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SitemapCopyright © 2005 - 2021 ProProfs.com. Why can't I see everybody who liked my tweet? To help compare different orders of magnitude, this section lists lengths between 10−7 and 10−6 m (100 nm and 1 μm). Maybe a Child's mind, as we can not touch it physically, so if we can not touch it physically, perhaps it is the smallest thing, yet it is, Humanities Greatest Resource, making it the biggest thing in our Universe. The real name of this planet is 55 Cancri e but this planet is also known as Diamond planet. To help compare different orders of magnitude, this section lists distances starting at 100 Zm (1023 m or 11 million light-years). To help compare different orders of magnitude, this section lists lengths between 10−2 m and 10−1 m (1 cm and 1 dm). Several endurance auto races are, or were, run for 1,000 km: 1.280 Mm – Diameter of the trans-Neptunian object, 13.300 Mm – Length of roads being rehabilitated and widened under the, 10 Mm – Approximate altitude of the outer boundary of the, 14.000 Mm – Smallest diameter of Jupiter's, 40.005 Mm – Polar circumference of the Earth, 40.077 Mm – Equatorial circumference of the Earth, 180 Mm – Average distance covered during life, 3 Gm – Total length of "wiring" in the human brain, 149.6 Gm (93.0 million mi; 1.0 au) – Distance between the, 591 Gm (4.0 au) – Minimum distance between the, 780 Gm (5.2 au) – Distance between Jupiter and the Sun, 965 Gm (6.4 au) – Maximum distance between the Earth and Jupiter, 5.7 Tm – 38.1 au – Perihelion distance of, 10 Tm – 67 AU – Diameter of a hypothetical, 12.9 Tm – 86.3 AU – Distance to 90377 Sedna in March 2014, 14.1 Tm – 94.3 AU – Estimated radius of the, 55.7 Tm – 371 AU – Aphelion distance of the, 1.9 Pm ± 0.5 Pm = 12,000 AU = 0.2 light-year radius of, 4.7 Pm = 30,000 AU = half-light-year diameter of, 7.5 Pm – 50,000 AU – Possible outer boundary of, 15 Pm – 1.59 light-years – Possible outer radius of, 20 Pm – 2.11 light-years – maximum extent of influence of the Sun's, 230 Pm – 24 light-years – Diameter of the, 373.1 Pm – 39.44 light-years – Distance to, 1.6 Em – 172 ± 12.5 light-years – Diameter of, 6.2 Em – 650 light-years – Distance to the, 13 Em – 1,300 light-years – Distance to the, 14 Em – 1,500 light-years – Approximate thickness of the, 14.2 Em – 1,520 light-years – Diameter of the, 47 Em – 5,000 light-years – Distance to the, 53 Em – 5,600 light-years – Distance to the, 150 Em – 16,000 light-years – Diameter of the, 200 Em – 21,500 light-years – Distance to, 240 Em – 25,000 light-years – Distance to the, 260 Em – 28,000 light-years – Distance to the center of the, 830 Em – 88,000 light-years – Distance to the, 1.7 Zm – 179,000 light-years – Distance to the, <1.9 Zm – <200,000 light-years – Revised estimated diameter of the disc of the, 2.0 Zm – 210,000 light-years – Distance to the, 2.8 Zm – 300,000 light-years – Distance to the, 8.5 Zm – 900,000 light-years – Distance to the, 24 Zm – 2.5 million light-years – Distance to the, 30.8568 Zm – 3.2616 million light-years – 1, 40 Zm – 4.2 million light-years – Distance to the, 49.2 Zm – 5.2 million light-years – Width of the, 57 Zm – 6 million light-years – Diameter of the supergiant, 95 Zm – 10 million light-years – Distance to the, 140 Zm – 15 million light-years – Distance to, 250 Zm – 27 million light-years – Distance to the, 280 Zm – 30 million light-years – Distance to the, 570 Zm – 60 million light-years – Approximate distance to the, 620 Zm – 65 million light-years – Approximate distance to the, 800 Zm – 85 million light-years – Approximate distance to the, 1.2 Ym – 127 million light-years – Distance to the closest observed, 1.3 Ym – 137 million light-years – Distance to the, 1.9 Ym – 201 million light-years – Diameter of the, 2.3 Ym – 225 to 250 million light-years – Distance light travels in vacuum in one, 2.8 Ym – 296 million light-years – Distance to the, 3.2 Ym – 338 million light-years – Distance to the, 4.7 Ym – 496 million light-years – Length of the, 6.1 Ym – 645 million light-years – Distance to the, 9.5 Ym – 996 million light-years – Diameter of the, 13 Ym – 1.38 billion light-years – Length of the, 18 Ym – redshift 0.16 – 1.9 billion light-years – Distance to the, 30.8568 Ym – 3.2616 billion light-years – 1 gigaparsec, 33 Ym – 3.5 billion light-years – Maximum distance of the, 37.8 Ym – 4 billion light-years – Length of the, 75 Ym – redshift 0.95 – 8 billion light-years – Approximate distance to the, 85 Ym – redshift 1.6 – 9 billion light-years – Approximate distance to the, 94.6 Ym – 10 billion light-years – Approximate distance to quasar OQ172, 94.6 Ym – 10 billion light-years – Length of the, 124 Ym – redshift 7.54 – 13.1 billion light-years –, 130 Ym – redshift 1,000 – 13.8 billion light-years – Distance (LTD) to the source of the, 260 Ym – 27.4 billion light-years – Diameter of the observable universe (double LTD), 440 Ym – 46 billion light-years – Radius of the universe measured as a, 590 Ym – 62 billion light-years – Cosmological, 886.48 Ym – 93.7 billion light-years – The diameter of the, >1,000 Ym – >105.7 billion light-years – Size of universe beyond the, This page was last edited on 3 January 2021, at 13:31. This is a partial list of Solar System objects by size, arranged in descending order of mean volumetric radius, and divided into several size classes.These lists can also be sorted according to an object's mass and, for the largest objects, volume, density and surface gravity, insofar as these values are available. Shown in this image is IC 1101: The single largest galaxy that has ever been found in the observable universe. Learn vocabulary, terms, and more with flashcards, games, and other study tools. What is the difference between Galaxy and Universe? To help compare different orders of magnitude, this section lists lengths between 10−9 and 10−8 m (1 nm and 10 nm). Click image to see more details and links to their scales. metres. Yellow Dwarf. To help compare orders of magnitude, this section lists lengths between 100 and 1,000 kilometres (105 and 106 metres). The moon is a powerful body in orbit around a planet. A solar system is a star and its planets, asteroids, comets, and other bodies. The solar system where we are living right now is just one of the many. Which planet is your favorite planet and why? From smallest to largest, the correct order in the solar system, galaxy, and universe. It also houses moons, dust, and rocks. Brown Dwarf. Some of them are too far away to be explored so it will nearly impossible at this point to try. Galaxy, universe. There are many differences between these three things. The universe is everything. This is the 10th Biggest Planets In The Universe and also on our list. 1.6 The order from smallest to largest is: atom → water molecule → planet → star → solar system → galaxy → universe Brown Dwarf. The term myriometre (abbr. People say that the universe may continue to grow, and no one knows exactly how big this is. In the list of Top 10 Biggest Planets In The Universe, 55 Cancri e is at no 10. Our solar system belongs in the Milky Way Galaxy which belongs in the universe. To help compare different orders of magnitude, this section lists distances starting at 10 Ym (1025 m or 1.1 billion light-years). Jupiter’s mass is more than 300 times that of Earth, and its diameter, at 140,000 km, is about 11 times Earth’s diameter. The correct answer to this question is C, Solar system. Starting below from the smallest to the largest that we know of right now; and in the years to come, we will discover many more sizes, from very small to very large, and everything in between. 10 years ago. Jamie. An asteroid resides in the asteroid belt between Mars and Jupiter. It is the altitude at which the FAI defines spaceflight to begin.  metres and Next is the galaxy. The solar system is home to the Sun and many planets like Earth, Mercury, and Jupiter. The solar system is approximately 4.571 billion years old. Can you rematch with someone you recently unmatched on Tinder? We only relate to what we can understand with our numbers. The Universe The Universe ???? Planet, star, universe, galaxy, galaxy cluster, star … The universe is known to be 93 billion light-years. To help compare different orders of magnitude, this section lists lengths between 10−17 m and 10−16 m (10 am and 100 am). To help compare different orders of magnitude, this section lists lengths between 10−15 metres and 10−14 metres (1 femtometre and 10 fm). You know that the moon is smaller … Red Dwarf. Smallest to largest in the universe? Universe is the biggest, I think. It's surprising what picayune stuff is being taught in astronomy classes these days. Start studying Hierarchy of Matter (from smallest to largest). Who deals with teeth problems and fix them. Moon, planet, star, solar system, galaxy, cosmos. The largest out of the three is the Universe. The zettametre (SI symbol: Zm) is a unit of length in the metric system equal to 1021 metres.[158]. The myriametre[117] (sometimes also spelled myriameter, myriometre and myriometer) (10,000 metres) is a deprecated unit name; the decimal metric prefix myria-[75] (sometimes also written as myrio-[118][119][120]) is obsolete[76][77][78] and not included among the prefixes when the International System of Units was introduced in 1960. In particle physics, this unit is more commonly called a fermi, also with abbreviation "fm". To help compare different orders of magnitude, this section lists distances starting at 10 Zm (1022 m or 1.1 million light-years). Earth would not have seasons if it-a. Our solar system belongs in the Milky Way Galaxy which belongs in the universe. It is comprised of billions of galaxies. The solar system is known to be smaller than the galaxy because it is always possible for different solar systems to be a part of the galaxy, but the galaxy cannot be placed in a solar system. To help compare different distances this section lists lengths starting at 1010 metres (10 gigametres (Gm) or 10 million kilometres, or 0.07 astronomical units). 139 metres – height of the world's tallest roller coaster, 187 metres – shortest wavelength of the broadcast, 341 metres – height of the world's tallest bridge, the, 400–800 metres – approximate heights of the, 555 metres – longest wavelength of the broadcast, 135–185 metres – the length of an Australian football field, 137.16 metres – total length of a Canadian football field, including the end zones (150 yards), 115.5 metres – height of the world's tallest. 10 10 metres (very rarely termed a decametre which is abbreviated as dam) is equal to: To compare different orders of magnitude this section lists lengths between 100 metres and 1,000 metres (1 kilometre). Reprise de la triangulation", Comité International des Poids et Mesures, "Dr. Charles Lindemann's Lab: Sperm Facts", "World's Biggest Sperm Belongs to a Tiny Fly", "CNN – Scientists discover biggest bacteria ever – April 15, 1999", "World's Smallest Frog Found—Fly-Size Beast Is Tiniest Vertebrate", NATO Infantry Weapons Standardization, Per G. Arvidsson, ChairmanWeapons & Sensors Working GroupLand Capability Group 1 – Dismounted Soldier NATO Army Armaments Group, "World's smallest vertebrate has a big secret", "USGA: Guide to the Rules on Clubs and Balls", "Driver Location Signs – Frequently Asked Questions", "Burj Dubai all set for 09/09/09 soft opening", "Tallest tree in the world: coast redwood", "Kosciuszko National Park lookouts and scenery", "Stratolab, an Evolutionary Stratospheric Balloon Project", "Turkey Building the World's Deepest Immersed Tube Tunnel", "Facts and History about the Panama Canal", "The development of a policy for the management of dingo populations in South Australia", "China's Great Wall far longer than thought: survey", "Solar System Exploration – Earth's Moon: Facts & Figures", "A New VLA-Hipparcos Distance to Betelgeuse and its Implications", "SI Brochure: The International System of Units (SI)", Cosmos – Journey from microcosmos to macrocosmos, https://en.wikipedia.org/w/index.php?title=Orders_of_magnitude_(length)&oldid=998033558, Articles needing additional references from January 2020, All articles needing additional references, Articles containing potentially dated statements from 2012, All articles containing potentially dated statements, Articles containing potentially dated statements from January 2007, Articles with unsourced statements from April 2020, Articles with unsourced statements from February 2009, Articles containing potentially dated statements from 2016, Articles containing potentially dated statements from 2010, Articles containing potentially dated statements from May 2010, Articles containing potentially dated statements from 2018, Articles with unsourced statements from April 2019, Articles with unsourced statements from March 2018, Articles containing potentially dated statements from 2019, Articles containing potentially dated statements from October 2018, Articles with unsourced statements from December 2008, Articles with unsourced statements from June 2016, Articles with unsourced statements from September 2014, Articles with unsourced statements from August 2019, Articles containing potentially dated statements from 2002, Articles with unsourced statements from November 2010, All articles with vague or ambiguous time, Articles containing potentially dated statements from December 2008, Articles containing potentially dated statements from August 2005, Articles with failed verification from December 2015, Articles needing additional references from March 2011, Articles containing potentially dated statements from October 2009, Articles needing additional references from April 2007, Articles with unsourced statements from January 2018, Creative Commons Attribution-ShareAlike License, Effective cross section radius of high-energy, Upper bound of the typical size range for "fundamental, Effective cross section radius of an 11 MeV, Typical size of a fog, mist, or cloud water droplet, Since 1983, defined as length of the path travelled by light in, Typical distance covered by the winner of the, Approximate length of the two longest rivers, the, Greatest mileage ever recorded by a car (3 million miles by a 1966, Total length of DNA molecules in all cells of an adult human body, Supposed outer boundary of the Oort cloud (~ 50,000 au). It is the supplier of light and heat. This holds billions of stars, which scientists approximate anywhere from 200 to 400 billion stars. To help compare different distances this section lists lengths starting at 1015 m (1 Pm or 1 trillion km or 6685 astronomical units (AU) or 0.11 light-years). The statement asks that the objects will be arranged from smallest to largest. 10 The first 4 star sizes are the smaller type stars. A. According to most experiments conducted to determine the smallest object in the universe visible to the human eye, the most accepted conclusion is that under the ideal conditions, we could see objects as small as 0.1 mm. However, the names of all SI mass units are based on gram, rather than on kilogram; thus 10 3 kg is a megagram (10 6 g), not a "kilokilogram". To help compare different distances this section lists lengths starting at 109 metres (1 gigametre (Gm) or 1 billion metres). just put them in order from LARGEST to smallest. The universe contains many galaxies, one of which being the Milky Way. Big Comet (It is believed that some comets are as large as 300 km in … 0 0. To help compare different orders of magnitude, this section lists lengths between 10−16 m and 10−15 m (100 am and 1 fm). This combines the solar system and the galaxies, as well as energy and matter. To study this information, NASA uses telescopes, which is how we can categorize them by size and other details. To help compare different orders of magnitude, this section lists distances starting at 100 Ym (1026 m or 11 billion light-years). To help compare different orders of magnitude, this section lists lengths between 10−4 m and 10−3 m (100 μm and 1 mm). To help compare different distances this section lists lengths starting at 1016 m (10 Pm or 66,800 AU, 1.06 light-years). In terms of size, the galaxy is known to be much larger. The yottametre, or yottameter in the US, (SI symbol: Ym) is a unit of length in the metric system equal to 1024 metres[158]. A. Range of lengths from the subatomic to the astronomical scales, "1mm" redirects here. The galaxy might seem big, but you have to remember that there are different galaxies that can be found in the universe, which means that out of the three, the universe is the biggest one of all. Lv 4. Nomenclature des "mesures républicaines". Click here to get an answer to your question  Which is the correct order of planet, galaxy, solar system, universe? To help compare different orders of magnitude, this section lists lengths between 10−3 m and 10−2 m (1 mm and 1 cm). mom, equivalent to 100 micrometres; frequently confused with the myriametre, 10 kilometres)[74] is deprecated; the decimal metric prefix myrio-[75] is obsolete[76][77][78] and was not included among the prefixes when the International System of Units was introduced in 1960. 10 centimetres (abbreviated to 10 cm) is equal to: To help compare different orders of magnitude, this section lists lengths between one metre and ten metres. Why do the Kardashians only date black guys? The star sizes starting by the smallest by type are: White Dwarf. Distance of these objects are derived from their measured redshifts, which depend on the cosmological models used. To help compare different orders of magnitude, this section lists lengths starting at 108 metres (100 megametres or 100,000 kilometres or 62,150 miles). The Largest Known Galaxy Compared to the Milky Way. To help compare different orders of magnitude this section lists lengths between 10−8 and 10−7 m (10 nm and 100 nm). Atom water molecule planet star solar system galaxy universe. To help compare different distances this section lists lengths between 1017 m (100 Pm or 11 light-years) and 1018 m (106 light-years). To help compare different distances this section lists lengths between 1018 m (1 Em or 105.7 light-years) and 1019 m (1,057 light-years). What are Jupiter, Saturn, Uranus, and Neptune commonly known as? The universe is known to be very vast and there is a big chance that it will get even larger in the long run. It is estimated to be 13.772 billion years old. Some say that it might be infinite. To help compare different orders of magnitude, this section lists lengths starting at 107 metres (10 megametres or 10,000 kilometres). Higgs Boson -> Galaxy Filaments. cw. This means that if the lighting, placement of the objects and color contrasts were all perfect, we could see the Proteus of an amoeba, a tiny aquatic organism called Paramecium and even … 35 A distance of 100 kilometres is equal to about 62 miles (or 62.13711922 miles). {\displaystyle 1.6\times 10^{-35}} 1500 metres – distance sound travels in water in one second; 5.727 km – height of Cerro Aucanquilcha, highest road in the world, located in, 1 km – very approximate size of the smallest-known, 1 mil, the unit of measure commonly used in. A length of 100 kilometres (about 62 miles), as a rough amount, is relatively common in measurements on Earth and for some astronomical objects. It is also home to dust and gas. The order is as follows: asteroid, moon, planet, star, solar system, galaxy, universe. Mr.D has Problems. To help compare different orders of magnitude, this section lists lengths shorter than 10−21 m (10 ym). Our sun is a star which is many times larger than all the planets. How does the discovery of radiations coming from all directions in space support the big bang theory? 1 decade ago. What is it called when two tectonic plates rub against each other in opposite directions? Most of us may be obsessed with the big things, but here is a list of the smallest things in the universe to show you how beautiful small things can be. How long does it take for Saturn to move around the sun? Answer Save. 1 decade ago. × The faint yellow glow around the Sun represents one light-minute. Planets are more significant than the moon. To help compare different orders of magnitude, this section lists lengths between 10−18 m and 10−17 m (1 am and 10 am). Starting below from the smallest to the largest that we know of right now; and in the years to come, we will discover many more sizes, from very small to very large, and everything in between. To help compare different orders of magnitude, this section lists lengths between 10−5 m and 10−4 m (10 μm and 100 μm). Find an answer to your question Place the components of the Universe in order from largest to smallest. 1 decade ago. The femtometre (symbol fm) is a unit of length in the metric system, equal to 10−15 metres. The universe is home to all of the galaxies, and it is estimated that there are billions of them. The following are examples of orders of magnitude for different lengths. The solar system where the earth is a part of is just one of the many solar systems that you can find in the galaxy that we belong in. 1 decade ago. Red Dwarf. What is the main difference between cholesterol and fat. To help compare different orders of magnitude, this section lists lengths starting at 106 m (1 Mm or 1,000 km). Think about this. Put the following in order from largest to smallest: solar system, galaxy, universe, Earth - 5144454 To help compare different distances this section lists lengths starting at 1014 m (100 Tm or 100 billion km or 670 astronomical units). The smallest is definitely going to be a solar system because there are different solar systems that are available in one galaxy. We called this planet Diamond planet because of its appearance and there are so many Diamonds that if somebody can take all this planet in our earth the price of Diamond can be is equal to sand. To help compare different orders of magnitude, this section lists lengths between 10−19 m and 10−18 m (100 zm and 1 am). Same with galaxies that can be found in the universe. To help compare different orders of magnitude, this section lists lengths between 10−14 m and 10−13 m (10 fm and 100 fm). The stars in the center of the galaxy are extremely small. 10 To help compare different orders of magnitude this section lists lengths between 10−11 and 10−10 m (10 pm and 100 pm). 0 0. To help compare different orders of magnitude, this section lists distances starting at 10 Em (1019 m or 1,100 light-years). 1 kilometre (unit symbol km) is equal to: To help compare different orders of magnitude, this section lists lengths between 10 and 100 kilometres (104 to 105 metres). a. a galaxy b. star clusters c. the Local Group d. a wall e. Virgo cluster f. Virgo supercluster g. a star. Commonly used units shown in, 5.7 Em – 600 light-years – Diameter of the, CS1 maint: multiple names: authors list (, radius = distance times sin(angular diameter/2) = 0.2, harv error: no target: CITEREFReedBalickHajianKlayton1999 (, diameter=sin(65 arcminutes)*1270 light-years=24; where "65.00 × 60.0 (arcmin)" sourced from. A planet is almost a spherical body that is in orbit around the sun. The order of size from the smallest to the largest is asteroids and moon, planet, star, solar system, galaxy, universe. We have no clue as Infinity IS. C is the right answer to this question. This planet is two times larger than our earth. To help compare different orders of magnitude this section lists lengths between 10−12 and 10−11 m (1 pm and 10 pm). 10 There are so many that are available right now. What is the difference between Geocentric and Heliocentric? Solar system, galaxy, universe is the answer that is ordered from smallest to largest. How would you describe the Planet Mercury? probes, satellites, space shuttles, telescopes Arrange the following terms in order, from largest to smallest: galaxy, stars, universe… To help compare different orders of magnitude this section lists lengths between 10−10 and 10−9 m (100 pm and 1 nm; 1 Å and 10 Å). {\displaystyle 10^{10^{10^{122}}}} To help compare different orders of magnitude, this section lists distances starting at 1 Ym (1024 m or 105.702 million light-years). d. The center of the galaxy consists of a dense cluster of stars. a. It is substantially larger than a star and a star is what planets orbit. To help compare different orders of magnitude, this section lists lengths between 10−21 m and 10−20 m (1 zm and 10 zm). What is the smallest thing in the universe? What is the difference between Bull and Ox? The star sizes starting by the smallest by type are: White Dwarf. 2) Put the Universe in Order: Size In this activity, students can organize the objects cards by their size starting with the smallest object and continuing to the largest. To help compare different orders of magnitude, this section lists lengths between 10 centimetres and 100 centimetres (10−1 metre and 1 metre). C is the correct answer to this question. The universe may be an unimaginable large expanse of space with billions of galaxies and stars, but it too is made up of tiny things. To help compare different orders of magnitude, this section lists some items with lengths between 10−6 and 10−5 m (between 1 and 10 micrometres, or μm). The largest planet in our solar system by far is Jupiter, which beats out all the other planets in both mass and volume. Favourite answer. − C is known to be the answer to this question. Solar system, galaxy, universe is the answer that is ordered from smallest to largest. To help compare distances at different orders of magnitude this section lists lengths starting at 1011 metres (100 gigametre or 100 million kilometres or 0.7 astronomical units). The universe is known to be vast. 1 decade ago. The first 4 star sizes are the smaller type stars. A lot of experts say that the universe is expected to grow even bigger in the future because it has grown a lot since the time that it was discovered. Planet, star, universe, galaxy, ga… 7 Answers. Learn how and when to remove this template message, high-resolution transmission electron microscope, average half-pitch of a memory cell expected to be manufactured circa 2022, average half-pitch of a memory cell expected to be manufactured circa 2019–2020, average half-pitch of a memory cell manufactured circa 2018, average half-pitch of a memory cell manufactured circa 2016, average half-pitch of a memory cell manufactured circa 2013, average half-pitch of a memory cell manufactured circa 2011–2012, average half-pitch of a memory cell manufactured circa 2009–2010, average half-pitch of a memory cell manufactured circa 2007–2008, average half-pitch of a memory cell manufactured circa 2005–2006, average half-pitch of a memory cell manufactured circa 2002–2003, largest earthquake ever recorded in the United Kingdom, gas pipeline from Iran to India via Pakistan, largest and most massive-known cosmic structure, 10.1175/1520-0469(1961)018<0671:AFFDSD>2.0.CO;2, "The four forces: The strong interaction", "CODATA Value: classical electron radius", "WebElements Periodic Table of the Elements / Sulfur / Radii", "Gram-scale CCVD synthesis of double-walled carbon nanotubes", https://www.theverge.com/circuitbreaker/2016/10/6/13187820/one-nanometer-transistor-berkeley-lab-moores-law, "Samsung announces industry-first mass production of System-on-Chip with 10nm FinFET technology", "Hard drive basics – Capacities, RPM speeds, interfaces, and mechanics", "Evaluation of corneal thickness and topography in normal eyes using the Orbscan corneal topography system", Order Siphonaptera – Fleas – BugGuide.Net, "What is a rapier – Renaissance swords Rapiers", http://www.ibiblio.org/chinesehistory/contents/07spe/specrep01.html#Quick%20Facts, "Twin Keck telescopes probe dual dust disks", "Sun's 'twin' an ideal hunting ground for alien life", "Disk stars in the Milky Way detected beyond 25 kpc from its center", "The Milky Way galaxy may be much bigger than we thought", "The Corrugated Galaxy—Milky Way May Be Much Larger Than Previously Estimated", "Size of the Milky Way Upgraded, Solving Galaxy Puzzle", "Buckminsterfullerene: Molecule of the Month", "Hard drive basics – Capacities, RPM speeds, interfaces and mechanics", https://www.pptaglobal.org/media-and-information/ppta-statements/1055-2019-novel-coronavirus-2019-ncov-and-plasma-protein-therapies, "Human sperm accumulation near surfaces: a simulation study", "Genes are real things :: DNA from the Beginning", Drop Size Distributions and Related Properties of Fog for Five Locations Measured From Aircraft, "La Loi Du 18 Germinal An 3 – Décision de tracer le mètre, unité fondamentale, sur une règle de platine. It is known to be expanding as time passes by. Relevance. The solar system is the smallest. Distance traveled by light in one year; at its current speed, As of March 2013, distance to nearest discovered, As of October 2010, distance to nearest discovered extrasolar planet with potential to support life as we know it (, Approximate radius of humanity's radio bubble, caused by high-power TV broadcasts leaking through the atmosphere into outer space, Diameter of the low surface brightness disc halo of the giant spiral galaxy, Lower bound of the (possibly infinite) radius of the universe, if it is a, According to the laws of probability, the distance one must travel until one encounters a volume of space identical to our, 1 ym – 1 yoctometre, the smallest named subdivision of the metre in the, 2 ym – the effective cross-section radius of 1, 2 zm – the upper bound for the width of a, 7 zm – radius of effective cross section for a, 100 am – all lengths shorter than this distance are not confirmed in terms of size, 1.75 fm – the effective charge diameter of a, 7 fm – the radius of the effective scattering, 570 fm – typical distance from the atomic nucleus of the two innermost electrons (electrons in the, 1 pm – reference value of particle displacement in acoustics, 25 pm – approximate radius of a helium atom, the smallest neutral atom, 1 nm – roughly the length of a sucrose molecule, calculated by, 5 nm – size of the gate length of a 16 nm processor, 13 nm – the length of the wavelength that is used for, 22 nm – Smallest feature size of production, 100 nm – greatest particle size that can fit through a, 120 nm – greatest particle size that can fit through a, 300 nm – greatest particle size that can fit through a, 6 μm – thickness of the tape in a 120-minute (C120), 10 μm – mean longest dimension of a human, 10.6 μm – wavelength of light emitted by a, 17 μm – minimum width of a strand of human hair, 25.4 μm – 1/1,000 inch, commonly referred to as 1, 100 μm – smallest distance that can be seen with the, 181 μm – maximum width of a strand of human hair, 200 μm – nominal width of the smallest commonly available mechanical pencil lead (0.2 mm), 560 μm – thickness of the central area of a human, 8 mm – width of old-format home movie film, 2 cm – approximate width of an adult human, 5.5 × 5.5 × 5.5 cm – dimensions of a 3x3x3, 8.6 cm × 5.4 cm – dimensions of a standard, 10 cm = 1.0 dm – wavelength of the highest, 100 cm = 10 dm – wavelength of the lowest, 60 cm = 6 dm – standard depth (front to back) of a domestic kitchen worktop in Europe (= 600 mm), 15 cm = 1.5 dm – approximate size of largest, 26.3 cm = 2.6 dm – length of average male human, 29.98 cm = 2.998 dm – distance light travels in one, 30 cm = 3.0 dm – maximum leg length of a Goliath birdeater, 84 cm = 8.4 dm – approximate diameter of 2008 TS26, a, 1 m – approximate height of the top part of a, 2.5 m – distance from the floor to the ceiling in an average residential house, 2.77–3.44 m – wavelength of the broadcast, 2.44 m – height of an association football, 2.45 m – highest high jump by a human being (, 3.05 m – (10 feet) height of the basket in, 8.95 m – longest long jump by a human being (, 1.63 m – (5 feet 4 inches) (or 64 inches) – height of average U.S. female, 1.75 m – (5 feet 8 inches) – height of average U.S. male, 2.72 m – (8 feet 11 inches) – tallest-known human being (, 25 metres – wavelength of the broadcast radio, 31 metres – wavelength of the broadcast radio, 40 metres – average depth beneath the seabed of the, 49 metres – wavelength of the broadcast radio, 18.44 metres – distance between the front of the pitcher's rubber and the rear point of home plate on a, 27.43 metres – distance between bases on a, 28 metres – length of a standard FIBA basketball court, 28.65 metres – length of an NBA basketball court (94 feet), 15 metres – approximate distance the tropical, the approximate distance travelled by light in 300. 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## Francis

Francis turbines (James Bicheno Francis) belong to the category of reaction machines.

Vertical Francis turbine

Horizzontal Francis turbine

The runner is fed with water under pressure because only one portion of the available head has been transformed into speed by means of the wicket gate. The reaction degree is defined as the difference between the available head and the head that has to be still transformed at the runner inlet, and can be expressed as  $\bf\chi =\frac { {V}_{1 }^{ 2 } }{ 2{\large g}H }$ [8]

Having indicated with H the available net head and with V1 the water speed at the runner inlet (fig. 1). On average, the reaction degree corresponds to 0.7 ÷0.8. One portion of the head operates on the runner inlet by IMPULSE, that is the one transformed into speed at the wicket gate outlet, while the remaining portion operates by REACTION.

Fig 1

Fig 2

In Impulse (Pelton) turbines, the axial thrust transmitted from the wheel to the motor shaft is null, on the contrary, in REACTION turbines one component of the axial thrust F1 is generated by the difference of motion quantity between runner inlet and outlet and has opposite direction with respect to the water discharge. Another thrust F2, generally of opposite direction with respect to the previous one and then following the way of the water, and of a much higher value, is the one that take place between runner and covers (fig. 2), to which, in case of vertical units, we must add the weight of the rotating parts.
$\bf{\small F }_{ 1 }=\large\frac {\Large \gamma\large Q }{ g({ V }_{ 1a }-{ V }_{ 2a }) }$                       F=F1-F2
There are various expedients to decrease the value of F, as for example to perform, where possible, holes on the runner crown with the purpose to put in touch the area under pressure with the one in depression at the runner downstream (fig. 2), or to adopt compensation pipes on the upper cover to put in touch the area between runner and cover with the outside environment under atmospheric pressure or in touch with the draft tube situated just below the runner where there is depression, and so on. In most cases, to nullify the thrust F it we adopt the thrust bearings. Differently from Pelton turbines, it is much more difficult to determine the diameter of the Francis runner, even if in first approximation. In the spirit and in the limits of this site, we propose the following table that will give a first indication about the runner dimensions. See (fig 4). Being $\bf{\small U }_{ 1e }=\frac {\Large \pi {\large D }_{ 1e }^{ }n }{ 60 }$ [9] and so for the other U relevant to the corresponding diameters. Zd is the number of gates and a0 is the maximum circle between two contiguous gates in rated opening position.

 nq 15 30 40 55 70 80 95 110 $\bf\Large\frac { { U }_{ 1e } }{ \sqrt { 2gH } }$ 0,65 0,686 0,745 0,828 0,920 1,020 1,130 1,240 $\bf\Large\frac { { U }_{ 1i } }{ \sqrt { 2gH } }$ 0,65 0,686 0,70 0,70 0,70 0,70 0,70 0,70 $\bf\Large\frac { { U }_{ 2e } }{ \sqrt { 2gH } }$ 0,40 0,495 0,633 0,78 0,92 1,04 1,155 1,27 $\bf\Large\frac { { U }_{ 2i } }{ \sqrt { 2gH } }$ 0,34 0,358 0,37 0,38 0,39 0,4 0,405 0,41 $\bf\Large\frac { B }{ { D }_{ 1e } }$ 0,05 0,150 0,175 0,225 0,27 0,315 0,35 0,39 $\bf\Large\frac { { D }_{ s } }{ { D }_{ 1e } }$ 0,525 0,690 0,85 0,995 1 1,02 1,022 1,025 $\bf\Large\frac { { Z }_{ d }{\LARGE a }_{ 0 } }{ { D }_{ 1e }}$ 0,80 1,15 1,45 1,65 1,82 1,95 2,07 2,15

no images were found

Fig 3 Francis runner in workshop

Fig 4

Example:
Calculate the main dimensions of one Francis runner that operates under the following data:
H=130 m            Q= 15 m3/s             n=428 rpm                  µ= 92%
The power output at the turbine shaft is (formula [a]) N= 17600 Kw and the characteristic speed nq=43 ( formula [b] ).
From the table $\bf\large\frac { { U }_{ 1e } }{ \sqrt { 2gH } }$=0,75 (about) and taking into account of (9), we obtain D1e= 1,68 m and going on with the data of the table, we obtain in the same D1i=1,58 m, D2e=1,43 m, D2i=0,83 m, B=0,295 m, Ds= 1,43 m. We choose Zd = 20 gates (*), a0=0,122 m. The speed the water reaches when it comes out from the gates when the machine is at full load is $\bf{\small V }_{\small 0 }=\large\frac { Q }{ { Z }_{ d }{\Large a }_{ 0 }B }$=21 m/s and neglecting the leaks through the wicket gate at the runner inlet we can consider V0=V1 and then the reaction [8] degree results to be  f=0,8.

Note. The values expressed in the table are merely indicative and have the only purpose to give an idea of the dimensions the hydraulic channel may reach.

(*) The ratio between number of gates and number of runner blades shall no be a whole number in order to prevent pulsations. In the previous example, if we suppose 13 runner blades also Zd= 24 is a correct value.

format: plain


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## jackyluvv 2 years ago Which inequality does not have the solution {x| x > 5}? a)−4x<−20 b)6x<30 c)1/4x>5/4 d)−3/5x<−3

1. Mathhelp346

Turn the sign into and equal sign 14+x=3 Subtract 14 from both sides x=-11

2. Mathhelp346

*an

3. Aylin

$x \le -11$

4. jackyluvv

thank you this helped me alot! Would you mind helping me with another one?

5. Aylin

Ok

6. jackyluvv

Which inequality does not have the solution {x| x > 5}? $a) -4x < -20$ $b) 6x < 30$ $c) 1/4x > 5/4$ $d) -3/5x < -3$

7. Aylin

a. $-4x < -20$$\frac{ -4x }{ -4 } > \frac{ -20 }{ -4 }$$x > 5$b.$6x < 30$$\frac{ 6x }{ 6 } < \frac{ 30 }{ 6 }$$x < 5$c$\frac{ x }{ 4 } > \frac{ 5 }{ 4 }$$\frac{ 4x }{ 4 }> \frac{ 4 \times 5 }{ 4 }$$x > 5$d. $\frac{ -3x }{ 5 } < -3$$\frac{ 5 \times -3 x }{ -3 \times 5 } > \frac{ 5 \times -3 }{ -3 }$$x > 5$

8. jackyluvv

so is it a?

9. Aylin

Look for the one that doesn't have x > 5

10. jackyluvv

oh i thought it was suppose to have that lol

11. jackyluvv

you have helped me a lot thank you

12. Aylin

You're welcome


text:
# MathSciDoc: An Archive for Mathematician ∫

#### Optimization and ControlConvex and Discrete Geometry mathscidoc:1705.27001

SIAM Journal on Imaging Sciences, 8, (4), 2239-2267, 2015
The alternating direction method of multipliers (ADMM) is a popular and efficient first-order method that has recently found numerous applications, and the proximal ADMM is an important variant of it. The main contributions of this paper are the proposition and the analysis of a class of inertial proximal ADMMs, which unify the basic ideas of the inertial proximal point method and the proximal ADMM, for linearly constrained separable convex optimization. This class of methods are of inertial nature because at each iteration the proximal ADMM is applied to a point extrapolated at the current iterate in the direction of last movement. The recently proposed inertial primal-dual algorithm [A. Chambolle and T. Pock, On the ergodic convergence rates of a first-order primaldual algorithm, preprint, 2014, Algorithm 3] and the inertial linearized ADMM [C. Chen, S. Ma, and J. Yang, arXiv:1407.8238, eq. (3.23)] are covered as special cases. The proposed algorithmic framework is very general in the sense that the weighting matrices in the proximal terms are allowed to be only positive semidefinite, but not necessarily positive definite as required by existing methods of the same kind. By setting the two proximal terms to zero, we obtain an inertial variant of the classical ADMM, which is to the best of our knowledge new. We carry out a unified analysis for the entire class of methods under very mild assumptions. In particular, convergence, as well as asymptotic $o(1/\sqrt{k})$ and nonasymptotic $O(1/\sqrt{k})$ rates of convergence, are established for the best primal function value and feasibility residues, where k denotes the iteration counter. The global iterate convergence of the generated sequence is established under an additional assumption. We also present extensive experimental results on total variation–based image reconstruction problems to illustrate the profits gained by introducing the inertial extrapolation steps.
alternating direction method of multipliers (ADMM), proximal point method (PPM), inertial PPM, proximal ADMM, inertial proximal ADMM
@inproceedings{caihua2015inertial,
title={Inertial Proximal ADMM for Linearly Constrained Separable Convex Optimization},
author={Caihua Chen, Raymond H. Chan, Shiqian Ma, and Junfeng Yang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530124951840325757},
booktitle={SIAM Journal on Imaging Sciences},
volume={8},
number={4},
pages={2239-2267},
year={2015},
}

Caihua Chen, Raymond H. Chan, Shiqian Ma, and Junfeng Yang. Inertial Proximal ADMM for Linearly Constrained Separable Convex Optimization. 2015. Vol. 8. In SIAM Journal on Imaging Sciences. pp.2239-2267. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170530124951840325757.


text:
# “… including any attempts you have made to solve it.”

Me again. Blind application of that criterion "ideally including any attempts you have made to solve it" just seems silly for some problems.

Consider this question. Seems like an excellent question to me - surely it's at least curious that such a bad question got four upvotes?

I mean I understand the point to the "missing context... include your attempts to solve it" thing - we want to discourage students from thoughtlessly asking routine questions that can be solved by standard methods covered in class. But this question is not that - if someone asked this question in class I'd be infinitely pleased to have such a thoughtful student.

Seems to me the difference between this question and the typical PSQ question that deserves to be closed is that MSE is a better place with this question than without it.

The "context" is clear from the, erm, context: We know that if $f$ is continuous it has an antiderivative; what sort of weaker result can we obtain under weaker hypotheses?

And regarding attempts to solve it, it's an actual problem, not an exercise - I spent all morning yesterday thinking about it and there's more or less nothing I could say about my "attempts to solve it". I mean I didn't "attempt" to make $F(x)=\int_0^x f(t) dt$ work because it's immediately obvious that the integral need not exist. And I have no idea what else I might "attempt".

Hence, to satisfy the people who are going to ask what my question is:

Question: Can anyone give me a hypothetical example of something the OP might have said about "attempts to solve it"?

If yes that would be great, might help me solve it. If, as I suspect, no, then closing it for that reason just seems wrong.

(Before making insulting conjectures regarding my motivation here you should note that I saw the OP had accepted my answer before seeing the question had been closed, and my reaction was to comment that the answer really shouldn't be accepted, since after all it didn't actually answer the question. Of course my saying that leads to the question of what the point to my answer was. The point was to point out that a counterexample must be fairly hairy, to save people from wasting time trying to construct counterexamples that can't possibly work.)

• Blind application of that criterion "ideally including any attempts you have made to solve it" just seems silly for some problems. Sure, I agree. That is why we have multiple methods to supply context, because we can't always rely on each one individually to be present. Are you under the impression that this one phrase is a deal-breaking criterion that people rely on for closing questions? Maybe for some, but I don't think many. In the case you mention, I think context could be pulled into this post from the previous related posts and the context passes muster. – rschwieb Jul 19 '18 at 13:55
• In other words, this question about "what could have been said about attempts to solve it" is misguided, the straw-man being that the forum rules closed the question for that specific reason (and not for other reasons) A question can have sufficient context without much in the way of a solution. The preceding questions for that user that led up to this question is a great example. – rschwieb Jul 19 '18 at 13:57
• @rschwieb Well, strawman or not, that's the reason given. And I can't think of another reason people might have had. Regarding pulling in context from the previous related posts, the OP did include links to two related posts... (Oh, maybe I misunderstood you - perhaps your point was that the OP did supply context this way?) – David C. Ullrich Jul 19 '18 at 13:59
• It is not the reason given: it is one of many pieces of generic advice beneath the reason given. Context takes many forms, not just attempts to solve. And, as I mention, I think the question has barely enough context to continue as opened. But I disagree with the premise of this post, that's all. If it hadn't already been reopened before I could cast a reopen vote, my name would be on the list. – rschwieb Jul 19 '18 at 14:00
• It also looks a bit like many of the poster's questions are weakly supported, so that may have had something to do with it. Like it or not, we all have to find some way of compromising in order to handle users who just simply post hard questions without context. I bet, though, if you went straight to the Reopen thread, it would have sailed through to reopening too. – rschwieb Jul 19 '18 at 14:05
• I voted to reopen. I have no idea what/where this "reopen thread" might be... – David C. Ullrich Jul 19 '18 at 14:11
• Perhaps it is worth saying that the full text of the missing context close reason is this (it includes the link): "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Martin Sleziak Jul 19 '18 at 14:12
• I'm also of the opinion that not every question should require such song and dance. A directly stated, sufficiently interesting question inherently satisfies its own requirements for context, if you ask me, at least from a closure standpoint. This is why people should not be voting based on question format alone. – Alexander Gruber Jul 19 '18 at 14:12
• Re: This is now moot, since the question in question has been reopened. Well, as you can see, the question already has a close vote now, so maybe there is no hurry to remove the meta thread. And since even among experienced users there seemed to be lack of clarity in what ways can context be provided, I think that discussion could be useful even if the question has already been reopened. – Martin Sleziak Jul 19 '18 at 14:19
• @DavidC.Ullrich Here's the thread: Requests for Reopen & Undeletion Votes (volume 07/2018 - today) An incarnation of this thread has been around for at least four years continuously, I think, and is referenced by numerous meta threads. – rschwieb Jul 19 '18 at 14:35
• @MartinSleziak Thanks, but I don't see how the full text changes anything here. First/again, I don't see what she could have said about her attempts, and nobody's made any suggestion in that regard. Is there is in fact nothing she could say about that then the rest of the text, explaining why it would be a good thing, seems irrelevant. "helps others identify where you have difficulties": Right, if it's a routine question. But here, since nobody has any idea how to solve it, people can't point out what she's missing... – David C. Ullrich Jul 19 '18 at 14:36
• @DavidC.Ullrich That would be tantamount to removing closure entirely, since 5 accounts could re-open every question permanently. But yeah, it also seems suboptimal to have no controls on how often/fast a question goes open/shut. Hard to do without tying the hands of our progeny and future selves. – rschwieb Jul 19 '18 at 15:26
• @DavidC.Ullrich I think the existing practice is already quite fair: when a user voted to close a post (and the post is closed because of their vote), they cannot vote to close it again if the post is reopened. – user99914 Jul 19 '18 at 16:05
• @rschwieb There is some limit on how often/quickly a question can cycle between open and closed, as one can only cast one close vote per question (perhaps per unit of time?). Thus once a question is reopened, the original closers cannot re-close it. – Xander Henderson Jul 19 '18 at 16:12
• @DavidC.Ullrich You keep asking for something else that the original asker could have added to improve the question. On a question like this, some explanation of why the question is interesting might be in order. For example your non-answer answer does a nice job of showing why the question is interesting, and several of the comments below that answer provide additional context. I would also like to suggest that the question you should be asking is not "What else could the OP have done?" and instead ask "What else can the OP do now?", with the goal being to end up with a good question. – Xander Henderson Jul 19 '18 at 16:17

## 1 Answer

I will repeat that the full text of the banner displayed after the question is put on hold looks like this:

This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level.

In particular, it links to: How to ask a good question. This FAQ item has also a section called Provide Context. You can see there that showing your own attempts is not the only possibility how to add context. In fact, many users advocate that other forms of context are quite often better (although perhaps they might be more difficult to provide by the asker). See the discussion here: Can we stop the “Show your work craze”?.

So even in the cases where it is difficult for the OP to show their work, they might have other options.

The question you are asking about at the time when it was closed looked like this:

Let $f:\mathbb{R}\to \mathbb{R}$ be continuous at $x$ for every $x\in I$ where $I\subset \mathbb R$ . Does there always exist a function $F:\mathbb{R}\to \mathbb{R}$ differentiable on $I$ and $F'(x) = f(x)$ for every $x \in I$. ?

Correct definition of antiderivative function

Existence of an antiderivative for a continuous function on an arbitrary subset of $\mathbb{R}$

You said yourself in the question here on meta:

The "context" is clear from the, erm, context: We know that if $f$ is continuous it has an antiderivative; what sort of weaker result can we obtain under weaker hypotheses?

The OP did not mention even that they know this.

Moreover, there were two links (one to another question, the other one to an answer) in the question without even mentioning what is the purpose of those links.

The same user asked several questions close to this one:

Adding a few words what the OP learned from those question and how they are actually different from this one could count as context too.

Personally, I would consider something like this certainly a sufficient context. (Although I'd guess I'm much less strict about context than most users.)


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# In Ireland, which of the following is known as “the Black Stuff”?

In Ireland, which of the following is known as “the Black Stuff”?

Guinness

Asphalt

Oil

Ground pepper


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# Browse by Journal

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Number of items: 20.

## B

 Brown, Brian Malcolm, Eastham, M.S.P., Wood, Ian (2009) Estimates for the lowest eigenvalue of a star graph. Journal of Mathematical Analysis and Applications, 354 (1). pp. 24-30. ISSN 0022-247X. (doi:10.1016/j.jmaa.2008.12.014) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:23936)

 Brown, B. Malcolm, Klaus, Martin, Malamud, Mark, Mogilevskii, Vadim, Wood, Ian (2019) Weyl Solutions and $$j$$-selfadjointness for Dirac Operators. Journal of Mathematical Analysis and Applications, 480 (2). ISSN 0022-247X. (doi:10.1016/j.jmaa.2019.07.034) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided) (KAR id:75785)

## C

 Common, Alan K., Sommen, F. (1993) Axial monogenic functions from holomorphic-functions. Journal of Mathematical Analysis and Applications, 179 (2). pp. 610-629. ISSN 0022-247X. (doi:10.1006/jmaa.1993.1372) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:20849)

 Common, Alan K. (1995) BI-Axial Gegenbauer Functions of the 2nd Kind. Journal of Mathematical Analysis and Applications, 190 (3). pp. 725-737. ISSN 0022-247X. (doi:10.1006/jmaa.1995.1106) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:19766)

 Constantin, Olivia (2010) Carleson embeddings and some classes of operators on weighted Bergman spaces. Journal of Mathematical Analysis and Applications, 365 (2). pp. 668-682. ISSN 0022-247X. (doi:10.1016/j.jmaa.2009.11.035) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31287)

 Constantin, Olivia, Ortega-Cerda, Joaquim (2011) Some spectral properties of the canonical solution operator to dbar on weighted Fock spaces. Journal of Mathematical Analysis and Applications, 377 (1). pp. 353-361. ISSN 0022-247X. (doi:10.1016/j.jmaa.2010.10.074) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31259)

 Common, Alan K., Sommen, F. (1994) Special Bi-Axial Monogenic Functions. Journal of Mathematical Analysis and Applications, 185 (1). pp. 189-206. ISSN 0022-247X. (doi:10.1006/jmaa.1994.1241) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:20465)

## D

Deaño, Alfredo, Huertas, Edmundo, Román, Pablo (2016) Asymptotics of orthogonal polynomials generated by a Geronimus perturbation of the Laguerre measure. Journal of Mathematical Analysis and Applications, 433 (1). pp. 732-746. ISSN 0022-247X. (doi:10.1016/j.jmaa.2015.08.002) (KAR id:51338)
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 Deaño, Alfredo, Huertas, Edmundo, Marcellán, Francisco (2013) Strong and ratio asymptotics for Laguerre polynomials revisited. Journal of Mathematical Analysis and Applications, 403 (2). pp. 477-486. ISSN 0022-247X. (doi:10.1016/j.jmaa.2013.02.039) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:70214)

## L

 Lipovan, Olivia (2006) Integral inequalities for retarded Volterra equations. Journal of Mathematical Analysis and Applications, 322 (1). pp. 349-358. ISSN 0022-247X. (doi:10.1016/j.jmaa.2005.08.097) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31552)

 Loureiro, Ana F. (2010) New results on the Bochner condition about classical orthogonal polynomials. Journal of Mathematical Analysis and Applications, 364 (2). pp. 307-323. ISSN 0022-247X. (doi:10.1016/j.jmaa.2009.12.003) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31561)

 Liu, Wenbin, Barrett, John W. (1993) A Remark on the Regularity of the Solutions of the p-Laplacian and Its Application to Their Finite Element Approximation. Journal of Mathematical Analysis and Applications, 178 (2). pp. 470-487. ISSN 0022-247X. (doi:10.1006/jmaa.1993.1319) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:36855)

 Loureiro, Ana F., Maroni, P., Rocha, Z. da (2006) The generalised Bochner condition about classical orthogonal polynomials revisited. Journal of Mathematical Analysis and Applications, 322 (2). pp. 645-667. ISSN 0022-247X. (doi:10.1016/j.jmaa.2005.09.026) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31538)

 Lipovan, Olivia (2000) A retarded Gronwall-like inequality and its applications. Journal of Mathematical Analysis and Applications, 252 (1). pp. 389-401. ISSN 0022-247X. (doi:10.1006/jmaa.2000.7085) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31641)

 Lipovan, Olivia (2003) A retarded integral inequality and its applications. Journal of Mathematical Analysis and Applications, 285 (2). pp. 436-443. ISSN 0022-247X. (doi:10.1016/S0022-247X(03)00409-8) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:31573)

## M

 Mansfield, Elizabeth L. (1999) The nonclassical group analysis of the heat equation. Journal of Mathematical Analysis and Applications, 231 (2). pp. 526-542. ISSN 0022-247X. (doi:10.1006/jmaa.1998.6250) (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:16919)

## P

Portaluri, Alessandro, Waterstraat, Nils (2013) On bifurcation for semilinear elliptic Dirichlet problems and the Morse-Smale index theorem. Journal of Mathematical Analysis and Applications, 408 (2). pp. 572-575. ISSN 0022-247X. (doi:10.1016/j.jmaa.2013.06.037) (KAR id:51396)
 Preview

Portaluri, Alessandro, Waterstraat, Nils (2014) On bifurcation for semilinear elliptic Dirichlet problems on geodesic balls. Journal of Mathematical Analysis and Applications, 415 (1). pp. 240-246. ISSN 0022-247X. (doi:10.1016/j.jmaa.2014.01.064) (KAR id:51397)
 Preview

## R

 Rogers, Colin, Bassom, Andrew P., Clarkson, Peter (2018) On integrable Ermakov-Painlevé IV systems. Journal of Mathematical Analysis and Applications, 462 (2). pp. 1225-1241. ISSN 0022-247X. (doi:10.1016/j.jmaa.2018.02.025) (KAR id:66116)

Roelands, Mark, Schwanke, C. (2019) Series and power series on universally complete complex vector lattices. Journal of Mathematical Analysis and Applications, 473 (2). pp. 680-694. ISSN 0022-247X. (doi:10.1016/j.jmaa.2018.12.041) (KAR id:80086)
 Preview

This list was generated on Tue Jul 14 00:26:59 2020 BST.


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# Summations on the same expression do not give the same result?

Posted 1 year ago
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 Hey guys:When I tried to take summation with respect to my expression Pmoe, I found that the Mathematica does not give consistent results if I put the summation symbol in different places. Please see my attachment where I use Pmoe1 and Pmoe2 to represent two different ways of summation, which should give the same result. It turns out that Pmoe1 is correct if you let Mathematica give values for each i and then sum all the values up. Appreciate anyone who can explain it a bit more.Thanks in advance. Attachments:
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Posted 1 year ago
 In your definition of Pmoe if you change = to := then the results of the two tables are identical.If you study the help pages for = and := then perhaps this will help you begin to understand the difference.The difference in your example depends on when the right hand side of Pmoe will be evaluated.
Posted 1 year ago
 Sorry I am not convinced.My question is why Pmoe1 and Pmoe2 are different, which are both defined by :=.My understanding for := is that the expression is evaluated on request and for = is that the expression is evaluated immediately. However, Pmoe1 and Pmoe2 equal in theoretical sense, which imply they have the values no matter when they are evaluated. I also tried to increase the precision level and the result do not change.
 I have a suspicion something is funky with the symbolic solution to the inner sum that produces the Hypergeometric1F1. When you use Set to define Pmoe, then Simplify[Pmoe1[A, \[Alpha], \[Beta], t, 1] == Pmoe2[A, \[Alpha], \[Beta], t, n] /. n -> 1] is True, but neither equals Pmoe2[A, \[Alpha], \[Beta], t, 1] that has already had the symbolic sum taken. On the other hand, using SetDelayed to define Pmoe we have Simplify[Pmoe1[A, \[Alpha], \[Beta], t, 1] == Pmoe2[A, \[Alpha], \[Beta], t, 1]] is True, but neither equals Pmoe2[A, \[Alpha], \[Beta], t, n] /. n -> 1. I think this means there is agreement only when the inner sum is either taken first or not taken first, but I am honestly a bit confused here.


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## Weekly review: week from 2012-04-22 to 05-05

### Last week

• Work
• [-] Continue to work on robust schedulability, try to finish, including coding.
• [X] Set up files for thesis (LaTeX, orgmode,…)
• [-] Work on/Write safe set computation & robust.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [X] MLE+ plan (with R’s students).
• [X] RTSS plan (with R and M).
• [ ] Read RL & continue to develop ML-based scheduling.
• [X] Update BibTeX of papers & docs.
• Later: attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design.
• Personal
• [-] Keep healthy lifestyle and exercise.
• [ ] Brainstorm and Plan.

### Plan for next week

• Work
• [ ] RTSS
• [ ] Finish robust schedulability, coding and example.
• [ ] Finish safe set computation & robust on paper & mindmap.
• [ ] Import all papers on desktop to BibTex & mindmap.
• [ ] Gather & organize all my hand writings.
• [ ] Habit of reviewing, updating, backing up my plan, results, references, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Check on MLE+ progress.
• Later: attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, ML-based scheduling.
• Personal
• [ ] Keep healthy lifestyle and exercise.
• [ ] Insurance & credit card for wife.
• [ ] Financial management.
• [ ] Clean up house.
• [ ] Brainstorm and Plan.

## Weekly review: week from 2012-04-15 to 04-21

### Last week

I decided not going to Germany.

• Work
• [X] Work on robust optimization & robust schedulability.
• [-] Work on/Write safe set computation & robust.
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [-] Read RL & continue to develop ML-based scheduling.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Update BibTeX of papers & docs.
• [0/10] Update ideas on mindmaps/outline:
• [ ] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability: how to solve optim
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [ ] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• Later: write up proofs and results I have so far, Update literature (BibTeX), attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, brainstorm MLE+.
• Personal
• [ ] Try to keep healthy lifestyle, exercise.
• [X] Make appointment for US visa in Canada.
• [X] Check out German visa requirements & procedure.
• [X] VEF DS-2019.
• [X] Preparation for H to US.

### Plan for next week

• Work
• [ ] Continue to work on robust schedulability, try to finish, including coding.
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [ ] Work on/Write safe set computation & robust.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] MLE+ plan (with R’s students).
• [ ] RTSS plan (with R and M).
• [ ] Read RL & continue to develop ML-based scheduling.
• [ ] Update BibTeX of papers & docs.
• [0/11] Update ideas on mindmaps/outline:
• [ ] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability
• [ ] robust periodic scheduling
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [ ] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• Later: attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design.
• Personal
• [ ] Keep healthy lifestyle and exercise.
• [ ] Brainstorm and Plan.

Posted in Weekly | 1 Comment

## Geometric computation and plotting with Yalmip

Yalmip is modeling language in Matlab for mathematical optimization (or programming in the language of Operation Research). There are many excellent optimization solvers out there, for Matlah or not, commercial or free or open source. However, each of them uses a different programming and modeling interface. Some are quite difficult to use. Most require you to transform your optimization problems into a standard form to be able to solved by the solver. Thus, it is unintuitive. Furthermore, in many practical applications, you must apply many technical tricks to transform or approximate your problems just to be able to solve them (efficiently). Manually doing this is both time-consuming and error-prone, and you may not know all the tricks, especially if you are not an expert.

Yalmip solves these difficulties by providing a consistent, well-designed, intuitive, and easy-to-use modeling language. The language is symbolic and uses a syntax very close to the mathematical languge used to formulate optimization problems. It also transforms your problems automatically, applies many useful tricks accurately, then calls external solvers to solve them for you. More information can be found on its website.

I have just discovered that Yalmip can also plot (constraint) sets. Basically, it samples the variable space with a grid and solves a sequence of optimization problems to calculate the feasible points. Then a (bounded convex) representation of the constraint set can be formed and plotted. This has been available in Yalmip for quite a while, but I only discovered it when I needed to plot a complex set and MPT could not handle the task. This feature is very helpful. To plot standard geometric objects such as a polytope or an ellipsoid, Yalmip is much slower than a specialized toolbox like MPT, but it is more flexible and more powerful. Therefore, you should stick to specialized toolboxes for standard objects, and use Yalmip for the rest.

Another more useful feature of Yalmip is the ability to perform geometric computation, such as Minkowski sum/difference and contracting/expanding sets. Examples can be found here. Although these computations can be performed by specialized toolboxes (MPT, ellipsoid), they are limited in capability. For example, using the polytope class in MPT, you can only compute the Minkowski difference between polytopic sets. Minkowski difference between a polytope and an ellipsoid (essentially shifting and contracting the polytope in a metric defined by the ellipsoid) can however be carried out by Yalmip, using its robust optimization framework and the robustify command. Another example is the range computation of a polytopic set, i.e. $\{ y | y = A x + b, x \in P\}$ where $P$ is a polytope, $A$ and $b$ are given matrix and vector. MPT can only compute this set if $A$ is non-singular (and of course, square). With Yalmip, you are able to compute this set when $A$ is singular and even non-square. Depending on the set and the dimensions you are working on, the computation can be very heavy and time-consuming, but at least it is possible.

All these computations will be implemented in a collection of Matlab functions for my research, and will be published on my github account.

## Weekly review: week from 2012-04-08 to 04-14

### Last week

• Work
• [X] Develop ML-based scheduling: finish experiment(s).
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [X] Code and plan for RTSS, delegate tasks to M.
• [-] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Start writing up hybrid computation.
• [2/10] Update ideas on mindmaps/outline:
• [X] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability: how to solve optim
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [X] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• [ ] (Optional) Work on robust optimization & robust schedulability.
• Later: write up proofs and results I have so far, Update literature (BibTeX), attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, brainstorm MLE+.
• Personal
• [-] Try to keep healthy lifestyle, exercise.
• [-] Make appointment for US visa in Canada, pay if necessary.
• [ ] Check out German visa requirements & procedure.
• [X] List of docs for wife’s visa, e.g. letter, bank statement, etc.
• [ ] Develop vision & plan (Hyatt).

### Plan for next week

• Work
• [ ] Work on robust optimization & robust schedulability.
• [ ] Work on/Write safe set computation & robust.
• [ ] Set up files for thesis (LaTeX, orgmode,…)
• [ ] Read RL & continue to develop ML-based scheduling.
• [ ] Habit of reviewing, updating, backing up my plan, results, data for thesis.
• [ ] Habit of writing a bit each day.
• [ ] Update BibTeX of papers & docs.
• [0/10] Update ideas on mindmaps/outline:
• [ ] ML scheduling
• [ ] hybrid computation: maximal safe set, approximation
• [ ] robust schedulability: how to solve optim
• [ ] multi-agent view (cf. the other thesis)
• [ ] hierarchical scheduling
• [ ] performance of periodic sched (J’s paper, my TECS)
• [ ] multiple modes
• [ ] system ID???
• [ ] adaptive???
• [ ] applications, implementation/simulation: need to update weekly
• Later: write up proofs and results I have so far, Update literature (BibTeX), attracting set for schedulability of more general dynamics, ML – bandit, tech report for CDC paper, mechanism design, brainstorm MLE+.
• Personal
• [ ] Try to keep healthy lifestyle, exercise.
• [ ] Make appointment for US visa in Canada.
• [ ] Check out German visa requirements & procedure.
• [ ] VEF DS-2019.
• [ ] Preparation for H to US.


text:
592 views

An algorithm is made up pf two modules $M1$ and $M2.$ If order of $M1$ is $f(n)$ and $M2$ is $g(n)$ then the order of algorithm is

1. $max(f(n),g(n))$
2. $min(f(n),g(n))$
3. $f(n) + g(n)$
4. $f(n) \times g(n)$

option A) max(f(n),g(n))
COMPLEXITY   BETTER

TO TAKE WROST CASE  SO WE GO WITH OPTION  A

option A will be correct

In order to find the order of the algorithm, there are three possible cases with f(n) and g(n)
Case-1 : if f(n) > g(n)
In this case we take O(f(n)) the complexity of the algorithm as g(n) is a lower order term, we can ignore this one .
Case-2 : f(n) < g(n)
In this case we take O(g(n)) the complexity of the algorithm as f(n) is a lower order term, we can ignore this one.
Case-3: f(n) = g(n)
Time Complexity can be either O(g(n)) or O(f(n)) (which is equal asymptotically). So the order of the algorithm is max(f(n), g(n))


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# Undirected graph G that has 12 vertices, 66 edges and 3 connected components?

Why would it be impossible to draw an undirected graph G that has 12 vertices, with 3 connected components if G had 66 edges?

• What have you tried? Where did you get stuck? We do not want to just do your (home-)work for you; we want you to gain understanding. However, as it is we do not know what your underlying problem is, so we can not begin to help. See here for a relevant discussion. If you are uncertain how to improve your question, why not ask around in Computer Science Chat? You may also want to check out our reference questions. – Raphael Jun 12 '15 at 11:45

Hint. How many edges does the complete graph on 12 vertices have?

• I am not sure about this but the complete question goes like this. (Draw a simple undirected graph G that has 12 vertices, 18 edges, and 3 connected components. Why would it be impossible to draw G with 3 connected components if G had 66 edges?) – amulamul Jun 11 '15 at 23:44

Consider the following problem:

What is the possible maximum number of edges in $G$, which has 12 vertices and consists of 3 components (I assume that loops and multiple edges are not allowed)?

Let $n_1, n_2, n_3$ be the numbers of vertices in the three separated components. Then you are lookin for

$$\max \frac{n_1(n_1 - 1)}{2} + \frac{n_2 (n_2 - 1)}{2} + \frac{n_3 (n_3 - 1)}{2}$$ $$\text{subject to } n_1 + n_2 + n_3 = 12$$

An optimal (intuitive) solution is $n_1 = n_2 = 1, n_3 = 10$ and the maximum value is 45.


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# 6.29: Error-Correcting Codes - Hamming Codes

Learning Objectives

• A description of some strategies for minimizing there errors in a transmitted bit-stream.

For the (7,4) example, we have 2N-K -1 =7 error patterns that can be corrected. We start with single-bit error patterns, and multiply them by the parity check matrix. If we obtain unique answers, we are done; if two or more error patterns yield the same result, we can try double-bit error patterns. In our case, single-bit error patterns give a unique result.

This corresponds to our decoding table: We associate the parity check matrix multiplication result with the error pattern and add this to the received word. If more than one error occurs (unlikely though it may be), this "error correction" strategy usually makes the error worse in the sense that more bits are changed from what was transmitted.

As with the repetition code, we must question whether our (7,4) code's error correction capability compensates for the increased error probability due to the necessitated reduction in bit energy. Fig. 6.29.1 shows that if the signal-to-noise ratio is large enough channel coding yields a smaller error probability. Because the bit stream emerging from the source decoder is segmented into four-bit blocks, the fair way of comparing coded and uncoded transmission is to compute the probability of block error: the probability that any bit in a block remains in error despite error correction and regardless of whether the error occurs in the data or in coding buts. Clearly, our (7,4) channel code does yield smaller error rates, and is worth the additional systems required to make it work.

Fig. 6.29.1 The probability of an error occurring in transmitted K=4 data bits equals (1-pe)4 equals the probability that the four bits are received without error. The upper curve displays how this probability of an error anywhere in the four-bit block varies with the signal-to-noise ratio. When a (7,4) single-bit error correcting code is used, the transmitter reduced the energy it expends during a single-bit transmission by 4/7, appending three extra bits for error correction. Now the probability of any bit in the seven-bit block being in error after error correction equals pe' (1-pe' where pe' is the probability of a bit error occurring in the channel when channel coding occurs. Here (7pe' (1-pe' equals the probability of exactly on in seven bits emerging from the channel in error; The channel decoder corrects this type of error, and all data bits in the block are received correctly.

Note that our (7,4) code has the length and number of data bits that perfectly fits correcting single bit errors. This pleasant property arises because the number of error patterns that can be corrected, 2N-K -1, equals the codeword length N. Codes that have 2N-K -1 = N are known as Hamming codes, and the following table provides the parameters of these codes. Hamming codes are the simplest single-bit error correction codes, and the generator/parity check matrix formalism for channel coding and decoding works for them.

Unfortunately, for such large blocks, the probability of multiple-bit errors can exceed the number of single-bit errors unless the channel single-bit error probability pe is very small. Consequently, we need to enhance the code's error correcting capability by adding double as well as single-bit error correction.

Exercise $$\PageIndex{1}$$

What must the relation between N and K be for a code to correct all single- and double-bit errors with a "perfect fit"?

Solution

In a length-N block, N single-bit and $\frac{N(N-1)}{2}$ double-bit errors can occur. The number of non-zero vectors resulting from $H\hat{c}$ must equal or exceed the sum of these two numbers.

$2^{N-K}-1\geq N+\frac{N(N-1)}{2}\; or\; 2^{N-K}\geq \frac{N^{2}+N+2}{2}$

The first two solutions that attain equality are (5,1) and (90,78) codes. However, no perfect code exists other than the single-bit error correcting Hamming code.

### Contributor

•  ContribEEOpenStax


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Status Documentation

# Whisper - Extended Features

## Deeper Down The Rabbit Hole

If you’re up for it, you can instead dive directly into the protocol specification.

Whisper is an identity-based messaging system which provides a non-application-specific API without being prejudiced by low-level hardware attributes and characteristics, particularly the notion of singular endpoints.

Alternatively, Whisper may be likened to a DHT with a per-entry configurable time-to-live (ttl) and conventions for the signing and encryption of values. Whisper also allows for the same entry to have multiple keys, some or all of which may be the same as other entries, which leads to collisions and is another means by which Whisper ensures plausible deniability.

## Envelopes

Envelopes are like items should you think of Whisper as a DHT. Should Whisper be considered a datagram messaging system, then envelopes become the packet format which house encrypted datagrams. Envelopes are necessarily comprehensible by any node (i.e. they themselves are unencrypted).

Envelopes are transmitted as RLP-encoded structures. The precise definition is given by:

[expiry: P, ttl: P, [topic0: B_4, topic1: B_4, ...], data: B, nonce: P]

param Description
expiry 4 bytes (the intended expiry UNIX time for the envelope in seconds).
ttl 4 bytes (time-to-live in seconds).
topic 4 bytes of arbitrary data. Can be an array.
data byte array of arbitrary size (contains encrypted message).
nonce 8 bytes of arbitrary data. This is used for the PoW calculation, calculated by taking the SHA3 of the concatenation of the nonce with the RLP packet less the nonce. The smaller it is, the higher the work proved.
AESNonce 12 bytes of random data (only present in case of symmetric encryption).

While envelopes are not encrypted, Whisper nodes know nothing about content of envelopes which they cannot decrypt.

## Topics

Topics are short strings - hashes to be precise - which are set by the sender (or at the application layer) and help categorize messages. In more technical language: topics are cryptographically secure, probabilistic, partial-classifications of the message.

Nodes pass envelopes around regardless of their ability to decode the message as this is an important component in Whisper’s dark communications strategy (detailed in the next page).

Upon receipt of a message, if the node detects a known topic, it tries to decrypt the message with the corresponding key. In case of failure, the node assumes that a topic collision has occurred, e.g. the message was encrypted with another key, and should be just forwarded further. Collisions are not only expected, they are necessary for plausible deniability.

Four bytes was chosen to minimise space should a large number of topics be mentioned, while still keeping a sufficient amount of space to avoid large-scale topic-collision (though it may yet be reviewed and possibly made dynamic in later revisions of the protocol).

## Messages

A message is formed as the concatenation of a single byte for flags, followed by any additional data (as stipulated by the flags) and finally the actual payload (i.e. message). This series of bytes is what forms the data item of the envelope and is always encrypted.

In the present protocol version, no explicit authentication token is given to indicate that the data field is encrypted; any would-be readers of the message must know ahead of time, through the choice of topic that they have specifically filtered for, that the message is encrypted with a particular key. This is likely to be altered to include a MAC.

Any determination that the message is indeed from a particular sender is left for a higher-level to address. This is achieved through the Javascript API, which allows the _to parameter to be passed only at the point of specifying the filter. Since the signature is a part of the message and not outside the envelope, those unable to decrypt the message data are also unable to access any signature. Any message is therefore constructed as follows:

1. flags: 1 byte
2. (signature: 65 bytes)
3. auxiliary field: up to 4 bytes

The first 2 bits of the flags field specifies the size of the auxiliary field and the third bit indicates whether a signature is present. A message is invalid if bit 2 is set but the total data is less than 66 bytes (since this wouldn’t allow it to contain a signature).

Encrypting

All messages are encrypted. Asymmetric encryption uses the standard Elliptic Curve Integrated Encryption Scheme with a SECP-256k1 public key. Symmetric encryption uses AES GCM algorithm with random 96-bit nonce.

Payloads are encrypted in one of two ways. If the message has a specific recipient, then it is encrypted using ECIES with the specific recipient’s SECP-256k1 public key. If the message has no recipient, then we use AES-256 with a randomly generated key. This key is then XORed with each of the full topics to form a salted topic. Each salted topic is stored prior to the encrypted data in the same order as the corresponding topics are in the envelope header.

Decrypting

Recipients decrypt messages in one of two ways. Through the use of topics, it should be known whether the envelope is meant for a specific recipient (in which case, use the private key to decrypt) or to a general multicast audience. If intended for a general audience, we assume that at least one topic is known (since otherwise, the envelope could not be properly “identified”). In this case, we match the known full topic to one of the abridged topics in the envelope, determine the index and de-salt the according salted-key at the beginning of the data segment in order to retrieve the final key.

The signature, if provided, is the SHA3-256 hash of the unencrypted payload signed using ECDSA with the insertion-identity’s secret key.

The signature portion is formed as the concatenation of the r, s and v parameters of the SECP-256k1 ECDSA signature, in that order. v is non-normalised and should be either 27 or 28. r and s are both big-endian encoded, fixed-width 32-byte unsigned.

The payload is otherwise unformatted binary data.

In the Javascript API, the distinction between envelopes and messages is blurred. This is because DApps should know nothing about envelopes whose message cannot be inspected.

Here’s a picture for those who don’t like so many words:

## Bloom Filters

Bloom filters are a probabilistic data structure that we can use to verify the presence - or absence - of an item within a list, or collection. To be more specific, it can verify with certainty that an item is NOT in the list, and it can say with probability that item IS in the list. It can do this in a fairly fast and space-efficient way.

This gets technical, so buckle in. The Bloom filter is used to identify a number of topics I may be interested in to my peers without compromising (too much) my privacy over precisely what topics interest me. Precise control over the information content (and thus efficiency of the filter) may be maintained through the addition of bits and is something that can be implemented client side, i.e. by the user.

Bloom filters are formed by the bitwise OR operation on a number of bloomed topics. The bloom function takes the topic and projects them onto a 512-bit slice. At most, three bits are marked for each bloomed topic.

The projection function is defined as a mapping from a 4-byte slice S to a 512-bit slice D; for ease of explanation, S will dereference to bytes, whereas D will dereference to bits.

LET D[*] = 0
FOREACH i IN { 0, 1, 2 } DO
LET n = S[i]
IF S[3] & (2 ** i) THEN n += 256
D[n] = 1
END FOR

Further information can be found in EIP 627.

## PoW Actual Calculation

The Proof of Work for Whisper envelope is defined as the average number of iterations required to find the current BestBit (the number of leading zero bits in the hash), divided by message size and ttl:

PoW = (2**BestBit) / (size * TTL)

PoW calculation:

fn short_rlp(envelope) = rlp of envelope, excluding nonce field.
fn pow_hash(envelope, nonce) = sha3(short_rlp(envelope) ++ nonce)
fn pow(pow_hash, size, ttl) = 2**leading_zeros(pow_hash) / (size * ttl)

where size is the size of the full RLP-encoded envelope.

## What Does It All Mean?

All the above features combine into a dark system: i.e. one that is uncompromising when it comes to information leakage from metadata. In its most secure mode of operation, Whisper can (at a considerable cost of bandwidth and latency) deliver 100% dark operation. Even better, this applies not only for metadata collection from inter-peer conduits (i.e. backbone dragnet devices), but even against a much more arduous 100% - 2 attack; i.e. where every node in the network is compromised (though functional) save a pair running ÐApps for people that wanted to communicate without anybody else knowing.

:mind_blown:


text:
## Friday, 3 December 2010

### Interpretability and importance of functionals in competing risks and multi-state models

Per Kragh Andersen and Niels Keiding have a new paper currently available as a Department of Biostatistics, Copenhagen research report. They argue that three principles should be adhered to when constructing functionals of the transition intensities in competing risks and illness-death models. The principles are:

1. Do not condition on the future.
2. Do not regard individuals at risk after they have died.
3. Stick to this world.

They identify several existing ideas that violate these principles. Unsurprising, the latent failure times model for competing risks rightly comes under fire for violating (3), i.e. to say anything about hypothetical survival distributions in the absence of the other risks requires making untestable assumptions. Semi-competing risks analysis where one seeks the survival distribution for illness in the absence of death has the same problem.

The subdistribution hazard from the Fine-Gray model violates principle 2 because it involves the form $\inline P(X(t + dt) = j | X(t) \neq j)$. Andersen and Keiding say this makes interpretation of regression parameters difficult because they are log(subdistribution hazard ratios). The problem seems to be that many practitioners interpret the coefficients as if they are standard hazard ratios. The authors go on to say that linking covariates directly to cumulative incidence functions is useful. The distinction between this and the Fine-Gray model is rather subtle as in the Fine-Gray model (when covariates are not time dependent): $\inline CIF(t; Z) = 1 - \exp{(-H(t)\exp{(b^{T}Z)})}$ i.e. b is essentially interpreted as a parameter in a cloglog model.
The conditional probability function recently proposed by Allignol et al has similar problems with principle 2.

Principle 1 is violated in the pattern-mixture parametrisation. This is where we consider the distribution of event times conditional on the event type, e.g. the sojourn in state i given the subject moved to state j. This is used for instance in flow-graph Semi-Markov models.

A distinction that is perhaps needed that isn't really made clear in the paper is that there is a difference between violating the principles for mathematical convenience e.g. for model fitting and violating the principles in terms of the actual inferential output. Functionals to be avoided should perhaps be those where no easily interpretable transformation to a sensible measure is available. Thus a pattern-mixture parametrisation for a semi-Markov model without covariates seems unproblematic, since we can retrieve the transition intensities. However, when covariates are present the transition intensities will have complicated relationships to the covariates without an obvious interpretation.

**** UPDATE : The paper is now published in Statistics in Medicine. *****