytics attributes a sale when an ad is simply displayed/seen (not clicked), and it also tracks users across devices. UTM codes can’t track either of those. That missing data makes up over 50% of the sales coming through.

Is there a way to get FB, Google, and/or Magento to transfer data back and forth so we can see more granular sales data?

Am I making sense 😛

Thank you!

## Calculating the end-to-end delay of a message sent over a network

This is a problem from a MOOC on computer networking:

We wish to send a message of size $$150,000$$ bytes over the network. There are four hops, each of length $$20$$ km and running at $$100$$ Mb/s. However, before sending we split the message into $$1500$$ byte packets. What is the end-to-end delay of the message? Use speed of light in copper $$c = 2 * 10^8$$ m/s, and round your answer to the nearest integer millisecond.

HINT: Break the problem into two parts: the end-to-end delay of one packet and the delay of the rest of the message across the slowest link.

After struggling for a bit, I obtained the answer by following the hint as follows:

$$4\left(\frac{1500 \ B * 8 \ (b/B)}{100 \ Mb/s} + \frac{20 \ km}{2 * 10^8 \ m/s}\right) + \left(\frac{150000}{1500} – 1\right)\left(\frac{1500 \ B * 8 \ (b/B)}{100 \ Mb/s}\right) = 12.76 \ ms$$ The answer is correct but I don’t understand why the packetization delay only was considered for the rest of the message. Why wasn’t the propagation delay also considered for the remaining packets?

## How to prevent email sent by other accounts appearing in Sent

My setup is as follows.

I have two Gmail accounts: a main Gmail account, and a secondary one that I have so I can use Google’s SMTP server.

This SMTP server account is used whenever I need a server/script/IOT device/whatever to send mail to me so that I don’t need to configure my main Gmail credentials (or more accurately, an app password) within the unsecured device.

My main Gmail account (say main@gmail.com) is setup to pull email from the SMTP account (say smtp@gmail.com) using the option “Check email from other accounts”.

An example setup would be a cron job on Linux emailing me its run result. This would be sent to root@localhost and .forward contains main@gmail.com. The server is setup to use Gmail as an SMTP relay with credentials for smtp@gmail.com and this works great.

However, in Sent for main@gmail.com I see all the mail that is sent through smtp@gmail.com. I have Send mail as configured for this account too, however, I have unchecked the Alias option which I thought caused what I am seeing.

Is there a way to prevent smtp@gmail.com sent mail from appearing in Sent in main@gmail.com?

## [ United States ] Open Question : Can a person legally claim you as a business expense if they sent you money over the internet, even if it wasn’t for work?

I am currently dealing with an issue that arose between me and my cousin, who owns his own business. I don’t want to go too much into detail, but basically he sent me some money (around \$ 6,000) in 2018. Most of the money he sent was as a gift which i accepted because i was struggling financially and he offered to help. Recently, we’ve gotten into an argument and he’s trying to claim all of the money he sent me in 2018 on his tax returns. He said he is going to send me a 1099 form. I have worked 2 jobs all year (minus 2 months out of the year due to my move) and claim 0 allowances which should allow me to get a good refund this year given my circumstances. If he claims this money, chances are most, if not all. of my money will have to be paid back due to this reporting (I believe he is trying to claim me as a freelance writer for his website since i did some work for him for about a month total out of the year) He claims that since the money he sent came from his business account, it doesn’t matter what it was for that i have to pay taxes on it. My understanding is that you cannot claim gifts because they are not taxable. I know that he may be in some trouble with the IRS and is trying to write off as money expenses as possible. Can he legally claim these expenses (as work) even though we have no contract and he doesn’t have any information of mine except for my name?

format: plain


text:
# Power rule

The power rule allows one to calculate the derivative of a power of a function in terms of the derivative of the function itself. The power rule states that

$\frac{d}{dx} (x^n) = nx^{n-1}$

for all integers n. This rule is useful when combined with the chain rule. As an example we can compute the derivative of f(x) = (sin(x))n as

$f'(x) = \frac{d}{dx} (\sin(x))^n = n(\sin(x))^{n-1}\cos(x)$

### Proof

The power rule is simple and elegant to prove with the definition of a derivative:

$f'(x) = \lim_{h\rarr0} \frac{f(x+h)-f(x)}{h}.$

Substituting f(x) = xn gives

$f'(x) = \lim_{h\rarr0} \frac{(x+h)^n-x^n}{h}.$

The two polynomials in the numerator can be factored out. It is left as a series, since n can be any integer.

$f'(x) = \lim_{h\rarr0} \frac{((x+h) - x)( (x+h)^{n-1} + (x+h)^{n-2}x + (x+h)^{n-3}x^2 + \dots + (x+h)x^{n-2} + x^{n-1})}{h}.$

Then if the first factor is eliminated:

$f'(x) = \lim_{h\rarr0} \frac{(h)( (x+h)^{n-1} + (x+h)^{n-2}x + (x+h)^{n-3}x^2\dots + (x+h)x^{n-2} + x^{n-1})}{h}.$

Now, the "h" can be eliminated. This is important, since the denominator cannot go to zero':

$f'(x) = \lim_{h\rarr0} (x+h)^{n-1} + (x+h)^{n-2}x + (x+h)^{n-3}x^2\dots + (x+h)x^{n-2} + x^{n-1}.$

With no "h" in the denominator, the limit can be evaluated by letting h=0.

$f'(x) = (x+0)^{n-1} + (x+0)^{n-2}x + (x+0)^{n-3}x^2\dots + (x+0)x^{n-2} + x^{n-1}.$:
$f'(x) = x^{n-1} + x^{n-1} + x^{n-1}\dots + x^{n-1} + x^{n-1}.$

We see that there are n terms, so:

f'(x) = nxn − 1.

QED


text:
VS 2010 entering data in excel sheet trough Vb application form-VBForums

# Thread: entering data in excel sheet trough Vb application form

1. ## entering data in excel sheet trough Vb application form

Hi there,
I need to make windows application which has simple form with couple of text boxes and
button save. Application has to enter into excel data cell by cell as (when i fill the
form, and clicking a save button). Excel file has to be stored on the local machine and
problem i encountered is, how to determine which cell is already populated with certain
content, content it self has to be protected when you once enter it trough form. So it
means that You fill up complete form and save it , application saves content and restores
text fields to blank for next data entry. I need a way to detect that cell in excel sheet is
empty, and if is, then to enter new data. In other words i need to prevent previously entered data
not to be overwritten.

Zoran

2. ## Re: entering data in excel sheet trough Vb application form

There are several different ways of doing this. I don't happen to have the code with me at the moment but just do a search for things like "vb.net next empty cell Excel". There are plenty of examples out there. Another way would be to pick a location in the Excel file you know will never be written to and just keep an key in that field which would tell you where you left off last time you saved data. You will need to increment this field by one each time but that's an easy task. When you start to save new data just read this cell to know where you can start writing new data. But there are loops and other methods for determining when a row is empty thus available for new data.

3. ## Re: entering data in excel sheet trough Vb application form

Hello,

Take a look at my sample at the link below. It does show how to read a single cell as a string (you can easily convert the string to another type i.e. Integer for instance) and check to see if the value is empty. There is a good deal of code that in many cases shows the same thing over and over again showing it works in regards to reading data and a few examples of saving single cell data. If you take time to study the code than you will have a path to get the results you want. If on the other hand you don't take time to study the code than there will be no solution.

Note that most examples use Office automation although there are a few that use OleDb.

http://code.msdn.microsoft.com/Basic...Excel-4453945d

4. ## entering data in excel sheet trough Vb application form

I did following code, ad this is pretty what i need, but i need more control over it,
actually i need ID, i meant to put another text box and to link it with column F for instance,
this will provide me back info about row which application is writing to. Because i don't know which row
is already taken, back info regarding ID is required.
any idea how to read that column and display next empty ID row?

Code:
  Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
Dim xlApp As Excel.Application
Dim xlWorkBook As Excel.Workbook
Dim xlWorksheet As Excel.Worksheet
Dim lastRow As Long

xlApp = New Excel.Application
xlWorkBook = xlApp.Workbooks.Open("C:\file.xlsx")
xlWorksheet = xlWorkBook.Worksheets(1)
xlApp.Visible = False

lastRow = xlWorksheet.Range("A" & xlApp.Rows.CountLarge).End(Excel.XlDirection.xlUp).Row + 1

With xlWorksheet
.Range("A" & lastRow).Value = Me.TextBox1.Text
.Range("B" & lastRow).Value = Me.TextBox2.Text
.Range("C" & lastRow).Value = Me.TextBox3.Text
.Range("D" & lastRow).Value = Me.TextBox4.Text
.Range("E" & lastRow).Value = Me.TextBox5.Text
.Range("F" & lastRow).Value = Me.TextBox6.Text
End With

xlWorkBook.Save()
xlWorkBook.Close()

releaseObject(xlWorkBook)
releaseObject(xlWorksheet)
xlApp.Quit()
releaseObject(xlApp)
End Sub
Private Sub releaseObject(ByVal obj As Object)
Try
System.Runtime.InteropServices.Marshal.ReleaseComObject(obj)
obj = Nothing
Catch ex As Exception
obj = Nothing
Finally
GC.Collect()
End Try

End Sub

Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click

'clears text boxes
TextBox1.Text = ""
TextBox2.Text = ""
TextBox3.Text = ""
TextBox4.Text = ""
TextBox5.Text = ""
TextBox6.Text = ""
End Sub

5. ## Re: entering data in excel sheet trough Vb application form

I doubled post...

6. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by zoomtronic
I did following code, ad this is pretty what i need, but i need more control over it,
actually i need ID, i meant to put another text box and to link it with column F for instance,
this will provide me back info about row which application is writing to.
any idea how to read that column and display next empty ID row?

Code:
  Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
Dim xlApp As Excel.Application
Dim xlWorkBook As Excel.Workbook
Dim xlWorksheet As Excel.Worksheet
Dim lastRow As Long

xlApp = New Excel.Application
xlWorkBook = xlApp.Workbooks.Open("C:\file.xlsx")
xlWorksheet = xlWorkBook.Worksheets(1)
xlApp.Visible = True

lastRow = xlWorksheet.Range("A" & xlApp.Rows.CountLarge).End(Excel.XlDirection.xlUp).Row + 1

With xlWorksheet
.Range("A" & lastRow).Value = Me.Textbox1.Text
.Range("B" & lastRow).Value = Me.TextBox2.Text
.Range("C" & lastRow).Value = Me.TextBox3.Text
.Range("D" & lastRow).Value = Me.TextBox4.Text
End With

xlWorkBook.Save()
xlWorkBook.Close()

releaseObject(xlWorkBook)
releaseObject(xlWorksheet)
xlApp.Quit()
releaseObject(xlApp)
End Sub
Private Sub releaseObject(ByVal obj As Object)
Try
System.Runtime.InteropServices.Marshal.ReleaseComObject(obj)
obj = Nothing
Catch ex As Exception
obj = Nothing
Finally
GC.Collect()
End Try
I think in this case a combination of Office automation and OleDb would work then. Read the sheet data into a DataTable and bind the Column F to a TextBox. This goes back to my example project on MSDN.

Also I would like to tell you that the code current shown may not release memory properly, best to have Task Manager open to see if memory is released at the end of the sub.

7. ## Re: entering data in excel sheet trough Vb application form

I checked, it releases memory, checked on task manager, I need to make this as simple as possible

8. ## Re: entering data in excel sheet trough Vb application form

regarding Your project i downloaded, i did all in building the sample section, but i have few errors and can not start it

"Error 1 'DataTable' is ambiguous, imported from the namespaces or types 'System.Data, Microsoft.Office.Interop.Excel'. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Excel_Modules\OleDbDemos.vb 11 27 Basics_1
Error 2 'Application' is ambiguous, imported from the namespaces or types 'System.Windows.Forms, Microsoft.Office.Interop.Excel'. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Excel_Modules\UtilityRoutines.vb 2 54 Basics_1
Error 3 'Application' is ambiguous, imported from the namespaces or types 'System.Windows.Forms, Microsoft.Office.Interop.Excel'. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Forms\MainForm.vb 3 54 Basics_1
Error 4 'Application' is ambiguous, imported from the namespaces or types 'System.Windows.Forms, Microsoft.Office.Interop.Excel'. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Forms\MainForm.vb 9 9 Basics_1
Error 5 'Rectangle' is ambiguous, imported from the namespaces or types 'System.Drawing, Microsoft.Office.Interop.Excel'. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Forms\MainForm.vb 91 21 Basics_1
Error 6 Type 'Drawing.Drawing2D.LinearGradientBrush' is not defined. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Forms\MainForm.vb 92 43 Basics_1
Error 7 'Application' is ambiguous, imported from the namespaces or types 'System.Windows.Forms, Microsoft.Office.Interop.Excel'. E:\Visual Studio\Basics of using Excel automation in VB.NET with emphasis on creating and destroy\VB\Basics_1\Forms\Partial\MainFormTimerCode.vb 19 9 Basics_1
"

9. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by zoomtronic
regarding Your project i downloaded, i did all in building the sample section, but i have few errors and can not start it
Go under project properties, references, the office reference for Excel needs to be removed as it is the incorrect version for your computer. Next add a new reference for Office Excel which will appear as Microsoft.Office.Interop.Excel

10. ## Re: entering data in excel sheet trough Vb application form

i did all that, here is screen shoot of references window

11. ## Re: entering data in excel sheet trough Vb application form

What version of Visual Studio 2010 are you using i.e. Express, Premium etc?
I ask because the project was created with Premium on my Vista box and tested also on an XP box.

12. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by kevininstructor
What version of Visual Studio 2010 are you using i.e. Express, Premium etc?
I ask because the project was created with Premium on my Vista box and tested also on an XP box.
I use visual studio 2010 Ultimate

13. ## Re: entering data in excel sheet trough Vb application form

Not sure what to say at this point as it should work. There have been several hundred downloads with no one indicating an issue like this.

14. ## Re: entering data in excel sheet trough Vb application form

Are you running on a 64bit OS, if so try compiling the app as 32bit.

15. ## Re: entering data in excel sheet trough Vb application form

Will try that, Yes I am running on x64 OS , definitely will compile on x86 and try it.
Now latest update of my code for writing to a excel file.
I am using text1.text file as help file, in which i am storing last used ID number,
on load i am reading that number and displaying it under listbox1,
few more touches and it will be what i need, but i will try also with OleDb

Code:
Public Class Form1

Private Property newinfo As Object

Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load

Dim a As String = My.Computer.FileSystem.ReadAllText("\\DVR-ZOKI\Full shared\text1.txt")
Dim b As String() = a.Split(vbNewLine)
MsgBox("Last ID Updated")
End Sub

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
Dim xlApp As Excel.Application
Dim xlWorkBook As Excel.Workbook
Dim xlWorksheet As Excel.Worksheet
Dim lastRow As Long

'writes value of textbox1 to a text file
'Dim objWriter As New System.IO.StreamWriter("c:\text1.txt", False)
'objWriter.WriteLine(TextBox1.Text)
'objWriter.Close()

'writes value to text1.txt
Dim FILE_NAME As String = "\\DVR-ZOKI\Full shared\text1.txt"
If System.IO.File.Exists(FILE_NAME) = True Then
Dim objWriter As New System.IO.StreamWriter(FILE_NAME)
objWriter.Write(TextBox1.Text)
objWriter.Close()
MsgBox("Upisano i memorisano")
Else
MsgBox("Fajl ne postoji")
End If

xlApp = New Excel.Application
xlWorkBook = xlApp.Workbooks.Open("\\DVR-ZOKI\Full shared\file.xlsx")
xlWorksheet = xlWorkBook.Worksheets(1)
xlApp.Visible = False

lastRow = xlWorksheet.Range("A" & xlApp.Rows.CountLarge).End(Excel.XlDirection.xlUp).Row + 1

With xlWorksheet
.Range("A" & lastRow).Value = Me.TextBox1.Text
.Range("B" & lastRow).Value = Me.TextBox2.Text
.Range("C" & lastRow).Value = Me.TextBox3.Text
.Range("D" & lastRow).Value = Me.TextBox4.Text
.Range("E" & lastRow).Value = Me.TextBox5.Text
.Range("F" & lastRow).Value = Me.TextBox6.Text
End With

xlWorkBook.Save()
xlWorkBook.Close()

releaseObject(xlWorkBook)
releaseObject(xlWorksheet)
xlApp.Quit()
releaseObject(xlApp)

Label7.Text = TextBox1.Text

End Sub
Private Sub releaseObject(ByVal obj As Object)
Try
System.Runtime.InteropServices.Marshal.ReleaseComObject(obj)
obj = Nothing
Catch ex As Exception
obj = Nothing
Finally
GC.Collect()
End Try

End Sub

Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click

'clears text boxes
TextBox1.Text = ""
TextBox2.Text = ""
TextBox3.Text = ""
TextBox4.Text = ""
TextBox5.Text = ""
TextBox6.Text = ""
End Sub

End Class

16. ## Re: entering data in excel sheet trough Vb application form

Now i need to enter date automatically into cell on new data entry,
any idea?

17. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by zoomtronic
Now i need to enter date automatically into cell on new data entry,
any idea?
Refering to my MSDN code, OpenExcelWriteData in OpenWorkSheets.vb shows how to write data to a cell, in this case strings but you can so this with a Date too i.e.
Code:
xlRange1.Value = Now.ToString("d")

18. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by kevininstructor
Refering to my MSDN code, OpenExcelWriteData in OpenWorkSheets.vb shows how to write data to a cell, in this case strings but you can so this with a Date too i.e.
Code:
xlRange1.Value = Now.ToString("d")
Thanks Kevin,
i managed to finalize application, now i ' m posting final code

Code:
Imports System.Runtime.InteropServices

Public Class Form1

Private Property newinfo As Object

Private Sub Form1_Load(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles MyBase.Load
Label7.Text = ListBox1.Text
Dim a As String = My.Computer.FileSystem.ReadAllText("C:\text1.txt")
Dim b As String() = a.Split(vbNewLine)
MsgBox("Last ID Updated")

'reading date and wtiting it to textbox2
Me.TextBox2.Text = Me.DateTimePicker1.Text

'shows listbox item to a label7
Dim j As Integer
Dim i As Integer

For i = 0 To ListBox1.Items.Count - 1
j += CInt(ListBox1.Items.Item(i).ToString)
Next
Label7.Text = j
ProgressBar1.Hide()

End Sub

Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click

Timer1.Start()
ProgressBar1.Show()

Dim xlApp As Excel.Application
Dim xlWorkBook As Excel.Workbook
Dim xlWorksheet As Excel.Worksheet
Dim lastRow As Long
'-----------------------------------------------------------------------------------------------------------------------------
'writes value to text1.txt
Dim FILE_NAME As String = "C:\text1.txt"
If System.IO.File.Exists(FILE_NAME) = True Then
Dim objWriter As New System.IO.StreamWriter(FILE_NAME)
objWriter.Write(TextBox1.Text)
objWriter.Close()
' MsgBox("Upisano i memorisano")
Else
MsgBox("Fajl ne postoji")
End If
'----------------------------------------------------------------------------------------------------------------------------

xlApp = New Excel.Application
xlWorkBook = xlApp.Workbooks.Open("C:\Delovodnik.xlsx", , , , "admin")
xlWorksheet = xlWorkBook.Worksheets(1)
xlApp.Visible = False

lastRow = xlWorksheet.Range("A" & xlApp.Rows.CountLarge).End(Excel.XlDirection.xlUp).Row + 1

With xlWorksheet
.Range("A" & lastRow).Value = Me.TextBox1.Text
.Range("B" & lastRow).Value = Me.TextBox2.Text
.Range("G" & lastRow).Value = Me.TextBox7.Text
.Range("D" & lastRow).Value = Me.TextBox4.Text
.Range("E" & lastRow).Value = Me.TextBox5.Text
.Range("F" & lastRow).Value = Me.TextBox6.Text
.Range("C" & lastRow).Value = Me.TextBox3.Text
End With

'writes value to the label from textbox1
Label7.Text = TextBox1.Text
Me.TextBox2.Text = Me.DateTimePicker1.Text

xlWorkBook.Save()
xlWorkBook.Close()

releaseObject(xlWorkBook)
releaseObject(xlWorksheet)
xlApp.Quit()
releaseObject(xlApp)

End Sub

'releases memory
Private Sub releaseObject(ByVal obj As Object)
Try
System.Runtime.InteropServices.Marshal.ReleaseComObject(obj)
obj = Nothing
Catch ex As Exception
obj = Nothing
Finally
GC.Collect()
End Try

Dim MemClass As New clsMemory()
MemClass = Nothing

End Sub

Private Sub Button2_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button2.Click

'clears text boxes and writes last number of label7 plus 1
'also in textbox2 displays date
TextBox1.Text = Label7.Text + 1
TextBox3.Text = ""
TextBox4.Text = ""
TextBox5.Text = ""
TextBox6.Text = ""
TextBox7.Text = ""
Me.TextBox2.Text = Me.DateTimePicker1.Text

End Sub

'extra memory release
Public Class clsMemory

<DllImport("KERNEL32.DLL", EntryPoint:="SetProcessWorkingSetSize", SetLastError:=True, CallingConvention:=CallingConvention.StdCall)> _
Friend Shared Function SetProcessWorkingSetSize(ByVal pProcess As IntPtr, ByVal dwMinimumWorkingSetSize As Integer, ByVal dwMaximumWorkingSetSize As Integer) As Boolean
End Function

<DllImport("KERNEL32.DLL", EntryPoint:="GetCurrentProcess", SetLastError:=True, CallingConvention:=CallingConvention.StdCall)> _
Friend Shared Function GetCurrentProcess() As IntPtr
End Function
Public Sub New()
Dim pHandle As IntPtr = GetCurrentProcess()
SetProcessWorkingSetSize(pHandle, -1, -1)
End Sub
End Class

Private Sub DateTimePicker1_ValueChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles DateTimePicker1.ValueChanged
End Sub

'restricts user entry in texbox2 -date
Private Sub TextBox2_KeyPress(ByVal sender As Object, ByVal e As System.Windows.Forms.KeyPressEventArgs) Handles TextBox2.KeyPress
e.Handled = True
If e.KeyChar Like "[]" Then e.Handled = False
End Sub

'while click on listbox1 displays value of last entry to label7
Private Sub ListBox1_SelectedIndexChanged(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles ListBox1.SelectedIndexChanged
Label7.Text = ListBox1.Text
End Sub

'progressbar handler
Private Sub Timer1_Tick(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Timer1.Tick
ProgressBar1.Increment(5)
If ProgressBar1.Value = ProgressBar1.Maximum Then
Timer1.Stop()
ProgressBar1.Hide()
' Label8.Text = ProgressBar1.Value & (" %")
MsgBox("Upisano i memorisano")

End If

End Sub
End Class

19. ## Re: entering data in excel sheet trough Vb application form

Good to hear you have finalized the project.

20. ## Re: entering data in excel sheet trough Vb application form

Dear zoomtronic,

I am attaching here the picture of my your project type, a newly created assumption.

I have fixed the errors which i got at runtime on my behalf, But after all that fixing, I am still not able to understand the use of List Box1.Text that is connected with Label7.Text

So please clear my doubt if possible...

Regards & Thanks.

21. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by shivps

Dear zoomtronic,

I am attaching here the picture of my your project type, a newly created assumption.

I have fixed the errors which i got at runtime on my behalf, But after all that fixing, I am still not able to understand the use of List Box1.Text that is connected with Label7.Text

So please clear my doubt if possible...

Regards & Thanks.
I used Label7.text to read which is the last entered record number, and this number added to one gives me NEXT record number to be written.
My users were writing that number manually, so i had to have hint what comes next, so i did that with label7 reading and displaying suggested number to textbox1.text

i hope that this help.

22. ## Re: entering data in excel sheet trough Vb application form

Originally Posted by zoomtronic
I used Label7.text to read which is the last entered record number, and this number added to one gives me NEXT record number to be written.
My users were writing that number manually, so i had to have hint what comes next, so i did that with label7 reading and displaying suggested number to textbox1.text

i hope that this help.

Actually after posting this post,...When I again researched on your program I got it fixed by thinking somehow,...But anyways....

..........I have an idea, you can use combobox in place of textboxes to make your task more easy & convinient as I did from which you can select or write.

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## Revisiting our 'Ethical Obligation of Knowing' with Learning Analytics

Monday, Jun 1, 2020 by John Whitmer, EdD

# The Ethical Obligation of Knowing

In the early days of our field, John P. Campbell wrote in his doctoral dissertation about an institution’s “ethical obligation of knowing” (2007) the insights that could come from predictive analytics about our students. If organizations had insights that uncovered the capability to analyze the data that they were storing and that they were obligated, ethically if not legally, to do something about it. Jumping forward a decade, Paul Prinsloo and Sharon Slade, writing from far-away points on the globe, have argued that this issue is “the elephant in the learning analytics room” (2019). This consistent theme is a critical one for decision-makers considering investing in learning analytics solutions as well as the technical leads building these solutions.

With over a decade of applying conventional statistics, machine learning, natural language processing and other techniques, we have a portfolio of problems that we know how to “solve” through algorithmic solutions with rigor and reliability. Predicting student course performance, analyzing discussion forum interactions to discover social networks , analyzing assessment results to identify valid (and problematic) students assessments are all examples of areas with well-established techniques that we can apply with confidence in any learning environment that uses educational technology platforms to a significant degree.

# Using Analytics to Address COVID-19 Challenges

Given this successful development of learning analytics, combined with the current fiscal climate that COVID-19 is bringing to academic institutions and state budgets, it is imperative upon all of us to be as effective as possible and apply analysis for accurate insights that can make a difference in student learning. Providing successful and high-quality online experiences will become a differentiator and quite possibly a survival tactic for many institutions to meet their obligations to students and provide a cohesive learning experience. Personal relationships, intuition, and hunches can provide powerful orientations but must be backed up with evidence and analysis.

There are many ways to get started with a campus analytics project; build, buy or borrow considerations can help campuses to evaluate potential solutions and ways to get this expertise in a way that meets the culture and resources available at a campus. Having a trusted internal or external partner that is independent of the outcomes is a key feature for any implementation of analytics, especially when considered in the context of decision-making, given potential biases and influences on the ability of people to make accurate inferences from the data.

Having a team with a balance of technical expertise, domain knowledge, and above all, vision for the best interests of the student is critical to getting these projects started. I also strongly advocate for starting with a small-scale “EDA” (exploratory data analysis) project to uncover what is feasible with the data available to a campus; too often I see campuses with good intent getting involved in extensive management planning projects (or data infrastructure efforts) without digging into their data to see what is feasible with the assets that they have at hand.

Please feel free to reach out if we can help get you started or make advances in your learning analytics efforts.

# Works Cited

Campbell, J. (2007). Utilizing student data within the course management system to determine undergraduate student academic success: An exploratory study. Retrieved from http://proquest.umi.com/pqdweb?did=1417816411&Fmt=7&clientId=11430&RQT=309&VNa e=PQD

Prinsloo, P., & Slade, S. (2017). An Elephant in the Learning Analytics Room: The Obligation to Act. Proceedings of the Seventh International Learning Analytics & Knowledge Conference, 46 55. https://doi.org/10.1145/3027385.3027406

## Stay in touch

Whether you have questions, need to schedule a demo, or have criticism, praise, suggestions or general feedback? We're here to help.


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Analytical solutions of the integrals for the mode-matching of symmetric rectanglular wave guide
2017-05-06

# Total power $$P$$ over the cross-section is normalized

## TE modes

\begin{aligned} E_z &= 0 \\ H_z &= \frac{j\,k_c}{\sqrt{ab|\beta|\omega\mu}}\; A \cos\frac{m\pi x}{a} \cos\frac{n\pi y}{b} \\ E_x &= \frac{-1}{k_c\sqrt{ab}}\; \sqrt{\frac{\omega\mu}{|\beta|}} \frac{n}{b} A \cos\frac{m\pi x}{a} \sin\frac{n\pi y}{b} \\ E_y &= \frac{1}{k_c\sqrt{ab}}\; \sqrt{\frac{\omega\mu}{|\beta|}} \frac{m}{a} A \sin\frac{m\pi x}{a} \cos\frac{n\pi y}{b} \\ H_x &= \frac{-\beta}{k_c\sqrt{ab}}\; \sqrt{\frac{1}{\omega\mu|\beta|}} \frac{m}{a} A \sin\frac{m\pi x}{a} \cos\frac{n\pi y}{b} \\ H_y &= \frac{-\beta}{k_c\sqrt{ab}}\; \sqrt{\frac{1}{\omega\mu|\beta|}} \frac{n}{b} A \cos\frac{m\pi x}{a} \sin\frac{n\pi y}{b} \end{aligned}

## TM modes

\begin{aligned} E_z &= \frac{v\,j\,k_c}{\sqrt{ab|\beta|\omega\epsilon}}\; B \sin\frac{m\pi x}{a} \sin\frac{n\pi y}{b} \\ H_z &= 0 \\ E_x &= \frac{v\,\beta}{k_c\sqrt{ab}}\; \sqrt{\frac{1}{\omega\epsilon|\beta|}} \frac{m}{a} B \cos\frac{m\pi x}{a} \sin\frac{n\pi y}{b} \\ E_y &= \frac{v\,\beta}{k_c\sqrt{ab}}\; \sqrt{\frac{1}{\omega\epsilon|\beta|}} \frac{n}{b} B \sin\frac{m\pi x}{a} \cos\frac{n\pi y}{b} \\ H_x &= \frac{-v}{k_c\sqrt{ab}}\; \sqrt{\frac{\omega\epsilon}{|\beta|}} \frac{n}{b} B \sin\frac{m\pi x}{a} \cos\frac{n\pi y}{b} \\ H_y &= \frac{v}{k_c\sqrt{ab}}\; \sqrt{\frac{\omega\epsilon}{|\beta|}} \frac{m}{a} B \cos\frac{m\pi x}{a} \sin\frac{n\pi y}{b} \\ \end{aligned}
where $$v=1$$ if forwards, $$-1$$ backwards; $$k_c = \sqrt{ \left(\frac{m\pi}{a}\right)^2 + \left(\frac{n\pi}{b}\right)^2 }$$ and $$\beta = \sqrt{k^2-k_c^2}$$

## Notes

• This normalization is only valid for both $$m$$ and $$n$$ non-zero. for TE$$_{m\ 0}$$ or TE$$_{0\ n}$$ there is a factor of 2 in power, i.e., $$\sqrt2$$ in amplitude.
• The name individual parts of $$E_x$$, $$E_y$$ are given for the coefficient pairs $$m/a$$, $$n/b$$ etc. for $$x$$, $$y$$ and their signs, respectively. Where as the common part means the rest terms with square roots, $$k_c$$, $$v$$ and eventually the $$\beta$$ with its sign (propogating direction).
• The coefficient of $$E_y$$ in TM mode is chosen to be positive real (or negative imaginary). A side effect is that this makes the junction reciprocal.

# Orthogonal Integration of Fields for an E-Plane Discontinuity

For E-plane discontinuities, $$\int H\mathrm{d}s$$ on the small aperture for the continuation of the field whereas $$\int E\mathrm{d}s$$ on the large aperture, in order to include the $$E_\perp=0$$ metal boundary.

Note: Weight (Base) functions should be conjugated to the transversal fields, however since we put $$j$$ into the common coefficiency, the conjugation can be omited.

## Orthogonal Integral 1

### Form

$$\begin{split} \int_{-\frac{a}{2}}^{\frac{a}{2}} \; \int_{-\frac{b}{2}}^{\frac{b}{2}} \quad &\sin\frac{m\pi\,(x+a/2)}{a} \cos\frac{n\pi\,(y+c/2)}{c} \\ &\sin\frac{p\pi\,(x+a/2)}{a} \cos\frac{q\pi\,(y+b/2)}{b} \quad \mathrm{d}y\; \mathrm{d}x \end{split}$$

### Solution (mathematica)

0 except $$m = p \ne 0$$ combining with
• $$c\,q \ne b\,n$$ $$-\frac{a b^2 c n \left(\sin \left(\frac{\pi n (c-b)}{2 c}\right)-(-1)^q \sin \left(\frac{\pi n (b+c)}{2 c}\right)\right)}{2 \pi (b n-c q) (b n+c q)}$$
• $$c\,q = b\,n$$ and $$q \ne 0$$ $$\frac{a b \left(\sin \left(\frac{\pi q (b-c)}{2 b}\right)+\sin \left(\frac{\pi q (3 b+c)}{2 b}\right)+2 \pi q \cos \left(\frac{\pi q (b-c)}{2 b}\right)\right)}{8 \pi q}$$
• $$c\,q = b\,n$$ and $$q = 0$$ $$\frac{a b}{2}$$

## Orthogonal Integral 2

### Form

$$\begin{split} \int_{-\frac{a}{2}}^{\frac{a}{2}} \; \int_{-\frac{b}{2}}^{\frac{b}{2}} \quad &\cos\frac{m\pi\,(x+a/2)}{a} \sin\frac{n\pi\,(y+c/2)}{c} \\ &\cos\frac{p\pi\,(x+a/2)}{a} \sin\frac{q\pi\,(y+b/2)}{b} \quad \mathrm{d}y\; \mathrm{d}x \end{split}$$

### Solution (mathematica)

0 except $$m = p$$ combining with
• $$c\,q = b\,n$$ and $$p = 0$$ (and $$q \ne 0$$) $$-\frac{a b \left(\sin \left(\frac{\pi q (b-c)}{2 b}\right)+\sin \left(\frac{\pi q (3 b+c)}{2 b}\right)-2 \pi q \cos \left(\frac{\pi q (b-c)}{2 b}\right)\right)}{4 \pi q}$$
• $$c\,q = b\,n$$ and $$p \ne 0$$ (and $$q \ne 0$$) $$-\frac{a b \left( \sin \left(\frac{\pi q (b-c)}{2 b}\right) + \sin \left(\frac{\pi q (3 b+c)}{2 b}\right) -2 \pi q \cos \left(\frac{\pi q (b-c)}{2 b}\right) \right)}{8 \pi q}$$
• $$c\,q \ne b\,n$$ and $$p = 0$$ $$-\frac{a b c^2 q \left(\sin \left(\frac{\pi n (c-b)}{2 c}\right)-(-1)^q \sin \left(\frac{\pi n (b+c)}{2 c}\right)\right)}{\pi (b n-c q) (b n+c q)}$$
• $$c\,q \ne b\,n$$ and $$p \ne 0$$ $$-\frac{a b c^2 q \left(\sin \left(\frac{\pi n (c-b)}{2 c}\right)-(-1)^q \sin \left(\frac{\pi n (b+c)}{2 c}\right)\right)}{2 \pi (b n-c q) (b n+c q)}$$


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# A new approach to counterexamples to $L^1$ estimates: Korn's inequality, geometric rigidity and regularity for gradients of separately convex functions

created on 26 Nov 2003
modified by maggi on 19 Dec 2005

[BibTeX]

Published Paper

Inserted: 26 nov 2003
Last Updated: 19 dec 2005

Journal: Arch. Ration. Mech. Anal.
Volume: 175
Number: 2
Pages: 287-300
Year: 2005
Notes:

Preprint Nr. 932003, Max Planck Institute for Mathematics in the Sciences, DOWNLOAD AT http:/www.mis.mpg.depreprints2003index.html

Abstract:

The derivation of counterexamples to $L^1$ estimates can be reduced to a geometric decomposition procedure along rank-one lines in matrix space. We illustrate this concept in two concrete applications. Firstly, we recover a celebrated, and rather complex, counterexample by Ornstein, proving the failure of Korn's inequality, and of the corresponding geometrically nonlinear rigidity result, in $L^1$. Secondly, we construct a function $f:R^2\rightarrow R$ which is separately convex but whose gradient is not in BV{loc}, in the sense that the mixed derivative $f_{12}$ is not a bounded measure.

Credits | Cookie policy | HTML 5 | CSS 2.1


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# A division and n-root algorithm for big numbers

In a previous post, we introduced a library for performing arithmetic operations with arbitrary precision, and in this update we optimized the multiplication algorithm using the Fast Fourier Transform factorization.

In this post, using the FFT-based multiplication algorithm as the cornerstone of our library, we will optimize the division algorithm and introduce some other methods for computing square and quartic roots. In a previous example, we succeeded to compute the largest known prime number at the time - the Mersenne prime $M_{43112609}$ - working with integer arithmetic. With the new ingredients, we will be able to compute some other interesting things, such as millions of decimals of $\pi$ or other irrational numbers using convergent series.

## A new division algorithm

We have already optimized the multiplication method, moving from a $O(n^2)$ time complexity algorithm to a $O(n\,log_2(n))$ one. But the division is still computed with a long division algorithm, with a time complexity of $O(n^2)$. We will try to find a faster algorithm using the Newton Raphson method to converge to the solution.

The problem is: given the numbers $a$ and $b$, we want to compute the quotient $c = \dfrac{a}{b}$. The following function has a zero at the desired quotient:

Applying the Newton-Raphson method to it, starting with an initial guess $x_0$, we can compute a sequence $\{x_k\},\,k=1,\,2,\,\ldots$ that converges quadratically to $\dfrac{a}{b}$ in the following way

Turns out that we didn’t make any progress yet, as long as we still need to compute a division with the same divisor $b$. But, conceiving the division $\dfrac{a}{b}$ as a multiplication by the inverse $a\,\left(b^{-1}\right)$, and being that inverse $b^{-1}$ a zero of the following trivial function:

we can build a series that converges quadratically to $b^{-1}$

Thus, we only need multiplications and subtractions to compute every element of the sequence. Once we have converged to the inverse, $x_{k} \simeq b^{-1}$, we only need to estimate the division as

A quadratic convergence means that the amount of figures found, should double from one iteration to the next one.

## A square root and n-root algorithm

In a similar way, we can build a sequence converging to the square root of a given number, which is a root of the following function

Or, if we want to avoid computing the division in each iteration, we can build a sequence converging to the inverse of the square root, being such number a zero of the function

Voilà, we only need multiplications and additions/subtractions in each iteration, and the solution will converge quadratically to $\dfrac{1}{\sqrt{a}}$. We can even compute the desired value ${\sqrt{a}}$ at the end without having to invert the solution, only multiplying by $a$

This method can be generalized for computing ${\sqrt[n]{a}}$ (the two previous examples correspond to $n = 1$ and $n = 2$):

Once we have the final solution $x_{k} \simeq \dfrac{1}{\sqrt[n]{a}}$, we can compute the n-root without inverting the solution, by means of

## Implementation details

The implementation in the project page adds the new features to the previous version:

• Inverse computation (file div.cc).
• Division algorithm using the inverse method (file div.cc). The long division algorithm was already implemented.
• Square and quartic roots (n-root not implemented) using the direct methods or the more efficient inverse ones (file sqrt.cc).

The plot below shows a scalability comparison of the methods implemented in the library. Notice the scalability problems of Long Division and Long Multiplication algorithms (the latest takes 10,000 times longer than the FFT multiplication algorithm to compute 1 million figures). The Newton inverse algorithm and its related algorithms (inverse division, square root and quartic root), perform well enough for our purposes (much better than the non inverse versions). The non inverse square and quartic root algorithms are based on an inverse division algorithm (they would perform much worse if based on a long division algorithm). There are many possible optimizations, but they are beyond the scope of this post.

Figure 1: Scalability of the algorithms implemented in the library.

Some other important issues we didn’t tackle yet:

• Initial guesses for the iterative methods: check the methods BigNumber::fromDouble(double, int) and toDouble(double&, int&) and their usage for computing an initial guess, i.e. for a multiplicative inverse.
• Convergence criterions: a typical stop criterion with a convergent sequence would be when $x_{k+1}$ and $x_{k}$ are very close each other, $x_{k+1} \simeq x_{k}$, and that means that all (or almost all) of their digits match up. Check the source code again for further detail.
• Rounding errors: using algorithms that converge to multiplicative inverses can incur rounding errors when working with finite arithmetic. These errors can be overcome, but no solution has been implemented in the code, nor discussed in this post. As a hint for the division algorithm, for example, once we get the approximate quotient $c_1 \simeq \dfrac{a}{b}$ using the inverse approach, we can compute a new quotient $c_2 \simeq \dfrac{r}{b}$ (where $r = a - b\,c_1$ is the first remainder), and estimate the final quotient as $c \simeq c_1 + c_2$. The second division can be performed with a more accurate Long Division algorithm, not taking too long given the small remainder.

## Application example

I always wanted to write my own program for computing millions of decimals of $\pi$, and now we have all the ingredients to do it by using, for instance, a 4th order Borwein’s algorithm (disclaimer: this is just an application of this general purpose library, not a specially optimized way to compute decimals of $\pi$). Let us start with the following values:

and then construct the sequences $\{y_k\}$ and $\{a_k\}$

the sequence $\{a_{k}\}$ converges with quartic order to $\dfrac{1}{\pi}$. You can get this result in a few minutes with a normal computer - as of 2012 - if you compute $\pi$ with 1,038,090 decimals (the last 7 decimals are wrong due to rounding errors, and the total amount of figures involved in computations is $2^{20}$ = 1,048,576). You can find the implementation in the file pi.cc.

Written on November 2, 2012


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How to prove Lagrange multiplier theorem in a rigorous but intuitive way?

Following some text books, the Lagrange multiplier theorem can be described as follows.

Let $U \subset \mathbb{R}^n$ be an open set and let $f:U\rightarrow \mathbb{R}, g:U\rightarrow \mathbb{R}$ be $C^1$ functions. Let $\mathbf{x}_{0} \in U, c=g(\mathbf{x}_0)$, and let $S$ be the level set of $g$ with value $c$. Suppose that $\nabla g(\mathbf{x}_0) \neq 0$.
If the function $f|_S$ has a local extremum at $\mathbf{x}_0$ then there is a $\lambda \in \mathbb{R}$ so that $\nabla f(\mathbf{x}_0)=\lambda g(\mathbf{x}_0)$

Some textbooks give a strict proof using implicit function theorem (see proof). The proof is very clear, however I can't build some intuition from the proof. Can someone help me prove this theorem in a rigorous but more intuitive way? Thanks.

• In what perspective are you going to use this theorem? Apr 27, 2016 at 9:26
• I would like to understand Lagrange multiplier theorem and KKT condition in a better way. I think it will help me to understand the optimization algorithms. Apr 27, 2016 at 10:04

Here's some intuition.

First suppose that $$x_0$$ is a local minimizer for the problem \begin{align} \tag{\spadesuit} \text{minimize} & \quad f(x) \\ \text{subject to} &\quad Ax = b. \end{align} If $$Au = 0$$, then the directional derivative $$D_u f(x_0) = \langle \nabla f(x_0),u \rangle$$ is nonnegative. Otherwise, it would be possible to improve $$x_0$$ by perturbing it a bit in the direction $$u$$.

It follows that if $$Au = 0$$, then $$\langle \nabla f(x_0),u \rangle = 0$$.

So, $$\nabla f(x_0)$$ is in the orthogonal complement of the null space of $$A$$.

BUT, according to the "four subspaces theorem" (which is beloved by Gilbert Strang), the orthogonal complement of the null space of $$A$$ is the range of $$A^T$$. Thus, $$\nabla f(x_0)$$ is in the range of $$A^T$$. In other words, there exists a vector $$\lambda$$ such that $$$$\nabla f(x_0) = A^T \lambda.$$$$ This is our Lagrange multiplier optimality condition, in the case where we have linear equality constraints.

Next, suppose that $$x_0$$ is a local minimizer for the problem \begin{align} \text{minimize} & \quad f(x) \\ \text{subject to} &\quad g(x) = 0, \end{align} where $$g:\mathbb R^n \to \mathbb R^m$$.

It seems plausible that $$x_0$$ is also a local minimizer for the problem we get by replacing $$g$$ with the local linear approximation to $$g$$ at $$x_0$$: \begin{align} \text{minimize} & \quad f(x) \\ \text{subject to} &\quad g(x_0) + g'(x_0)(x - x_0) = 0. \end{align} (Here $$g'(x_0)$$ is the Jacobian matrix of $$g$$ at $$x_0$$.) Assuming that $$x_0$$ is indeed a local minimizer for this modified problem, it follows that $$x_0$$ satisfies the optimality condition derived above: \begin{align} \nabla f(x_0) &= g'(x_0)^T \lambda \\ &= \nabla g_1(x_0) \lambda_1 + \cdots + \nabla g_m(x_0) \lambda_m \end{align} for some vector $$\lambda = \begin{bmatrix} \lambda_1 & \ldots & \lambda_m \end{bmatrix}^T \in \mathbb R^m$$. (Here $$g_1,\ldots,g_m$$ are the component functions of $$g$$, and we use the convention that the gradient is a column vector.) This is our Lagrange multiplier optimality condition in the case of nonlinear equality constraints.

I believe it's possible to view the proof using the implicit function theorem as a rigorous version of this intuition.

Edit: Now I'll show how a similar approach can handle inequality constraints, if we replace the "four subspaces theorem" with Farkas' lemma (which I call the four cones theorem).

Let $$x^*$$ be a local minimizer for the problem \begin{align} \tag{\heartsuit} \text{minimize} & \quad f(x) \\ \text{subject to} & \quad Ax \leq b. \end{align} Suppose that $$u \in \mathbb R^n$$ and $$Au \leq 0$$. Then the directional derivative $$D_uf(x^*) = \langle \nabla f(x^*),u \rangle \geq 0$$. Otherwise, we could improve $$x^*$$ by perturbing it a bit in the direction of $$u$$.

At this point, we would like to invoke something like the four subspaces theorem, to find some optimality condition that $$\nabla f(x^*)$$ must satisfy. While the four subspaces theorem is inapplicable here, there is a one-sided version of the four subspaces theorem that fits this situation perfectly.

The four cones theorem

We first recall a few facts from convex analysis. If $$C \subset \mathbb R^n$$ is a cone, then the polar of $$C$$ is defined by $$$$C^\circ = \{z \mid \langle x,z \rangle \leq 0 \,\, \forall \,\, x \in C \}.$$$$ Note that $$C^\circ$$ is a closed convex cone.
A convex cone is a "one-sided" version of a subspace, and the polar cone is a "one-sided" version of the orthogonal complement. Instead of $$\langle x,z \rangle = 0$$, we have $$\langle x, z \rangle \leq 0$$. Here's some support for this analogy:

• For a subspace $$W$$ of $$\mathbb R^n$$, we have the familiar equation $$W = W^{\perp \perp}$$. The one-sided version of this is that if $$C$$ is a closed convex cone, then $$C = C^{\circ \circ}$$.
• If $$W$$ is a subspace of $$\mathbb R^n$$, then any $$x \in \mathbb R^n$$ can be decomposed as $$x = \Pi_W(x) + \Pi_{W^\perp}(x)$$. The one-sided version of this is that if $$C \subset \mathbb R^n$$ is a closed convex cone, then any $$x \in \mathbb R^n$$ can be decomposed as $$x = \Pi_C(x) + \Pi_{C^\circ}(x)$$. Moreover, $$\Pi_C(x)$$ is orthogonal to $$\Pi_{C^\circ}(x)$$.

Let $$\mathcal R_+(A^T) = \{ A^T z \mid z \geq 0 \}$$. So $$\mathcal R_+(A^T)$$ is a one-sided version'' of the column space of $$A^T$$. I call it the column cone of $$A^T$$. Let $$\mathcal N_-(A) = \{x \mid Ax \leq 0 \}$$. So $$\mathcal N_-(A)$$ is a one-sided version of the null space of $$A$$. I call it the null cone of $$A$$. Note that $$\mathcal N_-(A)$$ and $$\mathcal R_+(A^T)$$ are both closed convex cones.

The four subspaces theorem can be stated as $$$$\mathcal N(A)^\perp = \mathcal R(A^T).$$$$ Here is our "one-sided" version of the four subspaces theorem: $$$$\mathcal N_-(A)^\circ = \mathcal R_+(A^T).$$$$ I call this the "four cones theorem".

Invoking the four cones theorem

We can use the "four cones theorem" to find an optimality condition for problem ($$\heartsuit$$), just as we used the four subspaces theorem to find an optimality condition for problem ($$\spadesuit$$). As noted previously, if $$A u \leq 0$$, then $$\langle \nabla f(x^*), u \rangle \geq 0$$. In other words, $$-\nabla f(x^*) \in \mathcal N_-(A)^\circ$$. By the four cones theorem, it follows that $$-\nabla f(x^*) \in \mathcal R_+(A^T)$$. Thus, there exists a vector $$z \geq 0$$ such that $$$$\nabla f(x^*) + A^T z = 0.$$$$ This, together with $$Ax^* \leq b$$, is our optimality condition (KKT condition) for the problem ($$\heartsuit$$) with linear inequality constraints.

Connection with Farkas's lemma

The four cones theorem can be stated as a theorem of the alternative''. If $$g \in \mathbb R^n$$, then $$g$$ either does or does not belong to $$\mathcal R_+(A^T)$$. In other words, either $$g$$ belongs to $$\mathcal R_+(A^T)$$, or else $$g$$ does not belong to the polar of $$\mathcal N_-(A)$$. This means that one and only one of the following two alternatives is true:

1. There exists $$z \geq 0$$ such that $$g = A^T z$$.
2. There exists $$u$$ such that $$Au \leq 0$$ and $$\langle g, u \rangle > 0$$.

This is equivalent to the statement of Farkas's lemma given in Boyd and Vandenberghe. The four cones theorem is Farkas's lemma.

Visualizing the four cones theorem

The "alternative" statement of the four cones theorem suggests a way of visualizing the four cones theorem that makes it seem obvious. The first alternative is that $$g$$ belongs to the convex cone generated by the columns of $$A^T$$. The second alternative is that there is a hyperplane through the origin that separates $$g$$ from the columns of $$A^T$$. (The vector $$u$$ is a normal vector to this separating hyperplane.)

Problem with linear equality and inequality constraints

This case is similar to the previous cases, except that we will use a different version of Farkas's lemma that involves a combination of equality and inequality constraints.

• Very helpful to me. Can this intuition be generalized to understand the proof of KKT condition? Apr 27, 2016 at 8:03
• Yes, and it's a beautiful story that's rarely told. We replace the four subspace theorem with Farkas' lemma (the four cone theorem). I added notes about this. Apr 27, 2016 at 9:01
• +1 very nice! I haven't fully understood the case with inequality constraints but I understand your (classic) strategy: work with linear function first, then work with general function (but locally approximately linear) Apr 27, 2016 at 10:02
• There is a tricky point in the intuition: we say (suppose we're talking about minimization, for concreteness) that if the gradient of $f$ were not parallel to the gradient of $g$, then we could find a vector which is orthogonal to the gradient of $g$ and which has a negative inner product with the gradient of $f$, and improve our candidate by moving in that direction. The tricky thing is that we can't move in that direction, strictly speaking, because those points are not on the surface (in the nonlinear constraint case).
– Ian
Apr 27, 2016 at 15:21
• To make sense of this directly without explicitly invoking the implicit function theorem, you should estimate how far away you are from the surface when you move along a tangent direction, and use that to conclude that if you project from the tangent direction down to the surface, you still decrease the objective function, provided you moved a small enough distance.
– Ian
Apr 27, 2016 at 15:21

Here's a different way to see that Lagrange multipliers are "intuitively" the correct way to go. To first order, the change in $f$ due to a change in $\vec r$ is simply:$$\delta f = f(\vec r + \delta\vec r) - f(\vec r) \approx \nabla f\cdot\delta\vec r.$$This has the obvious interpretation for $f$ above, "go in the direction of $\nabla f$ to increase $f$," but it also has an interpretation for constraints: to first order, the paths allowed by a constraint $g(\vec r) = c$ must be the ones such that $\nabla g \cdot \delta \vec r = 0,$ otherwise you would increase $c$ to first-order by following that tangent vector. That is, if you obey the constraint, we must have $\delta g = 0.$

Now we simply combine these two. At the constrained extremum of $f$ on $S,$ it must be the case that for all $\delta\vec r$ such that $\nabla g \cdot \delta \vec r = 0,$ we also have $\delta f = \nabla f\cdot\delta\vec r = 0,$ otherwise we can follow $\pm \delta\vec r$ to increase/decrease $f$, proving that this wasn't either sort of extremum on $S$ after all. So just to phrase the very condition for a constrained maximum, we would have to write it as $$\forall \vec a . (\nabla g \cdot \vec a = 0) \rightarrow (\nabla f \cdot \vec a = 0)$$

But that "for-all" is 100% sufficient to prove that they are proportional! Effectively, you can't have two linearly independent vectors $\vec a, \vec b$ such that the nullspaces of $(\vec a \cdot)$ and $(\vec b \cdot)$ are the same. Let's just prove this last aspect to complete the proof.

Consider $\vec p = \vec a - \alpha \vec b$ for $\alpha = \vec a \cdot \vec b / (\vec b \cdot \vec b)$, this satisfies by construction $\vec b \cdot \vec p = 0$ and therefore we must have $\vec a \cdot \vec p = 0$ due to the shared nullspace. But when you chug through the algebra of this it means ultimately that $(\vec a \cdot \vec a)(\vec b \cdot \vec b) = (\vec a \cdot \vec b)^2.$ That guarantees the = sign in a triangle inequality looking like either of $$|\vec a \pm \vec b|^2 = |\vec a|^2 + |\vec b|^2 \pm 2 (\vec a \cdot \vec b) ~\le~ (|\vec a| + |\vec b|)^2 = |\vec a|^2 + |\vec b|^2 + 2 |\vec a||\vec b|.$$ We know that those equals signs only hold when the vectors are degenerate, that is, $\vec a = \lambda \vec b.$

Look at the tangent space to $$S = g^{-1}(c)$$ at $$x_0$$, say $$S_{x_0}$$. Then $$S_{x_0} = \left[\nabla g(x_0) \right]^{\perp}$$. Therefore, $$S_{x_0}^\perp$$ is the one-dimensional subspace spanned by $$\nabla g(x_0)$$. Now, $$\nabla f(x_0) = \lambda \nabla g(x_0)\text{ for some } \lambda \in \Bbb{R} \iff \nabla f(x_0) \in S_{x_0}^\perp \iff \nabla f(x_0).v = 0 \text{ for all } v \in S_{x_0}.$$ But every $$v \in S_{x_0}$$ is of the form $$v = \dot\alpha(t_0)$$ for some parametrized curve $$\alpha:I \to S$$ and $$t_0 \in I$$ with $$\alpha(t_0) =x_0$$. Since $$x_0$$ is an extreme point of $$f$$ on $$S$$, $$t_0$$ is an extreme point of $$f \circ \alpha$$ on $$I$$. Hence $$0=(f \circ \alpha)'(t_0) = \nabla f(\alpha(t_0)).\dot\alpha(t_0) = \nabla f(x_0).v$$ for all $$v \in S_{x_0}$$ and so the result follows.

Caveat: Think where implicit function theorem is coming into this proof


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# Three boys are pulling 3 ropes joined at a point. The boy in the middle is exerting a pull of 100 N. The other two boys, whose ropes both make an angle of 150? with the center rope, are pulling with forces 100 N of 50?3 N & 50/?3 N. Find the magnitude of the resultant pull on the common point

Dear student,

"Three boys are pulling 3 ropes joined at a point. The boy in the middle is exerting a pull of 100 N. The other two boys, whose ropes both make an angle of 150 degree with the center rope, are pulling with forces 100 N, of $50\sqrt{3}$ N & $50\sqrt{3}$ N. Find the magnitude of the resultant pull on the common point"