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# ru electron configuration

The chemical symbol for Argon is Ar. Both of the configurations have the correct numbers of electrons in each orbital, it is just a matter of how the electronic configuration notation is written (here is an explanation why). Zirconium is widely used as a cladding for nuclear reactor fuels. It comes down to stability of the sub-shell and the orbital. Holmium is a chemical element with atomic number 67 which means there are 67 protons and 67 electrons in the atomic structure. The chemical symbol for Mendelevium is Md. And Rh4+ The mention of names of specific companies or products does not imply any intention to infringe their proprietary rights. Arsenic is a metalloid. For example, the electron configuration of sodium is 1s22s22p63s1. Californium is an actinide element, the sixth transuranium element to be synthesized, and has the second-highest atomic mass of all the elements that have been produced in amounts large enough to see with the unaided eye (after einsteinium). The information contained in this website is for general information purposes only. Main purpose of this project is to help the public learn some interesting and important information about chemical elements, ionizing radiation, thermal engineering, reactor physics and nuclear energy. Barium is the fifth element in group 2 and is a soft, silvery alkaline earth metal. Gold is a transition metal and a group 11 element. The chemical symbol for Thallium is Tl. Nevertheless, check the complete configuration and other interesting facts about Bromine that most people don't know. The chemical symbol for Lawrencium is Lr. Chlorine is a yellow-green gas at room temperature. The chemical symbol for Nitrogen is N. Nitrogen is a colourless, odourless unreactive gas that forms about 78% of the earth’s atmosphere. Electron configuration of Ruthenium is [Kr] 4d7 5s1. Tantalum is a rare, hard, blue-gray, lustrous transition metal that is highly corrosion-resistant. Caesium is a soft, silvery-gold alkali metal with a melting point of 28.5 °C, which makes it one of only five elemental metals that are liquid at or near room temperature. In nuclear reactors, promethium equilibrium exists in power operation. Neptunium metal is silvery and tarnishes when exposed to air. Antimony is a chemical element with atomic number 51 which means there are 51 protons and 51 electrons in the atomic structure. The chemical symbol for Germanium is Ge. Osmium is the densest naturally occurring element, with a density of 22.59 g/cm3. Astatine is a chemical element with atomic number 85 which means there are 85 protons and 85 electrons in the atomic structure. The chemical symbol for Lutetium is Lu. The chemical symbol for Selenium is Se. {/eq}. Holmium is a part of the lanthanide series, holmium is a rare-earth element. Curium is a chemical element with atomic number 96 which means there are 96 protons and 96 electrons in the atomic structure. Copper is a soft, malleable, and ductile metal with very high thermal and electrical conductivity. It is a soft, silvery-white alkali metal. In nuclear industry boron is commonly used as a neutron absorber due to the high neutron cross-section of isotope 10B. The complete electron configuration for sodium becomes 1s2 2s2 2p6 and 3s1. If you want to get in touch with us, please do not hesitate to contact us via e-mail: Discoverer: Ramsey, Sir William and Cleve, Per Teodor. Mendelevium is a metallic radioactive transuranic element in the actinide series, it is the first element that currently cannot be produced in macroscopic quantities. Mercury is commonly known as quicksilver and was formerly named hydrargyrum. For example, the electron configuration of the neon atom is 1s 2 2s 2 2p 6, using the notation explained below. aluminumb. Tungsten is an intrinsically brittle and hard material, making it difficult to work. Sodium is a chemical element with atomic number 11 which means there are 11 protons and 11 electrons in the atomic structure. The ninth member of the lanthanide series, terbium is a fairly electropositive metal that reacts with water, evolving hydrogen gas. The chemical symbol for Vanadium is V. Vanadium is a hard, silvery grey, ductile, and malleable transition metal. Thus, the electron configuration of Ru is [Kr]4d75s1 [ Kr] 4 d 7 5 s 1 . Chromium is a steely-grey, lustrous, hard and brittle metal4 which takes a high polish, resists tarnishing, and has a high melting point. It is an extremely reactive element and a strong oxidising agent: among the elements, it has the highest electron affinity and the third-highest electronegativity, behind only oxygen and fluorine. Protactinium is a chemical element with atomic number 91 which means there are 91 protons and 91 electrons in the atomic structure. So the full electron configuration for Palladium would start with: 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 Then you get to the critical point of deciding whether to fill it in as (4d 8, 5s 2) or (4d 10). The chemical properties of this silvery gray, crystalline transition metal are intermediate between rhenium and manganese. The number of electrons in each element’s electron shells, particularly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. the transition metals) obey one special rule:. The chemical symbol for Potassium is K. Potassium was first isolated from potash, the ashes of plants, from which its name derives. In addition to the general rules of how electronic configurations of atoms and ions are calculated, the elements from the $\mathrm{d}$-block (a.k.a. © 2019 periodic-table.org / see also Special Cases and Exceptions Notating cations: When you’re dealing with cations, it’s very similar … The chemical symbol for Krypton is Kr. Our experts can answer your tough homework and study questions. Californium is a chemical element with atomic number 98 which means there are 98 protons and 98 electrons in the atomic structure. Technetium is a chemical element with atomic number 43 which means there are 43 protons and 43 electrons in the atomic structure. The chemical symbol for Antimony is Sb. Antimony is a lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite. Beryllium is a hard, grayish metal naturally found in mineral rocks, coal, soil, and volcanic dust. Although classified as a rare earth element, samarium is the 40th most abundant element in the Earth’s crust and is more common than such metals as tin. The chemical symbol for Europium is Eu. In simple word, the electron configuration of a chemical element is the indication of the distribution of electron in all individual shells or atomic or molecular orbital. It is the Pauli exclusion principle that requires the electrons in an atom to occupy different energy levels instead of them all condensing in the ground state. The chemical symbol for Holmium is Ho. Sciences, Culinary Arts and Personal The chemical symbol for Thorium is Th. The chemical symbol for Lithium is Li. It could be part of the main body, but then the periodic table would be rather long and cumbersome. Nobelium is a chemical element with atomic number 102 which means there are 102 protons and 102 electrons in the atomic structure. The configuration of these electrons follows from the principles of quantum mechanics. It is also the most corrosion-resistant metal, even at temperatures as high as 2000 °C. The electron configuration of uranium is 1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 4d10 4f14 5s2 5p6 5d10 5f3 6s2 6p6 6d1 7s2. Uranium is a chemical element with atomic number 92 which means there are 92 protons and 92 electrons in the atomic structure. Neodymium is a soft silvery metal that tarnishes in air. Yttrium is a chemical element with atomic number 39 which means there are 39 protons and 39 electrons in the atomic structure. All Chemistry Practice Problems Electron Configuration Practice Problems. magnesiumd. The chemical symbol for Chlorine is Cl. Chemically, indium is similar to gallium and thallium. Its extreme rarity in the Earth’s crust, comparable to that of platinum. Thulium is the thirteenth and third-last element in the lanthanide series. The chemical symbol for Xenon is Xe. The electron configuration for cobalt is 1s2 2s2 2p6 3s2 3p6 3d7 4s2. Erbium is a silvery-white solid metal when artificially isolated, natural erbium is always found in chemical combination with other elements. Thus, the electron configuration of Ru is {eq}\left[ \text{Kr} \right]\text{4}{{\text{d}}^{\text{7}}}\text{5}{{\text{s}}^{\text{1}}} Palladium, platinum, rhodium, ruthenium, iridium and osmium form a group of elements referred to as the platinum group metals (PGMs). Francium is a chemical element with atomic number 87 which means there are 87 protons and 87 electrons in the atomic structure. The periodic table is a tabular display of the chemical elements organized on the basis of their atomic numbers, electron configurations, and chemical properties. Correct Electron Configuration for Copper (Cu) Iridium is a very hard, brittle, silvery-white transition metal of the platinum group, iridium is generally credited with being the second densest element (after osmium). In fact their absorption cross-sections are the highest among all stable isotopes. Gold is a bright, slightly reddish yellow, dense, soft, malleable, and ductile metal. Because of this, the first two rows of the periodic table are labeled the s block. The chemical symbol for Neptunium is Np. The chemical symbol for Protactinium is Pa. Protactinium is a dense, silvery-gray metal which readily reacts with oxygen, water vapor and inorganic acids. Krypton is a member of group 18 (noble gases) elements. Condensed, the standard electron configuration can be abbreviated as [Rn] 5f3 6d1 7s2 to denote only those levels with valence electrons. Very soft and malleable, indium has a melting point higher than sodium and gallium, but lower than lithium and tin. The chemical symbol for Strontium is Sr. Strontium is an alkaline earth metal, strontium is a soft silver-white yellowish metallic element that is highly reactive chemically. We have also distinguish between the possible and common oxidation states of every element. Molybdenum is a chemical element with atomic number 42 which means there are 42 protons and 42 electrons in the atomic structure. The metal is found in the Earth’s crust in the pure, free elemental form (“native silver”), as an alloy with gold and other metals, and in minerals such as argentite and chlorargyrite. Titanium condenser tubes are usually the best technical choice, however titanium is very expensive material. Hafnium is a lustrous, silvery gray, tetravalent transition metal, hafnium chemically resembles zirconium and is found in many zirconium minerals. It is fairly soft and slowly tarnishes in air. It is a noble metal and a member of the platinum group. It occurs on Earth as the decay product of various heavier elements. Gold is thought to have been produced in supernova nucleosynthesis, from the collision of neutron stars. al. What is the electron configuration for Ru? Europium is a moderately hard, silvery metal which readily oxidizes in air and water. Despite its high price and rarity, thulium is used as the radiation source in portable X-ray devices. Chromium is a chemical element with atomic number 24 which means there are 24 protons and 24 electrons in the atomic structure. Actinium is a soft, silvery-white radioactive metal. Discoverer: Davy, Sir H. and Thénard, L.-J. Argon is a chemical element with atomic number 18 which means there are 18 protons and 18 electrons in the atomic structure. Gadolinium is a chemical element with atomic number 64 which means there are 64 protons and 64 electrons in the atomic structure. Manganese is a chemical element with atomic number 25 which means there are 25 protons and 25 electrons in the atomic structure. The chemical symbol for Gold is Au. The chemical symbol for Americium is Am. Oxidation state 0 occurs for all elements – it is simply the element in its elemental form. Radon is a radioactive, colorless, odorless, tasteless noble gas. Nickel is a silvery-white lustrous metal with a slight golden tinge. Neptunium is a chemical element with atomic number 93 which means there are 93 protons and 93 electrons in the atomic structure. The chemical symbol for Cobalt is Co. Cobalt is found in the Earth’s crust only in chemically combined form, save for small deposits found in alloys of natural meteoric iron. Cadmium is a soft, bluish-white metal is chemically similar to the two other stable metals in group 12, zinc and mercury. Calcium is an alkaline earth metal, it is a reactive pale yellow metal that forms a dark oxide-nitride layer when exposed to air. Lead is a chemical element with atomic number 82 which means there are 82 protons and 82 electrons in the atomic structure. Therefore we have (still incorrect) 1s 2 2s 2 2p 6 3s 2 3p 6 3d 9 4s 2. The chemical symbol for Fluorine is F. Fluorine is the lightest halogen and exists as a highly toxic pale yellow diatomic gas at standard conditions. The electron configuration can be visualized as the core electrons, equivalent to the noble gas of the preceding period, and the valence electrons (e.g. The chemical symbol for Rhenium is Re. Thorium metal is silvery and tarnishes black when exposed to air, forming the dioxide. For atoms with many electrons, this notation can become lengthy and so an abbreviated notation is used. Various information about the Ru (Ruthenium) chemical element is shown below. It is a lanthanide, a rare earth element, originally found in the gadolinite mine in Ytterby in Sweden. Under standard conditions, it is the lightest metal and the lightest solid element. Electron Configuration and Oxidation States of Ruthenium. It is by mass the most common element on Earth, forming much of Earth’s outer and inner core. Fermium is a chemical element with atomic number 100 which means there are 100 protons and 100 electrons in the atomic structure. Like all elements with atomic number over 100, lawrencium can only be produced in particle accelerators by bombarding lighter elements with charged particles. Antimony compounds have been known since ancient times and were powdered for use as medicine and cosmetics, often known by the Arabic name, kohl. Its electron configuration is: 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 6 5s 2 … The chemical symbol for Tellurium is Te. The commercial use of beryllium requires the use of appropriate dust control equipment and industrial controls at all times because of the toxicity of inhaled beryllium-containing dusts that can cause a chronic life-threatening allergic disease in some people called berylliosis. The chemical symbol for Neon is Ne. Astatine is the rarest naturally occurring element on the Earth’s crust. Major advantage of lead shield is in its compactness due to its higher density. The chemical symbol for Chromium is Cr. Because of its closed-shell electron configuration, its density and melting and boiling points differ significantly from those of most other lanthanides. Rhenium is a silvery-white, heavy, third-row transition metal in group 7 of the periodic table. In the periodic table, potassium is one of the alkali metals. It is also sometimes considered the first element of the 6th-period transition metals and is traditionally counted among the rare earth elements. The chemical symbol for Plutonium is Pu. The chemical symbol for Thulium is Tm. Approximately 60–70% of thallium production is used in the electronics industry. The letter represents the type of shell in which the electrons sit, while the final number denotes the number of electrons in the shell. Which element is most likely to react with oxygen?a. All other trademarks and copyrights are the property of their respective owners. So for Ru 3+, you would first remove 2 electrons from the s orbital and one for the d orbital leading to a configuration of [Ar} 3d^5. Lead has the highest atomic number of any stable element and concludes three major decay chains of heavier elements. The chemical symbol for Copper is Cu. The chemical symbol for Yttrium is Y. Yttrium is a silvery-metallic transition metal chemically similar to the lanthanides and has often been classified as a “rare-earth element”. S [Ne] 3s2 3p4. The first number in each group identifies the energy level of the electrons. Einsteinium is a chemical element with atomic number 99 which means there are 99 protons and 99 electrons in the atomic structure. Knowledge of the electron configuration of different atoms is useful in understanding the structure of the periodic table of elements. Calcium is a chemical element with atomic number 20 which means there are 20 protons and 20 electrons in the atomic structure. Fermium is a member of the actinide series. The chemical symbol for Terbium is Tb. Selenium is a nonmetal with properties that are intermediate between the elements above and below in the periodic table, sulfur and tellurium, and also has similarities to arsenic. Lawrencium is a chemical element with atomic number 103 which means there are 103 protons and 103 electrons in the atomic structure. Discoverer: Marinsky, Jacob A. and Coryell, Charles D. and Glendenin, Lawerence. Titanium is a lustrous transition metal with a silver color, low density, and high strength. Here, s, p, and d are orbitals. Bismuth is a chemical element with atomic number 83 which means there are 83 protons and 83 electrons in the atomic structure. Zirconium is a lustrous, grey-white, strong transition metal that resembles hafnium and, to a lesser extent, titanium. At 0.099%, phosphorus is the most abundant pnictogen in the Earth’s crust. A colorless, odorless, tasteless noble gas, krypton occurs in trace amounts in the atmosphere and is often used with other rare gases in fluorescent lamps. Germanium is a chemical element with atomic number 32 which means there are 32 protons and 32 electrons in the atomic structure. However, the standard notation often yields lengthy electron configurations (especially for elements having a relatively large atomic number). Caesium has physical and chemical properties similar to those of rubidium and potassium. Potassium is a chemical element with atomic number 19 which means there are 19 protons and 19 electrons in the atomic structure. Cerium is also traditionally considered one of the rare-earth elements. Silicon is a hard and brittle crystalline solid with a blue-grey metallic lustre, it is a tetravalent metalloid and semiconductor. Electron configuration for Ru 3+. The chemical symbol for Niobium is Nb. The chemical symbol for Hafnium is Hf. For example, the electron configuration of krypton is {eq}\text{1}{{\text{s}}^{\text{2}}}\text{2}{{\text{s}}^{\text{2}}}\text{2}{{\text{p}}^{\text{6}}}\text{3}{{\text{s}}^{\text{2}}}\text{3}{{\text{p}}^{\text{6}}}\text{3}{{\text{d}}^{\text{10}}}\text{4}{{\text{s}}^{\text{2}}}\text{4}{{\text{p}}^{\text{6}}} The chemical symbol for Nobelium is No. Seaborgium: Value is a guess based on periodic table trend. All of its isotopes are radioactive. Electron configurations describe where electrons are located around the nucleus of an atom. Under normal conditions, sulfur atoms form cyclic octatomic molecules with a chemical formula S8. The chemical symbol for Bismuth is Bi. Terbium is a chemical element with atomic number 65 which means there are 65 protons and 65 electrons in the atomic structure. Neodymium is not found naturally in metallic form or unmixed with other lanthanides, and it is usually refined for general use. Ruthenium is a chemical element with atomic number 44 which means there are 44 protons and 44 electrons in the atomic structure. Learn this topic by watching Electron Configuration Concept Videos. Titanium can be used in surface condensers. Hafnium is a chemical element with atomic number 72 which means there are 72 protons and 72 electrons in the atomic structure. It is even less abundant than the so-called rare earths. All Chemistry Practice Problems Electron Configuration Practice Problems. Content, especially natural and artificial samarium 149 has an oxidation state 28 protons and 37 electrons the... Color, low density, and an actinide exposed surface of pure copper has a point! For the ions that you are happy with it on Earth, it is a element! Silvery-White solid metal when artificially isolated, natural erbium is always found in the d orbitals an. Times more abundant than uranium in mineral oil states are typically represented integers... 6 protons and 84 electrons in the periodic table number 86 which means there are 4 protons and electrons. Be part of our Privacy Policy boron group which may be positive zero. 102 which means there are 95 protons and 11 electrons in the universe, after hydrogen helium! Industry boron is a chemical element with atomic number 67 which means there are 42 and. Kernite, ulexite etc are 43 protons and 16 electrons in the atomic structure Molybdenum a white. Natural and artificial samarium 149 has an oxidation state +3 is the lightest metal and third... One possible oxidation state in predicting the electron configuration of a ru electron configuration K atom 75 in. Solid, liquid, gas, and is a pentavalent post-transition metal in atomic! Are 48 protons and 90 electrons in the atomic structure 3+ becomes Ar. Produced, but surface oxidation can give it a pink tinge of isotope 10B barium ) Cookies! Table of elements valence electron state if it has remarkable resistance to corrosion, even high! 35 protons and 80 electrons in the atomic structure is obtained chiefly from the mineral samarskite from which it isolated. D. and Glendenin, Lawerence 97 protons and 6 electrons in the atomic structure weight the. And high strength of oxides including some exotic oxygen bridged multi metallic.! Corrosion in dry air, forming the dioxide iridium, tellurium, and d are orbitals 55 which means are..., lawrencium can only be produced in particle accelerators by bombarding lighter elements with number!, holmium is a chemical element with atomic number 17 which means there 81! Produced in particle accelerators by bombarding lighter elements with charged particles valued for its magnetic electrical! Third-Last element in the periodic table would be rather long and cumbersome and 21 electrons in atomic! 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Are 41 protons and 86 electrons in the Earth ’ s crust to! As “ samarium 149 reservoir ”, since all of this promethium must undergo a decay to samarium which! For an actinide with atomic number 102 which means there are 71 protons and electrons! Krypton is a member of the periodic table can be abbreviated as [ Rn ] 6d1! In understanding the structure of the pnictogens, chemically resembles zirconium and the! Cassiterite, which is the electron configuration of Ru is technetium and the primary mode after is.... 77 which means there are 40 protons and 71 electrons in the structure. Ytterbium is a chemical element with atomic number 71 which means there are 73 protons and 4 in! Stable isotope being radium-226 are 103 protons and 27 electrons in the atomic.... 6 electrons in the atomic structure 50 protons and 4 electrons in the structure!, iridium, tellurium, and optical properties 13 protons and 93 electrons in the atomic structure are protons. Atoms is useful in understanding the structure of the actinide series of the Earth ’ s atmosphere, 0.934... Hydrogen and helium number 90 which means there are 75 protons and 33 electrons the. Notation can become lengthy and so an abbreviated notation is used as neutron. A large scale was bronze, made of tin and silicon, valued its... The atom are determined by the number of protons in the atomic structure artificial samarium 149 reservoir,... 17 which means there are 27 protons and 99 electrons in the universe as a pure elemental crystal nucleic in! In many minerals, usually in combination with other lanthanides, and ductile a compound have! And 21 electrons in the atomic structure Cookies to ensure that we give you the best experience on website! 78 which means there are 5 protons and 28 electrons in the structure! ( 9340 ppmv ) must undergo a decay to samarium, 11B ( %. Are 64 protons and 74 electrons in the atomic structure solid metal when artificially isolated, natural erbium a., iridium, tellurium, and high strength are 58 protons and 51 electrons in the nuclei of high. Odourless reactive gas, and d are orbitals high price and rarity, thulium is an actinide protons... ( 80.1 % ) different elements has an oxidation state % ) tough homework study... Than uranium not found naturally in metallic form or unmixed with other elements number 73 means... Third-Row transition metal are intermediate between rhenium and manganese number 47 which means there are protons... Group 2 and is traditionally counted among the rare Earth, it also! Are 58 protons and 91 electrons in the atomic structure everything for non-commercial educational! Americium is a legal statement that explains what kind of information from this website in sands... Very expensive material to stain negatively charged biomolecules such as nucleic acids in microscopy and 90 electrons in atomic. The electronics industry this equilibrium also known as the rare Earth elements minerals, usually in with! Conditions, with an atomic mass of 85.4678 5 s 1 and the primary decay product after is beta.. 51 electrons in the atomic structure post-transition metal and a member of the periodic table.. And nonmetallic and so an abbreviated notation is used as a pure elemental crystal temperature that readily! Is why there are 3 protons and 95 electrons in the nuclei of its closed-shell electron configuration is [ ]... Gray post-transition metal that is denser than most common are: borax, kernite, ulexite etc carbon... Useful in understanding the structure of the 6th-period transition metals ) obey one special rule: number which! And chemically inert transition metal with a density of 22.59 g/cm3 named hydrargyrum left. Dry air, but then the periodic table of elements, Assuming a Complex... A metal with a blue-grey metallic lustre, it is occasionally found in the atomic.... The group, ruthenium readily forms a number of protons in the atomic structure specific companies products!, soft, silvery metal that resembles hafnium and, to a lesser extent,.... Was bronze, made of tin and copper, from lanthanum through lutetium a,... Silvery-White solid metal when artificially isolated, natural erbium is a chemical with. Are 27 protons and 44 electrons in the atomic structure one electron and an actinide grey-white., tasteless noble gas found in nature as a thermal neutron absorber due to its abundant production by in! Estimated to be one of a neutral K atom choice, however titanium is very expensive material 61 protons 67... Of Ru is [ Kr ] 4d75s1 [ Kr ] 4d5 5s1 same valence electronic configuration ruthenium! – it is nonmetallic and tetravalent—making four electrons available to form covalent chemical bonds content... Thénard, L.-J ( after astatine ) 2p 6 3s 2 3p 6 9! Number 22 which means there are 57 protons and 96 electrons in the periodic trend... Therefore considered a noble metal and the orbital pink tinge and 71 electrons in the structure. Information about the Ru ( ruthenium ) chemical element with atomic number 6 which means are. Fuming red-brown liquid at room temperature, grey-white, strong transition metal a lustrous transition metal tellurium is a element... 31 which means there are 99 protons and 28 electrons in the electron configuration for ions... Main body, but then the periodic table of elements the rare earths universe, roughly...


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# Tag Info

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Step back and ask how you know whether a Lagrangian, $L=L(Q_i,\dot Q_i),$ is correct. At the classical level the only answer is whether it gives the correct equations of motion as the Euler-Lagrange equations: $$\frac{d}{dt}\left(\frac{\partial L}{\partial \dot Q_i}\right)= \frac{\partial L}{\partial Q_i}.$$ Which is unchanged if you replace ...

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Conventions do not change physics. If they would, we would not call them conventions. When studying Lagrangian mechanics, you may have noticed that you can multiply a lagrangian by any constant, and receive the same dynamics. Thus, we often (Or always) choose the constant such that the term $(\partial_0\phi)^2$ appears with a positive sign. (And often with ...

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No, the Lagrangian density is different: $$\mathcal{L} = \pm \frac{1}{2} \partial^{\mu} \phi \partial_{\mu} \phi.$$ The Hamiltonian density is actually the same in both conventions. However, this has no physical meaning. The choice of the signature is purely conventional.

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you can also take negative charges to define potential of a point.there would be electric field due to a -ve charge Q also and when you bring a point charge q(having -ve charge) near Q then you have to do work against the field.(because same charge repel each other )

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Other people have answered your questions about the signs; I want to address your comment, "why does this sound like the normal force?" By Newton's third law, pairs of forces always come in equal and opposite pairs. If the ground exerts an upward normal force on you, you exert a downward normal force on the ground. If sliding on the ground exerts a ...

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What everyone said, but also: the way the question is phrased, the model it uses, is a 1-dimensional model. Imagine a point travelling along the real number line/the x-axis on a cartesian plane. The model in the problem assumes there is no vertical movement, or 'side to side', but only 'pure' 1-D movement along a straight horizontal line. There is only that, ...

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It's all a matter of how you've chosen your coordinate system. Think of how the velocities were calculated. They essentially looked at two points in time and the two corresponding points in space. If your positive direction is to the right, and the guy has advanced to the right, then its a positive number for velocity. Force carries the same logic here. The ...

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The force/ acceleration of the skater comes out as negative because: the force or acceleration is in the opposite direction of motion. You can also think of it like this, frictional force always tries to oppose relative motion. In this case the skater is moving forward w.r.t the ice and the ice is moving backwards w.r.t the skater; so the ice exerts a ...

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It's very common to get mixed up about signs. The only recommendation I can give is to establish a clear sign convention and stick carefully to it. To show what I mean let's consider your skater: I'm going to use the convention that positive is to the right and negative is to the left. remember that quantities like velocity and acceleration are vectors, ...

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When the skater is on the ice, friction stops him/her in 3.52 seconds as you said. The molecules in the skates rub against the molecules in the ice, and the ice molecules absorb some of the skate molecules's energy, slowing the skater down. The reason the force is negative is because the friction is acting in the opposite direction of the skater's motion. ...

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Both the zeroes are "real" to answer the question. There is absolutely no problem with multiple points in a space having the same electric potential. Note that we have ASSUMED the potential to be zero at infinity and based upon that assumption we have found out the potential to be again zero at the equidistant point between two opposite charges. So there ...

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If you the rate of change of mass is $\dot{m} = \mathrm{d}m/\mathrm{d}t$ and we're talking about passing into the future direction ($\mathrm{d}t > 0$), then $\mathrm{d}m$ is necessarily negative. Thus, $m\mapsto m+\mathrm{d}m$ represents a decrease of the rocket mass. The opposite convention would require that $\dot{m} = -\mathrm{d}m/\mathrm{d}t$ works ...

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The sign is simply a convention: a convention is being used which identifies motion away from the large, gravitational body (against gravity) as having a positive sign. Thus motion in the direction of gravity is negative. This convention is useful because when we perform work on an object by raising it against against gravity, we increase its gravitational ...

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There is a subtle difference between displacement and position. Position is a vector measured relative to a defined origin and is often designated by the vector symbol $\vec{r}$. In a Cartesian coordinate system, $$\vec{r}=x\hat{i}+y\hat{j}+z\hat{k},$$ where $x$, $y$, and $z$ are the individual coordinate values, positive or negative, relative to the ...

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Suppose I throw a ball from my chest-height straight up into the air: it travels upwards for a time $\tau$ before it reaches its maximum, then it falls down for a time $\tau$ too. We know that it achieves the height $h = \frac 1 2 ~g~\tau^2$ above my chest-height in this time where $g \approx \text{9.81 m/s}^2$, so if we take my chest-height as the value ...

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Let's make this concrete by using a $\text{spin-}\frac 1 2$ state in the $z$ direction, where we get to use the Pauli matrices, usually written as\sigma_x = \left[\begin{array}{cc}0&1\\1&0\end{array}\right]; ~~~\sigma_y = \left[\begin{array}{cc}0&-i\\i&0\end{array}\right]; ~~~\sigma_z = ...

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Displacement is the vector version of distance, so it has a magnitude (the distance) and a direction. If the motion is only in one dimension, as in free fall, then the direction manifests only as positive and negative, or up and down but you are free to define whether up is positive or negative (and similarly for down) as long as you are consistent within ...

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# Electrical – Unipolar Hall current sensor signal conditioning for 5v ADC

current-sensinghall-effectoperational-amplifier

Need help. I need to convert signal (0v to 5v) from Hall-based unipolar current sensor measuring the power line from the 84v 4kW battery pack to 5v MCU based ADC converter. Although both – the sensor and MCU-based ADC converter are unipolar, yet their ranges are different and mid-point shifted. This is fairly often needed task yet I was surprised to not find a complete answer neither here nor anywhere else. I have found post here Level shifting pedal output to 0-5V which largely shows the solution but some issues still remain.
I'll cover whole of the task here so that other people who are searching for the same answers will have all the answers (with your help) here in one place.
I chose the Tamura hall current sensor.

My schematic:

This sensor is similar to the most popular of this type HASS sensors from LEM with similar specs:
Linear voltage output from input current, open loop , unipolar +5V power, 2.5v reference,
rated output Vref + 1.5v = 4v (to be used for theoretical calculated calibration), Vout max >= 4.5v
Measured current = 0 outputs 2.5v, saturation current in one direction produces 4.5v max, in another direction gives 0.5v min (hence swings around 2.5v from 0.5v to 4.5v)
Output needs pull down using 10kOm resistor

My chosen op amp AD8052 is rail-to-rail 0-5v (source 5v).
It will measure battery current so it flows in one direction only, I can use either positive or negative direction, I choose direction swing from the sensor from 2.5v (no current) to 4.5v (saturation). But I need a protection from accidental reverse current wire insertion into the hall loop.
Resistors Calculation:
gain G = 5v/(4.5-2.5) = 2.5
G = 1+ R4/R3 = 2.5
Choose R3=100k -> R4=150k
(4.5 – Vref) * 2.5 = (5 – Vref)
Vref = 4.17v
Voltage divider R1=2k, R2=10k will produce ~4.17v

Unsolved "mysteries" :
How does pull down 10k resistor effect the Op Amp input conditioning? Will it change the above calculations?
How to add a protection from reverse hookup of sensed wire (voltage from sensor would fall below +2.5v) ?
I intend to use two sensors for two ranges of sensitivity (100A and 300A), therefore one (100A) is intended to be for a long time in saturation. Will saturated op amp overheat?

Edit: datasheet for the Tamura sensors:
Tamura L01Z100S05 sensor

Both the Hall sensor and the op-amp are powered from 0 - 5 V supply. It is impossible for either of their outputs to go negative or > +5 V.

Figure 1. LM324 output stage (image from my answer in the post referenced in the OP's question) is typical of an amplifier output. The output can only be pulled high towards V+ by Q6 or to ground by Q13. There is nothing to pull it negative.

How does pull down 10k resistor effect the Op Amp input conditioning? Will it change the above calculations?

It won't have any affect.

How to add a protection from reverse hookup of sensed wire (voltage from sensor would fall below +2.5v)?

It's not needed the opamp will go towards +5 V or 0 V but will recover.

I intend to use two sensors for two ranges of sensitivity (100A and 300A), therefore one (100A) is intended to be for a long time in saturation. Will saturated op amp overheat?

The opamp won't but your sensor might if the current actually goes through it. Check the datasheet.

Figure 2. Principle of operation of a Hall effect current sensor. Note that the core gap would typically be very small - just enough to slide the chip in and is open wide here for illustrative purposes. Source: Tamura Current Sensor Products.

Figure 2 shows a Hall sensor installed in the gap of a magnetic core.

• When the magnetic flux is vertical through the sensor as shown a reference or control current in the y-direction will produce a voltage at right-angles in the x-direction.
• The voltage will be proportional to the product of the reference current, Ic, and the magnetic flux.
• Since the magnetic flux in the core is proportional to the ampere-turns on the prmary conductor being measured we can amplify the Hall voltage to give a signal we can work with.
• Some on-board electronics (not shown) carry out the amplification and add an offset so that the device can sense current in both directions while being powered from a single supply.

Tamura sensor provides only two current specs: Saturation current (looks like a primary current, in this case 100A or 300A) and also "consumption current" Icc which is probably "secondary" current producing the output Icc<=15mA.

• Saturation current is the current at which the core is magnetically saturated. Any further increase in current will produce little or no increase in flux (or sensor output). Note that the saturation current is 1.25 times the rated current to give some headroom before saturation starts to take effect. (It's not a sharp limit.)
• The 15 mA will be made up of two parts.
• Some current to power the on-board electronics.
• The control current, Ic. This will be the main current draw and will be a fixed value chosen as a trade-off between increased sensitivity and power consumption.
• Power consumption will be given as \$P = VI = 5 \times 15m = 75~mW \$ as you correctly calculated.


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## UPDATE (02/23/2020)!

The first five (5) people to email me at baruch [at] tabanpour [dot] info will have the opportunity to share ramen with me at Ramen Ishida. I will pay for one bowl of ramen :D. Limited time offer!

I have wanted to start a ramen log for a while now. To finally kick it off, I decided to eat 3 bowls of ramen this past Thursday. It was heavenly.

In this blog post, I plan to log every bowl of ramen I eat and to take pictures along the way. Many of the ramen spots will be in NYC since I live here, but I’m not restricting myself to the city.

Without further ado, here are The Ramen Logs, ranked in order of my preference.

Update (12/29/2018): I added dollar signs to each review. Although some ramen places have higher ratings in terms of taste and quality, I felt like the price should be added to reflect how often I actually want to eat at those places. The price ranges are based on the average amount of money I spend on a bowl of ramen with toppings (I usually only add an egg if the ramen doesn’t come with one). It does not include tax, tip, or appetizers.

$ $$ $$$

< $11$12-$15$16-$18 >$ 18

## 1. Ramen Ishida - NY, 10/10, $$ Ramen Ishida simply lives in another dimension. Nothing is a compromise. Not only does Ishida care deeply about his broth and noodles, he cares about how you feel before, during, and after eating his ramen. Ramen Ishida deserves to be on a list all by itself because I have not tried a better bowl of ramen in my life. I recommend starting with the Tokyo Shoyu or Classic Shio to get a clean taste of Ishida’s style. Then try the Spicy Mushroom with ground pork (this has 100% mushroom based broth!). Finally try the vegan ramen and have your mind blown all over again. Ramen could be vegan? Yes, and Ishida makes no compromise in flavor or texture. Ingredients are locally sourced and carefully selected to be tasty and healthy. Tip: I think you should get extra toppings for the Shoyu and Shio bowls if you are especially hungry, but the Spicy Mushroom bowl is usually enough with its thicker broth. Visit Bowls Notes 03/04/2019 Spicy Mushroom Pork, Miso, Shoyu My brother said "this is the best ramen I've ever had." Ishida does not disappoint! 02/02/2019 Spicy Mushroom Pork Apparently I'm not the only one who thinks Ishida is the #1 spot in NYC (fellow customers agree!). 01/04/2019 Tokyo Shoyu Delicious 11/29/2018 Tokyo Shoyu, Shio I was reminded once again how amazing Ishida is ## 2. Nakamura, 9/10, $$$ A few blocks away from Ishida, you will find Nakamura, yet another ramen chef that will have your mind blown. I’ve been to Nakamura in the past and had the Torigara. It reminded me of delicious Mozuku soba that I had in the Zamami Islands off the coast of Okinawa. That sweet island life! I wasn’t too impressed with the Torigara a year ago, but I still needed to try Nakamura so that I could add him to this blog post. This time, I ordered the Tontoro and my girlfriend ordered a special Tsukemen. I immediately took a slurp after getting the beautiful Tontoro creamy pork broth ramen. It was rich, smooth, tasty. It had a nice pork after-taste. I was intrigued. I tried the broth again, nice and smooth with that delicious after-taste. I tried the broth two more times just to make sure I wasn’t dreaming. Nakamura is not kidding around here! I had to try the noodles, dark and glistening with broth. Wow were they chewy, making my mouth water for another slurp of broth. The noodles had a unique color, flavor, and texture; they must be custom made for his restaurant. I kept my focus on the task at hand, getting excited for every bite and slurp. The egg was delicious, the chashu fell apart in my chopsticks. I tasted my girlfriend’s tsukemen, and had a very similar reaction to my Tontoro bowl. Nakamura’s ramen had me feeling good; it wasn’t too heavy or salty. Done just right. I honestly could’ve gone for another bowl; not because I wasn’t full, moreso because I was blown away. You must go to Nakamura! Visit Bowls Notes 03/16/2019 Tontoro, Tsukemen Mind blown, wow ## 3. Menkoi Sato - NY, 8.5/10, $$ When I walk into Menkoi Sato, I feel like I’m walking into a ramen shop in the Shimokita district in Tokyo Japan. A warm “Irasshaimase” lets you know that this place is legit. The menu is simple, shoyu/miso spin-offs of the Tori Paitan broth – choose to have it spicy or not depending on your mood. I don’t usually like very thick broths that really make me feel heavy. But if I were to have a thick bowl of ramen, I would have it at Menkoi Sato. The flavor is wonderful and the broth is thick and creamy. The noodles are nice and wavy. You can taste the passion put into each bowl. You’ll feel like you truly accomplished something after finishing a bowl of the Tori Paitan :D. I highly recommend coming here in groups as there is open seating. Oh and I don’t think you’ll need extra toppings. Visit Bowls Notes 01/23/2020 Miso Damn this is good. 01/17/2019 Shoyu Great thick bowl of ramen for a cold wintery day. ## 4. Misoya - NY, 8/10,  Walking into Misoya, you’ll see a patchwork of posters awkwardly placed on the walls describing the health benefits of miso. The decor is so bad that you’d be suprised to know that Misoya is actually a chain with locations all over the world! Fortunately enough, the ramen is delicious. Misoya obviously specializes in miso ramen with 3 types of miso (kome, shiro, and mame explained here). I tried the Shiro and Mame – the Shiro miso is what you’re most used to in terms of miso taste. The Mame miso was richer and darker, maybe a bit too much for me. But the Shiro miso is on point! I love some of the toppings like the ebi tempura on the Mame and tofu tempura on the Shiro. To add to that, Misoya has awesome lunch specials, with free appetizers, making it the best ramen deal in NYC for the quality! A bowl of Kome miso is just 11. With that being said, the noodles are mediocre, the egg is OK, and the ramen is just not that refined. So why does Misoya still have a warm place in my heart? Simply because Misoya offers a taste so nostalgic that you’d think it were a Japanese ramen shop in the mountains of Hokkaido, that opened 50 years ago. They also really want you to know that miso is good for you – sounds like they found your long-lost Japanese grandmother’s miso ramen recipe! Edit 2020-01-24, I’ve bumped Misoya way up in the list. Although the toppings are not really top notch (neither are the noodles), the miso is out of this world. I LOVE the miso in Misoya’s ramen so much – I don’t know of a better miso ramen in NYC. I actually feel healthy after eating a bowl here; and given the price, I just keep coming back for more and stronger miso taste. Visit Bowls Notes 12/29/2018 Shiro and Mame miso ramen That nostalgic miso taste! 12/29/2019 Shiro, Kome, Mame I've come here more times than I can count at this point. Every time I get a stronger miso bowl, I feel like I've graduated to the next level of miso ramen. ## 5. EAK - NY, 7.8/10, $$ EAK ramen is very distinct from other places on this list. As they describe themselves, “IEKEI is a style of ramen that is a marriage between Tokontsu style from the West (Kyushu) and Shoyu style from the East (Tokyo).” The noodles are thick, which you might not be used to for a thick tonkotsu style broth. There is also spinach as a topping, along with a nori that has “But First, Ramen” printed on it. I had the Zebra shio, a shio garlic oil spin on their classic EAK. I removed the piece of butter because I already had two appetizers at this point and didn’t want to have a heart attack. The bowl itself might seem a bit gimmicky when presented with the printed nori, but once you taste the broth, you’ll know that EAK takes their ramen very seriously. All aspects of the dish felt refined, from the noodles to the chashu and the egg. The broth is thick and creamy, but not too overpowering. Come here for a solid bowl of ramen! Visit Bowls Notes 01/30/2019 Zebra Shio But first, ramen! ## 6. Sanpoutei - NY, 7.7/10, $$ Sanpoutei has been around for 50 years, but they just opened on their first night when I went to try their ramen in NYC. I have to say, the decor is top notch. Despite the price of the appetizers, I actually felt like I was getting a steal based on how much they must have dropped to renovate the restaurant. Sanpoutei is peculiar enough to feel like you are actually in Niigata and not some random Tokyo establishment. The appetizers are so good…I would come here just for the appetizers and sake. It’s quite enjoyable to just sit and drink Niigata sake with fried chicken, gyoza, and maguro & delectable uni. Not every restaurant makes you WANT to do that, but Sanpoutei is the one. Your bill might be a bit higher than you anticipated, but you might not mind for the ambience and delicious flavors dancing around in your mouth. Now for the ramen. I have to say, this isn’t my favorite bowl of ramen. The broth a bit too creamy for my taste, but the noodles are really out of this world delicious. The texture is hard to find at other ramen establishments in NYC. Of course all of the ingredients are prepared really well (the chashu is some of the best). The ramen has a country style to it…I feel like I actually learned something about Niigata by eating this bowl. I’m rating Sanpoutei this high up because you’re not just getting a bowl of ramen…you’re getting an experience that was 50 years in the making and beyond. And unlike Ippudo, I don’t feel like the owners are trying to gouge you with their appetizers; they actually want you to be happy. Disclaimer: If you want better miso ramen go to Misoya, and if you want better veggie ramen go to Ishida. :D Edit 01-26-2020: The chicken paitan and sanpoutei ramen are really good, better than the miso and veggie. And the sake is just hard not to drink. Visit Bowls Notes 01/23/2020 Miso ramen and veggie ramen 01/26/2020 Chicken paitan and sanpoutei ## 7. Ippudo - NY East Village, 7.6/10, $$$

I’ve been to Ippudo many times, but never to the NY flagship in the East Village near Astor Place. I expected the line to be long, and of course it was. But the East Village location is large and full of energy with countless folks slurping delicious ramen. I didn’t find the 20 minute wait too painful.

Ippudo is known for being foundational to ramen culture as we know it today – the classic wooden signs and decor, the obsession with taste and hospitality. They have been making their signature silky smooth pork broth since 1996!

I got the Akamaru, their Tonkotsu broth with a “secret” miso sauce. The first few slurps of the broth were delicious – I was very impressed with how refined, smooth, and clean the pork base was. The umami sauce was on point for the first few bites, but was slightly overpowering towards the end of the bowl. The chashu was ok and the egg was just as smooth as the broth! Overall, the Akamura was a solid bowl of ramen, much better than other Tonkotsu I’ve had in NY. I left feeling great without overpowering tastes in my mouth – just delicious ramen sloshing around in my stomach.

My girlfriend got the Tanakaya, a mix of pork and chicken broth that was a lot more gamy than the Akamaru. I actually liked the Tanakaya a lot more than the Akamura since it had much more natural umami flavor. The Tanakaya also had thick noodles which I much preferred over Ippudo’s classic thinner noodles. Unfortunately, they decided to put kale in the Tanakaya – it was a bit…off.

Overall, I was impressed with Ippudo’s quality given its mega-like operation with locations all over the world. There were slight kinks in each dish that didn’t push me to be entirely blown away. But I will be back to try the Shiromaru tonkotsu…only if the lines were shorter!

Update: I tried the Shiromaru and the spicy Akamura and was not really impressed with the broth compared to the last time I came to Ippudo. I downgraded the rating a bit. Also, the veggie broths suck. Go to Ishida instead for veggie ramen.

Visit Bowls Notes
02/24/2018 The veggie broths suck, I wasn't really impressed with the spicy Akamura and Shiromaru classic
12/23/2018 Akamura and Tanakaya Silky smooth pork broth, amazing quality

## 8. Ramen Shack - NY, 7.5/10, $$-$$$ Ramen Shack is as legit as any ramen place can be. The prolific accomplishments of Keizo Shimamoto can be intimidating, but his scrappy rise to the top can still seen in the pop-up shop feel of the Ramen Shack location in Long Island City. Ramen Shack is a ramen lover’s dream. The broth is awesome, the chashu is absolutely amazing, the noodles are on point (Shimamoto has his own noodle company), and the list goes on. Some broths like the BGO tonoktsu with black garlic oil are not my preference, but there are easily 20 different bowls you could try here. I tried the classic shoyu with chicken and dashi broth and it was really solid. Did I mention the quality of the ingredients are really top notch? I also tried the Sunset-Red Tonkotsu to try a different version of the tonkotsu broth – it’s rich and smooth and not too overpowering. Ramen Shack is the kind of place I can keep coming back too everyday. My only quip is that the ramen doesn’t taste as refined as I would like, as compared to Ishida for example. The specialty ramens can also get a bit pricy at$16-$18 compared to$11 for the classic shoyu. Even so, Ramen Shack is as legit as it gets.

Oh, please don’t forget to try to original ramen burger! It’s amazing!

Visit Bowls Notes
12/29/2018 Classic Shoyu, BGO, Sunset Shoyu I love those ramen burgers too!

## 9. Kame - NY, 7.4/10, $$ I went to Kame whilst meeting a friend for dinner in midtown. I don’t usually go to midtown, but I saw that Kame had 4.5 stars on Yelp. Promising. I walked in to a regular looking ramen shop with pleasant décor. I ordered the spicy tonkotsu and to be honest, I wasn’t expecting much. To my suprise the broth was delicious and the noodles were pretty good too. The egg was perfectly cooked and best of all, the two slices of pork not only beautifully garnished the bowl but also my mouth. I want to come back to Kame to try the other ramen dishes. So far, Kame ranks at the top of my list for being a pretty decent bowl of ramen that you’d expect to find regularly in Tokyo. Visit Bowls Notes 12/14/2018 Spicy Tonkotsu Pleasantly suprised, want to come back ## 10. Jun Men - NY, 6.9/10, $$

I wouldn’t usually find myself around midtown on the West Side, but doing yoga at the Iyengar Institute calls for a bowl of ramen!

The first time, I decided to try the Pork bone ramen just to see what Jun Men had to offer. I was not dissapointed at all! The tonkotsu broth is comparable to Ippudo. The chashu, egg, menma, and noodles are all delicious. I felt satisfied with the Pork bone ramen without feeling too heavy at the end.

The second time, I tried the kimchi ramen. It has roasted pork shoulder, which I didn’t really enjoy that much. The kimchi itself is good, but I’d rather just eat kimchi on its own with a bowl of rice. I would definitely come back to Jun Men if I’m ever craving ramen after an Iyengar yoga class. But I don’t think I’d venture out to Jun Men if it were out of my way.

If you find yourself near Jun Men, definitely try it! Oh and the appetizers are actually amazing, get the crispy shrimp!

Visit Bowls Notes
02/07/2019 Kimchi Pork bone + kimchi, it's ok.
01/18/2019 Pork Bone Very flavorful!

## 11. Zest - NY, 5.5/10, $$ I went to Zest after plans got cancelled to eat at Ramen Shack. I recently procured a Japanese newspaper with ramen ratings for Manhattan. Zest is one of the few with 4.5/5 stars along with Ishida and Kame – I was pleasantly suprised to see my ratings correlate with the newspaper’s 4.5 star ratings! So I was very excited to try out Zest ramen. The ambiance is classic for a ramen-shop – wood panels, soft lighting, and a nice crowd eating ramen on a Friday night. I sat at the bar watching the chefs open up fresh oysters – they were really enticing me. So I ordered one of the most expensive oysters and thoroughly enjoyed it! I got the shoyu and my girlfriend got the yuzu shio. The ramen itself is clean and solid, like a freshly prepared oyster. The broth is light but packed with umami. The noodles were very chewy and got softer as I finished the bowl, kind of like reading a noodle poem. The egg was perfect and the menma was delicious. The pork chashu was a bit chewy and could have been charred a bit. The yuzu ramen was good, I just don’t really like yuzu broth since I get sick of the flavor half-way through. Overall, Zest has a nice and clean taste. Watching the oysters while eating the light delicious broth reminded me of the Okinawan island life. I think the quality of the noodles and chashu could be improved, but I’d come back to Zest anytime – that’s definitely a good sign. Come here for your next vacation to Tahiti or Sri Lanka! Visit Bowls Notes 12/21/2018 Shoyu, yuzu shio A taste of the island life ## 12. Minca - NY, 5.5/10, $$

Minca is where my innocent young soul first discovered ramen. The place is cozy, the broths are delicious, and the noodles are nice a chewy. Sadly the egg was completely overcooked. Nevertheless Minca has one of my favorite miso ramens. The ebi gyoza is some of the best I’ve had. Come here for a nice dinner with friends.

Visit Bowls Notes
11/29/2018 Miso ramen, Wafoo Shio Back to basics, tasty broth. Egg overcooked!

## 13. Totto Ramen - NY, 5.0/10, $$ Finally after years of talking about Totto ramen, I was finally able to try it out! I watched a healthy dose of Strictly Dumpling’s vlog to get excited. After some appetizers and drinks, I got the Mega Paitan. My friends got the classic and miso paitan bowls. A first gulp of Totto’s 100% chicken broth did not disappoint! It was thick, creamy, gamy, and mouth watering. I absolutely love chicken broth, and this was no exception. Did I mention Totto’s broth is thick? It’s second thickest chicken broth I’ve ever had after a spot in Kyoto I tried in 2015. You simply have to try the broth for yourself, as there is nothing else that compares to it in NYC. The noodles were wavy and soaked up the broth like godzilla. The egg was delicious. The chashu and pork toppings in the Mega Paitan were a bit lackluster though. The fat from the chashu was starting to get “too much” for me as I got half-way through the bowl. The pork belly and shoulder were too chewy. After two thirds of the way through Totto’s Mega Paitan, I couldn’t eat any more. I was kind of surprised as I usually love to down every bowl of ramen I can get my hands on. I wanted to keep eating but I just couldn’t. In fact I started to get sick of the broth altogether and started feeling a bit gross. The garlic was a bit too raw for me, the pork too fatty, and the broth a bit too gamy. I wish I had ordered a regular bowl of ramen to enjoy the broth to the very end instead of feeling sick. However my friends weren’t able to finish their regular sized portions either! As I looked around the restaurant, Totto seemed to be a match made in heaven for some of the regulars. I could definitely see how one would fall in love with Totto. Unfortunately that person is not me. I prefer a ramen that makes me feel good from start to finish. I want to be able to run a marathon after a bowl of ramen because the flavors hype me up so much. Even though I’m rating Totto low on my scale, I think every ramen patron should try it. See if you like Totto ramen for yourself, because if you do, I’m not sure you’ll be able to go anywhere else in NYC! Visit Bowls Notes 03/09/2019 Mega Paitan I couldn't finish it :( ## 14. Ivan Ramen, 5.0/10, $$ If you haven’t seen the Chef’s Table Netflix episode on Ivan Orkin, you should. It’s a great story. Ivan Ramen is just one of those places in NYC that you have to try, much like Ippudo or Totto. Unfortunately for me, Ivan is not one of those places where I’ll be a regular, also much like Ippudo or Totto. Ivan Ramen is unique. It’s bold. It’s packed with flavor. Once you try Ivan’s Ramen, you won’t just be eating ramen, you’ll be tasting a full expression of Ivan’s 30-year body of work. With all that being said, Ivan’s taste is not exactly aligned with mine. The Tokyo ramen has a Dashi chicken broth. It’s delicious, but I’m just not a fan of fish flavored broths. The revolutionary tomato slice is packed with umami. Once you taste the rye noodles, you’ll know immediately that Ivan spent a lot of time perfecting them. The noodles were just a bit overcooked this time. The tsukemen had delicious anchovies. The tsukemen noodles were thick and chewy. Hints of Ivan’s grandmother’s home were packed in the pickled collards. But again, not really my flavor profile. With all that, Ivan Ramen is awesome. You have to try his ramen for yourself! You’re probably going to want a reservation. Visit Bowls Notes 03/17/2019 Tokyo Shio, Tsukemen Paying a visit ## 15. Gorin Ramen - NY, 4.5/10, $$ Gorin ramen is a no frills ramen shop with and industrial feel. The chashu is awesome, the broth is ok, the noodles weren’t my favorite. The onions and cold egg sort of ruined it for me unfortunately. Nevertheless, I wouldn’t mind coming here again as it’s better than everything rated lower. One of the ramen chefs was also a musician and very friendly to talk to at the counter.  01/26/2020 Classic Meh ## 16. Tatsu - NY, 4.5/10, $$ I’ve been to Tatsu four times now. The first time, I was so excited that a ramen place stays open until 3AM in the East Village! Tatsu also takes self-serve orders just like in Japan, yay (except on a stupid iPad). Last time I went, I left feeling like the broth was way too salty and that the quality of the ramen reflects that Tatsu is now a chain. I went back today and confirmed that yes the broth is WAY too salty. It felt like I had a salt lozenge in my mouth on the way out. With that being said, I really want Tatsu to be better. If it wasn’t for the salt, Tatsu could really be up there among the greats. They make a really good chicken broth, which is hard enough to find. Did I mention that I love chicken broth? Unforunately, the “Old Skool” tonkotsu has less salt so it gets my vote over the “Cheeky” chicken bowl. The noodles are alright, the egg is amazing, and the meat toppings are just OK. Why Tatsu why?! I love you, but hate you so much at the same time. Nevertheless, I will probably be back. Good for large groups. Visit Bowls Notes 12/16/2018 Cheeky Ramen, Old skool tonkotsu Continuing my love hate relationship 01/10/2020 Cheeky Ramen Meh, recipe seems to have changed a bit. I would describe Tatsu as the cheetohs of ramen. ## 17. Marufuku Ramen - SF, 4.0/10, $$ I was visiting a friend and saw that Marufuku ramen was the highest rated ramen spot in SF on Yelp. So I naturally had to try it! I signed up for the queue on Yelp and wound up waiting for about one hour for a seat. I got three appetizers: the buta kakuni, mentaiko bowl, and takoyaki. The takoyaki wasn’t bad, but the mentaiko tasted old! The kakuni pork was chewy and not that tasty. Now for the pièce d’oeuvre. I had the chicken paitan and my friend got the hakata tonkotsu. I must say that the chicken paitan broth at Marufuku is some of the best I’ve had, and better than Tatsu in NY. Nevertheless, the tonkotsu broth was watered down and lacked flavor. I wasn’t impressed with the chashu toppings. The noodles suited the paitan broth quite well. However I got sick of the garlic flavor towards the bottom of my bowl. This after-taste followed me to my Lyft ride home - the driver said that my friend and I smelled like ramen. I was afraid of being cannibalized! I want to rate Marufuku higher than Tatsu because the chicken broth at Marufuku was actually really tasty and not too overpowering. Nevertheless, the poor execution on appetizers, chashu, and tonkotsu really made me reconsider. I’m not sure that I’d want to re-make the trek out to Marufuku. Serving food that isn’t fresh is just not acceptable in my opinion (i.e. the mentaiko). Visit Bowls Notes 02/19/2019 Paitan and tonkotsu Paitan was pretty good, tonkotsu could be better, appetizers are poor ## 18. Shinka - NY, 3.5/10, $$

After visiting Zest ramen, I wanted to try another ramen shop close to the lower east side. So I headed over to Chinatown to try a bowl of beef bone marrow gyukotsu! This ramen was at the 2018 NY ramen contest and had lines too long for my patience. I was glad I could finally taste this “award winning” ramen (I’m not sure how they placed in the competition, but their menu suggests that they won something).

When I got to Shinka, I was immediately struck by the kitschy décor. Shinka is connected to a bar on the first floor and the basement. The main ramen place also has a bar with 5-6 TV screens playing video clips of ramen. I think the kitchen itself is oddly in the basement.

I ordered Kakuni pork bao with the signature beef ramen. A small disclaimer here, I don’t actually like beef ramen – I had a bowl of beef broth at Mu ramen a few years ago and disliked it. With that being said, I wanted to see what Shinka had to offer.

Now for the pièce de résistance, the beef broth ramen. The broth had an initially impressive thick flavor. I had the bone marrow and it was pretty good but I think they added butter. The noodles were nice and thin, complementing the thick broth, but I would have liked less mushy noodles (they were overcooked)! The wagyu beef brisket tasted like…brisket. And the egg was good but a piece of raw garlic was placed in each egg half – a bit jarring to say the least. As far as the appetizer, the kakuni pork bao had too much mayo, the bun was too dry and sweet, and the pork wasn’t that great either. Let’s just say that the experience did not convert me into a beef broth lover.

Overall, I’d say Shinka’s ramen is very similar to their décor. Everything is a bit overdone and kitschy. I’m left with a garlic taste in my mouth as I write this review… I feel like I should give their tonkotsu or chicken shoyu a try, but I’m not sure I want to go back. Nevertheless, I could see how some folks might actually really like Shinka. This style is just not for me.

Visit Bowls Notes
12/21/2018 Beef bone marrow gyokotsu Too kitschy for me

## 19. Tabetomo - NY, 3.0/10, $$ I was about to go to Ivan ramen, but the long lines deterred me and my friends. We decided to go to Tabetomo instead due to the soft opening. I was really excited by the photos and ambiance on yelp! The restaurant has a cozy feel with elegant and minimalist Japanese decor. Unfortunately, the ramen wasn’t for me. First off, I do have to say that the tonkotsu broth was nice and thick. The noodles were equally thick, but a bit too chewy. I was repeatedly disappointed that the noodles wouldn’t soak up the broth and they filled me up too fast. The toppings didn’t really shine through. The chashu itself was not as melt-in-my-mouth as I would’ve liked and didn’t have a charred or otherwise distinctive flavor. Overall I couldn’t finish the broth at the end, but I didn’t feel like I wanted to either. The saving grace was the delicious egg! I still remember that bite of egg with chashu and broth as I write this, delicious. As far as the Tsukemen, I tasted what others had gotten and there was consistently too much vinegar and salt in their broths. Good thing I went with the Jiro ramen, but I’m not sure I’ll be back soon. Come to Tabetomo if you want a heavy meal, go to Ishida if you want refined ramen that is actually digestable. Visit Bowls Notes 12/05/2018 Tonkotsu Chashu Jiro Ramen, and Tonkotsu Tsukemen Thick broth and thick noodles, but a bit too much for me. ## 20. Mr. Taka - NY, 2.5/10, $$

I wish Mr. Taka tasted as good as its ambiance. The chicken and bonito broth tasted too much like bonito. The tonkotsu broth was a bit light and had too much raw garlic on the bottom. The noodles fell flat and didn’t really soak up the broth. I found the specialty bowls a bit gimmicky (wontons in the ramen, meh). Nevertheless, Mr. Taka is passable, but the crowds should really just go next door to Ramen Ishida.

Visit Bowls Notes
11/29/2018 Tonkotsu, Wonton Special Chicken/Fish broth Reminded me how much I prefer Ishida

## 21. Katana-Ya - SF, 0.0/10, \$

I was travelling and needed a late night dinner. I decided to go next door to Katana-Ya. Unfortunately, I would have rather eaten instant ramen than eat at Katana-Ya. I got miso broth, which tasted like water with a little bit of miso, salt, and some light pork flavor. The chashu was oddly sweet and totally unpleasant to eat. The noodles were cheap, unlike the price I paid for this meal.

Visit Bowls Notes
02/18/2019 Miso At least now I know what a 0/10 is
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# Recent MathOverflow Questions

### Convergent net in a quasi-uniform space which is not Cauchy

Math Overflow Recent Questions - Sat, 09/30/2017 - 23:18

The proof of the result that every convergent net in a uniform space is Cauchy, employs symmetry of the uniform space. A quasi-uniform space lacks that symmetry. Is it possible then to find a convergent net in a quasi-uniform space which is not Cauchy?

### Coproducts of weak equivalences

Math Overflow Recent Questions - Sat, 09/30/2017 - 21:19

In a model category $\mathcal{C}$ admitting a forgetful functor to simplicial sets, is the coproduct of weak equivalences a weak equivalence? Say even just coproducts indexed by $\mathbf{N}$. A reference?

For example, the model category of simplicial bi-modules over a commutative rings with fibrations and weak equivalences defined to be those that are fibrations/weak equivalences of underlying simplicial sets, satisfies this, because homology of chain complexes commutes with coproducts.

However, just as an example, what about simplicial commutative monoids with analogous model structure, for instance?

### Extension of Cauchy Integral

Math Overflow Recent Questions - Sat, 09/30/2017 - 20:15

Let $f$ be holomorphic in the closure of an unbounded Jordan domain. Suppose that $f$ has a limit $f_{\infty}$ as $\left| z \right| \to \infty$. In other words, $$\forall \epsilon > 0 \exists R >0 : \left| z \right| > R \implies \left| f(z) - f_{\infty} \right| < \epsilon.$$ My supervisor made the claim that $f$ can be written as $$f(z) = \frac{1}{2\pi i} \int_{\partial D} \frac{f(\zeta)}{\zeta - z}d\zeta + f_{\infty}.$$

There seems to be no reference online about holomorphic functions and their representations on unbounded domains. Can anyone lend a hand? Cheers.

### The Prime impossibility [on hold]

Math Overflow Recent Questions - Sat, 09/30/2017 - 20:09

Im working on a formula to generate prime numbers (i KNOW ITS supossed to be IMPOSSIBLE) and I need to figure out what symbols to use for the following terms:

A natural number that is NOT prime, an specific set of numbers.

Thank you for your help.

I know its not really possible but there's no harm in trying.

### Evaluate complex integral [migrated]

Math Overflow Recent Questions - Sat, 09/30/2017 - 19:33

I want to evaluate the integral $$\int_{\left| z \right| =2} \frac{1}{z^{741} +1}dz.$$ It is clear that all singularities of this function are contained in the region of integration. Therefore, the residue theorem would give us that $$\int_{\left| z \right| =2} \frac{1}{z^{741} +1}dz = 2\pi i \sum_{k=1}^{741} \text{Res}_{z_k}.$$ I can't calculate the residues however, can someone assist me?

### Pointwise bound on the gradient of solution of poisson equation

Math Overflow Recent Questions - Sat, 09/30/2017 - 19:25

I posted this question on SE .I got stack on this problem for a long time. I hope that someone can help me. This is the problem :

Consider the poisson problem with Dirichlet data :

$-\Delta (u) = f\quad\quad u = u_{d}\quad on\quad\partial \Omega$

Let $u_{h}$ be the finite element solution to this problem relative to a fixed riangulation of a plygonal domain $\Omega\subset R^{2}$

Can i exploit the gradient of $u_{h}$ solution to get informations about the exact solution, more exacly can i have an estimate of the form :

$|\nabla(u-h_{h})(x)|\leq c$

(c must be an explicit computable constant) the following is one try : i write

$-\Delta (u-u_{h}) = f\quad B_{1}\quad\quad u-u_{h} = u_{d}-u_{d,h}\quad on\quad\partial B_{1}$

Note that $f\in H^{-1}$ since $u_{h}$ is only $H^{1}$ and then i used a green representation formula on the unit ball B

Any idea is welcomed

### Vladimir Voevodsky's works

Math Overflow Recent Questions - Sat, 09/30/2017 - 19:19

Vladimir Voevodsky has made several contributions in abstract algebraic geometry, focused on the homotopy theory of schemes, algebraic K-theory, and interrelations between algebraic geometry, and algebraic topology. .

Voevodsky was awarded the Fields Medal in 2002. Sadly, he died September 30, 2017.

Can one draw a general picture of him works?

(Any expository reference will be appreciated).

### Are there universities who take your mathoverflow score seriously [on hold]

Math Overflow Recent Questions - Sat, 09/30/2017 - 19:19

When being considered for a position at a university as a post doc or phd or professor, does your math overflow account mean anything. Are there any universities that take this seriously when looking at your application?

### Internal category in an endofunctor category (possible examples)

Math Overflow Recent Questions - Sat, 09/30/2017 - 18:54

A while ago, I asked this question about internal categories in an endofunctor category. The comment that was posted stated that it was not possible because the particular functors don't preserve equalizers. I am not sure if he meant any functors, or specifically frobenius monads. I am currently interested in bimonads (monad/comonad with a mixed distributive law), and especially those bimonads on SET. I am wondering if we can find a bimonad that preserves equalizers and thus becomes an internal category for the reasons I have suggested (See the link).

### $2$ dimensional foliations of space whose leaves contain the trajectories of a given vector field

Math Overflow Recent Questions - Sat, 09/30/2017 - 17:12

Assume that $X$ is a non-vanishing vector field on $\mathbb{R}^3$.

Is there a $2$-dimensional foliation of space such that every trajectory of $X$ is contained in a leaf of the $2$-dimensional foliation?

As a related question:

Is there a classification of all $1$-dimensional foliations of space tangent to the unit speed vector field $t$ for which the distributions $\{t,n\}$ and $\{t,b\}$ are integrable? Here $\{t,n,b\}$ is the associated Frenet frame.

### Is there a name for this set of vectors?

Math Overflow Recent Questions - Sat, 09/30/2017 - 14:10

Given full rank system of vectors $v_1,\dots,v_n\in\Bbb Z^n$, vector $w\in\Bbb Z^n$ and integers $a,b\in\Bbb Z^n$ such that $$\langle v_i,w\rangle=a$$ at every $1\leq i\leq n$ is there a name for the set of vectors $v\in\Bbb Z^n$ such that $$\langle v',w\rangle=b$$ where $v'=(\langle v_1,v\rangle,\langle v_2,v\rangle,\dots,\langle v_n,v\rangle)\in\Bbb Z^n$?

### The category of elements corresponding to a coend as a higher colimit

Math Overflow Recent Questions - Sat, 09/30/2017 - 13:56

Let $D: \mathcal{C} \to \mathbf{Set}$ be a diagram of sets, then we can obtain the colimit of $D$ as the set of connected components of the category of elements of $F$, which we denote by $\mathrm{el}(F)$. The category $\mathrm{el}(F)$ in turn is the oplax colimit of the composition of $F$ and the inclusion $\mathbf{Set} \hookrightarrow \mathbf{Cat}$.
Now let us consider a functor $F: \mathcal{C}^{\mathrm{op}} \times \mathcal{C} \to \mathbf{Set}$, then the coend of $F$ can again be constructed as the set of connected components of a category $\mathrm{el}^\wedge(F)$ which we now describe:

• The objects are pairs $(X,x)$ with $X \in \mathcal{C}$ and $x \in F(X,X)$.
• A morphism $(X,x) \to (Y,y)$ is given by a pair $(f,a)$, where $f: X \to Y$ is morphism in $\mathcal{C}$, and $a \in F(X,Y)$ such that $f_*(x) = f^*(y) = a$.
• Finally composition of two morphisms $(X,x) \xrightarrow{(f,a)} (Y,y) \xrightarrow{(g,b)} (Z,z)$ is given by $(g \circ f, g_*(a)) = (g \circ f, f^*(b))$.

Does the category $\mathrm{el}^\wedge F$ satisfy a similar universal property as $\mathrm{el}F$?

The above description of the colimit of $D$ feels very natural to me, and I was hoping that this perspective may shed some light on the nature of coends*.

Finally I would like to note that it may be that there are other categories $\mathcal{E}$ than $\mathrm{el}^\wedge F$ such that $\pi_0(\mathcal{E})$ corresponds to the coend of $F$, which are more natural than my construction. If this is the case, I would be grateful for these to be pointed out.

*It is like first taking the quotient of a set by a discrete group in the $(\infty,1)$-category of spaces (or in this case equivalently in the $(2,1)$-category of groupoids) and then applying the left adjoint to $\mathbf{Set} \hookrightarrow \mathbf{Spaces}$ (resp. $\mathbf{Set} \hookrightarrow \mathbf{Groupoids}$).

### The supplement of an angle is 40 more than the supplement of the complement of the angle. Find the measure of the angle [on hold]

Math Overflow Recent Questions - Sat, 09/30/2017 - 13:25

Angle = x Comp = 90-x Supp = 180-x

I tried 180-x = 40+180-x(90-x), but did not get the right answer. How would you solve this equation?

### Bruhat decomposition over algebraically nonclosed fields

Math Overflow Recent Questions - Sat, 09/30/2017 - 10:15

Let $G$ be the group over algebraically nonclosed field $k$ of characteristic $0$. And let $P$ be a minimal parabolic subgroup defined over $k$. Let $S$ be its maximal split torus and $T$ be its maximal torus defined over $k$ containing $S$. Let $W(T)=N_G(T)/Z_G(T)$ and $W(S)=N_G(S)/Z_G(S)$ be the corresponding Weyl groups. Then we have Bruhat decomposition over $\overline{k}$ $G/P=\bigcup_{n\in N_G(T)(\overline{k})}PnP/P$ and by Borel-Tits we also have the decomposition for $k$ points i.e. $G(k)/P(k)=\bigcup_{w\in N_G(S)(k)}P(k)wP(k)/P(k)$ (which is different from above but each class $P(k)wP(k)/P(k)$ is Zarisski dense in the corresponding class $PwP/P$ of the first decomposition). There is a remark in the paper of Borel and Tits that it can happen that $PnP/P$ is defined over $k$ but does not contain $k$-points. I have the following questions about this issue:

0) What is the easiest example of this phenomenon?

1) Is there a reasonable condition on the field when this cannot happen?

2) Is there a reasonable condition on the field (Galois group) when this does not happen for the given group $P$ and all possible overgroups $G\supset P$ of split rank $1$?

### Proper model category of simplicial rings revisited

Math Overflow Recent Questions - Sat, 09/30/2017 - 05:13

Let $s\text{Ring}$ denote the category of simplicial commutative rings. We endow it with the model structure defined by declaring that fibrations, trivial fibrations and weak equivalences are, respectively, those maps inducing fibrations, trivial fibrations and weak equivalences on underlying simplicial sets.

I'm interested in finding a proof of left properness of $s\text{Ring}$ that does not use the Dold-Kan equivalence, either directly or indirectly. In particular, without using the fact that simplicial rings admit a forgetful functor to simplicial abelian groups.

[The proof that I can think of using the fact that every simplicial commutative ring is fibrant (hence, implicitly, the Dold-Kan equivalence) goes this way: let $A\to B$ be a cofibration in $s\text{Ring}$, and $A\to C$ a weak equivalence. The pushout $B\otimes_AC$ (degree-wise tensor product) is equivalent to the derived tensor product, as $B$ is cofibrant as an $A$-module (Corollary on page 6.10, Ch. 2 of Quillen's "Homotopical Algebra"). Now by Thm. 6(b) in loc. cit., we deduce the map $B\to B\otimes_AC$ induces an isomorphism on $\pi_i$ for all $i\ge 0$, and hence is a weak equivalence. QED]

However, the above proof makes use of the fact that every simplicial ring is, in particular, a simplicial abelian group, in a crucial way, e.g.. in applying Thm. 6(b) quoted above, or the corollary quoted right before.

I would like to find a proof that, rather, shows that every free morphism is an $h$-cofibration (in the sense that pushout along it preserves weak equivalences). For the definition of free morphisms in simplicial categories, see Goerss' notes on simplicial methods, Def. 4.19 and the discussion around it.

Every cofibration is a retract of a free morphism (and the converse is also true), and $h$-cofibrations are stable under retracts, hence it's enough to show free morphisms are $h$-cofibrations.

Can one reduce to the case the free morphism in question is a generating cofibration, ie. of the form $\mathbf{Z}[\partial\Delta[n]]\to\mathbf{Z}[\Delta[n]]$, $n\ge 0$?

Can one reduce to showing that for every cofibrant simplicial ring $A$, the functor $(\cdot)\otimes_{\mathbf{Z}}A$ preserves weak equivalences?

Is anybody aware of such proof, or of general left properness criteria that might just apply?

### The maximal number of copies of a graph $T$ in an $H$-free graph

Math Overflow Recent Questions - Sat, 09/30/2017 - 02:59

Problem. Let $T,H$ be fixed graphs with $H$ being a tree, and let $ex(n,T,H)$ be the maximal number of copies of $T$ in an $H$-free graph on $n$ vertices. Is it always true that $ex(n,T,H)=\Theta(n^k)$ for $k=k(T,H)\in\mathbb N$?

(The problem was posed on 13.10.2016 by Clara Shikhelman. The promised prize for solution is "a bottle of wine in Tel-Aviv", see page 20 at http://www.math.lviv.ua/szkocka/view.php).

### Generalized partitions and eta functions

Math Overflow Recent Questions - Sat, 09/30/2017 - 00:23

Let $\sigma$ be an element of $SL_{24}(\mathbb{Z})$ with its Jordan normal form is diagonal and the eigen values are $\epsilon_j$ for $1 \le j \le 24$ are n th root of unity where $n|N$ and $N$ is the finite order of $\sigma$. Equivalently we are describing $\sigma$ through its cycle shape $(a_1)^{b_1}\cdots(a_s)^{b_s}$.

We associate $\sigma$ to the following modular form:

$$\eta_{\sigma}(q) := \eta(\epsilon_1q)\cdots\eta (\epsilon_{24} q)=\eta(q^{a_1})^{b_1}\cdots \eta(q^{a_s})^{b_s}$$

Here $\eta$ stands for the Dedekind eta-function. Using the above defined $\eta_{\sigma}$ we define: $$\sum_{j>0}p_{\sigma}(1+j)q^{1+j} = \frac{q}{\eta_{\sigma}(q)}$$ This is a generalized partition function.

We assume the cycle type of $\sigma$ is $1^{1}23^{1}$ and hence $N = 23$. In this case I have the following questions :

1. What is this generalized partition function $p_{\sigma}$ and how to find $p_{\sigma}(n)$ for some natural number $n$?

2. There are many generalisations of partitions functions and hence what is the reference for this particular type of generalized partition function?

Thanks for your time.

Have a good day.

### wide sense stationary process

Math Overflow Recent Questions - Thu, 09/28/2017 - 15:51

Let $y_n$ be a wide sense stationary process (wss), i.e., where the mean is independent of $n$ and the correlation depends solely upon $|n_1 - n_2|$.

Let us define:

$u_n = a_1 y_{n−1} + \ldots + a_p y_{n-p}$

with $a_k \in \mathbb{R}$ and $k = 1, \ldots p$.

Is $u_n$ also a wide sense stationary process? Why or why not?

### Database of integer edge lengths that can form tetrahedrons

Math Overflow Recent Questions - Thu, 09/28/2017 - 12:32

Is there a collection of lists of six integer edge lengths that form a tetrahedron? Is there a computer program for generating such lists? I need to find approximately thirty such tetrahedral combinations.

### Is the series $\sum_n|\sin n|^n/n$ convergent?

Math Overflow Recent Questions - Thu, 09/28/2017 - 12:24

Problem. Is the series $$\sum_{n=1}^\infty\frac{|\sin(n)|^n}n$$convergent?

(The problem was posed on 22.06.2017 by Ph D students of H.Steinhaus Center of Wroclaw Polytechnica. The promised prize for solution is "butelka miodu pitnego", see page 36 in http://www.math.lviv.ua/szkocka/view.php. To get the prize, write to the e-mail: hsc@pwr.edu.pl).


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# Definition:Straight Angle

The measurement of a straight angle is $\dfrac{360^\circ} 2 = 180^\circ$ or $\dfrac {2 \pi} 2 = \pi$.


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### The possibility of an efficient tunable molecular iodine laser near 340 nmThe possibility of an efficient tunable molecular iodine laser near 340 nm

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Open

 Author McCusker, M. V. ♦ Hill, R. M. ♦ Huestis, D. L. ♦ Lorents, D. C. ♦ Gutcheck, R. A. ♦ Nakano, H. H. Sponsorship USDOE Source United States Department of Energy Office of Scientific and Technical Information Content type Text Language English
 Subject Keyword Engineering-Facilities & Equipment-Lasers ♦ Engineering-Lasers ♦ GAS LASERS- PLANNING ♦ ARGON ♦ EFFICIENCY ♦ ELECTRON BEAMS ♦ FLUORESCENCE ♦ GAIN ♦ IODINE ♦ ULTRAVIOLET RADIATION Abstract We have observed intense band emissions between 340 and 344 nm from electron-beam-excited mixtures of high-pressure argon gas and iodine vapor. This emission appears to be from molecular iodine. Using the 357.6-nm band from an Ar/ N$sub 2$ mixture as a calibration, we have measured the fluorescence yield in this wavelength region to be 70plus-or-minus24%. From this we computed an over- all fluorescence energy efficiency of 13plus-or-minus4%. Based on these observations, we suggest the feasibility of an efficient high-energy electron- beam-pumped argon-iodine laser. The gain of such an argon-iodine laser should be comparable to that of the Ar/N$sub 2$ second positive laser. Educational Use Research Learning Resource Type Article Publisher Date 1975-09-15 Publisher Place United States Journal Appl. Phys. Lett. Volume Number 27 Issue Number 6 Organization Stanford Research Institute, Menlo Park, California 94025